Home

GROMACS USER MANUAL Version 2.0

1. a a A aj Aap 4 7 Er flij where f 138 935 485 see chapter 2 ATEQ 4 3 Free energy calculations 63 Coulomb interaction with Reaction Field The coulomb interaction including a reaction field between two particles of which the charge varies with A is Ve y E keg iy ca Aa AgP 1 Jai AgP 4 78 OV 1 a ky r e Tij A a aP Aaf AGP aP af 1 AJa AP 479 Note that the constants krf and crs are defined using the dielectric constant epf of the medium see sec 4 1 4 Lennard Jones interaction For the Lennard Jones interaction between two particles of which the atom type varies with A we can write LEC A0B i NCAR ACE Vio AAA ee 4 80 rig ey VLJ CB Ch Ce C 4 81 A rip re It should be noted that it is also possible to express a pathway from state A to state B using o and e see eqn 4 5 It may seem to make sense physically to vary the forcefield parameters o and e rather than the derived parameters C12 and Ce However the difference between the pathways in parameter space is not large and the free energy itself does not depend on the pathway therefore we use the simple formulation presented above 4 3 1 Near linear thermodynamic integration In GROMACS the near linear thermodynamic integration NLTI method of Resat and Mezei has been implemented 46 This method avoids singularities at the end points of the TI
2. dummies3 Dummy from funct a d 5 1 2 3 2 0 5 0 105 for type 3fad like this dummies3 Dummy from funct d theta 5 1 2 3 3 0 5 120 for type 3out like this dummies3 Dummy from funct a b c 5 1 2 3 4 0 4 0 4 6 9281 for type 4fd like this dummies4 Dummy from funct a b d 5 1 2 3 4 1 0 33333 0 33333 0 105 This will result in the construction of a dummy atom number 5 first column Dummy based on the positions of 1 and 2 or 1 2 and 3 or 1 2 3 and 4 next two three or four columns from following the rules determined by the function number next column funct with the parameters specified last one two or three columns a b Note that any bonds defined between dummy atoms and or normal atoms will be removed by grompp after the exclusions have been generated This way exclusions will not be affected by an atom being defined as dummy atom or not but by the bonding configuration of the atom 5 3 Parameter files 5 3 1 Atoms A number of static properties are assigned to the atom types in the GROMACS force field Type Mass Charge e and see Table 5 2 The mass is listed in f atp see 5 2 1 whereas the charge is listed in ff rtp rtp residue topology parameter file see 5 3 5 This implies that the charges are only defined in the building blocks of 5 3 Parameter files 79 Property Symbol Type Mass a m u Charge electron epsilon kJ mol
3. It is also possible to analyse specific hydrogen bonds with sel This index file must contain a group of atom triplets Donor Hydrogen Acceptor in the following way selected 20 21 24 25 26 29 136 Note that the triplets need not be on separate lines Each atom triplet specifies a hydro gen bond to be analyzed note also that no check is made for the types of atoms ins turns on computing solvent insertion into hydrogen bonds In this case an additional group must be selected specifying the solvent molecules dumconn makes g_hbond assume a covalent bond exists between any dummy atom and the first preceding in sequence heavy atom This is used in searching Donor Hydrogen pairs Output num number of hydrogen bonds as a function of time zac average over all autocorrelations of the existence functions either 0 or 1 of all hydrogen bonds dist distance distribution of all hydrogen bonds ang angle distribution of all hydrogen bonds hx the number of n n i hydrogen bonds as a function of time where n and n i stand for residue numbers and i ranges from 0 to 6 This includes the n n 3 n n 4 and n n 5 hydrogen bonds associated with helices in proteins hbn all selected groups donors hydrogens and acceptors for selected groups all hydrogen bonded atoms from all groups and all solvent atoms involved in insertion hbm existence matrix for all hydrogen bonds over all frames this also contains information on sol
4. 1 1 1 4 a kof af Me Erf y Kre Erf Kre 4 18 r 2eErf Da Kre Er Ke 1 3epp 1 nr0 Ze nr Te 2er Da Kre En p nro Crf 4 19 where F is Faraday s constant R is the ideal gas constant T the absolute temperature ci the molar concentration for species 7 and z the charge number of species where we have K different species In the limit of zero ionic strength 0 eqns 4 18 and 4 19 reduce to the simple forms of eqns 4 14 and 4 15 respectively 4 1 5 Modified non bonded interactions In the GROMACS force field the non bonded potentials can be modified by a shift func tion The purpose of this is to replace the truncated forces by forces that are continuous and have continuous derivatives at the cut off radius With such forces the time step in tegration produces much smaller errors and there are no such complications as creating charges from dipoles by the truncation procedure In fact by using shifted forces there is no need for charge groups in the construction of neighbor lists However the shift func tion produces a considerable modification of the Coulomb potential Unless the missing long range potential is properly calculated and added through the use of PPPM Ewald or PME the effect of such modifications must be carefully evaluated The modification of the Lennard Jones dispersion and repulsion is only minor but it does remove the noise caused by cut off effects Ther
5. Exp al x Two parmeters y a2 Exp al x Three parmeter y a2 Exp al x 1 a2 Exp a3 x Startvalues for the fit procedure can be given on the commandline It is also possible to fix parameters at their start value use nfix with the number of the parameter you want to fix Three output files are generated the first contains the ACF an exponential fit to it with 1 2 or 3 parameters and the numerical derivative of the combination data fit The second file contains the real and imaginary parts of the frequency dependent dielectric constant the last gives a plot known as the Cole Cole plot in which the imaginary component is plotted as a fcuntion of the real component For a pure exponential relaxation Debye relaxation the latter plot should be one half of a circle Files f Mtot xvg Input xvgr xmer file d deriv xvg Output xvgr xmer file 0 epsw xvg Output xvgr xmgr file c cole xvg Output xvgr xmgr file Other options h bool no Print help info and quit nice int 19 Set the nicelevel b real 1 First frame ps to read from trajectory e real 1 Last frame ps to read from trajectory 182 Manual Pages w bool no View output using xvgr or ghostview fft bool no use fast fourier transform for correlation function x1 bool yes use first column as X axis rather than first data set eint real 5 Time were to end the integration of the data and start to use the fit bfit real 5 Begin time of fit efit real 500 End time of
6. Figure 3 9 The interaction matrix left and the same using action reaction right N 2 N 2 N 2 N 2 N 2 1 N 2 1 N 2 1 N 2 1 N 2 Table 3 1 The number of interactions between particles The number of j particles per i particle is a function of the total number of particles N and particle number 2 Note that here the operator is used for integer division i e truncating the reminder J i 01234567 Wi sone 012345 6 ol eeoe50 012345 0 00o 1 e 9 1 e 13 e 1 e 3 e ME e 3 e 4 e 3 e 410 5100 o 100 e 500 e 6100 e 5 00 60 7 0000 N mod 4 2 N mod 2 1 N mod 4 0 Figure 3 10 Interaction matrices for different N The number of j particles an particle interacts with depends on the total number of particles and on the particle number 36 Algorithms read_data reset_r_in_box communicate_r compute_forces X communicate _and_sum_f update_r_and_v output_step YES more steps Done Figure 3 11 The Parallel MD algorithm If the steps marked are left out we have the sequential algorithm again 3 12 Parallel Molecular Dynamics 37 Forces Coordinates Figure 3 12 Data flow in a ring of processors void communicate_r int nprocs int pid rvec vecs int start int homenr nprocs number of processor
7. T3 10 Pressure comp ling s gaor a ee A a a ed 117 7 3 11 Simulated annealing een 118 7 3 12 Velocity generation 2 2 2 2 202000 000000008 118 7 3 13 Solvent optimization aoa a 118 TSE BODAS e os Boa meee BR ek Megs Sapo ok eae Roe 119 1 3 15 NMRevefinement ace eG ee ee ee a e 120 7 3 16 Free Energy Perturbation e e e 121 7 3 17 Non equilibrium MD e e o o 121 13 18 Electricitelds 204 5 24 era aa E EA E a kg 122 3 19 User defined thingies i ete Sie a KE ee ee ee a E 122 TA Program Options 6 a 122 CONTENTS ix Goz Programs by tople cd serio Go Did WE te Seek aoe da Fee eo ee wee T 123 8 Analysis 127 8 1 Groups in AnalysiS ee 127 8 2 Looking at your trajectory s sco sb a a E a 128 8 3 General properties sie kde dc k ee Ws ee EO we y 129 8 4 Radial distribution functions 0 0 e 129 8 5 Correlation functionss 2645 eke ok 2 oe Pay Be OS E ee a S 131 8 5 1 Theory of correlation functions 131 8 5 2 Using FFT for computation of the ACF 132 8 5 3 Special forms of the ACF o e 000 132 8 5 4 Some Applications 2 0 0 02 02 ee ee 132 8 5 5 Mean Square Displacement o 133 8 6 Bonds angles and dihedrals o o 133 8 7 Radius of gyration and distances o a 136 8 8 Root mean square devia
8. To calculate the function 1 z using the previously mentioned iteration scheme it is clear that the first estimation of the solution must be accurate enough to get precise results The requirements for the calculation are e Maximum possible accuracy with the used IEEE format e Use only one iteration step for maximum speed The first requirement states that the result of 1 z may have a relative error e equal to the e of a IEEE 32 bit single precision floating point number From this the 1 z of the initial approximation can be derived rewriting the definition of the relative error for succeeding steps equation eqn B 34 En 2f A Erai eH B 35 So for the lookup table the needed accuracy is AY 12 y q B 36 which defines the width of the table that must be gt 13 bit At this point the relative error e of the lookup table is known From this the maximum relative error in the argument can be calculated as follows The absolute error Az is defined as Aga gt B 37 and thus Ar y B 38 and thus Az constant B 39 for the 1 z function Y Y x holds so Arx x constant This is a property of the used floating point representation as earlier mentioned The needed accuracy of the argument of the lookup table follows from Ax AY so using the floating point accuracy equation eqn B 36 A 7 252 B 41 This defines the length of the lookup table which should be gt 12 bit B 3 Com
9. Use water specific non bonded optimizations This string should match the solvent molecule name in your topology Check your run time to see if it is faster 7 3 14 Bonds constraints none No constraints i e bonds are represented by a harmonic or a Morse potential depending on the setting of morse and angles by a harmonic potential hbonds Only constrain the bonds with H atoms all bonds Constrain all bonds h angles Constrain all bonds and constrain the angles that involve H atoms by adding bond constraints all angles Constrain all bonds and constrain all angles by adding bond constraints constraint_alg lincs LINear Constraint Solver The accuracy in set with lincs_order which sets the number of matrices in the expansion for the matrix inversion 4 is enough for a normal MD simulation 8 is needed for LD with large time steps If a bond rotates more than lincs_warnangle degrees in one step a warning will be printed both to the log file and to stderr Lincs should not be used with coupled angle constraints shake Shake is slower and less stable than Lincs but does work with angle constraints The relative tolerance is set with shake_tol 0 0001 is a good value for normal MD unconstrained _start no apply constraints to the start configuration yes do not apply constraints to the start configuration shake_tol 0 0001 relative tolerance for shake 120 Run parameters and Programs lincs_o
10. a 3 3 Yi Yij b x round y b 3 4 Zij Bie Found a e 5 where the length of the box edges are denoted by a b c and the function round z delivers the integer number that is nearest to x The translation vector index is determined by the 27 combinations of the 1 0 or 1 values of the three round function results assuming that all primary particles are in the central box The particles will move during the simulation and may move outside the primary box Before a new pair list is made up all particles will be reset to the primary box which lies 3 4 Molecular Dynamics 19 Figure 3 4 The computational box in two dimensions divided into NS grid cells with three particles i j and k Each NS grid cell is of size gt r 2 in the positive quadrant with respect to an origin at ro by applying zi axround x zo a 2 a yi yi bx round y yo b 2 b zi 2 c round z zo c 2 c 3 8 Image calculation on a grid GROMACS uses an interaction list for non bonded interactions usually called the neighbor list This list is made every nstlist MD steps where nstlist is typically 10 MD steps To make the neighbor list all particles that are close i e within the cut off to a given particle must be found This searching usually called neighbor searching NS involves periodic boundary conditions and determining the image see sec 3 2 When
11. 312 3 Parallel PPPM lt a ee ee se hoe ee 40 3 12 4 Parallel sorting jos ch dk acd doc eels dM ik awk dear oo Al Force fields 43 4 1 Non bonded interactions 0 02 0 0 0 2 02 000 44 4 1 1 The Lennard Jones interaction 0 0 44 4 1 2 Buckingham potential e 45 4 1 3 Coulomb interaction e 46 4 1 4 Coulomb interaction with reaction field 46 4 1 5 Modified non bonded interactions 4 47 4 1 6 Modified short range interactions with Ewald summation 49 4 2 Bonded interactions yg o AE A A ek 50 AD BondistretCh ori ssns io a SO ee a ge E a E eae E e 50 4 2 2 Morse potential bond stretching 51 4 2 3 Bond angle vibration a 52 4 2 4 Improper dihedral qo morin A A a Ee 53 4 2 5 Proper dihedrals lt td A a SE EG ts 54 4 2 6 Special imteractions e 56 4 2 7 Position restraints e 56 4 2 8 Angle restraidts i h p a a a a 57 4 2 9 Distance restraints a aoaaa a 57 4 3 Free energy calculations eee ee 61 4 3 1 Near linear thermodynamic integration 63 AA Methods e rra BPG SR Gee AA EA ae a ks 65 4 4 1 Exclusions and 1 4 Interactions 0 0 65 AAD Charge Groupss ves ode Ce A ek Boe hd a PEC ie Ble a a 65 CONTENTS 4 43 Treatment of cut Of S e 00000048 4 5 Dumm
12. 57 water geom etry The symmetry axis will alternate between three coordinate axes in both directions NI e Three or four control atoms i j k 1 where the first always is the atom to which the H atoms are connected The other two or three depend on the code selected 5 3 7 Termini database The termini databases are stored in f 7 n tdb and f 7 c tdb for the N and C terminus respectively They contain information for the pdb2gmx program on how to connect new atoms to existing ones which atoms should be removed or changed and which bonded interactions should be added The format of the is as follows this is an example from the ffgmx c tdb None coo replace C C C 12 011 0 27 5 3 Parameter files 85 d w d 8 C CAN OM 15 9994 0 635 delete 2 0 0 impropers C 01 02 CA The file is organized in blocks each with a header specifying the name of the block These blocks correspond to different types of termini that can be added to a molecule In this example None is the first block corresponding to a terminus that leaves the molecule as it is C00 is the second terminus type corresponding to changing the terminal carbon atom into a deprotonated carboxyl group Block names cannot be any of the following replace add delete bonds angles dihedrals impropers this would interfere with the parameters of the block and would probably also be very confusing to human readers
13. Generating topologies and coordinates pdb2gmx converts pdb files to topology and coordinate files editconf edits the box and writes subgroups genbox solvates a system genion generates mono atomic ions on energetically favorable positions genconf multiplies a conformation in random orientations genpr generates position restraints for index groups protonate protonates structures Running a simulation grompp makes a run input file tpbconv makes a run input file for restarting a crashed run mdrun performs a simulation Viewing trajectories ngmx displays a trajectory trjconv converts trajectories to e g pdb which can be viewed with e g rasmol Processing energies g energy writes energies to xvg files and displays averages g enemat extracts an energy matrix from an energy file mdrun with rerun re calculates energies for trajectory frames 124 Run parameters and Programs Converting files editconf trjconv trjcat eneconv xmp2ps Tools make_ndx converts and manipulates structure files converts and manipulates trajectory files concatenates trajectory files converts energy files converts XPM matrices to encapsulated postscript or XPM makes index files mk_angndx generates index files for g_angle gmxcheck gmxdump g_analyze checks and compares files makes binary files human readable analyzes data sets Distances between structures g rms g_confrms g_cluster g_rmsf calculates rmsd s w
14. Index file o distrmsd xvg Output xvgr xmgr file rms rmsdist xpm Output Opt X PixMap compatible matrix file scl rmsscale xpm Output Opt X PixMap compatible matrix file mean rmsmean xpm Output Opt X PixMap compatible matrix file nmr3 nmr3 xpm Output Opt X PixMap compatible matrix file nmr6 nmr6 xpm Output Opt X PixMap compatible matrix file Other options h bool no Print help info and quit nice int 19 Set the nicelevel b real 1 First frame ps to read from trajectory e real 1 Last frame ps to read from trajectory w bool no View output using xvgr or ghostview nlevels int 40 Discretize rms in levels max real 1 Maximum level in matrices E 37 g_rmsf g rmsf computes the root mean square fluctuation RMSF i e standard deviation of atomic positions after first fitting to a reference frame When the optional pdb file is given the RMSF values are converted to B factor values and plotted with the experimental data With option aver the average coordinates will be calculated and used as reference for fitting which is useless usually They are also saved to a gro file which may be usefull With the option aniso g rmsf will compute anisotropic temperature factors and then it will also output average coordinates and a pdb file with ANISOU records corresonding to the oq option Please note that the U values are orientation dependent so before comparison with experimental data you should verify that you fit to
15. Opt Index file Other options h bool no Print help info and quit nice int 19 Set the nicelevel b real 1 First frame ps to read from trajectory e real 1 Last frame ps to read from trajectory pbc enum none PBC treatment none whole inbox or nojump center bool no Center atoms in box box vector 0 0 0 Size for new cubic box default read from input shift vector 000 All coordinates will be shifted by framenr shift fit bool no Fit molecule to ref structure in the structure file pfit bool no Progressive fit to the previous fitted structure prec int 3 Precision for xtc and gro writing in number of decimal places vel bool yes Read and write velocities if possible skip int 1 Only write every nr th frame dt real O Only write frame when t MOD dt first time t0 real O Starting time for trajectory default don t change trunc real 1 Truncate input trj file after this amount of ps dump real 1 Dump frame nearest specified time g87box bool yes Write a box for g87 exec string Execute command for every output frame with the frame number as argument timestep real O Change time step between frames app bool no Append output sep bool no Write each frame to a separate gro or pdb file checkdouble bool no Only write frames with time larger than previous frame E 62 wheel wheel plots a helical wheel representation of your sequence The input sequence is in the dat file where the first line contains the number of residues and
16. The force distribution over the pairs is proportional to r This means that a close pair feels a much larger force than a distant pair which might lead to a too rigid molecule The other option is an equal force distribution In this case each pair feels 1 N of the derivative 60 Force fields of the restraint potential with respect to ry The advantage of this method is that more conformations might be sampled but the non conservative nature of the forces can lead to local heating of the protons It is also possible to use ensemble averaging using multiple protein molecules In this case the bounds should be lowered as in rm rixM48 4 65 ro raxM7Y4 8 where M is the number of molecules The GROMACS preprocessor grompp can do this automatically when the appropriate option is given The resulting distance is then used to calculate the scalar force according to F 0 ry lt T1 kar rw r r LTN lt T2 4 66 kar re ri Fe TN gt T2 where 7 and j denote the atoms of all the pairs that contribute to the NOE signal Using distance restraints A list of distance restrains based on NOE data can be added to a molecule definition in your topology file like in the following example distance_restraints al aj type index type low upi up2 fac 10 16 1 0 1 0 0 0 3 0 4 1 0 10 28 1 1 1 0 0 0 3 0 4 1 0 10 46 1 1 1 0 0 0 3 0 4 1 0 16 22 1 2 1 0 0 0 3 0 4 2 5 16 34 1 3 1 0 0 0 5 0 6
17. The constraints are formally part of the Hamiltonian and therefore they give a contribu tion to the free energy In GROMACS this can be calculated using the LINCS algorithm only If we have a number of constraint equations gg 9k Tk dk 4 89 where rg is the distance vector between two particles and dy is the constraint distance between the two particles we can write this using a A dependent distance as dk Th a Adi y ME 4 90 the contribution C to the Hamiltonian using Lagrange multipliers A Cy Y Aok 4 91 k IC gt a a dit 4 92 4 4 Methods 65 1 1 3 i i 2 i 4 Figure 4 14 Atoms along an alkane chain 4 4 Methods 4 4 1 Exclusions and 1 4 Interactions Atoms within a molecule that are close by in the chain i e atoms that are covalently bonded or linked by one respectively two atoms are so called first neighbors second neigh bors and third neighbors see Fig 4 14 Since the interactions of atom i with i 1 and the interaction of atom i with atom i 2 are mainly quantum mechanical they can not be modeled by a Lennard Jones potential Instead it is assumed that these interactions are adequately modeled by a harmonic bond term or constraint i i 1 and a harmonic angle term i i 2 The first and second neighbors atoms i land i 2 are therefore excluded from the Lennard Jones interaction list of atom i atoms i 1 and i 2 are called exclusions of atom i For third neighbors the norma
18. dump neighbor list If set to a positive number the entire neighbor list is printed in the log file may be many megabytes Mainly for debugging purposes but may also be handy for porting to other platforms 148 Technical Details 2 IAMCOOL when set prints cool quotes otherwise your GROMACS life will be dull and boring 3 WHERE when set print debugging info on line numbers 4 LOG_BUFS the size of the buffer for file I O When set to 0 all file I O will be unbuffered and therefore very slow This can be handy for debugging purposes because it ensures that all files are always totally up to date 5 GMXNPRI for SGI systems only When set gives the default non degrading priority npri for mdrun nmrun g_covar and g_nmeig e g setting setenv GMXNPRI 250 causes all runs to be performed at near lowest priority by default Some other environment variables are specific to one program such as TOTAL for the do_shift program and DSPP for the do_dssp program Appendix B Some implementation details In this chapter we will present some implementation details This is far from complete but we deemed it necessary to clarify some things that would otherwise be hard to understand B 1 Single Sum Virial in GROMACS The virial can be written in full tensor form as y Y a E X ri 0 Fy B 1 i lt j where denotes the direct product of two vectors When this is computed in the inner loop of an MD program 9 multiplications
19. gt re 3 20 Algorithms the prefactor is large 125 the scaling behavior makes the algorithm far superior over the standard O N algorithm when the number of particles exceeds a few hundred In the example of Fig 3 4 the image ty 0 of particle will find 7 as a neighbor while image ty 1 of particle will find k as a neighbor Charge groups Where applicable neighbor searching is carried out on the basis of charge groups A charge group is a small set of nearby atoms that have net charge zero Charge groups are defined in the molecular topology If the nearest image distance between the geometrical centers of the atoms of two charge groups is less than the cutoff radius all atom pairs between the charge groups are included in the pair list This procedure avoids the creation of charges due to the use of a cut off when one charge of a dipole is within range and the other not which can have disastrous consequences for the behavior of the Coulomb interaction function at distances near the cut off radius If molecular groups have full charges ions charge groups do not avoid adverse cut off effects and you should consider using one of the lattice sum methods supplied by GROMACS 13 If appropriately constructed shift functions are used for the electrostatic forces no charge groups are needed Such shift functions are implemented in GROMACS see chapter 4 but must be used with care in principle they should be combined with a la
20. one often wants to remove the overall rotation and translation to look at the internal motion only This can be achieved by least square fitting to a reference structure Care has to be taken that the reference structure is representative for the ensemble since the choice of reference structure influences the covariance matrix One should always check if the principal modes are well defined If the 8 10 Hydrogen bonds 139 a Ta aa wD D A Figure 8 8 Geometrical Hydrogen bond criterion first principal component resembles a half cosine and the second resembles a full cosine you might be filtering noise A good way to check the relevance of the first few principal modes is to calculate the eigenvector subspace overlap between the first and second half of the simulation The overlap between two sets of n orthonormal vectors v1 Vn and W1 W can be quantified as follows 1 n n overlap v w vi wj 8 27 a D lv 8 27 The overlap is 1 when sets v and w span the same subspace Note that this can only be done when the same reference structure is used for the two halves The covariance matrix is built and diagonalized by g covar The principal components and subspace overlap any many more things can be plotted and analyzed with g anaeig 8 10 Hydrogen bonds g_hbond The program g hbond analyses the hydrogen bonds H bonds between all possible donors D and acceptors A To determine if an H bond exists a geometric
21. real tpr Input Generic run input tpr tpb tpa no Print help info and quit O Set the nicelevel 1 First frame ps to read from trajectory 1 Last frame ps to read from trajectory Bibliography 1 101 Ma 119 Berendsen H J C van der Spoel D van Drunen R GROMACS A message passing parallel molecular dynamics implementation Comp Phys Comm 91 43 56 1995 Kraulis P J MOLSCRIPT a program to produce both detailed and schematic plots of protein structures J Appl Cryst 24 946 950 1991 van der Spoel D Vogel H J Berendsen H J C Molecular dynamics simulations of N terminal peptides from a nucleotide binding protein PROTEINS Struct Funct Gen 24 450 466 1996 van Gunsteren W F Berendsen H J C Computer simulation of molecular dy namics Methodology applications and perspectives in chemistry Angew Chem Int Ed Engl 29 992 1023 1990 Fraaije J G E M Dynamic density functional theory for microphase separation kinetics of block copolymer melts J Chem Phys 99 9202 9212 1993 McQuarrie D A Statistical Mechanics New York Harper amp Row 1976 van Gunsteren W F Berendsen H J C Algorithms for macromolecular dynamics and constraint dynamics Mol Phys 34 1311 1327 1977 Nilges M Clore G M Gronenborn A M Determination of three dimensional structures of proteins from interproton distance data by dynamical simulated anneal ing fro
22. x However one may cast eqn D 2 in another form containing partial sums which allows for a sequential update algorithm Define the partial sum m i n and the partial variance E a Xn m 2 Onm 5 Ti Wee 1 D 6 166 Averages and fluctuations It can be shown that Xnm k Xn m ide D 7 and Xn Xnm k V Sami Cno HUG pe 1 Hk 1 m n 1 m n 1 D 8 k For n 1 one finds Xi X1m k 2 m m k Olm k Cim Om 1jm k aA eal D 9 and for n 1 and k 1 eqn D 8 becomes X1 Xim Olm 1 Olm T ee an m m 1 D 10 Xim MIm 1 ar ee D 11 Sl m m 1 where we have used the relation Xi m Xim Im 1 D 12 Using formulae eqn D 11 and eqn D 12 the average XN 2 D 13 a H D 13 and the fluctuation A 1 a IND 01 Ny 2 Az Ns D 14 can be obtained by one sweep through the data D 2 Implementation In GROMACS the instantaneous energies E m are stored in the energy file along with the values of 01 m and X1m Although the steps are counted from 0 for the energy and fluctuations steps are counted from 1 This means that the equations presented here are the ones that are implemented We give somewhat lengthy derivations in this section to simplify checking of code and equations later on D 2 1 Part of a Simulation It is not uncommon to perform a simulation where the first part e g 100 ps is taken as equilibration However the averages and fluctuati
23. 1 0 In this example a number of features can be found In columns ai and aj you find the atom numbers of the particles to be restrained The type column should always be 1 As explained in sec 4 2 9 multiple distances can contribute to a single NOE signal In the topology this can be set using the index column In our example the restraints 10 28 and 10 46 both have index 1 therefore they are treated simultaneously An extra requirement for treating restraints together is that the restraints should be on successive lines without any other intervening restraint The type column will usually be 1 but can be set to 2 to obtain a distance restraint which will never be time and ensemble averaged this can be useful for restraining hydrogen bonds The columns low up1 and up2 hold the values of ro r and r2 from eqn 4 59 In some cases it can be useful to have different force constants for some restraints this is controlled by the column fac The force constant in the parameter file is multiplied by the value in the column fac for each restraint Some parameters for NMR refinement can be specified in the grompp mdp file 4 3 Free energy calculations 61 disre type of distance restraining The disre variable sets the type of distance re straining no simple turns the distance restraining off on When multiple proteins or peptides are used in the simulation ensemble averaging can be turned on by setting disre ensemble disre weighting f
24. 1 Non bonded interactions 49 1 5 Normal Force Shifted Force Se es 1 0 L Shift Function J 0 0 1 0 2 0 3 0 4 0 5 0 r Figure 4 4 The Coulomb Force Shifted Force and Shift Function S r using r 2 and ee where C re r1 re r1 4 29 When r 0 the modified Coulomb force function is 1 5r 4r LT Se A 4 30 aa S 4 30 identical to the parabolic force function recommended to be used as a short range function in conjunction with a Poisson solver for the long range part 13 The modified Coulomb potential function is 1 5 5re y E os AO 4 31 r ro 3re i 3r4 r see also Fig 4 4 4 1 6 Modified short range interactions with Ewald summation When Ewald summation or particle mesh Ewald is used to calculate the long range inter actions the short range coulomb potential must also be modified similar to the switch function above In this case the short range potential is given by erfc Brij V r 2 qig 4 32 Tij where 6 is a parameter that determines the relative weight between the direct space sum and the reciprocal space sum and erfc x is the complementary error function For further details on long range electrostatics see sec 4 6 50 Force fields 200 150 100 A A y y V kJ mole 50 0 08 0 09 0 10 0 11 r nm Figure 4 5 Principle of bond stretching left a
25. 1 one planar hydrogen e g rings or peptide bond one hydrogen atom n is generated lying in the plane of atoms i j k on the line bisecting angle j i k at a distance of 0 1 nm from atom i such that the angles n i j and n i k are gt 90 degrees 2 one single hydrogen e g hydroxyl one hydrogen atom n is generated at a distance of 0 1 nm from atom i such that angle n i j 109 5 degrees and dihedral n i j k trans 3 two planar hydrogens e g NH2 two hydrogens n1 n2 are generated at a distance of 0 1 nm from atom i such that angle n1 i j n2 i j 120 degrees and dihedral n1 i j k cis and n2 i j k trans such that names are according to IUPAC standards 56 4 two or three tetrahedral hydrogens e g CH3 three n1 n2 n3 or two n1 n2 hydrogens are generated at a distance of 0 1 nm from atom i such that angle n1 1 3 n2 i 3 n3 1 3 109 5 dihedral n1 i j k trans n2 i j k trans 120 and n3 i j k trans 240 degrees 5 one tetrahedral hydrogen e g C3CH one hydrogen atom n1 is generated at a distance of 0 1 nm from atom i in tetrahedral conformation such that angle n1 i 3 n1 i k n1 i 1 109 5 degrees 6 two tetrahedral hydrogens e g C CH2 C two hydrogen atoms n1 n2 are generated at a distance of 0 1 nm from atom i in tetrahedral conformation on the plane bissecting angle i j k with angle nl i n2 n1 i j n1 i k 109 5 two water hydrogens two hydrogens are generated around atom i according to SPC
26. 2 or a Cray T3E consist of relatively small numbers of relatively fast scalar processors typically 8 to 256 The communication channels that are available in hardware on these machine are not directly visible for the programmer a software layer like MPI or PVM hides this and makes communication from all processors to all others possible In contrast in the GROMACS hardware 1 only communication in a ring was available i e each processor could communicate with its direct neighbors only It seems logical to map the computational box of an MD simulation system to a 3D grid of processors e g 4x4x4 for a 64 processor system This ensures that most interactions that are local in space can be computed with information from neighboring processors only However this means that there have to be communication channels in 3 dimensions too which is not necessarily the case Although this may be overcome in software such a mapping is complicated for the MD software as well without clear benefits in terms of performance for most parallel computers Therefore we opt for a simple one dimensional division scheme for the computational box Each processor gets a slab of this box in the X dimension For the communication between processors this has two main advantages 1 Simplicity of coding Communication can only be to two neighbors called left and right in GROMACS 2 Communication can usually be done in large chunks which makes it more efficien
27. 3 4 2 4 Communicate the NS grid to neighboring processors not necessarily to all proces sors The amount of neighboring NS grid cells Nyy to communicate is determined by the cut off length re according to Nox 3 51 where ly is the box length in the slabbing direction 5 On each processor compute the neighbor list for all charge groups in its slab using the normal grid neighbor searching For homogeneous system this is close to an optimal load balancing without actually doing load balancing For inhomogeneous system such as membranes or interfaces the dimension for slabbing must be chosen such that it is perpendicular to the interface in this fashion each processor has a little bit of everything The GROMACS utility program editconf has an option to rotate a whole computational box The following observations are important here e Particles may diffuse from one slab to the other therefore each processor must hold coordinates for all particles all the time and distribute forces back to all processors as well e Velocities are kept on the home processor for each particle where the integration of Newton s equations is done e Fixed interaction lists bonds angles etc are kept each on a single processor Since all processors have all coordinates it does not matter where interactions are calculated The division is actually done by the GROMACS preprocessor grompp and care is taken that as far as poss
28. 4 energies calculate Lennard Jones SR energies calculate Lennard Jones 1 4 energies calculate Buckingham energies calculate free energy reference temperature for free energy calculation g energy extracts energy components or distance restraint data from an energy file The user is prompted to interactively select the energy terms she wants When the viol option is set the time averaged violations are plotted and the running time averaged and instantaneous sum of violations are recalculated Additionally running time averaged and instantaneous distances between selected pairs can be plotted with the pairs option Average and RMSD are calculated with full precision from the simulation see printed manual Drift is calculated by performing a LSQ fit of the data to a straight line Total drift is drift multiplied by total time 186 Manual Pages With G a Gibbs free energy estimate is calculated using the formula G ln lt e E kT gt kT where k is Boltzmann s constant T is set by Gtemp and the average is over the ensemble or time in a trajectory Note that this is in principle only correct when averaging over the whole Boltzmann ensemble and using the potential energy This also allows for an entropy estimate using G H T S where H is the enthalpy H U p V and S entropy Files f ener edr Input Opt Generic energy edr ene s topol tpr Input Opt Generic run input tpr tpb tpa 0 energy xvg Output xvgr xmgr f
29. 57 i e 1 The first atom is oxygen the other two are hydrogens 2 The first atom has Lennard Jones sec 4 1 1 and coulomb sec 4 1 3 interactions the other two only have coulomb The loop also works for the SPC E 67 and TIP3P 38 water models No assumption is made about force field parameters or charges The gain of this implementation is that there are more floating point operations in a single loop which implies that some compilers can schedule the code better It turns out however that even some of the most advanced compilers have problems with scheduling implying that manual tweaking is necessary to get optimum performance This may include common subexpression elimination or moving code around The loop is used when a solvent optimization is selected in the mdp file B 2 Optimizations 153 B 2 2 Shake for Water SETTLE We have implemented the SETTLE algorithm 22 which is an analytical solution of shake specifically for water SETTLE can be selected in the topology file Check for instance the topology GMXLIB spc itp moleculetype molname nrexcl SOL 1 atoms nr at type res nr rennm at nm cg nr charge 1 OW 1 SOL OW1 1 0 82 2 HW 1 SOL HW2 1 0 41 3 HW 1 SOL HW3 1 0 41 settles OW funct doh dhh 1 1 0 1 0 16333 exclusions 1 2 3 2 1 3 3 1 2 The section settles defines the first atom of the watery molecule the settle funct is always one and the distance between O and H
30. B 3 6 Implementation The lookup tables can be generated by a small C program which uses floating point numbers and operations with IEEE 32 bit single precision format Note that because of the odd even information that is needed the fraction table is twice the size earlier specified 13 bit i s o 12 bit The function according to equation eqn B 29 has to be implemented Applied to the 1 z function equation eqn B 28 leads to 1 f 0 3 B 54 and so 2 fi B 55 sO Yn 1 Yn 7 B 56 ma or Unir 3 aya B 57 Where yo can be found in the lookup tables and y gives the result to the maximum accuracy It is clear that only one iteration extra in double precision is needed for a double precision result B 4 Tabulated functions 159 B 4 Tabulated functions In some of the inner loops of GROMACS lookup tables are used for computation of potential and forces The tables are interpolated using a cubic spline algorithm There are separate tables for electrostatic dispersion and repulsion interactions but for the sake of caching performance these have been combined into a single array The cubic spline interpolation looks like this 2 h n y t mi aa gt 0 my vi B 58 where e 1 9 and y and Y are the tabulated values of a function y x and its second derivative respectively Furthermore h Ti41 Ti B 59 le z h B 60 so that 0 lt e lt 1 eqn B 58 can be rew
31. Fi y Fi B 12 j l N F J Fi B 13 i 1 which is the total force on 2 resp j Because we use Newton s third law Fi P B 14 we must in the implementation double the term containing the shift 6 B 1 3 The intramolecular shift mol shift For the bonded forces and shake it is possible to make a mol shift list in which the periodicity is stored We simple have an array mshift in which for each atom an index in the shiftvec array is stored B 1 Single Sum Virial in GROMACS 151 The algorithm to generate such a list can be derived from graph theory considering each particle in a molecule as a bead in a graph the bonds as edges 1 represent the bonds and atoms as bidirectional graph 2 make all atoms white 3 make one of the white atoms black atom 7 and put it in the central box 4 make all of the neighbors of i that are currently white grey 5 pick one of the grey atoms atom 7 give it the correct periodicity with respect to any of its black neighbors and make it black 6 make all of the neighbors of j that are currently white grey 7 if any grey atom remains goto 5 8 if any white atom remains goto 3 Using this algorithm we can e optimize the bonded force calculation as well as shake e calculate the virial from the bonded forces in the single sum way again Find a representation of the bonds as a bidirectional graph B 1 4 Virial from Covalent Bonds The covalent bond force gives a contribution to the v
32. It is however not recommended to be used for long alkanes and lipids The GROMOS 96 force field differs from the GROMACS force field in a few aspects e the force field parameters e the parameters for the bonded interactions are not linked to atom types e a fourth power bond stretching potential sec 4 2 1 e an angle potential based on the cosine of the angle sec 4 2 3 There are two differences in implementation between GROMACS and GROMOS 96 which can lead to slightly different results when simulating the same system with both packages e in GROMOS 96 neighbor searching for solvents is performed on the first atom of the solvent molecule this is not implemented in GROMACS but the difference with searching with centers of charge groups is very small e the virial in GROMOS 96 is molecule based this is not implemented in GROMACS which uses atomic virials The GROMOS 96 force field was parameterized with a Lennard Jones cut off of 1 4 nm so be sure to use a Lennard Jones cut off of at least 1 4 A larger cut off is possible because the Lennard Jones potential and forces are almost zero beyond 1 4 nm 4 8 2 GROMOS 96 files GROMACS can read and write GROMOS 96 coordinate and trajectory files These files should have the extension g96 Such a file can be a GROMOS 96 initial final configura tion file or a coordinate trajectory file or a combination of both The file is fixed format 74 Force fields all floats are written as 15
33. Normalization lt pg gt local 9 Normalization volumes are colored grey Gromacs RDF OW1 OW1 3 0 7 2 0 H iI f S 1 0 0 LA 0 0 L L 0 0 0 5 1 0 15 20 r nm Figure 8 3 goo r for Oxygen Oxygen of SPC water 8 5 Correlation functions 131 This gag r 0 is useful for analyzing anisotropic systems Note that in this case the normalization lt pg gt local o is the average density in all angle slices from 0 to 0 d0 up to Tmax SO angle dependent see Fig 8 2D 8 5 Correlation functions 8 5 1 Theory of correlation functions The theory of correlation functions is well established 60 However we want to describe here the implementation of the various correlation function flavors in the GROMACS code The definition of the autocorrelation function ACF C t for a property f t is Crt FOSE 8 6 where the notation on the right hand side means averaging over i e over time origins It is also possible to compute cross correlation function from two properties f t and g t Crg t FOIE tte 8 7 however in GROMACS there is no standard mechanism to do this note you can use the xmgr program to compute cross correlations The integral of the correlation function over time is the correlation time Ty Tf O 8 8 In practice correlation functions are calculated based on data points with discrete time intervals At so that the ACF from an MD simu
34. Per block the following options are present e replace replace an existing atom by one with a different atom type atom name charge and or mass For each atom to be replaced on line should be entered with the following fields name of the atom to be replaced new atom name new atom type new mass new charge e add add new atoms For each group of added atom s a two line entry is necessary The first line contains the same fields as an entry in the hydrogen database number of atoms type of addition control atoms see 5 3 5 but the possible types of addition are extended by two more specifically for C terminal additions 8 two carbozxyl oxygens COO two oxygens n1 n2 are generated according to rule 3 at a distance of 0 136 nm from atom i and an angle n1 i j n2 i j 117 degrees 9 carboryl oxygens and hydrogen COOH two oxygens n1 n2 are generated according to rule 3 at distances of 0 123 nm and 0 125 nm from atom i for n1 and n2 resp and angles n1 i j 121 and n2 i j 115 degrees One hydrogen n is generated around n2 according to rule 2 where n i j and n i j k should be read as n n2 i and n n2 i j resp After this line another line follows which specifies the details of the added atom s in the same way as for replacing atoms i e 86 5 4 5 4 1 Topologies atom name atom type mass charge Like in the hydrogen database see 5 3 5 when more t
35. This is implemented using a freeze factor f which is a vector and differs for each freezegroup see sec 3 3 This vector contains only zero freeze or one don t freeze When we take this freeze factor and the external acceleration ap into account the update algorithm for the velocities becomes F t A A d F n At a At 3 29 vt 7 f A ult 3 where g and h are group indices which differ per atom 3 4 4 Constraint algorithms SHAKE Constraints can be imposed in GROMACS using the traditional SHAKE method 21 The SHAKE routine changes a set of unconstrained coordinates r to a set of coordinates r that fulfill a list of distance constraints using a set r as reference SHAKE r gt r r This action is consistent with solving a set of Lagrange multipliers in the constrained equations of motion SHAKE needs a tolerance TOL it will continue until all constraints 3 4 Molecular Dynamics 25 THE UPDATE ALGORITHM Given Positions r of all atoms at time Velocities v of all atoms at time t Accelerations F m on all atoms at time t Forces are computed disregarding any constraints Total kinetic energy and virial 4 1 Compute the scaling factors A and pu according to eqns 3 20 and 3 23 y 2 Update and scale velocities v A v aAt y 3 Compute new unconstrained coordinates r r v At y 4 Apply constraint algorithm to coordinates constrain r gt r r 4 5 Correct veloc
36. V kJ mol 100 A AAA Figure 4 6 The Morse potential well with bond length 0 15 nm 0 0 L ii L f L 100 0 110 0 120 0 130 0 140 0 0 Figure 4 7 Principle of angle vibration left and the bond angle potential right 4 2 3 Bond angle vibration Harmonic potential The bond angle vibration between a triplet of atoms 2 j k is also represented by a harmonic potential on the angle 0 1 Va ijk Sign ijk 0 4 44 As the bond angle vibration is represented by a harmonic potential the form is the same as the bond stretching Fig 4 5 4 2 Bonded interactions 53 i l l 0 O J k j k Figure 4 8 Principle of improper dihedral angles Out of plane bending for rings left substituents of rings middle out of tetrahedral right The improper dihedral angle is defined as the angle between planes i j k and 3 k 1 in all cases The force equations are given by the chain rule F Walon dV d L rij Trj p Craig where 934 arccos gt 4 45 k dry Tigh kj F F F The numbering 2 j k is in sequence of covalently bonded atoms with 7 denoting the middle atom see Fig 4 7 Cosine based potential In the GROMOS 96 force field a simplified function is used to represent angle vibrations 1 2 Va ijn 5 hii cos 0 1 cos 0 4 46 where ets cos jj4 22 4 47 Tigh kj The corresponding force can be derived by par
37. all Calpha atoms it is calced as sqrt SUM i x i y i N where N is the number of backbone atoms For an ideal helix the radius is 0 23 nm 2 Twist file twist xvg The average helical angle per residue is calculated For alpha helix it is 100 degrees for 3 10 helices it will be smaller for 5 helices it will be larger 3 Rise per residue file rise xvg The helical rise per residue is plotted as the difference in Z coordinate between Ca atoms For an ideal helix this is 0 15 nm 4 Total helix length file len ahx xvg The total length of the helix in nm This is simply the average rise see above times the number of helical residues see below 5 Number of helical residues file n ahx xvg The title says it all 6 Helix Dipole backbone only file dip ahx xvg 7 RMS deviation from ideal helix calculated for the Calpha atoms only file rms ahx xvg 8 Average Calpha Calpha dihedral angle file phi ahx xvg 9 Average Phi and Psi angles file phipsi xvg 10 Ellipticity at 222 nm according to Hirst and Brooks Files s topol tpr Input Generic run input tpr tpb tpa n index ndx Input Index file f traj xtc Input Generic trajectory xtc trr trj gro g96 pdb to gtraj g87 Output Opt Gromos 87 ASCII trajectory format cz zconf gro Output Generic structure gro g96 pdb co waver gro Output Generic structure gro g96 pdb Other options h bool no Print help info and quit nice int 19 Set the nicelevel b real 1 First
38. at 1 206 Manual Pages Files f conf gro Input Generic structure gro g96 pdb tpr tpb tpa n in ndx Input Opt Index file 0 index ndx Output Index file Other options h bool no Print help info and quit nice int O Set the nicelevel E 53 mdrun The mdrun program performs Molecular Dynamics simulations It reads the run input file s and distributes the topology over processors if needed The coordinates are passed around so that computations can begin First a neighborlist is made then the forces are computed The forces are globally summed and the velocities and positions are updated If necessary shake is performed to constrain bond lengths and or bond angles Temperature and Pressure can be controlled using weak coupling to a bath mdrun produces at least three output file plus one log file g per processor The trajectory file 0 contains coordinates velocities and optionally forces The structure file c contains the coordinates and velocities of the last step The energy file e contains energies the temperature pressure etc a lot of these things are also printed in the log file of processor 0 Optionally coordinates can be written to a compressed trajectory file x When running in parallel with PVM or an old version of MPI the np option must be given to indicate the number of processors The option dgdl is only used when free energy perturbation is turned on With rerun an input trajectory can be given
39. at http md chem rug nl gmx Often the output files are in xmgr format First in sec 8 1 the group concept in analysis is explained Then the different analysis tools are presented 8 1 Groups in Analysis make_ndx mk_angndx In chapter 3 it was explained how groups of atoms can be used in the MD program In most analysis programs an index file is necessary too to select groups to work on Let s consider a simulation of a binary mixture of components A and B When we want to calculate the radial distribution function rdf g4g r of A with respect to B we have to calculate 4rr gag r V deo 8 1 where V is the volume and P r is the probability to find a B atom at a distance r from an A atom By having the user define the atom numbers for groups A and B in a simple file we can calculate this gag in the most general way without having to make any assumptions in the rdfprogram about the type of particles 128 Analysis Water That Was Pretty Cool Time 0 00 ps KODEA Figure 8 1 The window of ngmx showing a box of water Groups can therefore consist of a series of atom numbers but in some cases also of molecule numbers It is also possible to specify a series of angles by triples of atom numbers dihedrals by quadruples of atom numbers and bonds or vectors in a molecule by couples of atom numbers When appropriate the type of index file will be specified for the foll
40. can add it yourself The program has limited intelligence it reads a number of database files that allow it to make special bonds Cys Cys Heme His etc if necessary this can be done manually The program can prompt the user to select which kind of LYS ASP GLU CYS or HIS residue she wants For LYS the choice is between LYS two protons on NZ or LYSH three protons default for ASP and GLU unprotonated default or protonated for HIS the proton can be either on ND1 HISA on NE2 HISB or on both HISH By default these selections are done automatically For His this is based on an optimal hydrogen bonding conformation Hydrogen bonds are defined based on a simple geometric criterium specified by the maximum hydrogen donor acceptor angle and donor acceptor distance which are set by angle and dist respectively During processing the atoms will be reordered according to Gromacs conventions With n an index file can be generated that contains one group reordered in the same way This allows you to convert a Gromos trajectory and coordinate file to Gromos There is one limitation reordering is done after the hydrogens are stripped from the input and before new hydrogens are added This means that should not turn off reth The gro and g96 file formats do not support chain identifiers Therefore it is useful to enter a pdb file name at the o option when you want to convert a multichain pdb file When using reth to keep all hydroge
41. compiler could not come up with The implementation is typically done by calling a set of library routines to send and receive data to and from other processors Almost all hardware vendors support this way of parallelism in their C and Fortran compilers 2 Data Parallel This method lets the user define arrays on which to operate in parallel Program ming this way is much like vectorizing recurrence is not parallelized e g for i 1 i lt MAX i a i ali 1 1 does not vectorise and not parallelize be cause for every i the result from the previous step is needed The advantage of data parallelism is that it is easier for the user the compiler takes care of the parallelism The disadvantage is that it is supported by a small though growing number of hardware vendors and that it is much harder to maintain a program that has to run on both parallel and sequential machines because the only standard language that supports it is Fortran 90 which is not available on many platforms Both methods allow for the MD algorithm to be implemented without much trouble Message passing MD algorithms have been published since the mid 80 s 32 33 and development is still continuing Data parallel programming is newer but starting from a well vectorized program it is not hard to do Our implementation of MD is a message passing one the reason for which is partly his torical the project to develop a parallel MD program started when F
42. component of the pressure can be coupled to a pressure bath The average surface tension y t can be calculated from the difference between the normal and the lateral pressure Lz z z s 1 f Pacat 2 A de 3 24 La pi Pet PO 8 25 24 Algorithms where L is the height of the box and n is the number of surfaces The pressure in the z direction is corrected by scaling the height of the box with pz AP Po P 3 26 Tp Hz 1 P AP 3 27 This is similar to normal pressure coupling except that the power of one third is missing The pressure correction in the z direction is then used to get the correct convergence for the surface tension to the reference value yy The correction factor for the box length in the x y direction is Hoy 14 Any 2 rato ar O 3 28 MeL The value of 3 is more critical than with normal pressure coupling Normally an incorrect compressibility will just scale Tp but with surface tension coupling it affects the conver gence of the surface tension When 3 is set to zero constant box height AP is also set to zero which is necessary for obtaining the correct surface tension The complete update algorithm The complete algorithm for the update of velocities and coordinates is given in Fig 3 6 The SHAKE algorithm of step 4 is explained below GROMACS has a provision to freeze prevent motion of selected particles which must be defined as a freeze group
43. cpp Specifying pp will get the pre processed topology file written out If your system does not have a c preprocessor you can still use grompp but you do not have access to the features from the cpp Command line options to the c preprocessor can be given in the mdp file See your local manual man cpp When using position restraints a file with restraint coordinates can be supplied with r otherwise constraining will be done relative to the conformation from the c option Starting coordinates can be read from trajectory with t The last frame with coordinates and velocities will be read unless the time option is used Note that these velocities will not be used when gen_vel yes in your mdp file If you want to continue a crashed run it is easier to use tpbconv Using the morse option grompp can convert the harmonic bonds in your topology to morse potentials This makes it possible to break bonds For this option to work you need an extra file in your GMXLIB with dissociation energy Use the debug option to get more information on the workings of this option look for MORSE in the grompp log file using less or something like that By default all bonded interactions which have constant energy due to dummy atom constructions will be removed If this constant energy is not zero this will result in a shift in the total energy All bonded interactions can be kept by turning off rmdumbds Additionally all constraints for distances w
44. default since it takes a couple of minutes but for large runs it will save time Turn it on by specifying optimize_fft yes in your mdp file When running in parallel the grid must be communicated several times and thus hurting scaling performance With PME you can improve this by increasing grid spacing while simultaneously increasing the interpolation to e g 6th order Since the interpolation is entirely local a this will improve the scaling in most cases 4 7 All hydrogen forcefield 73 4 7 All hydrogen forcefield The GROMACS all hydrogen forcefield is almost identical to the normal GROMACS forcefield since the extra hydrogens have no Lennard Jones interaction and zero charge The only differences are in the bond angle and improper dihedral angle terms This forcefield is only useful when you need the exact hydrogen positions for instance for distance restraints derived from NMR measurements 4 8 GROMOS 96 notes 4 8 1 The GROMOS 96 force field GROMACS supports the GROMOS 96 force fields 42 All parameters for the 43a1 43a2 development improved alkane dihedrals and 43b1 vacuum force fields are included All standard building blocks are included and topologies can be build automatically by pdb2gmx The GROMOS 96 force field is a further development of the GROMOS 87 force field on which the GROMACS forcefield is based The GROMOS 96 force field has improvements over the GROMACS force field for proteins and small molecules
45. detail is used except for hydrogen atoms bound to aliphatic carbon atoms which are treated as united atoms No special hydrogen bond term is included The last 10 atom types are extra atom types with respect to the GROMOS 87 force field 35 e F was taken from ref 39 e CP2 and CP3 from ref 36 and references cited therein e CR5 CR6 and HCR from ref 54 e OWTS from ref 38 e SD OD and CD from ref 40 Therefore if you use the GROMACS force field as it is make sure you use the references in your publications as mentioned above Note GROMACS makes use of the atom types as a name not as a number as e g in GROMOS 5 2 2 Dummy atoms Some force fields use dummy atoms virtual sites that are constructed from real atoms on which certain interaction functions are located e g on benzene rings to reproduce the correct quadrupole This is described in sec 4 5 To make dummy atoms in your system you should include a section dummies in your topology file where the stands for the number constructing atoms for the dummy atom This will be 2 for type 2 3 for types 3 3fd 3fad and 3out and 4 for type 4fd the different types are explained in sec 4 5 Parameters for type 2 should look like this dummies2 Dummy from funct a 5 1 2 1 0 7439756 78 Topologies for type 3 like this dummies3 Dummy from funct a b 5 1 2 3 1 0 7439756 0 128012 for type 3fd like this
46. distance between two atoms or the minimum distance between two groups of atoms e g protein side chains in a salt bridge To calculate these distances between certain groups there are several possibilities e The distance between the geometrical centers of two groups can be calculated with g sgangle as explained in sec 8 6 e The minimum distance between two groups of atoms during time can be calculated with the program g mindist It also calculates the number of contacts between these groups within a certain radius rmaz e To monitor the minimum distances between residues see chapter 5 within a protein molecule you can use the program g mdmat This minimum distance between two residues A and Aj is defined as the smallest distance between any pair of atoms i As j As The output is a symmetrical matrix of smallest distances between all residues To visualize this matrix you can use a program such as xv If you want 8 8 Root mean square deviations in structure 137 21 30 40 50 60 70 80 90 Residue Number 0 Distance nm 1 2 Figure 8 7 A minimum distance matrix for a peptide 3 to view the axes and legend or if you want to print the matrix you can convert it with xpm2ps into a Postscript picture see Fig 8 7 Plotting these matrices for different time frames one can analyze changes in the structure and e g forming of salt bridges 8 8 Root mean square deviations in structure g_rms g_rmsdist
47. divides the box in slices and sums all charges of the atoms in each slice It then integrates this charge density giving the electric field and the electric field giving the potential Charge density field and potential are written to xvgr input files The program g_coord is a very simple analysis program All it does is print the coordinates of selected atoms to three files containing respectively the z y and z coordinates of those atoms It can also calculate the center of mass of one or more molecules and print the coordinates of the center of mass to three files By itself this is probably not a very useful analysis but having the coordinates of selected molecules or atoms can be very handy for further analysis not only in interface systems The program g pvd calculates a lot of properties among which the density of a group in particles per unit of volume but not a density that takes the mass of the atoms into account The program g density also calculates the density of a group but takes the 144 Analysis masses into account and gives a plot of the density against a box axis This is useful for looking at the distribution of groups or atoms across the interface 8 13 Chemical shifts total do_shift You can compute the NMR chemical shifts of protons with the program do_shift This is just an GROMACS interface to the public domain program total 66 For further information read the article Appendix A Technical Detai
48. dssp program get it do dssp assumes that the dssp executable is in home mdgroup dssp dssp If that is not the case then you should set an environment variable DSSP pointing to the dssp executable as in setenv DSSP usr local bin dssp The structure assignment for each residue and time is written to an xpm matrix file This file can be visualized with for instance xv and can be converted to postscript with xpm2ps The number of residues with each secondary structure type and the total secondary structure sss count as a function of time are also written to file sc Solvent accessible surface per residue can be calculated both in absolute values A and in frac tions of the maximal accessible surface of a residue The maximal accessible surface is defined as the accessible surface of a residue in a chain of glycines Files f traj xtc Input Generic trajectory xtc trr trj gro g96 pdb s topol tpr Input Structure mass db tpr tpb tpa gro g96 pdb n index ndx Input Opt Index file map ss map Input Lib File that maps matrix data to colors 0 ss xpm Output X PixMap compatible matrix file sc scount xvg Output xvgr xmgr file a area xpm Output Opt X PixMap compatible matrix file ta totarea xvg Output Opt xvgr xmer file aa averarea xvg Output Opt xvgr xmgr file Other options h bool no Print help info and quit nice int 19 Set the nicelevel b real 1 First frame ps to read from trajectory e real 1 Last frame p
49. dummify all aromatic residues Note that when all hydrogen atoms are dummified also those inside the aromatic residues will be dummified i e hy drogens in the aromatic residues are treated differently depending on the treatment of the aromatic residues Parameters for the dummy constructions for the hydrogen atoms are inferred from the forcefield parameters vis bond lengths and angles directly by grompp while processing the topology file The constructions for the aromatic residues are based on the bond lengths and angles for the geometry as described in the forcefields but these parameters are hard coded into pdb2gmx due to the complex nature of the construction needed for a whole aromatic group 6 2 1 Hydrogen bond angle vibrations Construction of Dummy Atoms The goal of defining hydrogen atoms as dummy atoms is to remove all high frequency de grees of freedom from them In some cases not all degrees of freedom of a hydrogen atom should be removed e g in the case of hydroxyl or amine groups the rotational freedom of the hydrogen atom s should be preserved Care should be taken that no unwanted correlations are introduced by the construction of dummy atoms e g bond angle vibra tion between the constructing atoms could translate into hydrogen bond length vibration Additionally since dummy atoms are by definition mass less in order to preserve total system mass the mass of each hydrogen atom that is treated as dummy atom should be
50. eS 182 BAG e dipolesn s a2 oa bey Sak wee ae ee ae ERS ee a al D 182 Bil 22SEC ye sees oe Se Mo e Ae ed bs ke aes i Eo a 4 184 Bil82dist it wk Ae ek Be Ed a Rath eR Soe a 184 BOS eneM ab es os ei ee E a a ee a ae ee gh ae A 185 E 20 energy cuate 185 B2 Boy TAl Os de oak oh hte a Get ke A to E Sere at We toa ee ae Y 186 B22 ADO oopa par sire fe IS eh ge BE BS OG Pd a ee d 187 E23 0 Abod iso o Ke eae ee os a AO I a to ee a 187 B24 e helix e GA Pa ad Got e AI a Ae Pst ge Tabet a 189 E25 g mdmat epa e eae Se A A al eh aan eS 190 B26 mind ist igs eh a Pha eee aod oP on BAY aon we ae E 190 E27 g msd 2 eos E eee ee eal a a a et we el A 191 E 28 e nMel eg eai a Sees ade Re EE hea sh Ba Fedele Mea aa She a ea ee 191 B29 OMENS ee a Eo Pe ee en EO E 192 B30 BLE i sah doe eed Wa Bee a on Ss a he oe A hee a 192 Eo l e2 potentials sas 4 Fok Rok BO as ARA ee eee ga ets Ss 193 E IZLETIAMA cig ht ou eters GE eee K o ee ee eo ee 193 B33 BIEOS 5s Sie he a Be a ae O ea eee ae ae 194 E34 see Ob we Se ah BP Std ne A oe ARA ey GS ee sy a 194 BOO gm ese seve a A He cee es hc ee dee T 195 BE 36 e tmsdist sci ge eh Aa ROO RRS E BPS Me aoa ae 3 196 EOC germs AA PR oe ook ak ee Py ee ete Se ae eae des 4 196 POOL pa e o Sheets cai oo ates fac pe ita a ee E 197 EI salt br a atte ih oar AA eae Baas RG Ruel ees 198 TAO PSAs eho A sig ee Re cage A Sa a atthe ote aed cabana 198 xii E 42 g_velacc E 43 genbox E 44 genconf E 45 gendr E 46 genion E 47 g
51. energetically favorable positions g_potential calculates the electrostatic potential across the box g dipoles computes the total dipole plus fluctuations g_dielectric calculates frequency dependent dielectric constants Protein specific analysis do_dssp assigns secondary structure and calculates solvent accessible surface area g_chi calculates everything you want to know about chi and other dihedrals g_helix calculates everything you want to know about helices g rama computes Ramachandran plots xrama shows animated Ramachandran plots wheel plots helical wheels Interfaces g potential calculates the electrostatic potential across the box g density calculates the density of the system g_order computes the order parameter per atom for carbon tails g h2order computes the orientation of water molecules Covariance analysis g_covar calculates and diagonalizes the covariance matrix g_anaeig analyzes the eigenvectors Normal modes grompp makes a run input file mdrun finds a potential energy minimum nmrun calculates the Hessian g_nmeig diagonalizes the Hessian g_anaeig analyzes the normal modes g nmens generates an ensemble of structures from the normal modes 126 Run parameters and Programs Chapter 8 Analysis In this chapter different ways of analyzing your trajectory are described The names of the corresponding analysis programs are given Specific info on the in and output of these programs can be found in the on line manual
52. eqn 3 40 For MD calculations a fourth order expansion is enough For Position Langevin Dynamics with large time steps an eighth order expansion may be necessary The order is a parameter in the input file for mdrun The implementation of LINCS is done in such a way that the algorithm will never crash Even when it is impossible to to reset the constraints LINCS will generate a conformation which fulfills the constraints as well as possible However LINCS will generate a warning when in one step a bond rotates over more than a predefined angle This angle is set by the user in the input file for mdrun 3 4 5 Output step The important output of the MD run is the trajectory file name trj which contains particle coordinates and optionally velocities at regular intervals Since the trajectory files are lengthy one should not save every step To retain all information it suffices to write a frame every 15 steps since at least 30 steps are made per period of the highest frequency in the system and Shannon s sampling theorem states that two samples per period of the highest frequency in a band limited signal contain all available information But 3 5 Simulated Annealing 29 that still gives very long files So if the highest frequencies are not of interest 10 or 20 samples per ps may suffice Be aware of the distortion of high frequency motions by the stroboscopic effect called aliasing higher frequencies are mirrored with respect to the sampli
53. file Other options h bool no Print help info and quit nice int 19 Set the nicelevel p int O Number of positive ions pn string Na Name of the positive ion pq real 1 Charge of the positive ion n int O Number of negative ions nn string Cl Name of the negative ion nq real 1 Charge of the negative ion rmin real 0 6 Minimum distance between ions wi int 1 First water atom to be cosidered counting from 1 nw int O Number of water molecules random bool no Use random placement of ions instead of based on potential The rmin option should still work seed int 1993 Seed for random number generator E 47 genpr genpr produces an include file for a topology containing a list of atom numbers and three force constants for the X Y and Z direction A single isotropic force constant may be given on the command line instead of three components This list is used as the position restraint list E 48 gmxcheck 203 Files f conf gro Input Generic structure gro g96 pdb tpr tpb tpa n index ndx Input Opt Index file 0 posre itp Output Include file for topology Other options h bool no Print help info and quit nice int O Set the nicelevel fc vector 1000 1000 1000 force constants kJ mol 1 nm 2 E 48 gmxcheck gmxcheck reads a trajectory trj trr or xtc or an energy file ene or edr and prints out useful information about them For a coordinate file generic structure file e g gro gmxcheck will check for presence o
54. for time average A file with reference free energies can be supplied to calculate the free energy difference with some reference state Group names e g residue names in the reference file should correspond to the group names as used in the groups file but a appended number e g residue number in the groups will be ignored in the comparison Files f ener edr groups groups dat eref eref dat emat emat xpm etot energy xvg Other options h bool nice int b real e real w bool sum bool skip int mean bool nlevels int max real min real coul bool coulr bool coul14 bool 1j bool 1j14 bool bham bool free bool temp real no 19 i no no yes 20 1e 20 1e 20 yes no no yes no no yes 300 E 20 g_energy Input Opt Generic energy edr ene Input Generic data file Input Opt Generic data file Output X PixMap compatible matrix file Output xvgr xmgr file Print help info and quit Set the nicelevel First frame ps to read from trajectory Last frame ps to read from trajectory View output using xvgr or ghostview Sum the energy terms selected rather than display them all Skip number of frames between data points with groups calculates matrix of mean energies in stead of matrix for each timestep number of levels for matrix colors max value for energies min value for energies calculate Coulomb SR energies calculate Coulomb LR energies calculate Coulomb 1
55. frame ps to read from trajectory e real 1 Last frame ps to read from trajectory w bool no View output using xvgr or ghostview r0 int 1 The first residue number in the sequence q bool no Check at every step which part of the sequence is helical F bool yes Toggle fit to a perfect helix db bool no Print debug info ev bool no Write a new trajectory file for ED ahxstart int O First residue in helix ahxend int O Last residue in helix 190 Manual Pages E 25 g mdmat g mdmat makes distance matrices consisting of the smallest distance between residue pairs With frames these distance matrices can be stored as a function of time to be able to see differences in tertiary structure as a funcion of time If you choose your options unwise this may generate a large output file Default only an averaged matrix over the whole trajectory is output Also a count of the number of different atomic contacts between residues over the whole trajectory can be made The output can be processed with xpm2ps to make a PostScript tm plot Files f traj xtc Input Generic trajectory xtc trr trj gro g96 pdb s topol tpr Input Structure mass db tpr tpb tpa gro g96 pdb n index ndx Input Opt Index file mean dm xpm Output X PixMap compatible matrix file frames dmf xpm Output Opt X PixMap compatible matrix file no num xvg Output Opt xvgr xmer file Other options h bool no Print help info and quit nice int 19 Set the nicelevel b r
56. function for linear molecules by specifying two atoms i j in the index file EXAMPLES g rotacf P 1 nparm 2 fft n index o rotacf x P1 fa expfit x P1 beginfit 2 5 endfit 20 0 This will calculate the rotational correlation function using a first order Legendre polynomial of the angle of a vector defined by the index file The correlation function will be fitted from 2 5 ps till 20 0 ps to a two parameter exponential Files f traj xtc Input Generic trajectory xtc trr trj gro g96 pdb s topol tpr Input Generic run input tpr tpb tpa n index ndx Input Index file 0 rotacf xvg Output xvgr xmgr file a fitacf xvg Output Opt xvgr xmgr file Other options h bool no Print help info and quit nice int 19 Set the nicelevel b real 1 First frame ps to read from trajectory e real 1 Last frame ps to read from trajectory w bool no View output using xvgr or ghostview d bool no Use index doublets vectors for correlation function instead of triplets planes acflen int 1 Length of the ACF default is half the number of frames 198 Manual Pages normalize bool yes Normalize ACF P enum O Order of Legendre polynomial for ACF 0 indicates none 0 1 2 or nparm enum 1 Number of parameters in exponential fit 1 or 2 beginfit real O Time where to begin the exponential fit of the correlation function endfit real O Time where to end the exponential fit of the correlation function E 39 g_saltbr g saltbr plots the differen
57. info and quit nice int 19 Set the nicelevel time bool yes Expect a time in the input n int 1 Read sets seperated by amp d bool no Use the derivative bw real 0 1 Binwidth for the distribution errbar enum none Error bars for the average none stddev or error subav bool no Subtract the average before autocorrelating oneacf bool no Calculate one ACF over all sets acflen int 1 Length of the ACF default is half the number of frames normalize bool yes Normalize ACF P enum O Order of Legendre polynomial for ACF 0 indicates none 0 1 2 or nparm enum 1 Number of parameters in exponential fit 1 or 2 beginfit real O Time where to begin the exponential fit of the correlation function endfit real O Time where to end the exponential fit of the correlation function E 6 g angle g angle computes the angle distribution for a number of angles or dihedrals This way you can check whether your simulation is correct With option ov you can plot the average angle of a group of angles as a function of time With the all option the first graph is the average the rest are the individual angles With the of option g_angle also calculates the fraction of trans dihedrals only for dihedrals as function of time but this is probably only fun for a selected few With option oc a dihedral correlation function is calculated It should be noted that the indexfile should contain atom triples for angles or atom quadruplets for dihedrals Tf this i
58. is function type pert indicates if this interaction type can be modified during free energy perturbation a multiplicities can not be modified 0 the outer two atoms in the dihedral the inner two atoms in the dihedral For free energy perturbation the parameters for topology B lambda 1 should be added on the same line after the normal parameters in the same order as the normal parameters Table 5 3 The topology top file part 1 5 4 File formats 91 Molecule definition interaction directive f parameters pert mandatory moleculetype molecule name exclude neighbors bonds away for non bonded interactions mandatory atom type residue number residue name atom name charge group number q e m u bond bonds bo nm fe kJ mol nm G96 bond bonds bo nm fe kJ mol nm morse bonds bo nm D kJ mol 8 nm LJ 1 4 pairs ce kJ mol nm c12 kJ mol nm bo deg fe kJ mol rad bo deg fe kJ mol Omax deg fe kJ mol7 mult bo deg fe kJ mol trad Co Ci Ca C3 Ca Cs kJ mol bo nm bo nm don dyn nm angle angles G96 angle angles proper dih dihedrals improper dih dihedrals RB dihedral dihedrals constraint constraints constr n c constraints settle settles dummy2 dummies2 dummy3 dummies3 dummy3fd dummies3 dummy3fad dummies3 dummy3out dummies3 dummy4fd dummies4 position res position_restraints distance res dis
59. is set which also centers the solute The program editconf has more sophisticated options to change the box and center the solute Solvent molecules are removed from the box where the distance between any atom of the solute molecule s and any atom of the solvent molecule is less than the sum of the VanderWaals radii of both atoms A database vdwradii dat of VanderWaals radii is read by the program atoms not in the database are assigned a default distance vdw 3 Insert a number nmo1 of extra molecules ci at random positions The program iterates until nmol molecules have been inserted in the box To test whether an insertion is successful the same Vander Waals criterium is used as for removal of solvent molecules When no appropriately sized holes holes that can hold an extra molecule are available the program does not terminate but searches forever To avoid this problem the genbox program may be used several times in a row with a smaller number of molecules to be inserted Alternatively you can add the extra molecules to the solute first and then in a second run of genbox solvate it all The default solvent is Simple Point Charge water SPC The coordinates for this are read from GMXLIB spc216 gro Other solvents are also supported as well as mixed solvents The only restriction to solvent types is that a solvent molecule consists of exactly one residue The residue information in the coordinate files is used and should therefore be
60. more or less consistent In practice this means that two subsequent solvent molecules in the solvent coordinate file should have different residue number The box of solute is built by stacking the coordinates read from the coordinate file This means that these coordinates should be equlibrated in periodic boundary conditions to ensure a good alignment of molecules on the stacking interfaces The program can optionally rotate the solute molecule to align the longest molecule axis along a box edge This way the amount of solvent molecules necessary is reduced It should be kept in mind that this only works for short simulations as eg an alpha helical peptide in solution can rotate over 90 degrees within 500 ps In general it is therefore better to make a more or less cubic box Finally genbox will optionally remove lines from your topology file in which a number of solvent molecules is already added and adds a line with the total number of solvent molecules in your coordinate file Files cp protein gro Input Opt Generic structure gro g96 pdb tpr tpb tpa cs spc216 gro Input Opt Lib Generic structure gro g96 pdb tpr tpb tpa ci insert gro Input Opt Generic structure gro g96 pdb tpr tpb tpa 0 out gro Output Generic structure gro g96 pdb p topol top In Out Opt Topology file E 44 genconf 201 Other options h bool no Print help info and quit nice int 19 Set the nicelevel box vector 0 0 0 box size nmol int O no of extr
61. nearby heavy atoms in a predefined manner see also sec 4 5 For the hydrogens in water and in hydroxyl sulfhydryl or amine groups no degrees of freedom can be removed because rotational freedom should be preserved The only other option available to slow down these motions is to increase the mass of the hydrogen atoms at the expense of the mass of the connected heavy atom This will increase the moment of inertia of the water molecules and the hydroxyl sulfhydryl or amine groups without affecting the equilibrium properties of the system and without affecting the dynamical properties too much These constructions will shortly be described in subsec 6 2 1 and have previously been described in full detail 59 Using both dummy atoms and modified masses the next bottleneck is likely to be formed by the improper dihedrals which are used to preserve planarity or chirality of molecular groups and the peptide dihedrals The peptide dihedral cannot be changed without affect ing the physical behavior of the protein The improper dihedrals that preserve planarity mostly deal with aromatic residues Bonds angles and dihedrals in these residues can also be replaced with somewhat elaborate dummy atom constructions as will be described in sub sec 6 2 2 All modifications described in this section can be performed using the GROMACS topol ogy building tool pdb2gmx Separate options exist to increase hydrogen masses dummify all hydrogen atoms or also
62. nicelevel b real 1 First frame ps to read from trajectory e real 1 Last frame ps to read from trajectory w bool no View output using xvgr or ghostview pbc bool yes PBC check fit bool yes Fit to reference structure ns bool no ns on axis instead of ps prev int 0 Calculate rmsd with previous frame fitall bool no Fit all pairs of structures in matrix skip int 1 Only write every nr th frame to matrix skip2 int 1 Only write every nr th frame to matrix max real 1 Maximum level in RMSD matrix 196 Manual Pages min real 1 Minimum level in RMSD matrix bmax real 1 Maximum level in bond angle matrix bmin real 1 Minimum level in bond angle matrix nlevels int 40 Number of levels in the matrices E 36 g_rmsdist gsmsdist computes the root mean square deviation of atom distances which has the advantage that no fit is needed like in standard RMS deviation as computed by g_rms The reference structure is taken from the structure file The rmsd at time t is calculated as the rms of the differences in distance between atom pairs in the reference structure and the structure at time t g rmsdist can also produce matrices of the rms distances rms distances scaled with the mean distance and the mean distances and matrices with NMR averaged distances 1 r and 1 r aver aging Files f traj xtc Input Generic trajectory xtc trr trj gro g96 pdb s topol tpr Input Structure mass db tpr tpb tpa gro g96 pdb n index ndx Input Opt
63. of ihv b We can treat the bonds and bond angles as constraints in the equation of motion The rational behind this is that a quantum oscillator in its ground state resembles a constrained bond more closely than a classical oscillator A good prac tical reason for this choice is that the algorithm can use larger time steps when the highest frequencies are removed In practice the time step can be made four times as large when bonds are constrained than when they are oscillators 7 GROMACS has this option for the bonds and for the bond angles The flexibility of the latter is rather essential to allow for the realistic motion and coverage of configurational space 7 Electrons are in the ground state In MD we use a conservative force field that is a function of the positions of atoms only This means that the electronic motions are not considered the electrons are supposed to adjust their dynamics infinitely fast when the atomic positions change the Born Oppenheimer approximation and remain in their ground state This is really all right almost always But of course electron transfer processes and electronically excited states can not be treated Neither can chemical reactions be treated properly but there are other reasons to shy away from reactions for the time being Force fields are approximate Force fields provide the forces They are not really a part of the simulation method and their parameters can be user modified as the ne
64. often negligible Especially cut off s for the Coulomb interactions cause large errors in the energies forces and virial Even when using a reaction field or lattice sum method the errors are larger than or comparable to the errors due to the single precision Since MD is chaotic trajectories with very similar starting conditions will diverge rapidly the divergence is faster in single precision than in double precision For most simulations single precision is accurate enough In some cases double precision is required to get reasonable results 146 Technical Details normal mode analysis for the conjugate gradient minimization and the calculation and diagonalization of the Hessian calculation of the constraint force between two large groups of atoms energy conservation this can only be done without temperature coupling and with out cut off s A 3 Porting GROMACS The GROMACS system is designed with portability as one major design goal However there are a number of things we assume to be present on the system GROMACS is being ported on We assume the following features 1 the UNIX operating system BSD 4 x or SYSTEM V rev 3 or higher or UNIX like libraries 2 an ANSI C compiler 3 optionally a Fortran 77 compiler or Fortran 90 compiler for faster on some comput ers inner loop routines 4 optionally an XDR library which will allow you to use the portable versions of the GROMACS binary file types GROMACS files writte
65. pdb p topol top Output Topology file i posre itp Output Include file for topology n clean ndx Output Opt Index file q clean pdb Output Opt Generic structure gro g96 pdb Other options h bool no Print help info and quit nice int O Set the nicelevel inter bool no Set the next 6 options to interactive ss bool no Interactive SS bridge selection ter bool no Interactive termini selection iso charged lys bool no Interactive Lysine selection iso charged asp bool no Interactive Aspartic Acid selection iso charged glu bool no Interactive Glutamic Acid selection iso charged his bool no Interactive Histidine selection iso checking H bonds angle real 135 Minimum hydrogen donor acceptor angle for a H bond degrees dist real 0 3 Maximum donor acceptor distance for a H bond nm una bool no Select aromatic rings with united CH atoms on Phenylalanine Tryp tophane and Tyrosine sort bool yes Sort the residues according to database H14 bool no Use 3rd neighbor interactions for hydrogen atoms reth bool yes Retain hydrogen atoms that are in the pdb file alldih bool no Generate all proper dihedrals dummy enum none Convert atoms to dummy atoms none hydrogens or aromatics heavyh bool no Make hydrogen atoms heavy E 58 protonate protonate protonates a protein molecule Files f conf gro Input Generic structure gro g96 pdb tpr tpb tpa 210 Manual Pages 0 confout gro Output Generic structure gro g96 pdb Other options h bo
66. real O Time where to end the exponential fit of the correlation function E 21 g_gyrate g gyrate computes the radius of gyration of a group of atoms and the radii of gyration about the x y and z axes as a function of time The atoms are explicitly mass weighted Files f traj xtc Input Generic trajectory xtc trr trj gro g96 pdb s topol tpr Input Structure mass db tpr tpb tpa gro g96 pdb 0 gyrate xvg Output xvgr xmer file n index ndx Input Opt Index file E 22 g_h2order 187 Other options h bool no Print help info and quit nice int 19 Set the nicelevel b real 1 First frame ps to read from trajectory e real 1 Last frame ps to read from trajectory w bool no View output using xvgr or ghostview q bool no Use absolute value of the charge of an atom as weighting factor in stead of mass p bool no Calculate the radii of gyration about the principal axes E 22 g h2order Compute the orientation of water molecules with respect to the normal of the box The program determines the average cosine of the angle between de dipole moment of water and an axis of the box The box is divided in slices and the average orientation per slice is printed Each water molecule is assigned to a slice per time frame based on the position of the oxygen When nm is used the angle between the water dipole and the axis from the center of mass to the oxygen is calculated instead of the angle between the dipole and a box axis Files f traj x
67. sigma nm Table 5 2 Static atom type properties in GROMACS amino acids or user defined building blocks When generating a topology top using the pdb2gmx program the information from these files is combined The following dynamic quantities are associated with an atom e Position x e Velocity v These quantities are listed in the coordinate file gro see section File format 5 4 4 5 3 2 Bonded parameters The bonded parameters i e bonds angles improper and proper dihedrals are listed in f bon itp The term func can be ignored in GROMACS 2 0 because for bonds and angles we only use 1 function so far For the dihedral this is explained after this listing bondtypes ae j func bO kb C 0 1 0 12300 502080 C OM 1 0 12500 418400 angletypes i j k func tho cth HO OA C 1 109 500 397 480 HO OA CH1 1 109 500 397 480 dihedraltypes z i 1 func q0 cq NR5 NR5 2 0 000 167 360 NR5 NR5 2 0 000 167 360 dihedraltypes 3 j k func phi0 cp mult C OA 1 180 000 16 736 2 C N 1 180 000 33 472 2 80 Topologies dihedraltypes El Ryckaert Bellemans Dihedrals aj ak funct CP2 CP2 3 9 2789 12 156 13 120 3 0597 26 240 31 495 Also in this file are the Ryckaert Bellemans 55 parameters for the CP2 CP2 dihedrals in alkanes or alkane tails with the following constants kJ mol Co 9 28 Co 13 12 Cy 26 24 Ci 1216 C3 SRG Cs 315 Note The use of this potential implies
68. the cut off is large compared to the box edge 1 gt 0 41 searching is done using an O N algorithm that computes all distances and compares them to the cut off ree When the cut off is smaller than 0 4 in all directions x y and z searching is done using a grid the NS grid All particles are put on the NS grid with the smallest spacing gt r 2 in each of the directions We have depicted the computational box divided into NS grid cells in Fig 3 4 In each spatial dimension a particle has three images For each direction the image may be 1 0 or 1 corresponding to a translation over 1 0 or 1 box vector We do not search the surrounding NS grid cells for neighbors of and then calculate the image but rather construct the images first and then search neighbors corresponding to that image of i Since we demand that the number of NS grid cells gt 5 in each direction the same neighbor will not be found twice For every particle exactly 125 5 neighboring cells are searched Therefore the algorithm scales linear with the number of particles Although In fact the cut off is divided into sub blocks the number of which can be chosen by the user The default for this number gria is 2 such that the NS grid spacing must be gt r 2 For simplicity we will just use this particular choice in the remainder of the text However it can be easily understood that if dgrid 3 we need at least 2 gria 7 grid cells each of which has size
69. the experimental coordinates When a pdb input file is passed to the program and the aniso flag is set a correlation plot of the Uij will be created if any anisotropic temperature factors are present in the pdb file E 38 g_rotacf 197 Files s topol tpr Input Generic run input tpr tpb tpa f traj xtc Input Generic trajectory xtc trr trj gro g96 pdb q eiwit pdb Input Opt Protein data bank file 0q anisou pdb Output Opt Protein data bank file n index ndx Input Opt Index file 0 rmsf xvg Output xvgr xmgr file oc correl xvg Output Opt xvgr xmer file 0x xaver gro Output Opt Generic structure gro g96 pdb Other options h bool no Print help info and quit nice int 19 Set the nicelevel b real 1 First frame ps to read from trajectory e real 1 Last frame ps to read from trajectory w bool no View output using xvgr or ghostview aver bool no Calculate average coordinates first Requires reading the coordinates aniso bool no Compute anisotropic termperature factors E 38 g_rotacf grotacf calculates the rotational correlation function for molecules Three atoms i j k must be given in the index file defining two vectors ij and jk The rotational acf is calculated as the autocorrelation function of the vector n ij x jk i e the cross product of the two vectors Since three atoms span a plane the order of the three atoms does not matter Optionally controlled by the d switch you can calculate the rotational correlation
70. title in the Y label position alongside the Y axis With the rainbow option dull grey scale matrices can be turned into attractive color pictures Merged or rainbowed matrices can be written to an XPixelMap file with the xpm option Files f root xpm Input X PixMap compatible matrix file f2 root2 xpm Input Opt X PixMap compatible matrix file di ps m2p Input Lib Input file for mat2ps do out m2p Output Opt Input file for mat2ps 0 plot eps Output Opt Encapsulated PostScript tm file xpm root xpm Output Opt X PixMap compatible matrix file Other options h bool no Print help info and quit nice int O Set the nicelevel w bool no View output using xvgr or ghostview title enum top Show title at top ylabel or none legend enum both Show legend both first second or none diag enum first Diagonal first second or none bx real 0 Box x size also y size when by is not set by real O Box y size rainbow enum no Rainbow colors convert white to no blue or red F 64 xrama xrama shows a Ramachandran movie that is it shows the Phi Psi angles as a function of time in an X Window Static Phi Psi plots for printing can be made with g rama Some of the more common X command line options can be used bg fg change colors font fontname changes the font 214 Files f 8 Other options h nice b e Manual Pages traj xtc Input Generic trajectory xtc trr trj gro g96 pdb topol bool int real
71. use for example the OPLS 44 force field We note however that is not yet possible to use this in GROMACS 2 0 5 3 4 Exclusions and 1 4 interaction The exclusions for bonded particles are generated by grompp for neighboring atoms up to a certain number of bonds away as defined in the moleculetype section in the topology file see 5 4 1 Particles are considered bonded when they are connected by bonds bonds type 1 or 2 or constraints constraints type 1 There is a second constraint type constraints type 2 which fixes the distance but does not connect the atoms by a chemical bond Extra exclusions within a molecule can be added manually in a exclusions section Each line should start with one atom index followed by one or more atom indices All non bonded interactions between the first atom and the other atoms will be excluded The 1 4 interactions are also listed for the atom types in ff nb itp under pairtypes It is possible to change them there of course or add new parameters for different new atom types 5 3 5 Residue database The file holding the residue database is ff rtp Originally this file contained building blocks amino acids for proteins and is the GROMACS interpretation of the rt37c4 dat file of GROMOS So the residue file contains information bonds charge charge groups and improper dihedrals for a frequently used building block It is better not to change this file because it is st
72. which can be transformed using a forward FFT routine into the real space potential Finally the potential and forces are retrieved using interpo lation 53 It is not easy to calculate the full long range virial tensor with PPPM but it is possible to obtain the trace This means that the sum of the pressure components is correct and therefore the isotropic pressure but not necessarily the individual pressure components Using PPPM To use the PPPM algorithm in GROMACS specify the following lines in your mdp file eeltype PPPM rlist 1 0 rcoulomb 0 85 rcoulomb_switch 0 0 rvdw 1 0 fourierspacing 0 075 For details on the switch parameters see the section on modified long range interactions in this manual When using PPPM we recommend to take at most 0 075 nm per gridpoint e g 20 gridpoints for 1 5 nm PPPM does not provide the same accuracy as PME but is faster in most cases PPPM can not be used with pressure coupling 4 6 4 Optimizing Fourier transforms To get the best possible performance you should try to avoid large prime numbers for grid dimensions The FFT code used in GROMACS is optimized for grid sizes of the form 2 3 5 7411 13 where e f is 0 or 1 and the other exponents arbitrary See further the documentation of the FFT algorithms at http www fftw org It is also possible to optimize the transforms for the current problem by performing some calculations at the start of the run This is not done per
73. will assume here that the software is installed with PVM A sample PVM session is described below First set the PVM environment variables in your cshrc file setenv PVM_ROOT home pvm setenv PVM_ARG SGI You also need access to a number of workstations let s call them vince butch and mia we ll assume your username is wallace Make a rhosts file in your home directory vince wallace butch wallace mia wallace Now log off and on again to effectuate all this assuming you are sitting on vince Start the pvm front end 7 pvm pvm gt add butch mia 2 successful HOST DTID vince 80000 mia 100000 pvm gt quit pvmd still running Now you can use GROMACS with PVM You just have to add the option N 3 to your grompp and mdrun command lines Since the remotely running mdruns will start from your home directory give a full path for the log file e g g data pulp wallace speptide md PVM jobs can be stopped within the PVM command line utility with kill process All PVM s can be terminated with the halt command 6 4 Running with MPI 107 6 4 Running with MPI If you have installed the MPI Message Passing Interface on your computer s you can compile GROMACS with this communication library Some hardware vendors provide optimized MPI libraries for shared memory architectures or whatever is fast on their par ticular platform Compiling the GROMACS distribution with MPI support is straightfor ward Edit your Makefi
74. xvgr xmgr file 0e ekrot xvg Output Opt xvgr xmer file Other options h bool no Print help info and quit nice int 19 Set the nicelevel b real 1 First frame ps to read from trajectory e real 1 Last frame ps to read from trajectory E 11 g_confrms g confrms computes the root mean square deviation RMSD of two structures after LSQ fitting the second structure on the first one The two structures do NOT need to have the same number of atoms only the two index groups used for the fit need to be identical The superimposed structures are written to file In a pdb file the two structures will have chain identifiers A and B respectively When the option one is set only the fitted structure is written to file and the chain identifiers are not changed Files f1 conf1 gro Input Structure mass db tpr tpb tpa gro g96 pdb 180 Manual Pages f2 conf2 gro Input Generic structure gro g96 pdb tpr tpb tpa 0 fit pdb Output Generic structure gro g96 pdb n1 fiti ndx Input Opt Index file n2 fit2 ndx Input Opt Index file Other options h bool no Print help info and quit nice int 19 Set the nicelevel one bool no Only write the fitted structure to file pbc bool no Try to make molecules whole again E 12 g_covar g covar calculates and diagonalizes the mass weighted covariance matrix All structures are fitted to the structure in the structure file When this is not a run input file periodicity will not
75. 00 01900 02700 03500 01900 01900 01100 00800 00800 00800 00800 06000 84700 37000 00670 00670 97380 99940 01900 00670 00670 02700 08000 98980 45300 carbonyl oxygen C 0 carboxyl oxygen C0 hydroxyl oxygen 0H water oxygen peptide nitrogen N or NH terminal nitrogen NH2 terminal nitrogen NH3 aromatic N 5 ring 2 bonds aromatic N 5 ring 3 bonds porphyrin nitrogen bare carbon peptide C 0 C N aliphatic CH group aliphatic CH2 group aliphatic CH3 group aromatic CH group 5 ring united aromatic CH group 6 ring united bare carbon 5 6 ring hydrogen bonded to nitrogen hydroxyl hydrogen water hydrogen hydrogen bonded to sulfur sulfur iron zinc arg NH NH2 arg NE NH phosphor sugar or ester oxygen sugar CH group aromatic N 6 ring 2 bonds aromatic N 6 ring 3 bonds sugar CH2 group silicon sodium 1 chlorine 1 5 2 Particle type 17 CA 40 08000 calcium 2 MG 24 30500 magnesium 2 F 18 99840 fluorine cov bound CP2 14 02700 aliphatic CH2 group using Ryckaert Bell CP3 15 03500 aliphatic CH3 group using Ryckaert Bell CR5 12 01100 aromatic CH group 5 ring H CR6 12 01100 aromatic C bonded to H 6 ring H HCR 1 00800 H attached to aromatic C 5 or 6 ri OWT3 15 99940 TIP3P water oxygen SD 32 06000 DMSO Sulphur 0D 15 99940 DMSO Oxygen CD 15 03500 DMSO Carbon Atomic
76. 1 P x 1 Pila x Po x 3x 1 2 8 6 Bonds angles and dihedrals 133 The self diffusion coefficient can be calculated using the Green Kubo relation 60 1 00 Da gt f els dl 8 16 0 which is just the integral of the velocity autocorrelation function There is a widely held belief that the velocity ACF converges faster than the mean square displacement sec 8 5 5 which can also be used for the computation of diffusion constants However Allen amp Tildesly 60 warn us that the long time contribution to the velocity ACF can not be ignored so care must be taken Another important quantity is the dipole correlation time The dipole correlation function for particles A is calculated as follows by g dipoles Cala ple adO gt ica 8 17 with ui gt eirjgj The dipole correlation time can be computed using eqn 8 8 For some applications see 62 The viscosity of a liquid can be related to the correlation time of the Pressure tensor P 63 64 g energy can compute the viscosity but in our experience this is not very accurate actually the values do not converge 8 5 5 Mean Square Displacement To determine the self diffusion coefficient Dx of particles A one can use the Einstein relation 60 Jim lt ri t r 0 gt ica 6Dat 8 18 This Mean Square Displacement and D4 are calculated by the program g msd For molecules consisting of more than one atom r is the center of mass positions In tha
77. 12 425 1993 de Groot B L Amadei A van Aalten D M F Berendsen H J C Towards an exhaustive sampling of the configurational spaces of the two forms of the peptide hormone guanylin J Biomol Str Dyn 13 5 741 751 1996 BIBLIOGRAPHY 217 30 131 139 133 134 135 136 137 40 41 y 42 de Groot B L Amadei A Scheek R M van Nuland N A J Berendsen H J C An extended sampling of the configurational space of hpr from e coli PROTEINS Struct Funct Gen 26 314 322 1996 Vriend G WHAT IF a molecular modeling and drug design program J Mol Graph 8 52 56 1990 Fincham D Parallel computers and molecular simulation Mol Sim 1 1 1987 Raine A R C Fincham D Smith W Systolic loop methods for molecular dy namics simulation Comp Phys Comm 55 13 30 1989 Geist A Beguelin A Dongarra J Jiang W Manchek R Sunderam V PVM 3 user s guide and reference manual Oak Ridge National Laboratory Oak Ridge Tennessee 37381 1994 van Gunsteren W F Berendsen H J C Gromos 87 manual Biomos BV Nij enborgh 4 9747 AG Groningen The Netherlands 1987 van Buuren A R Marrink S J Berendsen H J C A molecular dynamics study of the decane water interface J Phys Chem 97 9206 9212 1993 Mark A E van Helden S P Smith P E Janssen L H M van Gunsteren W F Convergence properties of free energy calcula
78. 2 with 4 protein convention Because of the equalities cos 2 2 cos 1 and cos 3 4 cos 3cos one can translate the OPLS parameters to Ryckaert 56 Force fields Bellemans parameters as follows Co Vo Va 35 V Vs Ci 5 3V3 V1 Ca V O 2M 4 53 C 0 Cs 0 with OPLS parameters in protein convention and RB parameters in polymer convention Note Mind the conversion from kcal mol for OPLS and RB parameters in literature to kJ mol in GROMACS 4 2 6 Special interactions Special potentials are used for imposing restraints on the motion of the system either to avoid disastrous deviations or to include knowledge from experimental data In either case they are not really part of the force field and the reliability of the parameters is not important The potential forms as implemented in GROMACS are mentioned just for the sake of completeness 4 2 7 Position restraints These are used to restrain particles to fixed reference positions R They can be used during equilibration in order to avoid too drastic rearrangements of critical parts e g to restrain motion in a protein that is subjected to large solvent forces when the solvent is not yet equilibrated Another application is the restraining of particles in a shell around a region that is simulated in detail while the shell is only approximated because it lacks proper interaction from missing particles outside the shell Re
79. 2 Usage vil 66 67 69 69 70 71 72 73 73 73 73 75 75 75 76 TT 78 78 79 80 81 81 83 84 86 86 92 93 94 vill CONTENTS 61 37 QU put mati eee Goo eee ON ee a e da 101 A Lamitations ea jose bear s Ba lee eel ks Bed a dee ae c s Se 102 6 1 5 Implementation 0 0 00 0 2 eee ee eee ee 102 6 1 6 Future development 00000 eee eee 102 6 2 Removing fastest degrees of freedom 2 000004 102 6 2 1 Hydrogen bond angle vibrations 103 6 2 2 Out of plane vibrations in aromatic groups 105 6 3 Runnine with PV Misa a hese SA es RA Pg Se a a ek E e 106 6 4 Running with MPI 0 2 02 0 020000 107 Run parameters and Programs 109 7 1 Online and html manuals 0 0 2 0 20 0 020004 109 2 Wiley pes eis Pee See pes A ties See ee se A Ao ei 109 3 Run Parameters ins 4 jes gk lacks dod ale ERE E eae de eat aoa 109 Mal yGenerall sg s ep Soe he Gok ea AA bee BR hye EEO de 109 3 2 Preprocessing baa Ge ee Pe eS fh Poa eR Se a ed A 111 3 3 RUE CONTO fob ae dis oe ea a Siar We oe a EG 111 7 3 4 Langevin dynamics 2 200 002 0000008 112 7 3 5 Energy minimization 2 20 2 2 0002020200008 112 13 0 Output Control ei 64 Slee Rea A Pee da aU 112 Tof Neighbor Searching mo ei ae a Ae ee Se a aa 113 7 3 8 Electrostatics and VAW e e 114 7 3 9 Temperature coupling e 116
80. 26 1 624 1 679 0 1227 0 0580 0 0434 1WATER HW2 2 0 190 1 661 1 747 0 8085 0 3191 0 7791 1WATER HW3 3 0 177 1 568 1 613 0 9045 2 6469 1 3180 2WATER OW1 4 1 275 0 053 0 622 0 2519 0 3140 0 1734 2WATER HW2 5 1 337 0 002 0 680 1 0641 1 1349 0 0257 2WATER HW3 6 1 326 0 120 0 568 1 9427 0 8216 0 0244 1 82060 1 82060 1 82060 This format is fixed i e all columns are in a fixed position If you want to read such a file in your own program without using the GROMACS libraries you can use the following formats 5 4 File formats 95 C format 5i 58 58 451 8 31 8 3178 3178 4f78 4f78 4f Or to be more precise with title etc it looks like this sin Title 5din natoms for i 0 i lt natoms i 454 58 58 547 8 31 8 3 8 31 8 4f 8 41 8 4fAn residuenr residuename atomname atomnr Xx y Z VX VyY VZ 10 5 10 5 10 5 10 5 10 5 10 5 10 5 10 5 10 5f n box X X box Y Y box Z Z box X Y box X Z box Y X box Y Z box Z X box Z Y Fortran format i5 2a5 i5 3f8 3 3f8 4 So confin gro is the GROMACS coordinate file and is almost the same as the GROMOS 87 file for GROMOS users when used with ntx 7 The only difference is the box for which GROMACS uses a tensor not a vector 96 Topologies Chapter 6 Special Topics 6 1 Calculating potentials of mean force the pull code There are a number of options to calculate potentials of mean force and related t
81. 3 atom4 phi0 cp mult impropers optional atom1 atom2 atom3 atom4 q0 cq N C CA H C CA N 0 ZN atoms ZN ZN 2 000 0 5 3 Parameter files 83 The file is free format the only restriction is that there can be at most one entry on a line The first field in the file is the bondedtypes field which is followed by four numbers that indicate the interaction type for bonds angles dihedrals and improper dihedrals The file contains residue entries which consist of atoms and optionally bonds angles dihedrals and impropers The charge group codes denote the charge group numbers Atoms in the same charge group should always be below each other When using the hydrogen database with pdb2gmx for adding missing hydrogens the atom names defined in the rtp entry should correspond exactly to the naming convention used in the hydrogen database see 5 3 6 The atom names in the bonded interaction can be preceded by a minus or a plus indicating that the atom is in the preceding or following residue respectively Parameters can be added to bonds angles dihedrals and impropers these parameters override the standard parameters in the itp files This should only be used in special cases Instead of parameters a string can be added for each bonded interaction this is used in GROMOS96 rtp files These strings are copied to the topology file and can be replaced by force field parameters by the C preprocessor in grompp using define statement
82. 49 1 F 0 1 B 50 then 2 lt 1 F lt 2 holds This is not the exact valid range as defined for normalized floating point numbers in equation eqn B 42 The value 2 causes the problem By mapping this value on the nearest representation lt 2 this can be solved The small error that is introduced by this approximation is within the allowable range The integer representation of the exponent is the next problem Calculating 2775 1 introduces a fractional result if 127 E odd This is again easily accounted for by splitting up the calculation into an odd and an even part For 127 E even E in equation eqn B 49 can be exactly calculated in integer arithmetic as a function of E _ 127 E MES E 126 B 51 158 Some implementation details For 127 E odd equation eqn B 45 can be rewritten as 127 E1 1 F ya A an 8 52 thus 126 E E 127 B 53 2 which also can be calculated exactly in integer arithmetic Note that the fraction is automatically corrected for its range earlier mentioned so the exponent does not need an extra correction The conclusions from this are e The fraction and exponent lookup table are independent The fraction lookup table exists of two tables odd and even exponent so the odd even information of the exponent Isb bit has to be used to select the right table e The exponent table is an 256 x 8 bit table initialized for odd and even
83. 9 files can get huge GROMACS supports the following data blocks in the given order e Header block TITLE mandatory e Frame blocks TIMESTEP optional POSITION POSITIONRED mandatory VELOCITY VELOCITYRED optional BOX optional See the GROMOS 96 manual 42 for a complete description of the blocks Note that all GROMACS programs can read compressed or g zipped files Chapter 5 Topologies 5 1 Introduction GROMACS must know on which atoms and combinations of atoms the various contri butions to the potential functions see chapter 4 must act Tt must also know what parameters must be applied to the various functions All this is described in the topology file top which lists the constant attributes of each atom There are many more atom types than elements but only atom types present in biological systems are parameterized in the force field plus some metals ions and silicon The bonded and special interactions are determined by fixed lists that are included in the topology file Certain non bonded interactions must be excluded first and second neighbors as these are already treated in bonded interactions In addition there are dynamic attributes of atoms their positions velocities and forces but these do not strictly belong to the molecular topology This Chapter describes the set up of the topology file the top file what the parameters stand for and how where to change them if needed Note if you have con
84. At where kM lt N e Cp jAt EN f GMAt f iM j At 8 11 However one needs very long simulations to get good accuracy this way because there are many fewer points that contribute to the ACF 8 5 2 Using FFT for computation of the ACF The computational cost for calculating an ACF according to eqn 8 9 is proportional to N which is considerable However this can be improved by using fast Fourier transforms to do the convolution 60 8 5 3 Special forms of the ACF There are some important varieties on the ACF e g the ACF of a vector p P cos p t plt E d 8 12 where P w is the nt order Legendre polynomial Such correlation times can actually be obtained experimentally using e g NMR or other relaxation experiments GROMACS can compute correlations using the 1st and 2 order Legendre polynomial eqn 8 12 This can a o be used for rotational autocorrelation g rotacf dipole autocorrelation g_dipoles In order to study torsion angle dynamics we define a dihedral autocorrelation function as 61 C t cos 0 7 0 7 t 8 13 Note that this is not a product of two functions as is generally used for correlation func tions but it may be rewritten as the sum of two products C t cos r cos 7 t sin 0 7 sin 7 t 8 14 8 5 4 Some Applications The program g velacc calculates this Velocity Auto Correlation Function Cy T lt vilr vi 0 gt iea 8 15
85. C 7 will be output so that more sophisticated analysis e g using multi exponential fits can be used to get better estimates for THp An H bond existence map can be generated of dimensions H bondsx frames Index groups are output containing the analyzed groups all donor hydrogen atom pairs and acceptor atoms in these groups donor hydrogen acceptor triplets involved in hydrogen bonds between the analyzed groups and all solvent atoms involved in insertion Solvent insertion into H bonds can be analyzed see Fig 8 9 In this case an addi tional group identifying the solvent must be selected The occurrence of insertion will be indicated in the existence map Note that insertion into and existence of a specific H bond can occur simultaneously and will also be indicated as such in the existence map 8 11 Protein related items 141 0 100 200 300 400 600 700 800 900 1000 _ 500 Time ps U Coil Bend EJ Turn E A Helix E B Bridge Figure 8 10 Analysis of the secondary structure elements of a peptide in time e PIE p y 0 E H ha Figure 8 11 Definition of the dihedral angles and y of the protein backbone R 8 11 Protein related items do_dssp g_rama xrama wheel To analyze structural changes of a protein you can calculate the radius of gyration or the minimum residue distances during time see sec 8 7 or calculate the RMSD sec 8 8 You can also look at the changing of secondary structure elements durin
86. E is se ps 1 i m s 1 s 1 5s s 1 S 2 SE llora Li at e a pi m n 1 s li m Ao m n the terms with x3 cancel so that we can simplify to Xin m n 1 pn a 2 riti D 32 i ms 1 i m s s s 1 n Xs Xs 2 m n oi m n No m n 1 m n 1 or on NY y rir Sa x ae Ao D 33 i m s 1s s4 1 If we now expand the first term using eqn D 28 we obtain Sets es Xan ee y aa y Se Ao D 34 i m s 1 s s 1 which we can reformulate to E S n S S 2 gt O See 2 sia Ske D 35 s 1s s 1 i m s 1 s s 1 or S S y S n S i 2 X Xan X Xant OS Ao D 36 E s s4 1 s li m s s4 1 which gives Ss So E n S 2X Xin DO Se a SN Ao D 37 s 1 s s li m 1 m s s 1 Since we need all data points 2 to evaluate this in general this is not possible We can then make an estimate of can using only the data points that are available using the left hand side of eqn D 30 While the average can be computed using all time steps in the simulation the accuracy of the fluctuations is thus limited by the frequency with which energies are saved Since this can be easily done with a program such as xmgr this is not built in in GROMACS 170 Averages and fluctuations Appendix E Manual Pages E 1 do_dssp do_dssp reads a trajectory file and computes the secondary structure for each time frame or every dt ps by calling the dssp program If you do not have the
87. Generic trajectory xtc trr trj gro g96 pdb n index ndx Input Opt Index file E 14 g_dielectric 181 s topol tpr Input Generic run input tpr tpb tpa ei electrons dat Output Generic data file 0 density xvg Output xvgr xmgr file Other options h bool no Print help info and quit nice int 19 Set the nicelevel b real 1 First frame ps to read from trajectory e real 1 Last frame ps to read from trajectory w bool no View output using xvgr or ghostview d string Z Take the normal on the membrane in direction X Y or Z s1 int 10 Divide the box in nr slices number bool no Calculate number density instead of mass density Hydrogens are not counted ed bool no Calculate electron density instead of mass density count bool no Only count atoms in slices no densities Hydrogens are not counted Diagnostics e When calculating electron densities atomnames are used instead of types This is bad e When calculating number densities atoms with names that start with H are not counted This may be surprising if you use hydrogens with names like OP3 E 14 g dielectric dielectric calculates frequency dependent dielectric constants from the autocorrelation function of the total dipole moment in your simulation This ACF can be generated by g dipoles For an estimate of the error you can run g statistics on the ACF and use the output thus generated for this program The functional forms of the available functions are One parmeter y
88. Generic trajectory xtc trr trj gro g96 pdb s topol tpr Input Generic run input tpr tpb tpa n index ndx Input Opt Index file Other options h bool no Print help info and quit nice int O Set the nicelevel b real 1 First frame ps to read from trajectory e real 1 Last frame ps to read from trajectory 208 Manual Pages Diagnostics e Balls option does not work e Some times dumps core without a good reason E 56 nmrun nmrun builds a Hessian matrix from single conformation For usual Normal Modes like calculations make sure that the structure provided is properly energy minimised The generated matrix can be diagonalized by g nmeig Files s topol tpr Input Generic run input tpr tpb tpa m hessian mtx Output Hessian matrix g nm log Output Log file Other options h bool no Print help info and quit nice int 19 Set the nicelevel v bool no Verbose mode compact bool yes Write a compact log file E 57 pdb2gmx This program reads a pdb file lets you choose a forcefield reads some database files adds hydrogens to the molecules and generates coordinates in Gromacs Gromos format and a topology in Gromacs format These files can subsequently be processed to generate a run input file Note that a pdb file is nothing more than a file format and it need not necessarily contain a protein structure Every kind of molecule for which there is support in the database can be converted If there is no support in the database you
89. Groningen Machine for Chemical Simulations GROMACS USER MANUAL Version 2 0 Phospholipase A2 ready to attack a lecithin mono layer GROMACS USER MANUAL Version 2 0 November 5 1999 David van der Spoel Aldert R van Buuren Emile Apol Pieter J Meulenhoff D Peter Tieleman Alfons L T M Sijbers Berk Hess K Anton Feenstra Erik Lindahl Rudi van Drunen Herman J C Berendsen BIOSON c Copyright BIOSON Research Institute and Laboratory of Biophysical Chemistry University of Groningen Nijenborgh 4 9747 AG Groningen The Netherlands Fax 31 0 50 63 4800 Preface amp Disclaimer This manual is not complete and has no pretention to be complete due to lack of time of the contributors It is meant as a source of information and references for the GROMACS user It contains the background physics of MD simulations and is still being worked on which in some cases means that the information is not correct When citing this document in any scientific publication please refer to it as van der Spoel D A R van Buuren E Apol P J Meulenhoff D P Tieleman A L T M Sijbers B Hess K A Feenstra E Lindahl R van Drunen and H J C Berendsen Gromacs User Manual version 2 0 Nijenborgh 4 9747 AG Groningen The Netherlands Internet http md chem rug nl gmx 1999 or if you use BibTeX you can directly copy the following Manual gmx20 title Gromacs U ser M a
90. H 0 apaa 4 67 where 6 1 kBT with kg Boltzmann s constant and T the temperature p are the gen eralized momenta and q are the generalized coordinates We can split the Hamiltonian in the potential V and kinetic K parts H V q K p 4 69 2 N K NA 4 70 62 Force fields where N is the number of particles in the system and m are the masses of the particles G 1 In f exp 8V q dq f exp BK p dp or 4 71 G K p 1 8 ln f exp 8V q dq Here are the modified equations used to calculate the free energy Harmonic potentials The example given here is for the bond potential which is harmonic in GROMACS How ever these equations apply to the angle potential and the improper dihedral potential as well Y Ka A Akf b 1 A Ab 4 72 Se Lep af o abg anf 06 oP 1 nag 209 4 73 Proper dihedrals For the proper dihedrals the equations are somewhat more complicated Va 1 Akf Akg cos ng 1 A gs APH 4 74 Se K KI fa cos ngd 0 aeg 208 1 Aki Ak 69 do sin ng 1 A dG AP7 4 75 Note that the multiplicity ng can not be parameterized because the function should remain periodic on the interval 0 27 Coulomb interaction The Coulomb interaction between two particles of which the charge varies with is 1 Dal Ag 1 af Ag 4 76 a E tab aa Mal da
91. In periodic systems with filled boxes the overall rotational motion is coupled to other degrees of freedom and does not give any problems 3 4 2 Compute forces As mentioned in chapter 4 internal forces are either generated from fixed static lists or from dynamics lists The latter concern non bonded interactions between any pair of particles Pair lists generation The non bonded pair forces need to be calculated only for those pairs i j for which the distance r between 7 and the nearest image of j is less than a given cut off radius re Some of the particle pairs that fulfill this criterion are excluded when their interaction is already fully accounted for by bonded interactions GROMACS employs a pair list that contains those particle pairs for which non bonded forces must be calculated The pair list contains the particle numbers and an index for the image displacement vectors that must be applied to obtain the nearest image for all particle pairs that have a nearest image distance less than rshort The list is updated every nstlist steps where nstlist is typically 10 or 20 There is an option to calculate the total non bonded force on each particle due to all particle in a shell around the list cutoff i e at a distance between rshort and rlong This force is calculated during the pair list update and retained during nstlist steps The vector rj r ri connecting nearest images is found by constructing Tij Tij a round z
92. In that case beware and test the influence of system size This is especially important when using lattice sums for long range electrostatics since these are known to sometimes introduce extra ordering 1 3 Energy Minimization and Search Methods As mentioned in sec 1 1 in many cases energy minimization is required GROMACS provides a simple form of local energy minimization the steepest descent method The potential energy function of a macro molecular system is a very complex landscape or hyper surface in a large number of dimensions It has one deepest point the global minimum and a very large number of local minima where all derivatives of the potential energy function with respect to the coordinates are zero and all second derivatives are nonnegative The matrix of second derivatives which is called the Hessian matrix has nonnegative eigenvalues only the collective coordinates that correspond to translation and rotation for an isolated molecule have zero eigenvalues In between the local minima there are saddle points where the Hessian matrix has only one negative eigenvalue These points are the mountain passes through which the system can migrate from one local minimum 6 Introduction to another Knowledge of all local minima including the global one and of all saddle points would enable us to describe the relevant structures and conformations and their free energies as well as the dynamics of structural transitions Un
93. MXHOME src this only works if you have csh The program manual pages can also be found in Appendix E Furthermore standard UNIX manuals can be generated using make nroff In the GMXRC file an extension of the MANPATH has been set that allows one to use the manual e g man grompp 7 2 File types Table 7 1 lists the file types used by GROMACS along with a short description A more elaborate description of the file types can be found in your GROMACS directory at GMXHOME htm1 online files html and online at http md chem rug nl gmx online2 0 files html GROMACS files written in xdr format can be read on any architecture with a GROMACS version 1 6 or newer compiled with an XDR library 7 3 Run Parameters 7 3 1 General Default values are given in parentheses The first option is always the default option Units are given in square brackets The difference between a dash and an underscore is ignored 110 Run parameters and Programs Default Default Name Ext Type Option Description atomtp atp Atomtype file used by pdb2gmx eiwit brk f Brookhaven data bank file nnnice dat Generic data file user dlg Dialog Box data for ngmx sam edi ED sampling input sam edo ED sampling output ener edr Generic energy edr ene ener edr Energy file in portable xdr format ener ene Energy file eiwit ent Entry in the protein date bank plot eps Encapsulated PostScript tm file gtraj g87 Gromos 87 ASCII trajectory format conf g96 Coordinate file i
94. The numerics for the first step and the second step are very similar A complete derivation of the algorithm can be found in 23 Only a short description of the first step is given here A new notation is introduced for the gradient matrix of the constraint equations which appears on the right hand side of the equation 3 35 Notice that B is a K x 3N matrix it contains the directions of the constraints The following equation shows how the new constrained coordinates rTn41 are related to the unconstrained coordinates 7775 rine M B B M B B rt d l where T M B BM B The derivation of this equation from eqns 3 33 and 3 34 can be found in 23 This first step does not set the real bond lengths to the prescribed lengths but the pro jection of the new bonds onto the old directions of the bonds To correct for the rotation of bond i the projection of the bond on the old direction is set to pi 2d 2 3 37 where l is the bond length after the first projection The corrected positions are roi L TrBn rngi Trp 3 38 This correction for rotational effects is actually an iterative process but during MD only one iteration is applied The relative constraint deviation after this procedure will be 28 Algorithms less than 0 0001 for every constraint In energy minimization this might not be accurate enough so the number of iterations is equal to the order of the expansion see below Ha
95. The root mean square deviation RMSD of certain atoms in a molecule with respect to a reference structure can be calculated with the program g rms by least square fitting the structure to the reference structure t2 0 and subsequently calculating the RM SD eqn 8 20 ix 3 RMSD t to VW r t ri to 8 20 i 1 where r t is the position of atom 7 at time t NOTE that fitting does not have to use the same atoms as the calculation of the RMSD e g a protein is usually fitted on the backbone atoms N C C but the RMSD can be computed of the backbone or of the whole protein Instead of comparing the structures to the initial structure at time t 0 so for example a crystal structure one can also calculate eqn 8 20 with a structure at time t2 t T This gives some insight in the mobility as a function of 7 Also a matrix can be made with the RM SD as a function of t and ta this gives a nice graphical impression of a trajectory If there are transitions in a trajectory they will clearly show up in such a matrix 138 Analysis Alternatively the RMSD can be computed using a fit free method with the program grmsdist SS li RMSD t WZ 5 X ry t r 0 8 21 i 1 j 1 where the distance rj between atoms at time t is compared with the distance between the same atoms at time 0 In stead of comparing the structures to the initial structure at time t 0 so for example a crystal structure one can
96. Wek e oR RE RE a Ge wee ke amp 50 The Morse potential well with bond length 0 15 nm 52 Angle vibration vtr a aa ee a BG aa A A 52 Improper dihedral angles a 93 Improper dihedral potential 2 o ee 54 Proper dihedral angles ani tye ea et i a ee ee ee SE E 54 Ryckaert Bellemans dihedral potential o 55 Position restraint potential o a oa 57 Distance Restraint potential o 58 xiv LIST OF FIGURES 4 14 Atoms along an alkane chain ooa o 65 4 15 Dummy atom construction e 67 6 1 Schematic picture of pulling a lipid out of a lipid bilayer with AFM pulling Vrup is the velocity at which the spring is retracted Zjing is the atom to which the spring is attached and Zspring is the location of the spring 98 6 2 Overview of the different reference group possibilities applied to interface systems C is the reference group The circles represent the center of mass of 2 groups plus the reference group and de is the reference distance 99 6 3 Dummy atom constructions for hydrogen atoms 104 6 4 Dummy atom constructions for aromatic residues 105 8 1 The window of ngmx showing a box of water o 128 8 2 Definition of slices TERESA ee ee ae ee ee Ge 130 8 3 goo r for Oxygen Oxygen of SPC water o o o o 130 8 4 Mean Squ
97. _order 4 ewald_rtol le 5 In this case the fourierspacing parameter determines the maximum spacing for the FFT grid and pme_order controls the interpolation order Using 4th order cubic interpolation and this spacing should give electrostatic energies accurate to about 5 107 Since the Lennard Jones energies are not this accurate it might even be possible to increase this spacing slightly Pressure scaling works with PME but be aware of the fact that anisotropic scaling can introduce artificial ordering in some systems 4 6 3 PPPM The Particle Particle Particle Mesh methods of Hockney amp Eastwood can also be applied in GROMACS for the treatment of long range electrostatic interactions 50 52 53 With this algorithm the charges of all particles are spread over a grid of dimensions nz ny nz using a weighting function called the triangle shaped charged distribution Wir Wiz W y W z i E gt l lt 3 4 113 WAS ala ali 0 3h lt jl where is x y or z is the distance to a grid point in the corresponding dimension Only the 27 closest grid points need to be taken into account for each charge Then this charge distribution is Fourier transformed using a 3D inverse FFT routine In Fourier space a convolution with function G is performed i k G k ae 4 114 72 Force fields where g is the Fourier transform of the charge spread function g r This yield the long range potential b k on the mesh
98. a molecules to insert seed int 1997 random generator seed vdwd real 0 105 default vdwaals distance Diagnostics e Molecules must be whole in the initial configurations E 44 genconf genconf multiplies a given coordinate file by simply stacking them on top of each other like a small child playing with wooden blocks The program makes a grid of user defined proportions nbox and interspaces the grid point with an extra space dist When option rot is used the program does not check for overlap between molecules on grid points It is recommended to make the box in the input file at least as big as the coordinates Van der Waals radius If the optional trajectory file is given conformations are not generated but read from this file and translated appropriately to build the grid Files f conf gro Input Generic structure gro g96 pdb tpr tpb tpa 0 out gro Output Generic structure gro g96 pdb trj traj xtc Input Opt Generic trajectory xtc trr trj gro g96 pdb Other options h bool no Print help info and quit nice int Set the nicelevel nbox vector Number of boxes dist vector Distance between boxes seed int Random generator seed rot bool no Randomly rotate conformations maxrot vector 90 90 90 Maximum random rotation O re O re ooro Diagnostics e The program should allow for random displacement off lattice points E 45 gendr gendr generates a distance restraint entry for a gromacs topology from another f
99. ad from trajectory w bool no View output using xvgr or ghostview prot bool no Protonate protein every step This currently does not add terminal hydrogens and therefore works only when the termini are capped ntop int 6 Number of large violations that are stored in the log file every step E 18 g_dist g dist can calculate the distance between the centers of mass of two groups of atoms as a function of time Or when dist is set print all the atoms in group 2 that are closer than a certain distance to the center of mass of group 1 Files f traj xtc Input Generic trajectory xtc trr trj gro g96 pdb s topol tpr Input Generic run input tpr tpb tpa n index ndx Input Opt Index file 0 dist xvg Output Opt xvgr xmer file Other options h bool no Print help info and quit nice int 19 Set the nicelevel b real 1 First frame ps to read from trajectory e real 1 Last frame ps to read from trajectory dist real O Print all atoms in group 2 closer than dist to the center of mass of group 1 E 19 g enemat E 19 g_enemat 185 g enemat extracts an energy matrix from an energy file With groups a file must be supplied with on each line a group to be used For these groups a matrices of interaction energies will be calculated Also the total interaction energy energy per group is calculated An approximation of the free energy is calculated using E free EO kT log lt exp E E0 kT gt where lt gt stands
100. added to the bonded heavy atom 104 Special Topics Figure 6 3 The different types of dummy atom constructions used for hydrogen atoms The atoms used in the construction of the dummy atom s are depicted as black circles dummy atoms as grey ones Hydrogens are smaller than heavy atoms A fixed bond angle note that here the hydrogen is not a dummy atom B in the plane of three atoms with fixed distance C in the plane of three atoms with fixed angle and distance D construction for amine groups NH2 or NH7 see text for details Taking into account these considerations the hydrogen atoms in a protein naturally fall into several categories each requiring a different approach see also Fig 6 3 hydroxyl OH or sulfhydryl SH hydrogen The only internal degree of freedom in a hydroxyl group that can be constrained is the bending of the C O H angle This angle is fixed by defining an additional bond of appropriate length see Fig 6 3A This removes the high frequency angle bending but leaves the dihedral rotational freedom The same goes for a sulfhydryl group Note that in these cases the hydrogen is not treated as a dummy atom single amine or amide NH and aromatic hydrogens CH The position of these hydrogens cannot be constructed from a linear combination of bond vectors because of the flexibility of the angle between the heavy atoms In stead the hydrogen atom is positioned at a fixed distance from the bonded h
101. aert Bellemans potential the 1 4 interactions must be excluded from the non bonded list Proper dihedrals periodic type Proper dihedral angles are defined according to the IUPAC IUB convention where is the angle between the ijk and the kl planes with zero corresponding to the cis configuration i and l on the same side 4 2 Bonded interactions 55 Table 4 1 Constants for Ryckaert Bellemans potential kJ mol7 50 0 a 30 0 V kJ mole 20 0 10 0 P Je XN ff Ne L ES i L 0 0 90 0 180 0 270 0 360 0 Figure 4 11 Ryckaert Bellemans dihedral potential Valdij1 kg 1 cos nd do 4 50 Proper dihedrals Ryckaert Bellemans function For alkanes the following proper dihedral potential is often used see Fig 4 11 5 Vio Pijat Y En cos h 4 51 n 0 where Y 180 Note A conversion from one convention to another can be achieved by multiplying every coefficient Cn by 1 An example of constants for C is given in Table 4 1 Note The use of this potential implies exclusions of LJ interactions between the first and the last atom of the dihedral and y is defined according to the polymer convention trans 0 The RB dihedral function can also be used to include the OPLS dihedral potential 44 The OPLS potential function is given as the first four terms of a Fourier series VrolPijki Vo ima cos y Va 1 cos 2w V3 1 cos 34 4 5
102. aken from the structure file if one is supplied otherwise it is the first frame Use center to put the system in the center of the box This is especially useful for multimeric proteins since this procedure will ensure the subunits stay together in the trajectory due to PBC they might be separated providing they were together in the initial conformation With the option dt it is possible to reduce the number of frames in the output This option relies on the accuracy of the times in your input trajectory so if these are inaccurate use the timestep option to modify the time this can be done simultaneously Using trunc trjconv can truncate trj in place i e without copying the file This is useful when a run has crashed during disk I O one more disk full or when two contiguous trajectories must be concatenated without have double frames Also the option checkdouble may be used to remove all duplicate frames from such a concatenated trajectory this is done by ignoring all frames with a time smaller than or equal to the previous 212 Manual Pages frame trjcat is more suitable for concatenating trajectory files The option dump can be used to extract a frame at or near one specific time from your trajectory Files f traj xtc Input Generic trajectory xtc trr trj gro g96 pdb 0 trajout xtc Output Generic trajectory xtc trr trj gro g96 pdb s topol tpr Input Opt Structure mass db tpr tpb tpa gro g96 pdb n index ndx Input
103. al criterion is used see also Fig 8 8 THB 0 35nm PRR 8 28 IA IA r a The value of ryp 3 5A corresponds to the first minimum of the rdf of SPC water see also Fig 8 3 The program g_hbond analyses all hydrogen bonds existing between two groups of atoms which must be either identical or non overlapping or in specified Donor Hydrogen Ac ceptor triplets in the following ways e Donor Acceptor distance r distribution of all H bonds e Hydrogen Donor Acceptor angle a distribution of all H bonds e The total number of H bonds in each time frame 140 Analysis Figure 8 9 Insertion of water into an H bond 1 Normal H bond between two residues 2 H bonding bridge via a water molecule The number of H bonds in time between residues divided into groups n n 4 where n and n 1 stand for residue numbers and 7 goes from 0 to 6 The group for i 6 also includes all H bonds for i gt 6 These groups include the n n 3 n n 4 and n n 5 H bonds which provide a measure for the formation of a helices or 6 turns or strands The lifetime of the H bonds is calculated from the average over all autocorrelation functions of the existence functions either 0 or 1 of all H bonds C r lt s t sit 7 gt 8 29 with s 0 1 for H bond i at time t The integral of C T gives a rough estimate of the average H bond lifetime typ THB Pao 8 30 Both the integral and the complete auto correlation function
104. aling factor is given by At 1 3 u 14 PO Po 3 23 p Here is the isothermal compressibility of the system In general this is not known It suffices to take a rough estimate because the value of 6 only influences the non critical time constant of the pressure relaxation without affecting the average pressure itself For water at 1 atm and 300 K 8 4 5 x 1071 Pa t 4 5 x 1075 Bar7 which is 7 5 x 1074 MD units see chapter 2 Most other liquids have similar values In the present version of GROMACS the pressure coupling can be done anisotropically the x y z dimensions are scaled separately based on the diagonal elements of the pressure tensor This allows e g to couple one dimension to an external pressure while keeping a fixed surface area in the other two dimensions useful in membrane simulations The sys tem axes remain orthogonal the scaling method allows in principle also dynamic changes in box angles but this is not implemented yet Since the pressure fluctuates heavily it is recommended to take Tp not too small a value between 0 4 and 1 ps will often be satisfactory When using lattice sum methods it is easy to get pressure oscillations but this can be overcome by either slower scaling or by averaging the calculated pressure over several steps Surface tension coupling When a periodic system consists of more than one phase separated by surfaces which are parallel to the xy plane the surface tension and the z
105. als If you want to include Ryckaert Bellemans type dihedrals in a topology do the following in case of e g decane dihedrals ai aj ak al funct cO c1 c2 1 2 3 4 3 3 4 5 3 and do not forget to erase the 1 4 interaction in pairs position restraints harmonically restrain particles to reference positions sec 4 2 7 The reference positions are read from a separate coordinate file by grompp include spc itp includes a topology file that was already constructed see next section molecule itp system title of your system user defined 90 Topologies Parameters interaction directive H f parameters pert type at tp mandatory defaults non bonded function type combination rule generate pairs no yes fudge LJ fudge QQ mandatory atomtypes atom type m u q e particle type ce kJ mol nm c12 kJ mol nm bondtypes see Table 5 4 directive bonds constrainttypes see Table 5 4 directive constraints pairtypes see Table 5 4 directive pairs angletypes see Table 5 4 directive angles proper dih dihedraltypes 2 1 Omar deg fe kJ mol mult improper dih dihedraltypes 2 2 po deg f kJ mol trad RB dihedral dihedraltypes 20 3 Co Cy Co C3 Ca Cs kJ mol LJ nonbond params 2 1 c kJ mol nm c12 kJ mol nm Buckingham nonbond_params 2 2 a kJ mol b nm ce kJ mol nm at is the number of atom types f tp
106. als 135 Figure 8 5 Dihedral conventions A Biochemical convention B Polymer convention D Figure 8 6 Options of g sgangle A Angle between 2 vectors B Angle between a vector and the normal of a plane C Angle between two planes D Distance between the geometrical centers of 2 planes E Distances between a vector and the center of a plane 136 Analysis For planes it uses the normal vector perpendicular to the plane It can also calculate the distance d between the geometrical center of two planes see Fig 8 6D and the distances d and dz between 2 atoms of a vector and the center of a plane defined by 3 atoms see Fig 8 6D It further calculates the distance d between the center of the plane and the middle of this vector Depending on the input groups i e groups of 2 or 3 atom numbers the program decides what angles and distances to calculate For example the index file could look like this a_plane 1 2 3 a_vector 3 4 5 8 7 Radius of gyration and distances g_gyrate g_sgangle g_mindist g_mdmat xpm2ps To have a rough measure for the compactness of a structure you can calculate the radius of gyration with the program g gyrate as follows E Ry zm 8 19 where m is the mass of atom 7 and r the position of atom 7 with respect to the center of mass of the molecule It is especially useful to characterize polymer solutions and proteins Sometimes it is interesting to plot the
107. also calculate eqn 8 20 using a time shift 7 N 2 RMSD t rT E Y ri t rit 8 22 i 1 so comparing to a least square structure at t 7 This gives some insight in the mobility as a function of r Use the program g_run_rms 8 9 Covariance analysis Covariance analysis also called principal component analysis or essential dynamics 28 can find correlated motions It uses the covariance matrix C of the atomic coordinates E 1l 1 Cig Mi i xi x 27 M5 8 23 where M is a diagonal matrix containing the masses of the atoms mass weighted analysis or the unit matrix non mass weighted analysis C is asymmetric 3N x 3N matrix which can be diagonalized with an orthonormal transformation matrix T TOT diag A1 dQ gt A3n where Aq gt A2 gt some gt A3N 8 24 The columns of T are the eigenvectors also called principal or essential modes T defines a transformation to a new coordinate system The trajectory can be projected on the principal modes to give the principal components p t p t TTM x t x 8 25 The eigenvalue A is the mean square fluctuation of principal component i The first few principal modes often describe collective global motions in the system The trajectory can be filtered along one or more principal modes For one principal mode this goes as follows i X filtered t x M Tp t 8 26 When the analysis is performed on a macromolecule
108. and 9 additions are needed Here it is shown how it is possible to extract the virial calculation from the inner loop and also how the pressure is calculated in GROMACS B 1 1 Virial In a system with Periodic Boundary Conditions the periodicity must be taken into account for the virial N 1 a 3 2 ry Fy B 2 i lt j where rj denotes the distance vector of the nearest image of atom i from atom j In this definition we add a shift vector 6 to the position vector r of atom i The difference vector rij is thus equal to ay 7 6 fj B 3 or in shorthand Tj B 4 u v uva The calculation of Lennard Jones and Coulomb forces is about 50 floating point operations 150 Some implementation details In a triclinic system there are 27 possible images of 7 when truncated octahedron is used there are 15 possible images B 1 2 Virial from non bonded forces Here the derivation for the single sum virial in the non bonded force routine is given 1 j in all formulae below N z rjo Fy B 5 i lt j 1 N N gd bh rit 6 415 Fy B 6 i l j l 1 N N e 5 ri 6 8 Fij rj 8 Fij B 7 s ll eu gt ll pos A ri dj 8 Mz Mz M N No POL B 8 gt j l i l j l 1 amp N N N 7 5 r 0 e Y Fij Sor ey Fij B 9 i 1 j 1 j 1 i 1 1 amp N 4 Y r 6 QF Y 7 F B 10 i l j l 1 id ner d son B 11 i 1 i 1 In these formulae we introduced N
109. and distance between both H atoms must be given Note that the algorithm can also be used for TIP3P and TIP4P 38 TIP3P just has another geometry TIP4P has a dummy atom but since that is generated it does not need to be shaken nor stirred B 2 3 Fortran Code Unfortunately Fortran compilers are still better than C compilers for most machines anyway For some machines e g SGI Power Challenge the difference may be up to a factor of 3 in the case of vector computers this may be even larger Therefore some of the routines that take up a lot of computer time have been translated into Fortran On most machine calling a Fortran routine from C is not hard to do but we did not rigorously test this The default for compiling GROMACS is to not use Fortran loops except for machines where we have tested it but it may be turned on in your local Makefile CPU When you have problems with linking check your Fortran object files using the UNIX nm utility to see what the name of the function is and modify the code where the function is called Please note that C compilers usually add an underscore before or after each function name Also do not forget that C code unlike Fortran is case sensitive When the Fortran function name in the object file is in uppercase you probably need to put the call in uppercase as well 154 Some implementation details Here is a list of the functions that have a Fortran equivalent c coul inloopc c fcoul inloo
110. andard input for pdb2gmx but if changes are needed make them 82 Topologies in the top file see section Topology file 5 4 1 However in the ff rtp file the user can define a new building block or molecule see for example 2 2 2 trifluoroethanol TFE or n decane C10 But when defining new molecules non protein it is preferable to create a itp file This will be discussed in a next section section 5 4 2 The file rtp is only used by pdb2gmx As mentioned before the only extra infor mation this program needs from ff rtp is bonds charges of atoms charge groups and improper dihedrals because the rest is read from the coordinate input file in the case of pdb2gmx a pdb format file Some proteins contain residues that are not standard but are listed in the coordinate file You have to construct a building block for this strange residue otherwise you will not obtain a top file This also holds for molecules in the coordinate file like phosphate or sulphate ions The residue database is constructed in the following way bondedtypes mandatory bonds angles dihedrals impropers 1 1 1 2 mandatory GLY mandatory atoms mandatory name type charge chargegroup N N 0 280 0 H H 0 280 0 CA CH2 0 000 1 C C 0 380 2 0 O 0 380 2 bonds optional atom1 atom2 bO kb N H N CA CA C C 0 C N angles optional atom1 atom2 atom3 tho cth dihedrals optional atom1 atom2 atom
111. angles ai aj ak funct tho cth 1 3 4 1 1 200000e 02 2 928800e 02 1 3 5 1 1 200000e 02 2 928800e 02 4 3 5 1 1 200000e 02 3 347200e 02 1 6 7 1 1 200000e 02 2 928800e 02 1 6 8 1 1 200000e 02 2 928800e 02 7 6 8 1 1 200000e 02 3 347200e 02 2 1 3 1 1 215000e 02 5 020800e 02 2 1 6 1 1 215000e 02 5 020800e 02 3 1 6 1 1 170000e 02 5 020800e 02 dihedrals ai aj ak al funct phi cp 2 1 3 4 1 1 800000e 02 3 347200e 01 6 1 3 4 1 1 800000e 02 3 347200e 01 2 1 3 5 1 1 800000e 02 3 347200e 01 6 1 3 5 1 1 800000e 02 3 347200e 01 2 1 6 7 1 1 800000e 02 3 347200e 01 3 1 6 T 1 1 800000e 02 3 347200e 01 2 1 6 8 1 1 800000e 02 3 347200e 01 3 1 6 8 1 1 800000e 02 3 347200e 01 dihedrals al aj ak al funct q0 cq 3 4 5 1 2 0 000000e 00 1 673600e 02 6 7 8 1 2 0 000000e 00 1 673600e 02 1 3 6 2 2 0 000000e 00 1 673600e 02 position_restraints This you wouldn t use normally for a molecule like Urea but it s here for didactical purposes ai funct fc 1 1 1000 1000 1000 2 1 1000 0 1000 3 1 1000 0 Include SPC water topology include spc itp system Urea in Water molecules molecule name nr Urea 1 SOL 1000 Here follows the explanatory text mult 000000e 00 000000e 00 000000e 00 000000e 00 000000e 00 000000e 00 000000e 00 000000e 00 Restrain to a point Restrain to a line Y axis Topologies O Restrain to a plane Y Z plane 5 4 File formats 89 defaults e no
112. arameterization of aromatic interactions in the GROMOS force field Private Communication 1993 Ryckaert J P Bellemans A Far Disc Chem Soc 66 95 1978 on Biochemical Nomenclature I I C Abrreviations and symbols for the descrip tion of the conformation of polypeptide chains tentative rules 1969 Biochemistry 9 3471 3478 1970 Berendsen H J C Postma J P M van Gunsteren W F Hermans J Interaction models for water in relation to protein hydration In Intermolecular Forces Pullman B ed D Reidel Publishing Company Dordrecht 1981 331 342 de Loof H Nilsson L Rigler R Molecular dynamics simulations of galanin in aqueous and nonaqueous solution J Am Chem Soc 114 4028 4035 1992 Feenstra K A Hess B Berendsen H J C Improving efficiency of large time scale molecular dynamics simulations of hydrogen rich systems J Comp Chem 20 786 798 1999 BIBLIOGRAPHY 219 601 611 169 168 164 1651 166 1671 168 169 Allen M P Tildesley D J Computer Simulations of Liquids Oxford Oxford Science Publications 1987 van der Spoel D Berendsen H J C Molecular dynamics simulations of Leu enkephalin in water and DMSO Biophys J 72 2032 2041 1997 van der Spoel D van Maaren P J Berendsen H J C A systematic study of water models for molecular simulation J Chem Phys 108 10220 10230 1998 Smith P E van Gunsteren W F The
113. are Displacement of SPC water 00005 134 8 5 Dihedral conventions 0 2 ee ee 135 8 6 Options of g Sgang Les s eic A Gut ad de wa aig NA 135 8 7 A minimum distance matrix for a peptide 3 137 8 8 Geometrical Hydrogen bond criterion o e 139 8 9 Insertion of water into an H bond o a 140 8 10 Analysis of the secondary structure elements of a peptide in time 141 8 11 Definition of the dihedral angles and w of the protein backbone 141 8 12 Ramachandran plot of a small protein o o 142 8 13 Helical wheel projection of the N terminal helix of HPr 142 B 1 IEEE single precision floating point format 00 0 155 List of Tables 1 1 2 1 2 2 2 3 2 4 3 1 4 1 4 2 5 1 5 2 5 3 5 4 7 1 B 1 B 2 Typical vibrational frequencies 2 ee 3 Basic units used in GROMACS o 10 Derived INDESEADAS a sh ta a T 10 Some Physical Constants 0 2 0 0 02 e 11 Reduced Lennard Jones quantities 1 2 2 0 0 eee eee ees 11 The number of interactions between particles 35 Constants for Ryckaert Bellemans potential kJ molt 55 Parameters for the different functional forms of the non bonded interactions 66 Particle types in GROMACS o 76 Static atom type properties in GROMACS 79 The topology top file part 1 ri e Ta 90 T
114. armonic the average energy of a single bond is not equal to KT as it is for the normal harmonic potential 4 2 2 Morse potential bond stretching For some systems that require an anharmonic bond stretching potential the Morse po tential 43 between two atoms i and j is available in GROMACS This potential differs from the harmonic potential in having an asymmetric potential well and a zero force at infinite distance The functional form is Vinorse Tig Dij 1 exp Big rig big 4 38 see also Fig 4 6 and the corresponding force is Emorselrij 2DijbijTij expl Bij rij bij RT 1 exp 6ij rij bis et i where Dj is the depth of the well in kJ mol ij defines the steepness of the well in nm and bij is the equilibrium distance in nm The steepness parameter jj can be expressed in terms of the reduced mass of the atoms 2 and j the fundamental vibration frequency wij and the well depth D Pij wig y 225 4 40 and because w 1 k p one can rewrite Bij in terms of the harmonic force constant kij kij 2D Bi 4 41 For small deviations rj bij one can expand the exp term to first order in the Taylor expansion exp 2 1 zx 4 42 Substituting this in the functional from Vinorse tig Disll exp Gig rig bi5 1 Dyl 1 7105 ry 85 4 43 Sok as one recovers the harmonic bond stretching potential 52 Force fields 400 300 200
115. at atoms that fall between r and rc are weighted linearly from 1 to 0 going from r to rc As reasonable initial values we suggest r 1 0 and rc 1 5 but this will depend strongly on the exact system of interest update 1 The frequency with which the dynamic reference groups are recalculated Usually there is no reason to use anything other than 1 pullrate 0 00005 The pull rate in nm timestep for AFM pulling forceconstant 100 The force constant for the spring in AFM pulling in kJ mol nm width 0 Width of the umbrella sampling potential in kJ mol nm r0_group2 0 0 0 0 3 300 The initial location of the groups with respect to the reference group Only coor dinates selected with direction are taken into account The groups are moved to these initial positions before the actual creation of a series of starting structures commences tolerance 0 001 The accuracy with which the actual position of the groups must match the calculated ideal positions for a starting structure in nm translation_rate 0 00001 The rate of translation in all directions nm step As mentioned above normal MD force calculations and position updates also act on the groups transstep 0 2 The interval in nm at which structures are written out 6 1 3 Output The output file is a text file with forces or positions one per line If there are two groups they alternate in the output file Currently there is no supported analysis pr
116. atoms and the Z axis E Tr 0 Var ri rj kar 1 cos n 0 00 where 0 arccos 2 0 4 58 ral A multiplicity n of 2 is useful when you do not want to distinguish between parallel and anti parallel vectors 4 2 9 Distance restraints Distance restraints add a penalty to the potential when the distance between specified pairs of atoms exceeds a threshold value They are normally used to impose experimental restraints as from experiments in nuclear magnetic resonance NMR on the motion of the system Thus MD can be used for structure refinement using NMR data The potential 58 Force fields 15 1 1 i i i i h 10 F To r take 1 3 E E 1 1 gt it 1 ae 1 PE 1 ly gt 5t Y i I ji l ES 1 1 Ne E 0 pS fi ZA 0 0 1 0 2 0 3 0 4 r nm 0 5 Figure 4 13 Distance Restraint potential form is quadratic below a specified lower bound and between two specified upper bounds and linear beyond the largest bound see Fig 4 13 kar riz ro 0 Vat Sky ri 11 kar r2 11 Qri r2 11 The forces are Pi kap rij ro fe for 0 for F Ea kay rij r FI for kdr r2 r for ij Time averaging for for for for ro r T2 Tro r1 T2 IA IA IA IN IA IA Tij lt 19 Tij lt Y1 4 59 Tij lt Ya Tij lt ro lt ry 4 60 lt Ya Distance restraints based on instantaneous distance
117. ay Fig 3 13 Chapter 4 Force fields A force field is built up from two distinct components e The set of equations called the potential functions used to generate the potential energies and their derivatives the forces e The parameters used in this set of equations Within one set of equations various sets of parameters can be used Care must be taken that the combination of equations and parameters form a consistent set It is in gen eral dangerous to make ad hoc changes in a subset of parameters because the various contributions to the total force are usually interdependent In GROMACS 2 0 the force field is based on GROMOS 87 35 with a small modification concerning the interaction between water oxygens and carbon atoms 36 37 as well as 10 extra atom types 36 40 However the user is free to make her own modifications beware This will be explained in details in chapter 5 which deals with the Topology To accommodate the potential functions used in some popular force fields GROMACS offers a choice of functions both for non bonded interaction and for dihedral interactions They are described in the appropriate subsections The potential functions can be subdivided into three parts 1 Non bonded Lennard Jones or Buckingham and Coulomb or modified Coulomb The non bonded interactions are computed on the basis of a neighbor list a list of non bonded atoms within a certain radius in which exclusions are already re
118. be taken into account When the fit and analysis groups are identical and the analysis is non mass weighted the fit will also be non mass weighted The eigenvectors are written to a trajectory file v When the same atoms are used for the fit and the covariance analysis the reference structure is written first with t 1 The average structure is written with t 0 the eigenvectors are written as frames with the eigenvector number as timestamp The eigenvectors can be analyzed with g anaeig Files f traj xtc Input Generic trajectory xtc trr trj gro g96 pdb s topol tpr Input Structure mass db tpr tpb tpa gro g96 pdb n index ndx Input Opt Index file o eigenval xvg Output xvgr xmgr file v eigenvec trr Output Full precision trajectory trr trj av average pdb Output Generic structure gro g96 pdb 1 covar log Output Log file Other options h bool no Print help info and quit nice int 19 Set the nicelevel b real 1 First frame ps to read from trajectory e real 1 Last frame ps to read from trajectory fit bool yes Fit to a reference structure mwa bool no Mass weighted covariance analysis last int 1 Last eigenvector to write away 1 is till the last E 13 g_ density Compute partial densities across the box using an index file Densities in gram cubic centimeter number densities or electron densities can be calculated For electron densities each atom is weighed by its atomic partial charge Files f traj xtc Input
119. ble definition of a reaction coordinate extension to groups that are parts of molecules that use SHAKE or LINCS and a combination of the starting structure calculation with constraints for faster convergence of starting structures 6 2 Removing fastest degrees of freedom The maximum time step in MD simulations is limited by the smallest oscillation pe riod that can be found in the simulated system Bond stretching vibrations are in their quantum mechanical ground state and are therefore better represented by a constraint than by a harmonic potential For the remaining degrees of freedom the shortest oscillation period as measured from a simulation is 13 fs for bond angle vibrations involving hydrogen atoms Taking as a guide line that with a Verlet leap frog integration scheme a minimum of 5 numerical integration steps should be performed per period of a harmonic oscillation in order to integrate it with reasonable accuracy the maximum time step will be about 3 fs Disregarding these very fast oscillations of period 13 fs the next shortest periods are around 20 fs which will allow a maximum time step of about 4 fs 6 2 Removing fastest degrees of freedom 103 Removing the bond angle degrees of freedom from hydrogen atoms can best be done by defining them as dummy atoms in stead of normal atoms Where a normal atoms is connected to the molecule with bonds angles and dihedrals a dummy atom s position is calculated from the position of three
120. calculation A 0 or 1 for the case of creation or annihilation of particles State B should the correspond to no particle The modified equations for the Lennard Jones contribution are PCR A UP TE eee Vig ea Md eet 4 82 7 g Vi CB 1 AICA _MCB 1 A CA E a a a ij ij It can be seen immediately that when CB CP 0 no particle and 1 both Vz and Pu are zero This means they need not be evaluated either For the coulomb 64 Force fields contribution we have w 2 1 AP Xai 1 Aaf 7a 4 84 Epia aV 2 Ag 1 Ea Ma Mg 4 85 Aq 1 AJ A A a Aa a Resat and Mezei have tested which exponents to A resp 1 A are best and found that 4 for the repulsion 3 for the dispersion and 2 for the Coulomb interaction to give good results 46 Although this method is an improvement over linear scaling for small A there still can be large forces and or energies and therefore careful equilibration should be done Kinetic Energy When the mass of a particle changes there is also a contribution of the kinetic energy to the free energy note that we can not write the momentum p as mv since that would result in the sign of ook being incorrect 47 2 1 p Ek gt 4 NE ame 14 00 OEk 1 2 mB mA gh ASE _ gt 4 87 Or 2 1 A m4 AmB after taking the derivative we can insert p mv such that OEk _ lo B A Constraints
121. can select the number of starting points and the interval in picoseconds between starting points More starting points implies more CPU time Files f traj xtc Input Generic trajectory xtc trr trj gro g96 pdb s topol tpr Input Structure mass db tpr tpb tpa gro g96 pdb n index ndx Input Opt Index file 0 msd xvg Output xvgr xmer file m mol xvg Output Opt xvgr xmer file d diff xvg Output Opt xvgr xmer file Other options h bool no Print help info and quit nice int 19 Set the nicelevel b real 1 First frame ps to read from trajectory e real 1 Last frame ps to read from trajectory w_ bool no View output using xvgr or ghostview type enum no Compute diffusion coefficient in one direction no x y Or z lateral enum no Calculate the lateral diffusion in a plane perpendicular to no x y ngroup int 1 Number of groups to calculate MSD for mw bool yes Mass weighted MSD nrestart int 1 Number of restarting points in trajectory dt real O Time between restarting points in trajectory only with nrestart gt 1 Diagnostics e The diffusion constant given in the title of the graph for lateral diffusion has to be multiplied by 6 4 E 28 g_nmeig g nmeig calculates the eigenvectors values of a Hessian matrix which can be calculated with nmrun The eigenvectors are written to a trajectory file v The structure is written first with t 0 The eigenvectors are written as frames with the eigenvector number as timestamp The e
122. ce between all combination of charged groups as a function of time The groups are combined in different ways A minimum distance can be given eg the cut off then groups that are never closer than that distance will not be plotted Output will be in a number of fixed filenames min min xvg min plus xvg and plus plus xvg or files for every individual ion pair if selected Files f traj xtc Input Generic trajectory xtc trr trj gro g96 pdb s topol tpr Input Generic run input tpr tpb tpa Other options h bool no Print help info and quit nice int 19 Set the nicelevel b real 1 First frame ps to read from trajectory e real 1 Last frame ps to read from trajectory t real 1000 trunc distance sep bool no Use separate files for each interaction may be MANY E 40 g_sas g sas computes hydrophobic and total solvent accessible surface area Files f traj xtc Input Generic trajectory xtc trr trj gro g96 pdb s topol tpr Input Generic run input tpr tpb tpa 0 area xvg Output xvgr xmgr file q connelly pdb Output Opt Protein data bank file Other options h bool no Print help info and quit nice int 19 Set the nicelevel b real 1 First frame ps to read from trajectory e real 1 Last frame ps to read from trajectory w bool no View output using xvgr or ghostview solsize real 0 14 Radius of the solvent probe nm ndots int 24 Number of dots per sphere more dots means more accuracy qmax real 0 2 The maximum charge e ab
123. celevel temp real 300 Temperature in Kelvin seed int 1 Random seed 1 generates a seed from time and pid num int 100 Number of structures to generate first int 7 First eigenvector to use 1 is select last int 1 Last eigenvector to use 1 is till the last E 30 g order Compute the order parameter per atom for carbon tails For atom i the vector i 1 i 1 is used together with an axis The index file has to contain a group with all equivalent atoms in all tails for each atom the order parameter has to be calculated for The program can also give all diagonal elements of the order tensor and even calculate the deuterium order parameter Scd default If the option szonly is given only one order tensor component specified by the d option is given and the order parameter per slice is calculated as well If szonly is not selected all diagonal elements and the deuterium order parameter is given Files f traj xtc Input Generic trajectory xtc trr trj gro g96 pdb n index ndx Input Index file s topol tpr Input Generic run input tpr tpb tpa 0 order xvg Output xvgr xmer file od deuter xvg Output xvgr xmer file os sliced xvg Output xvgr xmgr file E 31 g_potential Other options h nice szonly unsat E 31 g_ potential bool int real real bool enum int bool bool no 19 f no no no 193 Print help info and quit Set the nicelevel First frame ps to read from trajectory Last frame ps to r
124. ces are evaluated during neighbor list generation The virial is calculated from the sum of the short and long range forces This means that the virial can be slightly asymmetrical at non NS steps In single precision the virial is almost always asymmetrical because the off diagonal elements are about as large as each element in the sum In most cases this is not really a problem since the fluctuations in de virial can be 2 orders of magnitude larger than the average Except for the plain cut off all of the interaction functions in Table 4 2 require that neighbor searching is done with a larger radius than the re specified for the functional form because of the use of charge groups The extra radius is typically of the order of 0 25 nm roughly the largest distance between two atoms in a charge group plus the distance a charge group can diffuse within neighbor list updates Coulomb Plain cut off Reaction field Shift function Switch function VdW Plain cut off Shift function Switch function Table 4 2 Parameters for the different functional forms of the non bonded interactions 4 5 Dummy atoms 67 9 7 o o J 4 Oo 3out 4fd 3fd 3fad Figure 4 15 The six different types of dummy atom construction in GROMACS the constructing atoms are shown as black circles the dummy atoms in grey 4 5 Dummy atoms Dummy atoms can be used in GROMACS in a number of ways We write the position of the dummy particle rg as a function of th
125. ch we use in the next step 3 Convolute k with the Fourier transform of the charge spread function k which we have tabulated before to obtain the potential k As an optimization we store the g k in transposed form as well matching the transposed form of k which we get from the FFTW routine After this step we have the potential b k in Fourier space but still on the transposed FFT grid 4 Do an inverse transform of k to obtain r Since the algorithm must do a transpose of the data this step actually yields the wanted result the un transposed potential in real space 5 Interpolate the potential r in real space at the particle positions to obtain forces and energy For this bit the same considerations towards parallelism hold as for the charge spreading However in this case more neighboring grid cells are needed such that we need the following set of FFT grid slabs in the x direction len l lan trunc 3 lt ig lt trunc 6 1 4 3 54 The algorithm as sketched above requires communication for spreading the charges for the FFTW forward and backward and for interpolating the forces The GROMACS bits of the program use only left and right communication i e using two communication channels The FFTW routines actually use other forms of communication as well and these routines are coded with MPI routines for message passing This implies that GROMACS can only perform the PPPM algorithm on pa
126. clic peptides and crambin J Am Chem Soc 110 1657 1666 1988 Torda A E Scheek R M van Gunsteren W F Time dependent distance re straints in molecular dynamics simulations Chem Phys Lett 157 289 294 1989 Resat H Mezel M Studies on free energy calculations I Thermodynamic integra tion using a polynomial path J Chem Phys 99 6052 6061 1993 van Gunsteren W F Mark A E Validation of molecular dynamics simulations J Chem Phys 108 6109 6116 1998 Berendsen H J C van Gunsteren W F Molecular dynamics simulations Tech niques and approaches In Molecular Liquids Dynamics and Interactions et al A J B ed NATO ASI C 135 Reidel Dordrecht The Netherlands 1984 475 500 Ewald P P Die Berechnung optischer und elektrostatischer Gitterpotentiale Ann Phys 64 253 287 1921 Darden T York D Pedersen L Particle mesh Ewald An N log N method for Ewald sums in large systems J Chem Phys 98 10089 10092 1993 Essmann U Perera L Berkowitz M L Darden T Lee H Pedersen L G A smooth particle mesh ewald potential J Chem Phys 103 8577 8592 1995 Hockney R W Eastwood J W Computer simulation using particles New York McGraw Hill 1981 Luty B A Tironi I G van Gunsteren W F Lattice sum methods for calculating electrostatic interactions in molecular simulations J Chem Phys 103 3014 3021 1995 King P M Mark A E van Gunsteren W F Re p
127. constraints all of which are described below Temperature coupling For several reasons drift during equilibration drift as a result of force truncation and integration errors heating due to external or frictional forces it is necessary to control the temperature of the system GROMACS uses the weak coupling scheme 17 that mimics weak coupling with first order kinetics to an external heat bath with given temperature To See ref 18 for a comparison of this temperature control method with the Nos Hoover scheme 19 20 The effect of the algorithm is that a deviation of the system temperature from To is slowly corrected according to dT To T eas E 3 19 dt T which means that a temperature deviation decays exponentially with a time constant 7 This method of coupling has the advantage that the strength of the coupling can be varied and adapted to the user requirement for equilibration purposes the coupling time can be taken quite short e g 0 01 ps but for reliable equilibrium runs it can be taken much longer e g 0 5 ps in which case it hardly influences the conservative dynamics The heat flow into or out of the system is effected by scaling the velocities of each particle every step with a time dependent factor A given by 1 2 A Est 3 20 Tr T t at The parameter Tr is close to but not exactly equal to the time constant 7 of the temper ature coupling eqn 3 19 T 2Cytr Nak 3 21 where Cy is the
128. culetype before is meaningless and generates a warning 87 without e using molecules without having used system before is meaningless and generates a warning e after system the only allowed directive is molecules e using an unknown string in causes all the data until the next directive to be ignored and generates a warning Here is an example of a topology file urea top Example topology file The force field files to be included include ffgmx itp moleculetype name nrexcl Urea 3 atoms nr type 1 C 2 0 3 NT 4 H 5 H 6 NT 7 H 8 H bonds ai aj funct 3 4 1 3 5 1 6 T 1 6 8 1 1 2 1 1 3 1 1 6 1 pairs ai aj funct 2 4 1 2 5 1 2 T 1 2 8 1 3 7 1 3 8 1 resnr RRARpaR Rep O O CTO OGO residu UREA UREA UREA UREA UREA UREA UREA UREA PRPRPrPRPRP PB bO 000000e 01 000000e 01 000000e 01 000000e 01 230000e 01 330000e 01 330000e 01 c6 000000e 00 000000e 00 000000e 00 000000e 00 000000e 00 000000e 00 wWwwow ww uw Ooo00o0ooo atom C1 02 N3 H4 H5 N6 H7 H8 kb 744680e 05 744680e 05 744680e 05 744680e 05 020800e 05 765600e 05 765600e 05 c12 000000e 00 000000e 00 000000e 00 000000e 00 000000e 00 000000e 00 Q 09 B K WUUNNNR EF charge 683 683 622 346 276 622 346 276 88 4 6 1 0 000000e 00 0 000000e 00 5 6 1 0 000000e 00 0 000000e 00
129. d by the artifact of periodic conditions If a crystal is simulated such boundary conditions are desired although motions are naturally restricted to periodic motions with wavelengths fitting into the box If one wishes to simulate non periodic systems as liquids or solutions the periodicity by itself causes errors The errors can be evaluated by comparing various system sizes they are expected to be less severe than the errors resulting from an unnatural boundary with vacuum 14 Algorithms 0 O O O O i O j Re Ne e Figure 3 1 Periodic boundary conditions in two dimensions There are several possible shapes for space filling unit cells Some as the truncated oc tahedron 11 approach a spherical shape better than a cubic box and are therefore more economical for studying an approximately spherical macromolecule in solution since less solvent molecules are required to fill the box given a minimum distance between macromolecular images However a periodic system based on the truncated octahedron is equivalent to a periodic system based on a triclinic unit cell The latter shape is the most general space filling unit cell it comprises all possible space filling shapes 12 Therefore GROMACS will in future versions be based on the triclinic unit and will not contain other unit cell shapes However in the present version only rectangular boxes are allowed GROMACS uses periodic boundary conditions combi
130. e When writing pdb files B factors can be added with the bf option B factors are read from a file with with following format first line states number of entries in the file next lines state an index followed by a B factor The B factors will be attached per residue unless an index is larger than the number of residues or unless the atom option is set Obviously any type of numeric data can be added instead of B factors legend will produce a row of CA atoms with B factors ranging from the minimum to the maximum value found effectively making a legend for viewing Finally with option label editconf can add a chain identifier to a pdb file which can be useful for analysis with e g rasmol Files f conf gro Input Generic structure gro g96 pdb tpr tpb tpa n index ndx Input Opt Index file 0 out gro Output Generic structure gro g96 pdb bf bfact dat Input Opt Generic data file Other options h bool no Print help info and quit nice int O Set the nicelevel ndef bool no Choose output from default index groups d real O Distance between the solute and the rectangular box dc real O Distance between the solute and the cubic box box vector 000 Size of box c bool no Center molecule in box implied by d dc box center vector Coordinates of geometrical center rotate vector Rotation around the X Y and Z axes in degrees princ bool no Orient molecule s along their principal axes E 3 eneconv 173 scale vector 1 1 1 Scal
131. e i Tyr q Trp His y Figure 6 4 The different types of dummy atom constructions used for aromatic residues The atoms used in the construction of the dummy atom s are depicted as black circles dummy atoms as grey ones Hydrogens are smaller than heavy atoms A phenylalanine B tyrosine note that the hydroxyl hydrogen is not a dummy atom C tryptophane D histidine atoms are constructed as linear combinations of the two carbon mass vectors and their outer product resulting in an amine group with rotational freedom intact but without other internal degrees of freedom See Fig 6 3D 6 2 2 Out of plane vibrations in aromatic groups The planar arrangements in the side chains of the aromatic residues lends itself perfectly for a dummy atom construction giving a perfectly planar group without the inherently in stable constraints that are necessary to keep normal atoms in a plane The basic approach is to define three atoms or dummy masses with constraints between them to fix the geom etry and create the rest of the atoms as simple dummy type 3 atoms see section sec 4 5 from these three Each of the aromatic residues require a different approach Phenylalanine C Cea and Cez are kept as normal atoms but with each a mass of one third the total mass of the phenyl group See Fig 6 3A Tyrosine The ring is treated identical to the phenylalanine ring Additionally constraints are defined between Ce and Ce2 and O The origi
132. e 2 and using this notation Tij Tj fri 2 1 rig rij The force on particle i is denoted by F and F j force on i exerted by j 2 3 Please note that we changed notation as of ver 2 0 to rj rj r since this is the notation commonly used If you encounter an error let us know 2 2 MD units GROMACS uses a consistent set of units that produce values in the vicinity of unity for most relevant molecular quantities Let us call them MD units The basic units in this system are nm ps K electron charge e and atomic mass unit u see Table 2 1 Consistent with these units are a set of derived units given in Table 2 2 The electric conversion factor f 7 138 935 485 9 kJ mol nm e7 It relates the mechanical quantities to the electrical quantities as in 2 2 q q 10 Definitions and Units nm 107 m u atomic mass unit 1 6605402 10 x 107 kg 1 12 of the mass of a C atom 1 6605402 10 x 107 kg time ps 1072 s charge e electronic charge 1 60217733 49 x 1071 C temperature energy kJ mol Force kJ mol nm pressure kJ mol nm 10 N yy Pa 1 66054 x 10 Pa 16 6054 Bar velocity nm ps 1000 m s dipole moment enm electric potential kJ mol e7 0 010364 272 3 Volt electric field kJ mol nm e7 1 036 427 2 3 x 107 V m Table 2 2 Derived units Electric potentials and electric fields E are intermediate quantities in the calculation of energies and forces T
133. e for the potential and get a graphical representation of it than to modify the inner loops of the MD program 160 Some implementation details rtab xvg Repulsion dtab xvg Dispersion x f x f x UG 1 ctab xvg Coulomb Table B 2 User specified potential function data f x denotes the n derivative of f x with respect to x B 4 1 Your own potential function You can also use your own potential functions without editing the GROMACS code When you add the following lines in your mdp file electrostatics User rshort 1 0 rlong 1 0 the MD program will expect to find three files with five columns of table lookup data according to Table B 2 As an example for the normal dispersion interaction the file would contain x x cox 42x78 286K The x should run from 0 to re 0 5 with a spacing of 0 002 nm when you run in single precision or 0 0005 when you run in double precision This and other functions contain a singularity at x 0 but since atoms are normally not closer to each other than 0 1 nm the function value at x 0 is not important In this context re denotes the single cut off denoted by the variables rshort and rlong see above These variables should be the same but need not be 1 0 and consistent with the table data The neighbor searching algorithm will search all atom pairs within a distance rlong and compute the interactions using your potential functions This mechanism allows the user to
134. e is no fundamental difference between a switch function which multiplies the poten tial with a function and a shift function which adds a function to the force or potential 48 Force fields The switch function is a special case of the shift function which we apply to the force function F r related to the electrostatic or Van der Waals force acting on particle i by particle j as F cF r 4 20 Tij For pure Coulomb or Lennard Jones interactions F r F r r The shifted force F r can generally be written as F r Falr r lt ry F r Falr S r r lt r lt re 4 21 Er 0 Te Lr When r 0 this is a traditional shift function otherwise it acts as a switch function The corresponding shifted coulomb potential then reads V3 rij f0s r 5 q 9 4 22 where r is the potential function 00 f F a de 4 23 r The GROMACS shift function should be smooth at the boundaries therefore the following boundary conditions are imposed on the shift function S ri 0 So Flr caa Sre Falre das polynomial of tetona S r A r r1 B r r1 4 25 fulfills these requirements The constants A and B are given by the boundary condition at re a 4 r a 1 r1 A oe 4 26 ee ja a 3 re a 1 r rot q r1 Thus the total force function is ROS A ae O TA 4 27 S pat T 1 T 1 and the potential function reads 1 A B r pal dl r1 ae ri C 4 28 4
135. e overlap of the eigenvectors in file v2 with eigenvectors first to last in file v inpr calculate a matrix of inner products between eigenvectors in files v and v2 All eigen vectors of the first file will be used unless first and last have been set explicitly Files v eigenvec trr Input Full precision trajectory trr trj v2 eigenvec2 trr Input Opt Full precision trajectory trr trj f traj xtc Input Opt Generic trajectory xtc trr trj gro g96 pdb s topol tpr Input Opt Structure mass db tpr tpb tpa gro g96 pdb n index ndx Input Opt Index file disp eigdisp xvg Output Opt xvgr xmer file proj proj xvg Output Opt xvgr xmer file 2d 2dproj xvg Output Opt xvgr xmgr file 3d 3dproj pdb Output Opt Generic structure gro g96 pdb filt filtered xtc Output Opt Generic trajectory xtc trr trj gro g96 pdb extr extreme pdb Output Opt Generic trajectory xtc trr trj gro g96 pdb over overlap xvg Output Opt xvgr xmer file inpr inprod xpm Output Opt X PixMap compatible matrix file Other options h bool no Print help info and quit nice int 19 Set the nicelevel b real 1 First frame ps to read from trajectory e real 1 Last frame ps to read from trajectory first int 1 First eigenvector for analysis 1 is select last int 8 Last eigenvector for analysis 1 is till the last skip int 1 Only analyse every nr th frame max real O Maximum for projection of the eigenvector on the average structure max 0 g
136. e positions of other particles rj rq f r rp The dummy which may carry charge or can be involved in other interactions can now be used in the force calculation The force acting on the dummy particle must be redistributed over the atoms in a consistent way A good way to do this can be found in ref 48 We can write the potential energy as V Virari tn V ri ra 4 93 The force on the particle 7 is then ave V Org AV Pret Fr 4 94 Or Or Or Ora Bs F the first term of which is the normal force The second term is the force on particle due to the dummy particle which can be written in tensor notation OTa oya Oza Peah a i 4 95 Oy Oy OY OTa OYa Oza where Fy is the force on the dummy particle and xg yq and zg are the coordinates of the dummy particle In this way the total force and the total torque are conserved 48 There are six ways to construct dummies from surrounding atoms in GROMACS which we categorize based on the number of constructing atoms Note that all dummies types men tioned can be constructed from types 3fd normalized in plane and 3out non normalized out of plane However the amount of computation involved increases sharply along this list so it is strongly recommended to always use the first dummy type that will be sufficient for a certain purpose An overview of the dummy constructions is given in Fig 4 15 2 As a linear combi
137. each consecutive line contains a residuename Files f nnnice dat Input Generic data file 0 plot eps Output Encapsulated PostScript tm file Other options h bool no Print help info and quit nice int 19 Set the nicelevel r0 int 1 The first residue number in the sequence rot0 real 0 Rotate around an angle initially 90 degrees makes sense E 63 xpm2ps 213 T string Plot a title in the center of the wheel must be shorter than 10 char acters or it will overwrite the wheel nn bool yes Toggle numbers E 63 xpm2ps xpm2ps makes a beautiful color plot of an XPixelMap file Labels and axis can be displayed when they are supplied in the correct matrix format Matrix data may be generated by programs such as do_dssp g rms or g mdmat Parameters are set in the m2p file optionally supplied with di Reasonable defaults are supplied in a library file With f2 a 2nd matrix file can be supplied both matrix files will be read simultaneously and the upper left half of the first one f is plotted together with the lower right half of the second one 2 The diagonal will contain values from the matrix file selected with diag Plotting of the diagonal values can be suppressed altogether by setting diag to none If the color coding and legend labels of both matrices are identical only one legend will be displayed else two separate legends are displayed title can be set to none to suppress the title or to ylabel to show the
138. ead from trajectory View output using xvgr or ghostview Direction of the normal on the membrane z x or y Calculate order parameter as function of boxlength dividing the box in nr slices Only give Sz element of order tensor axis can be specified with d Calculate order parameters for unsaturated carbons Note that this cannot be mixed with normal order parameters Compute the electrostatical potential across the box The potential iscalculated by first summing the charges per slice and then integratingtwice of this charge distribution Periodic boundaries are not taken into account Reference of potential is taken to be the left side ofthe box It s also possible to calculate the potential in sphericalcoordinates as function of r by calculating a charge distribution inspherical slices and twice integrating them epsilon_r is taken as 1 2 is more appropriate in many cases Files f traj n index s topol o potential 0c charge of field Other options h bool nice int b real e real w bool d string s1 int cb int ce int tz real spherical bool Diagnostics xtc Input Generic trajectory xtc trr trj gro g96 pdb ndx Input Index file tpr Input Generic run input tpr tpb tpa xvg Output xvgr xmgr file xvg Output xvgr xmgr file xvg Output xvgr xmgr file no Print help info and quit 19 Set the nicelevel 1 First frame ps to read from trajectory 1 Last frame ps to read from trajectory no View output using xvg
139. eal 1 First frame ps to read from trajectory e real 1 Last frame ps to read from trajectory t real 1 5 trunc distance nlevels int 40 Discretize distance in levels dt real 0 Only analyze a frame each dt picoseconds E 26 g_mindist g mindist computes the distance between one group and a number of other groups Both the smallest distance and the number of contacts within a given distance are plotted to two separate output files Files f traj xtc Input Generic trajectory xtc trr trj gro g96 pdb n index ndx Input Index file od mindist xvg Output xvgr xmer file on numcont xvg Output xvgr xmer file o atm pair out Output Generic output file Other options h bool no Print help info and quit nice int 19 Set the nicelevel b real 1 First frame ps to read from trajectory e real 1 Last frame ps to read from trajectory w bool no View output using xvgr or ghostview matrix bool no Calculate half a matrix of group group distances d real 0 6 Distance for contacts E 27 g_msd 191 E 27 g msd g msd computes the mean square displacement MSD of atoms from their initial positions This provides an easy way to compute the diffusion constant using the Einstein relation If the d option is given the diffusion constant will be printed in addition to the MSD Mean Square Displacement calculations and Correlation functions can be calculated more accu rately when using multiple starting points see also Gromacs Manual You
140. eavy atom on a line going through the bonded heavy atom and a point on the line through both second bonded atoms see Fig 6 3B planar amine NH2 hydrogens The method used for the single amide hydrogen is not well suited for planar amine groups because no suitable two heavy atoms can be found to define the direction of the hydrogen atoms In stead the hydrogen is constructed at a fixed distance from the nitrogen atom with a fixed angle to the carbon atom in the plane defined by one of the other heavy atoms see Fig 6 3C amine group umbrella NH2 or NH7 hydrogens Amine hydrogens with rotational freedom cannot be constructed as dummy atoms from the heavy atoms they are connected to since this would result in loss of the rotational freedom of the amine group To preserve the rotational freedom while removing the hydrogen bond angle degrees of freedom two dummy masses are constructed with the same total mass moment of inertia for rotation around the C N bond and center of mass as the amine group These dummy masses have no interaction with any other atom except for the fact that they are connected to the carbon and to each other resulting in a rigid triangle From these three particles the positions of the nitrogen and hydrogen 6 2 Removing fastest degrees of freedom 105 e p C xa p d A f a e e se e S e E 2 1 4 y oman i n o gt e gt e o oo e A w s g PA a Ph
141. ed arises or knowledge improves But the form of the forces that can be used in a particular program is subject to limitations The force field that is incorporated in GROMACS is described in Chapter 4 In the present version the force field is pair additive apart from long range coulomb forces it cannot incorporate polarizabilities and it does not contain fine tuning of bonded interactions This urges the inclusion of some limitations in this list below For the rest it is quite useful and fairly reliable for bio macro molecules in aqueous solution The force field is pair additive This means that all non bonded forces result from the sum of non bonded pair in teractions Non pair additive interactions the most important example of which is interaction through atomic polarizability are represented by effective pair potentials 1 3 Energy Minimization and Search Methods 5 Only average non pair additive contributions are incorporated This also means that the pair interactions are not pure i e they are not valid for isolated pairs or for situations that differ appreciably from the test systems on which the models were parameterized In fact the effective pair potentials are not that bad in practice But the omission of polarizability also means that electrons in atoms do not provide a dielectric constant as they should For example real liquid alkanes have a dielectric constant of slightly more than 2 which reduce the long range electros
142. ed as with r as defined in eqn 4 102 dcos 0 dsin 6 5 Pi F F4 cos Fe Q S Tii Tik m4 Fa Iris ri Pig Pig dcos O dsin 6 Tig Fi ra Tr ULA pp F3 rn 35 Tij Tij Tij dsin 6 F ZAR r_ ri F ri F ri F where F Fy rij Fy F fr and F ir Tij Pij TESTE Tij Tij 4 103 4 6 Long Range Electrostatics 69 3out As a non linear combination of three atoms out of plane Fig 4 15 3out Ta T ari brik cles x ik 4 104 this enables the construction of dummies out of the plane of the other atoms The force on particles i j and k due to the force on the dummy can be computed as a TCZik CYik F CZik a c zik Fa TCVYik Lik a b C Zij C Yij 4 105 F C Zij b C Tij Fa CYij C Tij b Fi F Fj F 4fd From four atoms with a fixed distance Fig 4 15 4fd Tij ar jk br j Tq rite 4 106 rig orgie br in this case the dummy is at a distance of c from i The force on particles 7 j k and due to the force on the dummy can be computed as Fi F Fa p c F 1 a b Fa p VO rig arj br where pa F 4 107 F ay Fa p Oop Tid Ti Fl _ by Fg _ p id id 4 6 Long Range Electrostatics 4 6 1 Ewald summation The total electrostatic energy of N particles and the periodic images are given by B 4 108 E Ne Ny N i aon Ny Ny Nz n is the box index vector and the star indicates
143. ed in reciprocal space is controlled by fourierspacing The relative accuracy of direct reciprocal space is controlled by ewald_rtol NOTE Ewald scales as O N and is thus extremely slow for large systems It is included mainly for reference in most cases PME will perform much better PME Fast Particle Mesh Ewald electrostatics Direct space is similar to the Ewald sum while the reciprocal part is performed with FFTs Grid dimensions are controlled with fourierspacing and the interpolation order with pme_order With a grid spacing of 0 1 nm and cubic interpolation the electrostatic forces have an accuracy of 2 3e 4 Since the error from the vdw cutoff is larger than this you might try 0 15 nm When running in parallel the interpolation paral lelizes better than the FFT so try decreasing grid dimensions while increasing interpolation PPPM Particle Particle Particle Mesh algorithm for long range electrostatic interac tions Use for example rlist 1 0 rcoulomb_switch 0 0 rcoulomb 0 85 rvdw_switch 1 0 and rvdw 1 0 The grid dimensions are controlled by fourierspacing Reasonable grid spacing for PPPM is 0 05 0 1 nm See Shift for the details of the particle particle potential NOTE the pressure in incorrect when using PPPM Reaction Field Reaction field with Coulomb cut off rcoulomb where rcoulomb gt rvdw gt rlist The dielectric constant beyond the cut off is epsilon_r The dielectric constant can be set to infinity by setting e
144. eleration af will be imposed This is equivalent to an external force This feature makes it possible to drive the system into a non equilibrium state and enables to perform non equilibrium MD to obtain transport properties Energy monitor group Mutual interactions between all energy monitor groups are compiled during the simulation This is done for Lennard Jones and Coulomb terms separately In principle up to 256 groups could be defined but that would lead to 256x256 items Better use this concept sparingly The use of groups in analysis programs is described in chapter 8 3 4 Molecular Dynamics A global flow scheme for MD is given in Fig 3 2 Each MD or EM run requires as input a set of initial coordinates and optionally initial velocities of all particles involved This chapter does not describe how these are obtained for the setup of an actual MD run check the online manual at http md chem rug nl gmx 16 Algorithms THE GLOBAL MD ALGORITHM 1 Input initial conditions Potential interaction V as a function of atom positions Positions r of all atoms in the system Velocities v of all atoms in the system y repeat 2 3 4 required number of steps 2 Compute forces The force on any atom a OW F or is computed by calculating the force between non bonded atom pairs F Fij plus the forces due to bonded interactions which may depend on 1 2 3 or 4 atoms plus restraining and or external forces The pote
145. enpr E 48 gmxcheck E 49 gmxdump E 50 grompp E 51 highway E 52 make ndx E 53 mdrun E 58 protonate E 59 tpbconv HOO 41 Cat ters sce acy Gok ere oe E E 61 trjconv E 62 wheel E 63 xpm2ps E 64 xrama Bibliography Index E 57 pdb2gmx CONTENTS List of Figures 3 1 3 2 3 3 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 3 13 4 1 4 2 4 3 4 4 4 5 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 Periodic boundary conditions in two dimensions 14 The global MD algorithm e e 16 A Maxwellian distribution generated from random numbers 17 The computational box in two dimensions 0245 19 The Leap Frog integration method o 21 The MD update algorithm o e 25 The three position updates needed for one time step 27 Free ener ey Cycles carr A a ee ES 32 The interaction Matrix 35 Interaction matrices for different N o a 35 The Parallel MD algorithm e e 36 Data flow in a ring of processors e 37 Index in the coordinate array e 39 The Lennard Jones interaction ee ee 44 The Buckingham interaction e e 45 The Coulomb interaction with and without reaction field 46 The Coulomb Force Shifted Force and Shift Function S r 49 Bondsstretchings ao fox mowed eGo
146. erence group possibilities applied to interface systems C is the reference group The circles represent the center of mass of 2 groups plus the reference group and de is the reference distance com The center of mass of the group given under reference_group calculated each step from the current coordinates com_t0 The center of mass of the group given under reference_group calculated each step from the current coordinates but corrected for atoms that have crossed the box If the reference group consists of all the water molecules in the system and a single water molecule moves across the box and enters from the other side the c o m will show a slight jump This is simply due to the periodic boundary conditions and shows that the center of mass in a simulation in periodic boundary conditions is ill defined if the group used to calculate it is e g a slab of liquid If the real positions are used instead of the coordinates that have been reset to be inside the box the center of mass of the whole system is conserved dynamic In a phospholipid bilayer system it may be of interest to calculate the pmf of a lipid as function of its distance from the whole bilayer The whole bilayer can be taken as reference group in that case but it might also be of interest to define the reaction coordinate for the pmf more locally dynamic does not use all the atoms of the reference_group but instead only those within a cylinder with radius r below
147. esnr residu atom cgnr charge 1 C 1 UREA C1 1 0 683 8 H 1 UREA H8 3 0 276 bonds ai aj funct c0 c1 3 4 1 1 000000e 01 3 744680e 05 1 6 1 1 330000e 01 3 765600e 05 pairs ai aj funct c0 c1 2 4 1 0 000000e 00 0 000000e 00 5 6 1 0 000000e 00 0 000000e 00 angles ai aj ak funct cO cl 1 3 4 1 1 200000e 02 2 928800e 02 3 1 6 1 1 170000e 02 5 020800e 02 ai aj ak al funct c0 c1 c2 2 1 3 4 1 1 800000e 02 3 347200e 01 2 000000e 00 3 1 6 8 1 1 800000e 02 3 347200e 01 2 000000e 00 dihedrals ai aj ak al funct c0 c1 3 4 5 1 2 0 000000e 00 1 673600e 02 5 4 File formats 93 00000e 00 1 673600e 02 20 0 2 0 000000e 00 1 673600e 02 This results in a very short top file as described in the previous section but this time you only need to include files The force field files to be included tinclude ffgmx itp Include urea topology include urea itp Include SPC water topology include spc itp system Urea in Water molecules molecule name number Urea 1 SOL 1000 5 4 3 Ifdef option A very powerful feature in GROMACS is the use of ifdef statements in your top file By making use of this statement different parameters for one molecule can be used in the same top file An example is given for TFE where there is an option to use different charges on the atoms charges derived by De Loof et al 58 or by Van Buuren and Berendsen 39 In fact you can use all the options of the C Preproc
148. essor cpp because this is used to scan the file The way to make use of the ifdef option is as follows e in grompp mdp the GROMACS preprocessor input parameters use the option define DDeloof or define DVanBuuren e put the ifdef statements in your top as shown below atoms nr type resnr residu atom cgnr charge mass ifdef DeLoof Use Charges from DeLoof 1 C 1 TFE C 1 0 74 2 F 1 TFE F 1 0 25 3 F 1 TFE F 1 0 25 4 F 1 TFE F 1 0 25 5 CH2 1 TFE CH2 1 0 25 6 DA 1 TFE DA 1 0 65 T HO 1 TFE HO 1 0 41 else Use Charges from VanBuuren 94 Topologies 1 C 1 TFE C 1 0 59 2 F 1 TFE F 1 0 2 3 F 1 TFE F 1 0 2 4 F 1 TFE F 1 0 2 5 CH2 1 TFE CH2 1 0 26 6 OA 1 TFE OA 1 0 55 7 HO 1 TFE HO 1 0 3 Hendif ifdef BONDS bonds ai aj funct cO cl 6 7 1 1 000000e 01 3 138000e 05 1 2 1 1 360000e 01 4 184000e 05 1 3 1 1 360000e 01 4 184000e 05 1 4 1 1 360000e 01 4 184000e 05 1 5 1 1 530000e 01 3 347000e 05 5 6 1 1 430000e 01 3 347000e 05 else constraints ai aj funct dist 6 7 1 1 000000e 01 1 2 1 1 360000e 01 1 3 1 1 360000e 01 1 4 1 1 360000e 01 1 5 1 1 530000e 01 5 6 1 1 430000e 01 Hendif Also in this example is the option ifdef BONDS which results in constraints instead of normal bonds 5 4 4 Coordinate file Files with the gro file extension contain a molecular structure in GROMOS87 format A sample piece is included below MD of 2 waters reformat step PA aug 91 6 1WATER OW1 1 0 1
149. exclusions of LJ interactions between the first and the last atom of the dihedral and is defined according to the polymer convention Pirans 0 So there are three types of dihedrals in the GROMACS force field e proper dihedral funct 1 with mult multiplicity so the number of possible angles e improper dihedral funct 2 e Ryckaert Bellemans dihedral funct 3 In the file bon itp you can add bonded parameters If you want to include pa rameters for new atom types make sure you define this new atom type in f atp as well 5 3 3 Non bonded parameters The non bonded parameters consist of the Van der Waals parameters A and C as listed in nb itp where ptype is the particle type see Table 5 1 atomtypes name mass charge ptype c6 c12 0 15 99940 0 000 A 0 22617E 02 0 74158E 06 OM 15 99940 0 000 A 0 22617E 02 0 74158E 06 nonbond_params 3 i j func c6 c12 0 0 1 0 22617E 02 0 74158E 06 O OA 1 0 22617E 02 0 13807E 05 5 3 Parameter files 81 pairtypes sra j func cs6 cs12 THESE ARE 1 4 INTERACTIONS 0 0 1 0 22617E 02 0 74158E 06 O OM 1 0 22617E 02 0 74158E 06 With A and C being defined as Ai 4e o 5 1 and computed according to the combination rules 1 1 Cig CC 5 4 It is also possible to use the combination rules based on the Lennard Jones parameters and o with E Tij 0 055 5 5 Eij yentj 5 6 This is useful if you want to
150. f gendr genion genpr egmxcheck gmxdump gmxrc gromos 87 gromos 96 files gromos 96 force field grompp 179 179 139 180 180 181 182 182 184 184 185 168 185 186 187 187 189 190 190 191 31 191 192 192 193 193 194 194 195 196 196 197 198 198 199 199 200 201 201 202 202 203 203 147 43 73 73 89 103 204 hessian highway html manual hydrogen database hydrogen bond hypercube improper dihedral install interaction list kinetic energy langevin dynamics leap frog lennard jones license form limitations lincs log file make_ndx maxwellian distribution mdrun mesoscopic dynamics message passing mirror image mk_angndx modified mass molecular modeling mpi nearest image neighbor list neighbor searching neighborlist ngmx nmr refinement nmrun non bonded parameters non equilibrium md normal mode analysis nucleus online manual opls parabolic force INDEX 30 205 109 83 TT 33 80 145 19 65 20 112 21 111 44 63 145 3 26 64 119 113 166 205 17 206 2 33 53 207 103 1 38 107 146 18 19 20 113 113 207 57 120 31 208 80 15 121 30 see particles 109 55 81 49 INDEX parallel md 37 parallel virtual machines see pvm parallelization 32 parameters 75 particle decomposition 34 particle mesh ewald see pme particle particle particle mesh see pppm particles 75 pdb2gmx 57 79 103 208 pe
151. f coordi nates velocities and box in the file for close contacts smaller than vdwfac and not bonded i e not between bonlo and bonhi all relative to the sum of both Van der Waals radii and atoms outside the box these may occur often and are no problem If velocities are present an estimated temperature will be calculated from them The program will compare run input tpr tpb or tpa files when both s1 and s2 are supplied Files f traj xtc Input Opt Generic trajectory xtc trr trj gro g96 pdb s1 top1 tpr Input Opt Generic run input tpr tpb tpa s2 top2 tpr Input Opt Generic run input tpr tpb tpa c topol tpr Input Opt Structure mass db tpr tpb tpa gro g96 pdb e ener edr Input Opt Generic energy edr ene e1 ener1 edr Input Opt Generic energy edr ene e2 ener2 edr Input Opt Generic energy edr ene Other options h bool no Print help info and quit nice int Set the nicelevel vdwfac real Fraction of sum of VdW radii used as warning cutoff bonlo real Min fract of sum of VdW radii for bonded atoms bonhi real Max fract of sum of VdW radii for bonded atoms tol real Tolerance for comparing energy terms between different energy files ooo ON FOO E 49 gmxdump gmxdump reads a run input file tpa tpr tpb a trajectory trj trr xtc or an energy file ene edr and prints that to standard output in a readable format This program is essential for checking your run input file in case of proble
152. fit tail real 500 Length of function including data and tail from fit A real O Start value for fit parameter A tau1 real O Start value for fit parameter taul tau2 real O Start value for fit parameter tau2 eps0 real 80 Epsilon 0 of your liquid epsRF real 78 5 Epsilon of the reaction field used in your simulation fix string Fix this parameter at its start value e g A taul or tau2 nparm int 2 Number of parameters for fitting nsmooth int 3 Number of points for smoothing E 15 g dih g dih can do two things The default is to analyze dihedral transitions by merely computing all the dihedral angles defined in your topology for the whole trajectory When a dihedral flips over to another minimum an angle time plot is made The opther option is to discretize the dihedral space into a number of bins and group each conformation in dihedral space in the appropriate bin The output is then given as a number of dihedral conformations sorted according to occupancy Files f traj xtc Input Generic trajectory xtc trr trj gro g96 pdb s topol tpr Input Generic run input tpr tpb tpa 0 hello out Output Generic output file Other options h bool no Print help info and quit nice int 19 Set the nicelevel b real 1 First frame ps to read from trajectory e real 1 Last frame ps to read from trajectory w_ bool no View output using xvgr or ghostview sa bool no Perform cluster analysis in dihedral space instead of analysing dihe dral transi
153. for which forces and energies will be re calculated ED essential dynamics sampling is switched on by using the ei flag followed by an edi file The edi file can be produced using options in the essdyn menu of the WHAT IF program mdrun produces a edo file that contains projections of positions velocities and forces onto selected eigenvectors The options pi po pd pn are used for potential of mean force calculations and umbrella sampling See manual When mdrun receives a TERM signal it will set nsteps to the current step plus one which causes the run to end after one step and write all the usual output When running with MPI a TERM signal to one of the mdrun processes is sufficient this signal should not be sent to mpirun or the mdrun process that is the parent of the others Files s topol tpr Input Generic run input tpr tpb tpa 0 traj trr Output Full precision trajectory trr trj x traj xtc Output Opt Compressed trajectory portable xdr format c confout gro Output Generic structure gro g96 pdb e ener edr Output Generic energy edr ene 8 md log Output Log file dgdl dgdl xvg Output Opt xvgr xmer file rerun rerun xtc Input Opt Generic trajectory xtc trr trj gro g96 pdb ei sam edi Input Opt ED sampling input e0 sam edo Output Opt ED sampling output E 54 mk_angndx 207 pi pull ppa Input Opt Pull parameters po pullout ppa Output Opt Pull parameters pd pull pdo Output Opt Pull data output p
154. fortunately the dimensionality of the configurational space and the number of local minima is so high that it is impossible to sample the space at a sufficient number of points to obtain a complete survey In particular no minimization method exists that guarantees the determination of the global minimum However given a starting configuration it is possible to find the nearest local minimum Nearest in this context does not always imply nearest in a geometrical sense i e the least sum of square coordinate differences but means the minimum that can be reached by systematically moving down the steepest local gradient Finding this nearest local minimum is all that GROMACS can do for you sorry If you want to find other minima and hope to discover the global minimum in the process the best advice is to experiment with temperature coupled MD run your system at a high temperature for a while and then quench it slowly down to the required temperature do this repeatedly If something as a melting or glass transition temperature exists it is wise to stay for some time slightly below that temperature and cool down slowly according to some clever scheme a process called simulated annealing Since no physical truth is required you can use your phantasy to speed up this process One trick that often works is to make hydrogen atoms heavier mass 10 or so although that will slow down the otherwise very rapid motions of hydrogen atoms it will hardly infl
155. g to a bath In Computer Simulations in Material Science Meyer M Pon tikis V eds Kluwer 1991 139 155 Nos S Title J Chem Phys 81 511 1984 Hoove W G Title Phys Rev E 48 1695 1985 Ryckaert J P Ciccotti G Berendsen H J C Numerical integration of the carte sian equations of motion of a system with constraints molecular dynamics of n alkanes J Comp Phys 23 327 341 1977 Miyamoto S Kollman P A SETTLE An analytical version of the SHAKE and RATTLE algorithms for rigid water models J Comp Chem 13 952 962 1992 Hess B Bekker H Berendsen H J C Fraaije J G E M LINCS A linear constraint solver for molecular simulations J Comp Chem 18 1463 1472 1997 Levitt M Sander C Stern P S The normal modes of a protein Native bovine pancreatic trypsin inhibitor Proc Natl Acad Sci USA 10 181 199 1983 Go N Noguti T Nishikawa T Dynamics of a small globular protein in terms of low frequency vibrational modes Proc Natl Acad Sci USA 80 3696 3700 1983 Brooks B Karplus M Harmonic dynamics of proteins Normal modes and fluctua tions in bovine pancreatic trypsin inhibitor Proc Natl Acad Sci USA 80 6571 6575 1983 Hayward S Go N Collective variable description of native protein dynamics Annu Rev Phys Chem 46 223 250 1995 Amadei A Linssen A B M Berendsen H J C Essential dynamics of proteins PROTEINS Struct Funct Gen 17 4
156. g your run For this you can use the program do dssp which is an interface for the commercial program dssp 65 For further information see the dssp manual A typical output plot of do_dssp is given in Fig 8 10 One other important analysis of proteins is the so called Ramachandran plot This is the projection of the structure on the two dihedral angles and y of the protein backbone see Fig 8 11 To evaluate this Ramachandran plot you can use the program grama A typical output is given in Fig 8 12 It is also possible to generate an animation of the Ramachandran plot in time This can be of help for analyzing certain dihedral transitions in your protein You can use the program xrama for this When studying a helices it is useful to have a helical wheel projection of your peptide to see whether a peptide is amphipatic This can be done using the wheel program Two examples are plotted in Fig 8 13 142 Analysis Ramachandran Plot 180 0 120 0 60 0 0 0 Psi 60 0 120 0 f 180 0 Ec o y 180 0 120 0 60 0 0 0 60 0 120 0 180 0 Phi Figure 8 12 Ramachandran plot of a small protein 2 Sy HPr A Figure 8 13 Helical wheel projection of the N terminal helix of HPr 8 12 Interface related items 143 8 12 Interface related items g_order g_density g_potential g_coord When simulating molecules with long carbon tails it can be interesting to calculate their average orientat
157. he buffer will send the buffer to the indicated processor in our case always the neighboring processor The routine does not wait until the transfer is finished extern void gmx_tx_wait int pid This routine waits until the previous or the ongoing transmission is finished extern void gmx_txs int pid void buf int bufsize This routine implements a synchronous send by calling the a synchronous routine and then the wait It might come in handy to code this differently extern void gmx_rx int pid void buf int bufsize extern void gmx_rx_wait int pid extern void gmx_rxs int pid void buf int bufsize The very same routines for receiving a buffer and waiting until the reception is finished extern void gmx_init int pid int nprocs This routine initializes the different devices needed to do the communication In general it sets up the communication hardware if it is accessible or does an initialize call to the lower level communication subsystem extern void gmx_stat FILE fp char msg With this routine we can diagnose the ongoing communication In the current im plementation it prints the various contents of the hardware communication registers of the Intel 4860 multiprocessor boards to a file A 4 Environment Variables GROMACS programs may be influenced by the use of environment variables First of all the variables set in the GMXRC file are essential for running and compiling GROMACS Other variables are 1 DUMP_NL
158. he topology top file part 2 ooa o 91 Fh GROMACS file types E wie eye a ee RN 110 List of C functions and their Fortran equivalent plus the source files 154 User specified potential function data ee es 160 xvi LIST OF TABLES Chapter 1 Introduction 1 1 Computational Chemistry and Molecular Modeling GROMACS is an engine to perform molecular dynamics simulations and energy minimiza tion These are two of the many techniques that belong to the realm of computational chemistry and molecular modeling Computational Chemistry is just a name to indicate the use of computational techniques in chemistry ranging from quantum mechanics of molecules to dynamics of large complex molecular aggregates Molecular modeling indi cates the general process of describing complex chemical systems in terms of a realistic atomic model with the aim to understand and predict macroscopic properties based on detailed knowledge on an atomic scale Often molecular modeling is used to design new materials for which the accurate prediction of physical properties of realistic systems is required Macroscopic physical properties can be distinguished in a static equilibrium properties such as the binding constant of an inhibitor to an enzyme the average potential energy of a system or the radial distribution function in a liquid and b dynamic or non equilibrium properties such as the viscosity of a liquid diffusion p
159. hen one atom is connected to an existing one a number will be appended to the end of the atom name delete delete existing atoms One atom name per line bonds angles dihedrals and impropers add additional bonded parameters The format is identical to that used in the f 77 rtp see 5 3 5 File formats Topology file The topology file is built following the GROMACS specification for a molecular topology A top file can be generated by pdb2gmx Description of the file layout semicolon and newline surround comments on a line ending with the newline character is ignored directives are surrounded by and the topology consists of three levels the parameter level see Table 5 3 the molecule level which should contain one or more molecule definitions see Table 5 4 the system level system molecules items should be separated by spaces or tabs not commas atoms in molecules should be numbered consecutively starting at 1 the file is parsed once only which implies that no forward references can be treated items must be defined before they can be used exclusions can be generated from the bonds or overridden manually the bonded force types can be generated from the atom types or overridden per bond descriptive comment lines and empty lines are highly recommended 5 4 File formats e using one of the atoms bonds pairs 1 angles etc having used mole
160. hey do not occur inside GROMACS If they are used in evaluations there is a choice of equations and related units We recommend strongly to follow the usual practice to include the factor f in expressions that evaluate and E ir 1 0 2 5 J Ir ej B yE 25 J With these definitions gq is an energy and qE is a force The units are those given in Table 2 2 about 10 mV for potential Thus the potential of an electronic charge at a distance of 1 nm equals f 140 units 1 4 V exact value 1 439965 V Note that these units are mutually consistent changing any of the units is likely to produce inconsistencies and is therefore strongly discouraged In particular if are used instead of nm the unit of time changes to 0 1 ps If the kcal mol 4 184 kJ mol is used instead of kJ mol for energy the unit of time becomes 0 488882 ps and the unit of temperature changes to 4 184 K But in both cases all electrical energies go wrong because they will still be computed in kJ mol expecting nm as the unit of length Although careful rescaling of charges may still yield consistency it is clear that such confusions must be rigidly avoided In terms of the MD units the usual physical constants take on different values see Table 2 3 All quantities are per mol rather than per molecule There is no distinction between 2 3 Reduced units 11 Valu Avogadro s number 6 022 136 7 36 x 10 mol gas constant 8 314 510 70 x 107 kJ mo
161. hich will be constant anyway because of dummy atom constructions will be removed If any constraints remain which involve dummy atoms a fatal error will result To verify your run input file please make notice of all warnings on the screen and correct where necessary Do also look at the contents of the mdout mdp file this contains comment lines as well as the input that grompp has read If in doubt you can start grompp with the debug option which will give you more information in a file called grompp log along with real debug info Finally you can see the contents of the run input file with the gmxdump program Files f grompp mdp Input grompp input file with MD parameters po mdout mdp Output grompp input file with MD parameters c conf gro Input Generic structure gro g96 pdb tpr tpb tpa E 51 highway r conf gro n index ndx p topol top pp processed top 0 topol tpr t traj trr Other options h bool no nice int 0 v bool yes time real 1 np int 1 shuffle bool no rmdumbds bool yes maxwarn int 10 Diagnostics 205 Input Opt Generic structure gro g96 pdb tpr tpb tpa Input Opt Index file Input Topology file Output Opt Topology file Output Generic run input tpr tpb tpa Input Opt Full precision trajectory trr trj Print help info and quit Set the nicelevel Be loud and noisy Take frame at or first after this time Generate statusfile for processors Shuffle molecules over processors Remove con
162. ial variance from the two components we have to make a correction Ao On ofn Pm Ao D 22 if we define gon as the combined and renumbered set of data points we can write AB YE AB in i Oln m 2 S givens D 23 and thus If ap Xim Bla A lo Am 2 e FA 2 e r 2 i Ao D 24 168 Averages and fluctuations or n m XAB XAB 2 3 amy 2 AB Lat y D 25 2 2 n m leer 20p Hen 2 Ao all the x terms drop out and the terms independent of the summation counter can be simplified Kien t Bn AS AE D 26 n m n m o An 5 AB Xin Xf le Li 2 a 2 A RTA 2 ti ty af a 2 j we recognize the three partial sums on the second line and use eqn D 21 to obtain mXfn nXBn Ao nm n m D 27 if we check this by inserting m 1 we get back eqn D 11 D 2 3 Summing energy terms The g energy program can also sum energy terms into one e g potential kinetic total For the partial averages this is again easy if we have S energy components s n S S n S E A D 28 i m s 1 s li m s 1 For the fluctuations it is less trivial again considering for example that the fluctuation in potential and kinetic energy should cancel Nevertheless we can try the same approach as before by writing S y Onn DO D 29 1 if we fill in eqn D 6 lt i Xn gt 5 man i A D 30 E 2 E e ia E D 2 Implementation 169 which we can expand to S ser E 2
163. ible every processor gets the same number of bonded interactions 40 Algorithms In all this makes for a mixed particle decomposition domain decomposition scheme for parallelization of the MD code The communication costs are four times higher than for the simple particle decomposition method described in sec 3 11 the whole coordinate and force array are communicated across the whole ring rather than half the array over half the ring However for large numbers of processors the improved load balancing compensates this easily 3 12 3 Parallel PPPM A further reason for domain decomposition is the PPPM algorithm This algorithm works with a 3D Fast Fourier Transform It employs a discrete grid of dimensions nz ny nz the FFT grid The algorithm consist of five steps each of which have to be parallelized 1 Spreading charges on the FFT grid to obtain the charge distribution p r This bit involves the following sub steps a put particle in the box b find the FFT grid cell in which the particle resides c add the charge of the particle times the appropriate weight factor see sec 4 6 3 to each of the 27 grid points 3 x 3 x 3 In the parallel case the FFT grid must be filled on each processor with its share of the particles and subsequently the FFT grids of all processors must be summed to find the total charge distribution It may be clear that this induces a large amount of unnecessary work unless we use domain decompositio
164. ic system or systems where shear forces are imposed 1 N Exin a Y mwivi 3 12 i Pressure and virial The pressure tensor P is calculated from the difference between kinetic energy Ekin and the virial E 2 3V where V is the volume of the computational box The scalar pressure P which can be used for pressure coupling in the case of isotropic systems is computed as P Erin 5 3 13 P trace P 3 3 14 The virial tensor is defined as 1 3 3 ri 9 Fi 3 15 i lt j In sec B 1 the implementation in GROMACS of the virial computation is described 3 4 3 Update configuration The GROMACS MD program utilizes the so called leap frog algorithm 14 for the inte gration of the equations of motion The leap frog algorithm uses positions r at time t and velocities v at time t At it updates positions and velocities using the forces F t determined by the positions at time t At At F t v v t EO a 3 16 2 2 m r t At r t v t at 3 17 22 Algorithms The algorithm is visualized in Fig 3 5 It is equivalent to the Verlet 15 algorithm F t r t At 2r t r At FO ae O At 3 18 The algorithm is of third order in r and is time reversible See ref 16 for the merits of this algorithm and comparison with other time integration algorithms The equations of motion are modified for temperature coupling and pressure coupling and extended to include the conservation of
165. ics Simulations e 1 3 Energy Minimization and Search Methods 0 Definitions and Units 22 Notation a 3 5 rat Re Eee Be Pot A ee BE Oe eS 2 2 M Dunit sy HR 08 Ba Sa Rok Ee A e A ee ee eee T 2 3 Reduced Umts sts goa Wa y e RA gue OE a Te aie a Algorithms Bill IntPoducthiOnugs 26 dae Bobs A ke ES EE Ee eS eee es 3 2 Periodic boundary conditions 2 00 00 eee ee 3 3 The eroup CONCEDA ls 3 4 Molecular Dynamics 3 41 Anitidl Conditions 24 edad ls Be a A 3 4 2 Compute forces cc a a a RA ee aS D 3 43 Update configurati0d ee ee 3 4 4 Constraint algorithms 000000004 3 4 5 Output Step dh aod a aa oth ode aoe 3 0 simulated Amelia a Ea a oe a a eg 3 6 Langevin Dynamics 3 7 Energy Minimization 0 aoaaa ee 3 7 1 Steepest Descent 2 2 000 ee ee 3 12 Conjigate Gradient x ge oe Se e Be Ek OREN ESS 3 8 Normal Mode Analysis e e vi CONTENTS 3 9 Free energy perturbation 2 2 0 0 a 31 3 10 Essential Dynamics Sampling e 31 3 11 Parallelization s 4 4 vou oe Ae SOR al ae Se bee AR Gk ae 32 3 11 1 Methods of parallelization 2 0 ee es 32 3 11 2 MD on a ring of processors ee 34 3 12 Parallel Molecular Dynamics 02 02 0004 37 3 12 1 Domain decomposition 002002 eee eee 38 3 12 2 Domain decomposition for non bonded forces 38
166. id at low temperature is another example where classical me chanics breaks down While helium may not deeply concern us the high frequency vibrations of covalent bonds should make us worry The statistical mechanics of a classical harmonic oscillator differs appreciably from that of a real quantum oscilla tor when the resonance frequency v approximates or exceeds kgT h Now at room temperature the wavenumber o 1 1 v c at which hv kgT is approximately 200 cm Thus all frequencies higher than say 100 cm are suspect of misbe havior in classical simulations This means that practically all bond and bond angle vibrations are suspect and even hydrogen bonded motions as translational or libra tional H bond vibrations are beyond the classical limit see Table 1 1 What can we do Well apart from real quantum dynamical simulations we can do either of two things a If we perform MD simulations using harmonic oscillators for bonds we should 4 Introduction make corrections to the total internal energy U Egin Epot and specific heat Cy and to entropy S and free energy A or G if those are calculated The corrections to the energy and specific heat of a one dimensional oscillator with frequency v are 6 1 x M _ l USM UF r 30 145 1 3 250 QM _ l Te where z hv kT The classical oscillator absorbs too much energy kT while the high frequency quantum oscillator is in its ground state at the zero point energy level
167. igenvectors can be analyzed with g anaeig An ensemble of structures can be generated from the eigenvectors with g nmens Files f hessian mtx Input Hessian matrix s topol tpr Input Structure mass db tpr tpb tpa gro g96 pdb o eigenval xvg Output xvgr xmer file v eigenvec trr Output Full precision trajectory trr trj 192 Manual Pages Other options h bool no Print help info and quit nice int 19 Set the nicelevel m bool yes Divide elements of Hessian by product of sqrt mass of involved atoms prior to diagonalization This should be used for Normal Modes analyses first int 1 First eigenvector to write away last int 100 Last eigenvector to write away E 29 g_nmens g nmens generates an ensemble around an average structure in a subspace which is defined by a set of normal modes eigenvectors The eigenvectors are assumed to be mass weighted The position along each eigenvector is randomly taken from a Gaussian distribution with variance kT eigenvalue By default the starting eigenvector is set to 7 since the first six normal modes are the translational and rotational degrees of freedom Files v eigenvec trr Input Full precision trajectory trr trj e eigenval xvg Input xvgr xmgr file s topol tpr Input Structure mass db tpr tpb tpa gro g96 pdb n index ndx Input Opt Index file o ensemble xtc Output Generic trajectory xtc trr trj gro g96 pdb Other options h bool no Print help info and quit nice int 19 Set the ni
168. ile viol violaver xvg Output Opt xvgr xmgr file pairs pairs xvg Output Opt xvgr xmer file corr enecorr xvg Output Opt xvgr xmer file vis visco xvg Output Opt xvgr xmer file Other options h bool no Print help info and quit nice int 19 Set the nicelevel b real 1 First frame ps to read from trajectory e real 1 Last frame ps to read from trajectory w bool no View output using xvgr or ghostview G bool no Do a free energy estimate Gtemp real 300 Reference temperature for free energy calculation zero real O Subtract a zero point energy sum bool no Sum the energy terms selected rather than display them all dp bool no Print energies in high precision mutot bool no Compute the total dipole moment from the components skip int O Skip number of frames between data points aver bool no Print also the X1 t and sigmal t only if only 1 energy is requested nmol int 1 Number of molecules in your sample the energies are divided by this ndf int 3 Na of degrees of freedom per molecule Necessary for calculating the heat capacity fluc bool no Calculate autocorrelation of energy fluctuations rather than energy acflen int 1 ln of the ACF default is half the number of frames normalize bool yes Normalize ACF P enum O Order of Legendre polynomial for ACF 0 indicates none 0 1 2 or nparm enum 1 Number of parameters in exponential fit 1 or 2 beginfit real O Time where to begin the exponential fit of the correlation function endfit
169. iles not frames E 4 g_anaeig g anaeig analyzes eigenvectors The eigenvectors can be of a covariance matrix g covar or of a Normal Modes anaysis g nmeig When a trajectory is projected on eigenvectors all structures are fitted to the structure in the eigenvector file if present otherwise to the structure in the structure file When no run input file is supplied periodicity will not be taken into account Most analyses are done on eigenvectors first to last but when first is set to 1 you will be prompted for a selection disp plot all atom displacements of eigenvectors first to last 174 Manual Pages proj calculate projections of a trajectory on eigenvectors first to last 2d calculate a 2d projection of a trajectory on eigenvectors first and last 3d calculate a 3d projection of a trajectory on the first three selected eigenvectors filt filter the trajectory to show only the motion along eigenvectors first to last extr calculate the two extreme projections along a trajectory on the average structure and in terpolate nframes frames between them or set your own extremes with max The eigenvector first will be written unless first and last have been set explicitly in which case all eigen vectors will be written to separate files Chain identifiers will be added when writing a pdb file with two or three structures you can use rasmol nmrpdb to view such a pdb file over calculate the subspac
170. ing factor density real 1000 Density g l of the output box achieved by scaling pbc bool no Remove the periodicity make molecule whole again atom bool no Force B factor attachment per atom legend bool no Make B factor legend label string A Add chain label for all residues Diagnostics e For complex molecules the periodicity removal routine may break down in that case you can use trjconv E 3 eneconv When f is not specified Concatenates several energy files in sorted order In case of double time frames the one in the later file is used By specifying settime you will be asked for the start time of each file The input files are taken from the command line such that the command eneconv o fixed edr edr should do the trick With f specified Reads one energy file and writes another applying the dt offset t0 and settime options and converting to a different format if necessary indicated by file extentions settime is applied first then dt offset followed by b and e to select which frames to write Files f ener edr Input Generic energy edr ene 0 fixed edr Output Opt Generic energy edr ene Other options h bool no Print help info and quit nice int 19 Set the nicelevel b real 1 First time to use e real 1 Last time to use dt real O Only write out frame when t MOD dt offset offset real O Time offset for dt option settime bool no Change starting time interactively sort bool yes Sort energy f
171. ino acid backbone and sidechains It can compute dihedral angle as a function of time and as histogram distributions Output is in form of xvgr files as well as a LaTeX table of the number of transitions per nanosecond Order parameters S2 for each of the dihedrals are calculated and output as xvgr file and optionally as a pdb file with the S2 values as B factor If option c is given the program will calculate dihedral autocorrelation functions The function used is C t lt cos chi tau cos chi tau t gt The use of cosines rather than angles themselves resolves the problem of periodicity Van der Spoel amp Berendsen 1997 Biophys J 72 2032 2041 The option r generates a contour plot of the average omega angle as a function of the phi and psi angles that is in a Ramachandran plot the average omega angle is plotted using color coding Files s topol tpr Input Generic run input tpr tpb tpa f traj xtc Input Generic trajectory xtc trr trj gro g96 pdb 0 order xvg Output xvgr xmgr file p order pdb Output Opt Protein data bank file jc Jcoupling xvg Output xvgr xmer file c dihcorr xvg Output Opt xvgr xmer file g chi log Output Log file Other options h bool no Print help info and quit nice int 19 Set the nicelevel b real 1 First frame ps to read from trajectory e real 1 Last frame ps to read from trajectory w bool no View output using xvgr or ghostview r0 int 1 starting residue phi bool no Outpu
172. ion There are several flavors of order parameters most of which are related The program g_order can calculate order parameters using the equation 3 1 D 5 cos 0z 3 8 31 where 0 is the angle between the z axis of the simulation box and the molecular axis under consideration The latter is defined as the vector from C 1 to Cn 1 The parameters Sy and Sy are defined in the same way The brackets imply averaging over time and molecules Order parameters can vary between 1 full order along the interface normal and 1 2 full order perpendicular to the normal with a value of zero in the case of isotropic orientation The program can do two things for you It can calculate the order parameter for each CH2 segment separately for any of three axes or it can divide the box in slices and calculate the average value of the order parameter per segment in one slice The first method gives an idea of the ordering of a molecule from head to tail the second method gives an idea of the ordering as function of the box length The electrostatic potential 4 across the interface can be computed from a trajectory by evaluating the double integral of the charge density p z We p fae oleae Je 8 32 where the position z oo is far enough in the bulk phase that the field is zero With this method it is possible to split the total potential into separate contributions from lipid and water molecules The program g potential
173. ion or umbrella sampling group 1 MB21_1 group 2 MB21_2 The groups with the atoms to act on The first group is mandatory the second optional reference _group OCTA The reference group Distances are calculated betweeen group 1 and group _2 if specified and this group If e g the constraint force between two ions is needed you would specifiy group 1 as a group with 1 ion and reference_group as the other ion reftype com The type of reference group Options are com com_t0 dynamic dynamic_t0 as explained above reflag 1 The position of the reference group can be taken as average over a number of steps specified by reflag see above direction 0 0 0 0 1 0 Distances are calculated weighted by x y z as specified in direction Setting them all to 1 0 calculates the distance between two groups setting the first two to 0 0 and the third to 1 0 calculates the distance in the z direction only 6 1 Calculating potentials of mean force the pull code 101 reverse to_reference This option selects the direction in which the groups are moved with respect to the reference group for AFM pulling and starting structure calculations The options are to_reference from_reference r 0 If dynamic reference groups are selected dynamic dynamic_t0 r is the radius of the cylinder used to define which atoms are part of the reference group see above With dynamic reference groups the cylinder can be smoothly switched so th
174. iplications are needed The method is more stable and faster than SHAKE but it can only be used with bond constraints and isolated angle constraints such as the proton angle in OH Because of its stability LINCS is especially useful for Langevin Dynamics LINCS has two parameters which are explained in the subsection parameters The LINCS formulas We consider a system of N particles with positions given by a 3N vector r t For Molecular Dynamics the equations of motion are given by Newton s law a S MF 3 33 where F is the 3N force vector and M isa3Nx3N diagonal matrix containing the masses of the particles The system is constrained by K time independent constraint equations g r r ri d 0 1 1 K 3 34 3 4 Molecular Dynamics 27 A o y A o Y p 18 d A d L p Y y Ag y t unconstrained projecting out correction for update forces working gt rotational along the bonds lengthening Figure 3 7 The three position updates needed for one time step The dashed line is the old bond of length d the solid lines are the new bonds dcos 0 and p 2d 12 In a numerical integration scheme LINCS is applied after an unconstrained update just like SHAKE The algorithm works in two steps see figure Fig 3 7 In the first step the projections of the new bonds on the old bonds are set to zero In the second step a correction is applied for the lengthening of the bonds due to rotation
175. irial we have b Ir ll B 15 1 Vi grb bo B 16 Fi VWVV B 17 rh kb bo B 18 Es Fi B 19 The virial contribution from the bonds then is 1 3r 8 Fi E r F B 20 1 ti Fi B 21 2 152 Some implementation details B 1 5 Virial from Shake An important contribution to the virial comes from shake Satisfying the constraints a force G is exerted on the particles shaken If this force does not come out of the algorithm as in standard shake it can be calculated afterwards when using leap frog by At F Ar ri t At r t vi t gt Att At B 22 i miAr G E E B 23 but this does not help us in the general case Only when no periodicity is needed like in rigid water this can be used otherwise we must add the virial calculation in the inner loop of shake When it is applicable the virial can be calculated in the single sum way ieee B ae r F B 24 i where Ne is the number of constrained atoms B 2 Optimizations Here we describe some of the optimizations used in GROMACS apart from parallelism One of these the implementation of the 1 0 sqrt x function is treated separately in sec B 3 The most important other optimizations are described below B 2 1 Inner Loop for Water In GROMACS a special inner loop that calculates non bonded interactions for a water molecule with something else is implemented This loop assumes that the water model is like SPC
176. ith a reference structure and rmsd matrices fits two structures and calculates the rmsd clusters structures calculates atomic fluctuations Distances in structures over time g mindist g_dist g mdmat g rmsdist calculates the minimum distance between two groups calculates the distances between the centers of mass of two groups calculates residue contact maps calculates atom pair distances averaged with power 2 3 or 6 Mass distribution properties over time g com g gyrate g_msd g_rotacf g_rdf g_rdens calculates the center of mass calculates the radius of gyration calculates mean square displacements calculates the rotational correlation function for molecules calculates RDF s calculates radial densities Analyzing bonded interactions g bond calculates bond length distributions mk_angndx generates index files for g_angle g_angle g_dih calculates distributions and correlations for angles and dihedrals analyzes dihedral transitions Structural properties 7 5 Programs by topic 125 g hbond computes and analyzes hydrogen bonds g_saltbr computes salt bridges g sas computes solvent accessible surface area g_order computes the order parameter per atom for carbon tails g sgangle computes the angle and distance between two groups g_disre analyzes distance restraints Kinetic properties g_velacc calculates velocity autocorrelation functions Electrostatic properties genion generates mono atomic ions on
177. ith time constant tau_p ps The compressibility and ref erence pressure are set with compressibility bar and ref_p bar one value is needed semiisotropic Pressure coupling which is isotropic in the x and y direction but different in the z direction This can be useful for membrane simulations 2 values are needed for x y and z directions respectively anisotropic Idem but 3 values are needed for x y and z directions respectively Beware that isotropic scaling can lead to extreme deformation of the simulation box surface tension Surface tension coupling for surfaces parallel to the xy plane Uses normal pressure coupling for the z direction while the surface tension is coupled to the x y dimensions of the box The first ref_p value is the reference surface tension times the number of surfaces bar nm the second value is the reference z pressure bar The two compressibility bar values are the compressibility in the x y and z direction respectively The value for the z compressibility should be reasonably accurate since it influences the converge of the surface tension it can also be set to zero to have a box with constant height triclinic Not supported yet tau_p 1 ps time constant for coupling compressibility bar compressibility NOTE this is now really in bar For water at 1 atm and 300 K the compressibility is 4 5e 5 bar 1 ref_p bar reference pressure for coupling 118 Run parameter
178. ities are not available the program can generate initial atomic velocities v i 1 3N from a Maxwellian distribution Fig 3 3 at a given absolute temperature T 2 ae Mi _ M0 ploi P 3 2 where k is Boltzmann s constant see chapter 2 To accomplish this normally distributed random numbers are generated by adding twelve random numbers Ry in the range 0 lt Ry lt 1 and subtracting 6 0 from their sum The result is then multiplied by the standard deviation of the velocity distribution ykT m Since the resulting total energy will not correspond exactly to the required temperature T a correction is made first the center of mass motion is removed and then all velocities are scaled such that the total energy 18 Algorithms corresponds exactly to T see eqn 3 10 Center of mass motion The center of mass velocity is normally set to zero at every step Normally there is no net external force acting on the system and the center ofmass velocity should remain constant In practice however the update algorithm develops a very slow change in the center of mass velocity and thus in the total kinetic energy of the system specially when temperature coupling is used If such changes are not quenched an appreciable center of mass motion develops eventually in long runs and the temperature will be significantly misinterpreted The same may happen due to overall rotational motion but only when an isolated cluster is simulated
179. ities for constraints v r r At y 6 Scale coordinates and box r ur b ub Figure 3 6 The MD update algorithm 26 Algorithms are satisfied within a relative tolerance TOL An error message is given if SHAKE cannot reset the coordinates because the deviation is too large or if a given number of iterations is surpassed Assume the equations of motion must fulfill K holonomic constraints expressed as oklri ny 0 hea Ve dS 3 30 e g r1 r2 b 0 Then the forces are defined as O K V A 3 31 Dr gia 2 101 3 31 where Az are Lagrange multipliers which must be solved to fulfill the constraint equations The second part of this sum determines the constraint forces G defined by Gi y reds 3 32 1 a Ori The displacement due to the constraint forces in the leap frog or Verlet algorithm is equal to G m At Solving the Lagrange multipliers and hence the displacements requires the solution of a set of coupled equations of the second degree These are solved iteratively by SHAKE For the special case of rigid water molecules that often make up more than 80 of the simulation system we have implemented the SETTLE algorithm 22 sec B 2 2 The LINCS algorithm LINCS is an algorithm that resets bonds to their correct lengths after an unconstrained update 23 The method is non iterative as it always uses two steps Although LINCS is based on matrices no matrix matrix mult
180. ives the extremes nframes int 2 Number of frames for the extremes output E 5 g_analyze g analyze reads an ascii file and analyzes data sets A line in the input file may start with a time see option time and any number of y values may follow Multiple sets can also be read when they are seperated by option n in this case only one y value is read from each line All lines starting with and are skipped All analyses can also be done for the derivative of a set option d Option ac produces the autocorrelation function s E 6 g_angle 175 Option msd produces the mean square displacement s Option dist produces distribution plot s Option av produces the average over the sets optionally with error bars errbar Option ee produces error estimates using block averaging A set is divided in a number of blocks and averages are calculated for each block The error for the total average is calculated from the variance between the block averages These errors are plotted as a function of the block size For a good error estimate the block size should be at least as large as the correlation time but possibly much larger Files f graph xvg Input xvgr xmgr file ac autocorr xvg Output Opt xvgr xmgr file msd msd xvg Output Opt xvgr xmer file dist distr xvg Output Opt xvgr xmer file av average xvg Output Opt xvgr xmer file ee errest xvg Output Opt xvgr xmer file Other options h bool no Print help
181. l K7 Boltzmann s constant idem Planck s constant 0 399 031 32 24 kJ mol ps Dirac s constant 0 063 507 807 38 kJ mol ps velocity of light 299 792 458 nm ps Table 2 3 Some Physical Constants Length r a Mass m Time t Temperature T Energy Force Pressure Velocity Density Table 2 4 Reduced Lennard Jones quantities Boltzmann s constant k and the gas constant R their value is 0 008 31451 kJ mol K 2 3 Reduced units When simulating Lennard Jones LJ systems it might be advantageous to use reduced units 7 e setting Cii Mi kp 1 for one type of atoms This is possible When specifying the input in reduced units the output will also be in reduced units There is one exception the temperature which is expressed in 0 008 31451 reduced units This is a consequence of the use of Boltzmann s constant in the evaluation of temperature in the code Thus not T but kgT is the reduced temperature A GROMACS temperature T 1 means a reduced temperature of 0 008 units if a reduced temperature of 1 is required the GROMACS temperature should be 120 2717 In Table 2 4 quantities are given for LJ potentials Vig 4e 2 2 l 2 7 12 Definitions and Units Chapter 3 Algorithms 3 1 Introduction In this chapter we first give describe two general concepts used in GROMACS periodic boundary conditions sec 3 2 and the group concept sec 3 3 The MD algori
182. l Lennard Jones repulsion is sometimes still too strong which means that when applied to a molecule the molecule would deform or break due to the internal strain This is especially the case for Carbon Carbon interactions in a cis conformation e g cis butane Therefore for some of these interactions the Lennard Jones repulsion has been reduced in the GROMOS force field which is implemented by keeping a separate list of 1 4 and normal Lennard Jones parameters In other force fields such as OPLS 44 the standard Lennard Jones parameters are reduced by a factor of two but in that case also the dispersion r and the coulomb interaction are scaled GROMACS can use either of these methods 4 4 2 Charge Groups In principle the force calculation in MD is an O N problem Therefore we apply a cut off for non bonded force NBF calculations only the particles within a certain distance of each other are interacting This reduces the cost to O N typically 100N to 200N of the NBF It also introduces an error which is in most cases acceptable except when applying the cut off implies the creation of charges in which case you should consider using the lattice sum methods provided by GROMACS Consider a water molecule interacting with another atom When we would apply the cut off on an atom atom basis we might include the atom Oxygen interaction with a charge of 0 82 without the compensating charge of the Hydrogens and so induce a large dip
183. lation is N 1 j CIGAN 7 Y HAN RG DAS 8 9 1 0 where N is the number of available time frames for the calculation The resulting ACF is obviously only available at time points with the same interval At Since for many applications it is necessary to know the short time behavior of the ACF e g the first 10 ps this often means that we have to save the atomic coordinates with short intervals Another implication of eqn 8 9 is that in principle we can not compute all points of the ACF with the same accuracy since we have N 1 data points for C At but only 1 for Cy N 1 At However if we decide to compute only an ACF of length MAt where M lt N 2 we can compute all points with the same statistical accuracy 1 N 1 M Cy jAt i Y fiAt f i j At 8 10 1 0 here of course j lt M M is sometimes referred to as the time lag of the correlation function When we decide to do this we intentionally do not use all the available points for very short time intervals j lt lt M but it makes it easier to interpret the results 132 Analysis Another aspect that may not be neglected when computing ACFs from simulation is that usually the time origins eqn 8 6 are not statistically independent which may introduce a bias in the results This can be tested using a block averaging procedure where only time origins with a spacing at least the length of the time lag are included e g using k time origins with spacing of M
184. le CPU in the gmxhome src makef directory and set the USE_MPI variable to yes and recompile all sources If all is well you can now run with MPI There usually is a program called mpirun with which you can fire up the parallel processes A typical command line looks like mpirun p goofus doofus fred 10 mdrun s topol v N 30 this runs on each of the machines goofus doofus fred with 10 processes on eacht If you have a single machine with multiple processors you don t have to use the mpirun command but you can do with an extra option to mdrun mdrun np 8 s topol v N 8 In this example MPI reads the first option from the command line Since mdrun also wants to know the number of processes you have to type it twice Please note that no automatic nicing is done which means that only the first process will be niced by default Check your local manuals or online manual for exact details of your MPI implementation The online manual for MPI on the web can be found at http www mcs anl gov mpi index html This example taken from Silicon Graphics manual 108 Special Topics Chapter 7 Run parameters and Programs 7 1 Online and html manuals All the information in this chapter can also be found on GMXHOME html online html and online on the GROMACS web site http md chem rug nl gmx online2 0 html The program manual pages as referenced by GMXHOME html online html should be generated by executing make html in G
185. lect part of your trajectory and write it out to a new trajectory file in order to save disk space e g for leaving out the water from a trajectory of a protein in water ALWAYS put the original trajectory on tape We recommend to use the portable xtc format for your analysis to save disk space and to have portable files There are two options for fitting the trajectory to a reference either for essential dynamics analysis or for whatever The first option is just plain fitting to a reference structure in the structure file the second option is a progressive fit in which the first timeframe is fitted to the reference structure in the structure file to obtain and each subsequent timeframe is fitted to the previously fitted structure This way a continuous trajectory is generated which might not be the case when using the regular fit method e g when your protein undergoes large conformational transitions The option pbc sets the type of periodic boundary condition treatment whole makes broken molecules whole a run input file is required pbc is changed form none to whole when fit or pfit is set inbox puts all the atoms in the box nojump checks if atoms jump across the box and then puts them back This has the effect that all molecules will remain whole provided they were whole in the initial conformation note that this ensures a continuous trajectory but molecules may diffuse out of the box The starting configuration for this procedure is t
186. les rather than the center of geometry in the calcula tion of distance dependent Kirkwood factors acflen int 1 Length of the ACF default is half the number of frames normalize bool yes Normalize ACF P enum O Order of Legendre polynomial for ACF 0 indicates none 0 1 2 or nparm enum 1 Number of parameters in exponential fit 1 or 2 beginfit real O Time where to begin the exponential fit of the correlation function endfit real O Time where to end the exponential fit of the correlation function 184 Manual Pages E 17 g_disre g_disre computes violations of distance restraints If necessary all protons can be added to a protein molecule The program allways computes the instantaneous violations rather than time averaged because this analysis is done from a trajectory file afterwards it does not make sense to use time averaging An index file may be used to select out specific restraints for printing Files s topol tpr Input Generic run input tpr tpb tpa f traj xtc Input Generic trajectory xtc trr trj gro g96 pdb ds drsum xvg Output xvgr xmgr file da draver xvg Output xvgr xmgr file dn drnum xvg Output xvgr xmer file dm drmax xvg Output xvgr xmer file dr restr xvg Output xvgr xmer file 1 disres log Output Log file n viol ndx Input Opt Index file Other options h bool no Print help info and quit nice int 19 Set the nicelevel b real 1 First frame ps to read from trajectory e real 1 Last frame ps to re
187. lf of the CPU time goes to inverting the constraint coupling matrix B M B7 which has to be done every time step This K x K matrix has 1 m 1 m on the diagonal The off diagonal elements are only non zero when two bonds are connected then the element is cos p M where me is the mass of the atom connecting the two bonds and is the angle between the bonds The matrix T is inverted through a power expansion A K x K matrix S is introduced which is the inverse square root of the diagonal of B M B This matrix is used to convert the diagonal elements of the coupling matrix to one B M B SS B M B s s a0 S SB M BTS 1S S I An S l The matrix A is symmetric and sparse and has zeros on the diagonal Thus a simple trick can be used to calculate the inverse I An I An 4 A H 3 40 This inversion method is only valid if the absolute values of all the eigenvalues of A are smaller than one In molecules with only bond constraints the connectivity is so low that this will always be true even if ring structures are present Problems can arise in angle constrained molecules By constraining angles with additional distance constraints multiple small ring structures are introduced This gives a high connectivity leading to large eigenvalues Therefore LINCS should NOT be used with coupled angle constraints The LINCS Parameters The accuracy of LINCS depends on the number of matrices used in the expansion
188. lly but the force is used H 3 47 __ OV Ox 3 48 from which the Hessian is computed numerically It should be noted that for a usual Normal Mode calculation it is necessary to completely minimize the energy prior to com putation of the Hessian This should be done with conjugate gradient in double precision A number of GROMACS programs are involved in these calculations First nmrun which computes the Hessian and secondly g nmeig which does the diagonalization and sorting of normal modes according to frequencies Both these programs should be run in dou ble precision An overview of normal mode analysis and the related principal component analysis see sec 8 9 can be found in 27 3 9 Free energy perturbation Free energy perturbation calculations can be performed in GROMACS using slow growth methods An example problem might be calculate the difference in free energy of binding of an inhibitor I to an enzyme E and to a mutated enzyme E It is not feasible with computer simulations to perform a docking calculation for such a large complex or even releasing the inhibitor from the enzyme in a reasonable amount of computer time with reasonable accuracy However if we consider the free energy cycle in Fig 3 8A we can write AG1 NGG AG AG4 3 49 If we are interested in the left hand term we can equally well compute the right hand term If we want to compute the difference in free energy of binding
189. lp info and quit nice int 19 Set the nicelevel E 10 g com 179 b real 1 First frame ps to read from trajectory e real 1 Last frame ps to read from trajectory w bool no View output using xvgr or ghostview dista bool no Use RMSD of distances instead of RMS deviation nlevels int 40 Discretize RMSD matrix in levels cutoff real 0 1 RMSD cut off nm for two structures to be similar max real 1 Maximum level in RMSD matrix skip int 1 Only analyze every nr th frame av bool no Write average iso middle structure for each cluster method enum linkage Method for cluster determination linkage jarvis patrick monte carlo or diagonalization binary bool no Treat the RMSD matrix as consisting of 0 and 1 where the cut off is given by cutoff M int 10 Number of nearest neighbors considered for Jarvis Patrick algorithm 0 is use cutoff P int 3 Number of identical nearest neighbors required to form a cluster seed int 1993 Random number seed for Monte Carlo clustering algorithm niter int 10000 Number of iterations for MC kT real 0 001 Boltzmann weighting factor for Monte Carlo optimization zero turns off uphill steps E 10 g com g com computes the translational and rotational motion of a group of atoms i e a protein as a function of time Files f traj xtc Input Generic trajectory xtc trr trj gro g96 pdb s topol tpr Input Structure mass db tpr tpb tpa gro g96 pdb n index ndx Input Opt Index file 0X xcm xvg Output
190. ls A 1 Installation The GROMACS code is distributed in SOURCE form by our WWW server at http md chem rug nl gmx On this server you will find all the information you need to install the software as well as the license form that you have to submit before you are allowed to down load the code When you have filled in this license form a user name and password will be sent to you by e mail with which you can down load the files The e mail address you specify on your license sheet will also be used to send you information on updates bug fixes etc For commercial use of the software please contact us directly gromacs chem rug nl A 2 Single or Double precision GROMACS can be compiled in both single and double precision Double precision will be 0 to 50 slower than single precision depending on the architecture you are running on Double precision will use somewhat more memory and run input energy and full precision trajectory files will be almost twice as large The energies in single precision are accurate up to the last decimal the last one or two decimals of the forces are non significant The virial is less accurate than the forces since the virial is only one order of magnitude larger than the size of each element in the sum over all atoms sec B 1 In most cases this is not really a problem since the fluctuations in de virial can be 2 orders of magnitude larger than the average In periodic charged systems these errors are
191. lways written nstxtcout 0 steps frequency to write coordinates to xtc trajectory xtc_precision 1000 real precision to write to xtc trajectory xtc_grps group s to write to xtc trajectory default the whole system is written if nstxtcout is larger than zero energygrps group s to write to energy file 7 3 7 Neighbor searching nstlist 10 steps frequency to update neighborlist ns_type grid Make a grid in the box and only check atoms in neighboring grid cells when constructing a new neighbor list every nstlist steps The number of grid cells per Coulomb cut off length is set with deltagrid this number should be 2 for optimal performance In large systems grid search is much faster than simple search simple Check every atom in the box when constructing a new neighbor list every nstlist steps deltagrid 2 number of grid cells per Coulomb cut off length box rectangular Selects a rectangular box shape none Selects no box for use in vacuum simulations 114 Run parameters and Programs rlist 1 nm cut off distance for making the neighbor list 7 3 8 Electrostatics and VdW coulombtype Cut off Twin range cut off s with neighborlist cut off rlist and Coulomb cut off rcoulomb where rlist lt rvdw lt rcoulomb The dielectric constant is set with epsilon_r Ewald Classical Ewald sum electrostatics Use eg rlist 0 9 rvdw 0 9 rcoulomb 0 9 The highest magnitude of wave vectors us
192. m and not to describe the algorithms that are in practical use for molecular systems with their complex variety of atoms and terms in the force field descriptions We shall therefore consider as an example a simple system consisting only of a single type of atoms with a simple form of the interaction potential The emphasis will be on the special problems that arise when the algorithm is implemented on a parallel computer The simple model problem already contains the bottleneck of all MD simulations the com putationally intensive evaluation of the non bonded forces between pairs of atoms based on the distance between particles Complex molecular systems will in addition involve many different kinds of bonded forces between designated atoms Such interactions add to the complexity of the algorithm but do not modify the basic considerations concerning parallelization 3 11 1 Methods of parallelization There are a number of methods to parallelize the MD algorithm each of them with their own advantages and disadvantages The method to choose depends on the hardware and compilers available We list them here 3 11 Parallelization 33 1 Message Passing In this method which is more or less the traditional way of parallel programming all the parallelism is explicitly programmed by the user The disadvantage is that it takes extra code and effort the advantage is that the programmer keeps full control over the data flow and can do optimizations a
193. m a random array of atoms FEBS Lett 239 129 136 1988 van Schaik R C Berendsen H J C Torda A E van Gunsteren W F A structure refinement method based on molecular dynamics in 4 spatial dimensions J Mol Biol 234 751 762 1993 Zimmerman K All purpose molecular mechanics simulator and energy minimizer J Comp Chem 12 310 319 1991 Adams D J Adams E M Hills G J The computer simulation of polar liquids Mol Phys 38 387 400 1979 Bekker H Dijkstra E J Renardus M K R Berendsen H J C An efficient box shape independent non bonded force and virial algorithm for molecular dynamics Mol Sim 14 137 152 1995 216 13 114 115 16 171 118 19 20 21 na 199 193 194 195 126 1271 198 199 BIBLIOGRAPHY Berendsen H J C Electrostatic interactions In Computer Simulation of Biomolec ular Systems van Gunsteren W F Weiner P K Wilkinson A J eds ESCOM Leiden 1993 161 181 Hockney R W Goel S P J Comp Phys 14 148 1974 Verlet L Phys Rev 34 1311 1327 1967 Berendsen H J C van Gunsteren W F Practical algorithms for dynamics simu lations Berendsen H J C Postma J P M DiNola A Haak J R Molecular dynamics with coupling to an external bath J Chem Phys 81 3684 3690 1984 Berendsen H J C Transport properties computed by linear response through weak couplin
194. moved 2 Bonded covalent bond stretching angle bending improper dihedrals and proper dihedrals These are computed on the basis of fixed lists 3 Special position restraints and distance restraints based on fixed lists 44 Force fields 0 4 o2 E 2 gt 0 0 0 2 fi fi f 0 4 0 5 0 6 0 7 0 8 r nm Figure 4 1 The Lennard Jones interaction 4 1 Non bonded interactions Non bonded interactions in GROMACS are pair additive and centro symmetric V ri ry Ye Vi r5 4 1 i lt j Wig Tig Tij F Y L4t Fj 4 2 gt drij Tij The non bonded interactions contain a repulsion term a dispersion term and a Coulomb term The repulsion and dispersion term are combined in either the Lennard Jones or 6 12 interaction or the Buckingham or exp 6 potential In addition partially charged atoms act through the Coulomb term 4 1 1 The Lennard Jones interaction The Lennard Jones potential Vrz between two atoms equals c32 y i i Vtg rij ple 3 6 4 3 ij ij see also Fig 4 1 The parameters oa and as depend on pairs of atom types consequently they are taken from a matrix of LJ parameters The force derived from this potential is 12 IN o F r 12 6 4 4 uray re r rij 4 1 Non bonded interactions 45 1 5 1 0 lo e E 05 gt 0 0 0 5 02 03 04 05 06 07 08 r nm Figure 4 2 The Buckingham interacti
195. ms Files s topol tpr Input Opt Generic run input tpr tpb tpa f traj xtc Input Opt Generic trajectory xtc trr trj gro g96 pdb e ener edr Input Opt Generic energy edr ene 204 Manual Pages Other options h bool no Print help info and quit nice int O Set the nicelevel nr bool yes Show index numbers in output leaving them out makes comparsion easier but creates a useless topology E 50 grompp The gromacs preprocessor reads a molecular topology file checks the validity of the file expands the topology from a molecular description to an atomic description The topology file contains in formation about molecule types and the number of molecules the preprocessor copies each molecule as needed There is no limitation on the number of molecule types Bonds and bond angles can be converted into constraints separately for hydrogens and heavy atoms Then a coordinate file is read and velocities can be generated from a Maxwellian distribution if requested grompp also reads parameters for the mdrun eg number of MD steps time step cut off and others such as NEMD parameters which are corrected so that the net acceleration is zero Eventually a binary file is produced that can serve as the sole input file for the MD program grompp calls the c preprocessor to resolve includes macros etcetera To specify a macro preprocessor other than lib cpp such as m4 you can put a line in your parameter file specifying the path to that
196. n If each processor only has particles in a certain region of space it only has to calculate the charge distribution for that region of space Since GROMACS works with slabs this means that each processor fills the FFT grid cells corresponding to it s slab in space and addition of FFT grids need only be done for neighboring slabs To be more precise the slab x for processor 7 is defined as ly ly iG CD 3 52 Particle with this x coordinate range will add to the charge distribution on the following range of of FFT grid slabs in the x direction l l trunc i 1 lt i lt trunc 6 aA 2 3 53 where trunc indicates the truncation of a real number to the largest integer smaller than or equal to that real number 2 Doing the Fourier transform of the charge distribution p r in parallel to obtain p k This is done using the FFTW library http 1cs theory mit edu fftw which employs the MPI library for message passing programs note that there are also shared memory versions of the FFTW code This FFT algorithm actually use slabs as well good thinking Each processor does 3 12 Parallel Molecular Dynamics 41 2D FFTS on its slab and then the whole FFT grid is transposed in place i e without using extra memory This means that after the FFT the X and Y components are swapped To complete the FFT this swapping should be undone in principle by transposing back Happily the FFTW code has an option to omit this whi
197. n Gromos 96 format conf gro Generic structure gro g96 pdb tpr tpb tpa out gro Generic structure gro g96 pdb conf gro Coordinate file in Gromos 87 format polar hdb Hydrogen data base topinc itp Include file for topology run log Log file ps m2p Input file for mat2ps ss map File that maps matrix data to colors ss mat Matrix Data file grompp mdp grompp input file with MD parameters hessian mtx Hessian matrix index ndx Index file hello out Generic output file eiwit pdb Protein data bank file pull pdo Pull data output pull ppa Pull parameters residue rtp Residue Type file used by pdb2gmx doc tex LaTeX file topol top Topology file topol tpa Ascii run input file topol tpb i Binary run input file topol tpr Generic run input tpr tpb tpa topol tpr Structure mass db tpr tpb tpa gro g96 pdb topol tpr Portable xdr run input file traj trj i Trajectory file cpu specific traj trr Full precision trajectory trr trj traj trr Trajectory in portable xdr format root xpm X PixMap compatible matrix file traj xtc Generic trajectory xtc trr trj gro g96 pdb traj xtc Compressed trajectory portable xdr format graph xvg xver xmer file Table 7 1 The GROMACS file types 7 3 Run Parameters 111 A sample mdp file is available This should be appropriate to start a normal simulation Edit it to suit your specific needs and desires 7 3 2 Preprocessing title this is redundant so you can type anything you want cpp lib cpp your preproces
198. n bond type 1 Lennard Jones or 2 Buckingham note when using the Buckingham potential no combination rule can be used and a full interaction matrix must be provided under the nonbond params section combination rule 1 based on Van der Waals or 2 based on o and e generate pairs no get 1 4 interactions from pair list or yes generate 1 4 interac tions from normal Lennard Jones parameters using FudgeLJ and FudgeQQ FudgeLJ factor to change Lennard Jones 1 4 interactions e FudgeQQ factor to change electrostatic 1 4 interactions note FudgeLJ and FudgeQQ only need to be specified when generate pairs is set to yes include ffgmx itp this includes the bonded and non bonded GROMACS param eters the gmx in ffgmx will be replaced by the name of the forcefield you are actually using moleculetype defines the name of your molecule in this top and nrexcl 3 stands for excluding non bonded interactions between atoms that are no further than 3 bonds away atoms defines the molecule where nr and type are fixed the rest is user defined So atom can be named as you like cgnr made larger or smaller if possible the total charge of a charge group should be zero and charges can be changed here too bonds no comment pairs 1 4 interactions angles no comment dihedrals in this case there are 9 proper dihedrals funct 1 3 improper funct 2 and no Ryckaert Bellemans type dihedr
199. n in XDR format can be read on any architecture with a GROMACS version compiled with XDR 5 If you want to use the graphics the X window system version 11 Release 4 or higher and the X lib graphics libraries These are the requirements of a single processor system If you want to compile GRO MACS on a multi processor environment there is another requirement 1 Message passing architecture 2 Ring structure One can understand that a message passing architecture also can be mapped onto a shared memory machine This implementation is left to the reader as an exercise in parallel programming Also the ring structure can be mapped onto e g a hypercube A 3 1 Multi processor Porting In the case you want to run the GROMACS software on a multi processor machine you have two options 1 Install MPI or PVM The GROMACS WWW page has some pointers to relevant documents A 4 Environment Variables 147 2 Write communication routines yourself It may be clear that you will hardly ever need to write the routines yourself but if you can t avoid it here are some clues The interface between these routines and the rest of the GROMACS system is described in the file GMXHOME src include network h We will give a short description of the different routines below extern void gmx_tx int pid void buf int bufsize This routine when called with the destination processor number a pointer to a byte oriented transfer buffer and the size of t
200. n pull ndx Input Opt Index file Other options h bool no Print help info and quit nice int 19 Set the nicelevel deffnm string Set the default filename for all file options v bool no Be loud and noisy compact bool yes Write a compact log file E 54 mk_angndx mk_angndx makes an index file for calculation of angle distributions etc It uses a run input file tpx for the definitions of the angles dihedrals etc Files s topol tpr Input Generic run input tpr tpb tpa n angle ndx Output Index file Other options h bool no Print help info and quit nice int O Set the nicelevel type enum angle Type of angle angle g96 angle dihedral improper ryckaert bellemans or phi psi E 55 ngmx ngmx is the Gromacs trajectory viewer This program reads a trajectory file a run input file and an index file and plots a 3D structure of your molecule on your standard X Window screen No need for a high end graphics workstation it even works on Monochrome screens The following features have been implemented 3D view rotation translation and scaling of your molecule s labels on atoms animation of trajectories hardcopy in PostScript format user defined atom filters runs on MIT X real X open windows and motif user friendly menus option to remove periodicity option to show computational box Some of the more common X command line options can be used bg fg change colors font fontname changes the font Files f traj xtc Input
201. nal improper dihedral angles will keep both triangles one for the ring and one with O in a plane but due to the larger moments of inertia this construction will be much more stable The bond angle in the hydroxyl group will be constrained by a constraint between C and H note that the hydrogen is not treated as a dummy atom See Fig 6 3B e Tryptophane Cg is kept as a normal atom and two dummy masses are created at the center of mass of each of the rings each with a mass equal to the total mass of the respective ring C 2 and C 2 are each counted half for each ring This keeps the overall center of mass and the moment of inertia almost but not quite equal to what it was See Fig 6 3C Histidine C Ca and N 2 are kept as normal atoms but with masses redistributed such that the center of mass of the ring is preserved See Fig 6 3D 106 Special Topics 6 3 Running with PVM If you have a parallel computer it may be equipped with PVM Parallel Virtual Ma chines see also chapter 3 otherwise have your system administrator install it The package is public domain software and supports virtually every commercially available computer such as an SGI Power Challenge Paragon Intel 7860 box Thinking machines CM 5 CRAY J9036287 Convex MPP etc or on a cluster of workstations The GROMACS software can work with the PVM library but only on computers with the same processor it is not possible to mix e g Sparc and MIPS chips We
202. nation of two atoms Fig 4 15 2 Ta T ari 4 96 68 3 d 3fad Force fields in this case the dummy is on the line through atoms and 7 The force on particles i and j due to the force on the dummy can be computed as F 1 a Fa F a 4 97 As a linear combination of three atoms Fig 4 15 3 Tq Ti arij brik 4 98 in this case the dummy is in the plane of the other three particles The force on particles 2 j and k due to the force on the dummy can be computed as Fl 1 a b F pos a Fa 4 99 Fi b Fa In the plane of three atoms with a fixed distance Fig 4 15 3fd Tij T ar jk ra ri b 4 100 rij ar jr in this case the dummy is in the plane of the other three particles at a distance of b from 7 The force on particles 7 j and k due to the force on the dummy can be computed as F Fa 7 Fa p r ee Fl 1 a 7y Fa p where rag arse 4 101 _ ria Fa In the plane of three atoms with a fixed angle and distance Fig 4 15 3fad rq ri dcos0 m dsin0 where ri Tjk Ta Tie po 4 102 ri Irl Tij Pij in this case the dummy is in the plane of the other three particles at a distance of d from 7 at an angle of a with r Atom k defines the plane and the direction of the angle Note that in this case b and must be specified in stead of a and b see also sec 5 2 2 The force on particles i j and k due to the force on the dummy can be comput
203. nd line options are valid If this is not the case the program will be halted All GROMACS programs have 4 hidden options option type default description hidden bool yes hidden Print hidden options quiet bool no hidden Do not print help info man enum tex hidden Write manual and quit no html tex nroff java ascii or completion debug bool no hidden Write file with debug information e When compiled with the HAVE_MOTIF option all GROMACS programs have an ad ditional option 7 5 Programs by topic 123 7 5 X bool no Use dialog box GUI to edit command line options When compiled on an SGI IRIX system all GROMACS programs have an additional option npri int O Set non blocking priority try 128 Enumerated options enum should be used with one of the arguments listed in the option description the argument may be abbreviated The first match to the shortest argument in the list will be selected Vector options can be used with 1 or 3 parameters When only one parameter is supplied the two others are also set to this value All GROMACS programs can read compressed or g zipped files There might be a problem with reading compressed xtc trr and trj files but these will not compress very well anyway Most GROMACS programs can process a trajectory with less atoms than the run input or structure file but only if the trajectory consists of the first n atoms of the run input or structure file Programs by topic
204. nd the bond stretching potential right 4 2 Bonded interactions Bonded interactions are based on a fixed list of atoms They are not exclusively pair interactions but include 3 and 4 body interactions as well There are bond stretching 2 body bond angle 3 body and dihedral angle 4 body interactions A special type of dihedral interaction called improper dihedral is used to force atoms to remain in a plane or to prevent transition to a configuration of opposite chirality a mirror image 4 2 1 Bond stretching Harmonic potential The bond stretching between two covalently bonded atoms 7 and j is represented by a harmonic potential 1 Vo rij shia Mis bj 4 33 see also Fig 4 5 with the force es Fj rig hij rig big 4 34 ij Fourth power potential In the GROMOS 96 force field 42 the covalent bond potential is written for reasons of computational efficiency as 1 2 Vp rij qe r3 bij 4 35 the corresponding force is F ri ke re b7 Tij 4 36 4 2 Bonded interactions 51 The force constants for this form of the potential is related to the usual harmonic force constant k harm sec 4 2 1 as E NS 4 37 The force constants are mostly derived from the harmonic ones used in GROMOS 87 35 Although this form is computationally more efficient because no square root has to be evaluated it is conceptually more complex One particular disadvantage is that since the form is not h
205. ned with the minimum image con vention only one the nearest image of each particle is considered for short range non bonded interaction terms For long range electrostatic interactions this is not always accurate enough and GROMACS therefore also incorporates lattice sum methods like Ewald Sum PME and PPPM The box can be of arbitrary dimensions but must be rectangular An isolated cluster of molecules can of course be simulated as well within these restrictions by defining the periodic box size to be much larger than the cluster size The minimum image convention implies that the cut off radius used to truncate non bonded interactions must not exceed half the smallest box size 1 Re lt zminla b c 3 1 otherwise more than one image would be within the cut off distance of the force When a macromolecule such as a protein is studied in solution this restriction does not suf fice In principle a single solvent molecule should not be able to see both sides of the macromolecule This means that an edge a of the box must exceed the length of the 3 3 The group concept 15 macromolecule in the direction of that edge plus two times the cut off radius Re It is common to compromise in this respect and make the solvent layer somewhat smaller in order to reduce the computational cost Each unit cell cubic rectangular or triclinic the latter not being implemented in GRO MACS is surrounded by 26 translated images Thus a par
206. ng frequency and appear as lower frequencies 3 5 Simulated Annealing The well known simulated annealing SA protocol is implemented in a simple way into GROMACS A modification of the temperature coupling scheme is used as a very ba sic implementation of the SA algorithm The method works as follows the reference temperature for coupling To eqn 3 19 is not constant but can be varied linearly To step To Ao AA x step 3 41 if Ao 1 and Ad is 0 this is the plain MD algorithm Note that for standard SA AA must be negative When To step lt 0 it is set to 0 as negative temperatures do not have a physical meaning This feature allows for an annealing strategy in which at first the temperature is scaled down linearly until 0 K and when more steps are taken the simu lation proceeds at 0 K Since the weak coupling scheme does not couple instantaneously the actual temperature will always be slightly higher than 0 K 3 6 Langevin Dynamics The Position Langevin Dynamics algorithm is implemented in GROMACS is note NOT Velocity Langevin Dynamics This applies to over damped systems i e systems in which the inertia effects are negligible The equations are cee he dt y 3 42 where y is the friction coefficient amu ps and r t is a noise process with r t Ti 0 20 t 0 k T y In GROMACS the equations are integrated with an explicit scheme At At Pnl Tn Eln 2k T pe 3 43 where r is Gau
207. nge contribution to the virial 60 1 00 Bie c No Arr Zdr 2 Pe CO 12NmpCs r dr Ye 4AnC6N pr C 10 The corresponding correction to the pressure is Pr SO sp rz8 C 11 C 1 Dispersion 163 Using the same example of a water box the correction to the virial is 3 kJ mol the corresponding correction to the pressure for SPC water at liquid density is approx 280 bar For homogeneous mixtures we can again use the average dispersion constant Cg eqn C 6 4 P 37 Ce piro C 12 For inhomogeneous systems eqn C 12 can be applied under the same restriction as holds for the energy see sec C 1 1 164 Long range corrections Appendix D Averages and fluctuations D 1 Formulae for averaging Note this section was taken from ref 69 When analyzing a MD trajectory averages 1 and fluctuations ay le Py 0 1 of a quantity x are to be computed The variance 0 of a series of N values x can be computed from Ne 1 Ne y gt 2 X i i 1 z i 1 1 Unfortunately this formula is numerically not very accurate especially when o is small compared to the values of z The following equivalent expression is numerically more accurate Nz os Sle 2 D 3 with 1 amp 2 Do D 4 Using eqns D 2 and D 4 one has to go through the series of x values twice once to determine x and again to compute oz whereas eqn D 1 requires only one sequential scan of the series
208. nice int 19 Set the nicelevel b real 1 First frame ps to read from trajectory e real 1 Last frame ps to read from trajectory width real 0 12 bin width for radial axis E 34 g_rdf g rdf calculates radial distribution functions in different ways The normal method is around a set of particle s the other method is around the center of mass of a set of particles Tf a run input file is supplied s exclusions defined in that file are taken into account when calculating the rdf The option cut is meant as an alternative way to avoid intramolecular peaks in the rdf plot It is however better to supply a run input file with a higher number of exclusions For eg benzene a topology with nrexcl set to 5 would eliminate all intramolecular contributions to the rdf Files f traj xtc Input Generic trajectory xtc trr trj gro g96 pdb s topol tpr Input Opt Structure mass db tpr tpb tpa gro g96 pdb n index ndx Input Opt Index file 0 rdf xvg Output xvgr xmgr file E 35 g_rms 195 Other options h bool no Print help info and quit nice int 19 Set the nicelevel b real 1 First frame ps to read from trajectory e real 1 Last frame ps to read from trajectory w bool no View output using xvgr or ghostview bin real 0 005 Binwidth nm com bool no RDF with respect to the center of mass of first group cut real 0 Shortest distance nm to be considered E 35 g_rms gms computes the root mean square deviation RMSD of a s
209. ns from the pdb file the names of the hydrogens in the pdb file must match the names in the database E 58 protonate 209 sort will sort all residues according to the order in the database sometimes this is necessary to get charge groups together al1dih will generate all proper dihedrals instead of only those with as few hydrogens as possible this is useful for use with the Charmm forcefield The option dummy removes hydrogen and fast improper dihedral motions Angular and out of plane motions can be removed by changing hydrogens into dummy atoms and fixing angles which fixes their position relative to neighboring atoms Additionally all atoms in the aromatic rings of the standard amino acids i e PHE TRP TYR and HIS can be converted into dummy atoms elminating the fast improper dihedral fluctuations in these rings Note that in this case all other hydrogen atoms are also converted to dummy atoms The mass of all atoms that are converted into dummy atoms is added to the heavy atoms Also slowing down of dihedral motion can be done with heavyh done by increasing the hydrogen mass by a factor of 4 This is also done for water hydrogens to slow down the rotational motion of water The increase in mass of the hydrogens is subtracted from the bonded heavy atom so that the total mass of the system remains the same Files f eiwit pdb Input Generic structure gro g96 pdb tpr tpb tpa 0 conf gro Output Generic structure gro g96
210. nstant e may be set in the in the input for grompp 4 1 4 Coulomb interaction with reaction field The coulomb interaction can be modified for homogeneous systems by assuming a con stant dielectric environment beyond the cut off re with a dielectric constant of epp The interaction then reads a 1 r Ge 8 Vers s2 3 T PTE 4 12 Tij Zepp 1155 Te 2Epp 1 in which the constant expression on the right makes the potential zero at the cut off r We can rewrite this for simplicity as Vers 49 1 Tae ok krf ry ca 4 13 Tij 4 1 Non bonded interactions 47 with 1 erp 1 k pa A EE ac 4 14 rf 7a 2er 1 1 1 3E E taap aa a y 4 15 Crf re E rf Te ro 2er EE 1 for large epf the krf goes to 0 5 ES while for epp 1 the correction vanishes This makes it possible to use the same expression with and without reaction field albeit at some computational cost In Fig 4 3 the modified interaction is plotted and it is clear that the derivative with respect to rj force goes to zero at the cut off distance The force derived from this potential reads 1 Tij F rij fig gt 2krfrij 4 16 Tironi et al have introduced a generalized reaction field in which the dielectric continuum beyond the cut off re also has an ionic strength J 41 In this case we can rewrite the constants k and cpf using the inverse Debye screening length x 21 F P E y 4 17 E0Erf RT Eger fRT 2 ne
211. nstdisreout 100 steps frequency to write the running time averaged and instantaneous distances of all atom pairs involved in restraints to the energy file can make the energy file very large 7 3 16 Free Energy Perturbation free_energy no Only use topology A yes Change the system from topology A lambda 0 to topology B lambda 1 and calculate the free energy difference The starting value of lambda is init_lambda the increase per time step is delta lambda init_lambda 0 starting value for lambda delta_lambda 0 increase per time step for lambda 7 3 17 Non equilibrium MD acc_grps groups for constant acceleration e g Protein Sol all atoms in groups Protein and Sol will experience constant acceleration as specified in the accelerate line accelerate 0 nm ps acceleration for acc_grps x y and z for each group e g 0 1 0 0 0 0 0 1 0 0 0 0 means that first group has constant acceleration of 0 1 nm ps in X direction second group the opposite freezegrps Groups that are to be frozen i e their X Y and or Z position will not be updated e g Lipid SOL freezedim specifies for which dimension the freezing applies freezedim dimensions for which groups in freezegrps should be frozen specify Y or N for X Y and Z and for each group e g Y Y N N N N means that particles in the first group can move only in Z direction The particles in the second group can move in any direction 122 Run parame
212. ntial and kinetic energies and the pressure tensor are computed y 3 Update configuration The movement of the atoms is simulated by numerically solving Newton s equations of motion dr a F di mi dr y dv F U dt dt om Y 4 if required Output step write positions velocities energies temperature pressure etc Figure 3 2 The global MD algorithm 3 4 Molecular Dynamics 17 Probability 0 0 Velocity Figure 3 3 A Maxwellian distribution generated from random numbers 3 4 1 Initial conditions Topology and force field The system topology including a description of the force field must be loaded These items are described in chapter 4 All this information is static it is never modified during the run Coordinates and velocities Then before a run starts the box size and the coordinates and velocities of all particles are required The box size is determined by three vectors nine numbers b1 b2 b3 which represent the three basis vectors of the periodic box While in the present version of GROMACS only rectangular boxes are allowed three numbers suffice but the use of three vectors already prepares for arbitrary triclinic boxes to be implemented in a later version If the run starts at t to the coordinates at t t must be known The leap frog algorithm used to update the time step with At see 3 4 3 requires that the velocities must be known at t ty At If veloc
213. nual version 2 0 author David van der Spoel and Aldert R van Buuren and Emile Apol and Pieter J Meulenhoff and D Peter Tieleman and Alfons L T M Sij bers and Berk Hess and K Anton Feenstra and Erik Lindahl and Rudi van Drunen and Herman J C Berendsen address Nij enborgh 4 9747 AG Groningen The Netherlands Internet http md chem rug nl gmx year 1999 Please do also cite the original GROMACS paper 1 Any comment is welcome please send it by e mail to gromacs chem rug nl Groningen November 5 1999 BIOSON Research Institute and Department of Biophysical Chemistry University of Groningen Nijenborgh 4 9747 AG Groningen The Netherlands Fax 31 50 634800 Online Manual If you have access to a WWW browser such as NCSA mosaic or Netscape please look up our HTML page http md chem rug nl gmx Violated Copyrights The following commercial thingies may be mentioned here and there in the text plus some that we forgot here GROMOS is a trademark of Biomos B V SPARC is a trademark of Sun Microsystems inc and Texas Instruments inc CM5 is a trademark of Thinking Machines inc Quanta is a trademark of Molecular Simulations inc Cerius is a trademark of Molecular Simulations inc HyperChem is a trademark of AutoDesk inc The figure on front page was made with Molscript 2 Contents Introduction 1 1 Computational Chemistry and Molecular Modeling 1 2 Molecular Dynam
214. of atoms For constrained runs the distance between the reference group and the other groups is kept constant at the distance they have in the input coordinate file tpr file 98 Special Topics Figure 6 1 Schematic picture of pulling a lipid out of a lipid bilayer with AFM pulling Vrup is the velocity at which the spring is retracted Zz my is the atom to which the spring is attached and Zspring is the location of the spring 6 1 2 Usage Input files The mdrun programs needs 4 additional files 2 input files and 2 output files pi pull ppa If this file is specified the pull code will be used It contains the parameters that control what type of calculation is done A full explanation of all the options is given below pn index ndx This file defines the different groups for use in all pull calculations The groups are referred to by name so the index file can contain other groups that are not used as well po pullout ppa A formatted copy of the input parameter file with the parameters that were actually used in the run pdo pull pdo The data file with the calculated forces AFM pulling constraint force or positions umbrella sampling Definition of groups The way the reference groups and different reference types work is summarized in figure 6 2 There are four different possibilities for the reference group 6 1 Calculating potentials of mean force the pull code 99 Figure 6 2 Overview of the different ref
215. of two inhibitors I and P to an enzyme E Fig 3 8B we can again use eqn 3 49 to compute the desired property 3 10 Essential Dynamics Sampling The results from an Essential Dynamics ED analysis 28 of a protein can be used to guide MD simulations The idea is that from an initial MD simulation or from other sources a definition of the collective fluctuations with largest amplitude is obtained The position along one or more of these collective modes can be constrained in a second MD simulation in a number of ways for several purposes For example the position along a certain mode may be kept fixed to monitor the average force free energy gradient on that coordinate in that position Another application is to enhance sampling efficiency with respect to usual MD 29 30 In this case the system is encouraged to sample its available 32 Algorithms hah oe Cee 0 Figure 3 8 Free energy cycles A to calculate AG12 or the free energy difference between the binding of inhibitor I to enzymes E respectively E B to calculate AG 2 which is the free energy difference for binding of inhibitors I respectively I to enzyme E configuration space more systematically than in a diffusion like path that proteins usually take All available constraint types are described in the appropriate chapter of the WHAT IF 31 manual 3 11 Parallelization The purpose of this section is to discuss the parallelization of the principle MD algorith
216. ogram to read this file but it is simple to parse 102 Special Topics 6 1 4 Limitations Apart from obvious limitations that are simply not implemented e g a better umbrella sampling and analysis scheme there is one important limitation constraint forces can only be calculated between molecules or groups of molecules If a group contains part of a molecule of which the bondlengths are constrained SHAKE or LINCS and the constraint force calculation here will interfere with each other making the results unreliable If a constraint force is wanted between two atoms this can be done through the free energy perturbation code In summary e pull code between molecules or groups of molecules e free energy perturbation code between single atoms e not possible currently between groups of atoms that are part of a larger molecule for which the bonds are constrained with SHAKE or LINCS 6 1 5 Implementation The code for the options described above can be found in the files pull c pullinit c pullio c pullutil c and the headerfiles pull h and pulls h This last file defines a few datatypes pull h explains the main functions 6 1 6 Future development There are several additional features that would be useful including more advanced um brella sampling an analysis tool to analyse the output of the pull code incorporation of the input parameters and index file into the grompp program input files extension to more groups more flexi
217. ol no Print help info and quit nice int O Set the nicelevel E 59 tpbconv tpbconv can edit run input files in two ways 1st by creating a run input file for a continuation run when your simulation has crashed due to e g a full disk or by making a continuation run input file Note that a frame with coordinates and velocities is needed which means that when you never write velocities you can not use tpbconv and you have to start the run again from the beginning 2nd by creating a tpx file for a subset of your original tpx file which is useful when you want to remove the solvent from your tpx file or when you want to make e g a pure Ca tpx file WARNING this tpx file is not fully functional Files s topol tpr Input Generic run input tpr tpb tpa f traj trr Input Opt Full precision trajectory trr trj n index ndx Input Opt Index file 0 tpxout tpr Output Generic run input tpr tpb tpa Other options h bool no Print help info and quit nice int O Set the nicelevel time real 1 Continue from frame at this time instead of the last frame E 60 trjcat trjcat concatenates several input trajectory files in sorted order In case of double time frames the one in the later file is used By specifying settime you will be asked for the start time of each file The input files are taken from the command line such that a command like trjconv o fixed trr trr should do the trick Files 0 trajout xtc Output Generic trajectory x
218. ole moment over the system Therefore we have to keep groups of atoms with total charge 0 together the so called charge groups 66 Force fields 4 4 3 Treatment of cut offs GROMACS is quite flexible in treating cut offs which implies that there are quite a number of parameters to set The parameters are set in the input file for grompp One should distinguish two parts of the parameters firstly the parameters that describe the function Coulomb VDW Table 4 2 and secondly the parameters that describe neighbor searching In summary for both Coulomb and VdW there are a type selector wdwtype resp coulombtype and two parameters for a total of six parameters See sec 7 3 1 for a complete description of these parameters The neighbor searching NS maybe done using a single range or a twin range approach Since the former is merely a special case of the latter we will discuss the more general twin range In this case NS is described by two radii rlist and max rcoulomb rvdw Usually one builds the neighbor list every 10 time steps or every 20 fs parameter nstlist In the neighbor list all interaction pairs that fall within rlist are stored Further more the interactions between pairs that do not fall within rlist but do fall within and max rcoulomb rvdw are computed during NS and the forces and energy are stored separately and added to short range forces at every time step between successive NS If rlist max rcoulomb rvdw no for
219. on The LJ potential may also be written in the following form 12 6 Vis riz 45 2 4 5 In constructing the parameter matrix for the non bonded LJ parameters two types of combination rules can be used within GROMACS ap oP sof Ed E oy i gane or alternatively A i an 4 1 2 Buckingham potential The Buckingham potential has a more flexible and realistic repulsion term than the Lennard Jones interaction but is also more expensive to compute The potential form is Cs Von rij Aij exp Bijrij y 4 8 ij see also Fig 4 2 the force derived from this is ey ee ee ana a Ja 4 9 i riz ig Bijrij exP Bijriy Pia are 4 9 6 rij ij 46 Force fields 1500 Coulomb With RF RF C 1000 as De br A E X 2 gt 500 3 Se a 0 1 i Spe A A 0 0 0 2 0 4 0 6 0 8 1 0 r nm Figure 4 3 The Coulomb interaction for particles with equal signed charge with and without reaction field In the latter case was 78 and re was 0 9 nm The dot dashed line is the same as the dashed line except for a constant 4 1 3 Coulomb interaction The Coulomb interaction between two charge particles is given by Vo ri pis 4 10 El ij see also Fig 4 3 where f 138 935 485 see chapter 2 ATEQ The force derived from this potential is id Tij Fly fae 4 11 a ae 4 11 In GROMACS the relative dielectric co
220. on of a representative equilibrium ensemble two methods are available a Monte Carlo simulations and b Molecular Dynamics simulations For the generation of non equilibrium ensembles and for the analysis of dynamic events only the second method is appropriate While Monte Carlo simulations are more simple than MD they do not require the computation of forces they do not yield significantly better statistics than MD in a given amount of computer time Therefore MD is the more universal technique If a starting configuration is very far from equilibrium the forces may be excessively large and the MD simulation may fail In those cases a robust energy minimization is required Another reason to perform an energy minimization is the removal of all kinetic energy from the system if several snapshots from dynamic simulations must be compared energy minimization reduces the thermal noise in the structures and potential energies so that they can be compared better 1 2 Molecular Dynamics Simulations MD simulations solve Newton s equations of motion for a system of N interacting atoms Or mi Ae F i 1 N 1 1 The forces are the negative derivatives of a potential function V r1 r2 rN OV F 1 2 OK 1 2 Molecular Dynamics Simulations 3 type of wavenumber type of bond vibration cm7 stretch 3000 3500 stretch 1700 2000 bending 1600 stretch 1400 1600 sciss rock 1000 1500 bending 800 1000 libra
221. ons as printed in the log file are D 2 Implementation 167 computed over the whole simulation The equilibration time which is now part of the simulation may in such a case invalidate the averages and fluctuations because these numbers are now dominated by the initial drift towards equilibrium Using eqns D 7 and D 8 the average and standard deviation over part of the trajectory can be computed as Xm lm k Xim k Xi ym D 15 Kine ages i m m k m m gt k k D 16 Om 1 m k or more generally with p gt 1 and q gt p Xp q Xia A ipi D 17 Xip 1 _ Xi p 1 q D 18 p 1 q qa p i Opq Tlg Olp 1 Note that implementation of this is not entirely trivial since energies are not stored every time step of the simulation We therefore have to construct Xj p 1 and 01p 1 from the information at time p using eqns D 11 and D 12 X1p 1 Xip Tp D 19 Xi p 1 9 1 ay 1 G A D 20 Ol p 1 Ol p D 2 2 Combining two simulations Another frequently occurring problem is that the fluctuations of two simulations must be combined Consider the following example we have two simulations A of n and B of m steps in which the second simulation is a continuation of the first However the second simulation starts numbering from 1 instead of from n 1 For the partial sum this is no problem we have to add Xin from run A Ri Brae is D 21 When we want to compute the part
222. opics In the current version of GROMACS this is implemented through some extra files for mdrun 6 1 1 Overview Four different types of calculation are supported 1 Constraint forces The distance between the centers of mass of two groups of atoms can be constrained and the constraint force monitored The distance can be in 1 2 or 3 dimensions This method uses the SHAKE algorithm but only needs 1 iteration to be exact if only two groups are constrained 2 Umbrella sampling A simple umbrella sampling with an harmonic umbrella po tential that acts on the center of mass of a group of atoms 3 AFM pulling A spring is connected to an atom and slowly retracted This has the effect of pulling an atom or group of atoms away from its initial location The rate constant and spring constant for the spring can be varied to study e g the unbinding of a protein and a ligand see figure 6 1 4 Starting structures This option creates a number of starting structures for po tential of mean force calculations moving 1 or 2 groups of atoms at a specified rate towards or away from a reference group writing out a coordinate file at specified intervals Note that the groups given in the index file are translated a specified dis tance each step but in addition also undergo the normal MD subject to definitions of e g temperature coupling groups freeze groups and the like In the calculations there has to be 1 reference group and 1 or 2 other groups
223. orce weighting in restraints with multiple pairs The distance restraint force can be distributed equally over all the pairs involved in the restraint by setting disre_weighting equal The option disre_veighting conservative gives conservative forces when disre_tau 0 disre_mixed how to calculate the violations disre_mixed no gives normal time averaged violations When disre mixed yes the square root of the product of the time averaged and the instantaneous violations is used disre fc force constant kar for distance restraints kg eqn 4 59 can be set as variable disre_fc 1000 for a force constant of 1000 kJ mol nm This value is multiplied by the value in the fac column in the distance restraint entries in the topology file disre_tau time constant for restraints 7 eqn 4 63 can be set as variable disre_tau 10 for a time constant of 10 ps Time averaging can be turned off by setting disre_tau to 0 nstdisreout pair distance output frequency Determines how often the time aver aged and instantaneous distances of all atom pairs involved in distance restraints are written to the energy file 4 3 Free energy calculations Free energy perturbation calculations can be performed in GROMACS using either the slow growth method or using umbrella sampling This requires modification of the Hamiltonian H which can be derived using the partition function Z If we write the Gibbs free energy G using Z Z p B
224. ored in time by the program g com It is however recommended to remove the center of mass velocity every step see chapter 3 8 4 Radial distribution functions g_rdf The radial distribution function rdf or pair correlation function g4p r between particles of type A and B is defined in the following way lt pglr gt lt PB gt local 1 1 2a Ns rij r 8 3 ire FO aa lt PB gt local Na CAjEB gaB r with lt pg r gt the particle density of type B at a distance r around particles A and lt PB gt local the particle density of type B averaged over all spheres around particles A with radius rmaz see Fig 8 2C Usually the value of rmaz is half of the box length The averaging is also performed in time In practice the analysis program g_rdf divides the system into spherical slices from r to r dr see Fig 8 2A and makes a histogram in stead of the 6 function An example of the rdf of Oxygen Oxygen in SPC water 57 is given in Fig 8 3 With g rdf it is also possible to calculate an angle dependent rdf g1p r 0 where the angle 0 is defined with respect to a certain laboratory axis e see Fig 8 2B Na NB 1 ri r 0 0 4800 5H gt 8 4 7 al lt PB gt tocal 0 N mE 2rr sin 0 l Tij e cos 0 8 5 llrz ll lel 130 Analysis Figure 8 2 Definition of slices in g rdf A g4p r B gapl r 0 The slices are colored grey C Normalization lt pg gt local D
225. ormat The format of the input file must be resnr i resname i atomnm i resnr j resname j atomnm j lower upper where lower and upper are the distance bounds The entries must be separated by spaces but may be otherwise in free format Some expansion of templates like MB gt HB1 HB2 is done but this is not really well tested 202 Manual Pages Files s topol tpr Input Generic run input tpr tpb tpa d nnnice dat Input Generic data file 0 topinc itp Output Include file for topology m expmap dat Input Generic data file Other options h bool no Print help info and quit nice int O Set the nicelevel r int 1 starting residue number E 46 genion genion replaces water molecules by monoatomic ions Ions can be placed at the water oxygen positions with the most favorable electrostatic potential or at random The potential is calculated on all atoms using normal GROMACS particle based methods in contrast to other methods based on solving the Poisson Boltzmann equation The potential is recalculated after every ion insertion If specified in the run input file a reaction field or shift function can be used The potential can be written as B factors in a pdb file for visualisation using e g rasmol For larger ions e g sulfate we recommended to use genbox Files s topol tpr Input Generic run input tpr tpb tpa 0 out gro Output Generic structure gro g96 pdb 8 genion log Output Log file pot pot pdb Output Opt Protein data bank
226. ortran 90 was still in the making and no compilers were expected to be available At current we still believe that message passing is the way to go after having done some experiments with data parallel programming on a Connection Machine CM 5 because of portability to other hardware the poor performance of the code produced by the compilers and because this way of programming has the same drawback as vectorization the part of the program that is not vectorized or parallelized determines the runtime of the program Amdahl s law The approach we took to parallelism was a minimalist one use as little non standard elements in the software as possible and use the simplest processor topology that does the job We therefore decided to use a standard language ANSI C with as little non standard routines as possible We only use 5 communication routines that are non standard It is therefore very easy to port our code to other machines For an O N problem like MD one of the best schemes for the interprocessor connections is a ring so our software demands that a ring is present in the interprocessor connections A ring can almost always be mapped onto another network like a hypercube a bus interface Ethernet e g using Parallel Virtual Machines PVM 34 or a tree CM 5 Some hardware vendors have very luxurious connection schemes that connect every processor to every 34 Algorithms other processor but we do not really need it and so do n
227. ot use it even though it might come in handy at times When using a message passing scheme one has to divide the particles over processors which can be done in two ways e Space Decomposition An element of space is allocated to each processor when dividing a cubic box with edge b over P processors this can be done by giving each processor a slab of length b P This method has the advantage that each processor has about the same number of interactions to calculate at least when the simulated system has a homogeneous density like a liquid or a gas The disadvantage is that a lot of bookkeeping is nec essary for particles that move over processor boundaries When using more complex systems like macromolecules there are also 3 and 4 atom interactions that would complicate the bookkeeping so much that this method is not used in our program e Particle Decomposition Every processor is allocated a number of particles When dividing N particles over P processors each processor will get N P particles The implementation of this method is described in the next section 3 11 2 MD on a ring of processors When a neighbor list is not used the MD problem is in principle an O N problem as each particle can interact with every other This can be simplified using Newton s third law Fy Fj 3 50 This implies that there is half a matrix of interactions without diagonal a particle does not interact with itself to consider Fig 3 9 When we
228. over the whole range and the forces decay smoothly to zero between rvdw_switch and rvdw The neighbor search cut off rlist should be 0 1 to 0 3 nm larger than rvdw to accommodate for the size of charge groups and diffusion between neighbor list updates User mdrun will now expect to find two files with user defined functions rtab xvg for Repulsion dtab xvg for Dispersion These files should contain 5 columns the x value and the function value with its 1 to 3 derivative The x should run from 0 nm to rvdw 0 5 nm with a spacing of 0 002 nm when you run in single precision or 0 0005 nm when you run in double precision The function value at x 0 is not important When you want to use LJ correction make sure that rvdw corresponds to the cut off in the user defined function rvdw switch 0 nm where to start switching the LJ potential rvdw 1 nm distance for the LJ or Buckingham cut off bDispCorr 116 Run parameters and Programs no don t apply any correction yes apply long range dispersion corrections for Energy and Pressure fourierspacing 0 12 nm The maximum grid spacing for the FFT grid when using PPPM or PME For ordi nary Ewald the spacing times the box dimensions determines the highest magnitude to use in each direction In all cases each direction can be overridden by entering a non zero value for fourier_n fourier_nx 0 fourier_ny 0 fourier_nz 0 Highest magnitude of wave vectors in recip
229. owing analysis programs To help creating such index files index ndx there are a couple of programs to generate them using either your input configuration or the topology To generate an index file consisting of a series of atom numbers as in the example of gap use make_ndx To generate an index file with angles or dihedrals use mk_angndx Of course you can also make them by hand The general format is presented here Oxygen 1 4 T Hydrogen 2 3 5 6 8 9 First the group name is written between square brackets The following atom numbers may be spread out over as many lines as you like The atom numbering starts at 1 8 2 Looking at your trajectory ngmx Before analyzing your trajectory it is often informative to look at your trajectory first There is a special graphics program ngmx to show your binary trajectory It is also possible to generate a hard copy in Encapsulated Postscript format see Fig 8 1 8 3 General properties 129 8 3 General properties g_energy g_com To analyze some or all energies and other properties such as total pressure pressure tensor density box volume and box sizes use the program g energy A choice can be made from a list a set of energies like potential kinetic or total energy or individual contributions like Lennard Jones or dihedral energies The center of mass velocity defined as V Ey J mijv 8 2 com i T 4 1 2 with M pale m the total mass of the system can be monit
230. particle density p N V where V is the volume is 60 1 oo Vie No Arr g r V r dr C 3 Ye 162 Long range corrections which we can integrate assuming that the radial distribution function g r is 1 beyond the cut off re 2 Vir NprCor C 4 If we consider for example a box of pure water simulated with a cut off of 0 9 nm and a density of 1 g cm this correction is 0 25 kJ mol7 For a homogeneous mixture of M components j with N particles each we can write the long range contribution to the energy as M 2N N e Vin Artio C5 14 This can be rewritten if we define an average dispersion constant Cg NiN Co D Mioi C 6 ij Ve Npn Cs r7 C 7 A special form of a non homogeneous system in this respect is a pure liquid in which the atoms have different Cg values In practice this definition encompasses almost every molecule except mono atomic molecules and symmetric molecules like Nj or Oz Therefore we always have to determine the average dispersion constant Cg in simulations In the case of inhomogeneous simulation systems e g a system with a lipid interface the energy correction can be applied if Cg for both components is comparable C 1 2 Virial and pressure The scalar virial of the system due to the dispersion interaction between two particles i and j is given by 1 The pressure is given by 2 P zy Erin gt C 9 We can again integrate the long ra
231. pf f Coulomb interaction c_ljc inloopc c flje inloopf f Lennard Jones and Coulomb interaction c coul inloopc c fcoul8 inloopf f Coulomb c_ljc inloopc c fljc8 inloopf f LJ Coulomb cwater inloopc c fwater inloopf f Water Loop cshake shakef c fshake fshake f Shake cshake shakef c fshake8 fshake f Shake csettle csettle c fsettle fsettle f Settle csettle csettle c fsettle8 fsettle f Settle Table B 1 List of C functions and their Fortran equivalent plus the source files Note that the Fortan and C source files are both generated from one m4 file The 8 refers to double precision version of the same routine In C it is not necessary to use a special version of the code due to the use of typedef B 3 Computation of the 1 0 sqrt function B 3 1 Introduction The GROMACS project started with the development of a 1 x processor which calcu lates Y z Ta B 25 As the project continued the Intel 1860 processor was used to implement GROMACS which now turned into almost a full software project The 1 y x processor was imple mented using a Newton Raphson iteration scheme for one step For this it needed lookup tables to provide the initial approximation The 1 xz function makes it possible to use two almost independent tables for the exponent seed and the fraction seed with the IEEE floating point representation B 3 2 General According to 68 the 1 x can be calculated using the Newton Raph
232. psilon_r 0 Generalized Reaction Field Generalized reaction field with Coulomb cut off rcoulomb where rcoulomb gt rvdw gt rlist The dielectric constant beyond the cut off is epsilon_r The ionic strength is computed from the number of charged i e with non zero charge charge groups The temperature for the GRF potential is set with ref_t K 7 3 Run Parameters 115 Shift The Coulomb potential is decreased over the whole range and the forces decay smoothly to zero between rcoulomb_switch and rcoulomb The neighbor search cut off rlist should be 0 1 to 0 3 nm larger than rcoulomb to accommo date for the size of charge groups and diffusion between neighbor list updates User Specify rshort and rlong to the same value mdrun will now expect to find a file ctab xvg with user defined functions This files should contain 5 columns the x value and the function value with its 1 to 3 derivative The x should run from 0 nm to rlist 0 5 nm with a spacing of 0 002 nm when you run in single precision or 0 0005 nm when you run in double precision The function value at x 0 is not important rcoulomb_switch 0 nm where to start switching the Coulomb potential rcoulomb 1 nm distance for the Coulomb cut off epsilon_r 1 dielectric constant vdwtype Cut off Twin range cut off s with neighbor list cut off rlist and VdW cut off rvdw where rvdw gt rlist Shift The LJ not Buckingham potential is decreased
233. putation of the 1 0 sqrt function 157 B 3 5 Separate exponent and fraction computation The used IEEE 32 bit single precision floating point format specifies that a number is represented by a exponent and a fraction The previous section specifies for every possible floating point number the lookup table length and width Only the size of the fraction of a floating point number defines the accuracy The conclusion from this can be that the size of the lookup table is length of lookup table earlier specified times the size of the exponent 21225 1Mb The 1 z function has the property that the exponent is independent of the fraction This becomes clear if the floating point representation is used Define Peay 1 F B 42 see Fig B 1 where 0 lt S lt 1 0 lt E lt 255 1 lt 1 F lt 2 and S E F integer normalization conditions The sign bit S can be omitted because 1 z is only defined for x gt 0 The 1 y z function applied to x results in ylz VE B 43 gt B 44 2127 1 F this can be rewritten as y x 257127 eis QU 2 1 B 45 Define peto Oe B 46 Le 1 F B 47 then a lt 1 F lt 1 holds so the condition 1 lt 1 F lt 2 which is essential for normalized real representation is not valid anymore By introducing an extra term this can be cor rected Rewrite the 1 z function applied to floating point numbers equation eqn B 45 as y a a 2 1 F 7 B 48 and pee p B
234. r or ghostview Z Take the normal on the membrane in direction X Y or Z 10 Calculate potential as function of boxlength dividing the box in nr 0 Deca first nr slices of box for integration O Discard last nr slices of box for integration O Translate all coordinates lt distance gt in the direction of the box no Calculate spherical thingie e Discarding slices for integration should not be necessary E 32 g rama g rama selects the Phi Psi dihedral combinations from your topology file and computes these as a function of time Using simple Unix tools such as grep you can select out specific residues 194 Manual Pages Files f traj xtc Input Generic trajectory xtc trr trj gro g96 pdb s topol tpr Input Generic run input tpr tpb tpa 0 rama xvg Output xvgr xmer file Other options h bool no Print help info and quit nice int 19 Set the nicelevel b real 1 First frame ps to read from trajectory e real 1 Last frame ps to read from trajectory w bool no View output using xvgr or ghostview E 33 g_rdens Compute radial densities across the box in three flavors probability density number density real density Files f traj xtc Input Generic trajectory xtc trr trj gro g96 pdb n index ndx Input Index file s topol tpr Input Generic run input tpr tpb tpa op p rdens xvg Output xvgr xmer file on nrdens xvg Output xvgr xmgr file or rrdens xvg Output xvgr xmgr file Other options h bool no Print help info and quit
235. r systems For molecular mod eling this has two important consequences e The knowledge of a single structure even if it is the structure of the global energy minimum is not sufficient It is necessary to generate a representative ensemble at a given temperature in order to compute macroscopic properties But this is not enough to compute thermodynamic equilibrium properties that are based on free energies such as phase equilibria binding constants solubilities relative stability of molecular conformations etc The computation of free energies and thermodynamic potentials requires special extensions of molecular simulation techniques e While molecular simulations in principle provide atomic details of the structures and motions such details are often not relevant for the macroscopic properties of interest This opens the way to simplify the description of interactions and average over irrelevant details The science of statistical mechanics provides the theoretical framework for such simplifications There is a hierarchy of methods ranging from considering groups of atoms as one unit describing motion in a reduced number of collective coordinates averaging over solvent molecules with potentials of mean force combined with stochastic dynamics 4 to mesoscopic dynamics describing densities rather than atoms and fluxes as response to thermodynamic gradients rather than velocities or accelerations as response to forces 5 For the generati
236. raction computation 157 B 3 65 Implementation a hata Ge BR e a ae oe 158 B 4 Tabulated functions e 159 B 4 1 Your own potential function e e 160 Long range corrections 161 EA Dispersion s ge 4 i vase ea A Ee eee EE a E Eee eS 161 ill ENT ia go ah cee Sg asia N ste RE Spe Set ie A 161 C 1 2 Virial and pressure ee 162 Averages and fluctuations 165 D 1 Formulae for averaging moi tos a a a a ee eee 165 D 2 Implementation A A A ee a ie 166 D 2 1 Part ofa Simulation e 166 D 2 2 Combining two simulations 167 D 2 3 Summing energy derMs e 168 Manual Pages 171 LAO ASSP a Gh wo id Bok Hee A 171 E2 editcont ir A Be ed we A ee A a we RS 172 E3 COCO g rio Pla Oh A o Belo Pa Peete E ha Pe ER a gs 173 BA Caneel sl cick Sioa Gtk A ee A ete Wid ae o 173 Bib ganalyz sks ee A Qe ae oe ae Ale ak ade a he A A AA 174 E6 Sl doe tected ea ha ee Ge a ae EG ey A A 175 Bee SO OMG irae 5 6 ees a Bike RAR 176 CONTENTS xi ES PC A AR A ee ae mie Y 177 A Es e s mour Ge a ae ee ee ee ow eR sy a we ee 178 EJLOELCO ioe oe a eee She EN eo A ee ae a ae A 179 EA COMAS Si sce oils Yo ge Bike huge wed Mc te cake Boel Ge ec Ales he oe Ae oe oS 179 BLD Pe COVAT sc S A dow te a Daten We HORE a ce BE ARO me We tw ee a 180 ESPANA eS ee A 180 Be l4ve dielectric se es8 sgt dees Gok ea ee Ge a a Gd eee 181 ELO gdib e e oo Sorge Be eee ee ae A en Ge ae ee at we ln
237. rallel computers computers that support MPI However most shared memory computers such as the SGI Origin also support MPI using the shared memory for communication 3 12 4 Parallel sorting For the domain decomposition bit of GROMACS it is necessary to sort the coordinates or rather the index to coordinates every time a neighbor list is made If we use brute force and sort all coordinates on each processor which is technically possible since we have all the coordinates then this sorting procedure will take a constant time proportional to N logN independent of the number of processors We can however do a little better if we assume that particles diffuse only slowly A parallel sorting algorithm can be conceived as follows At the first step of the simulation 1 Do a full sort of all indices using e g the quick sort algorithm that is built in in the standard C library 2 Divide the sorted array into slabs as described above see Fig 3 13 42 Algorithms At subsequent steps of the simulation 1 Send the indices for each processor to the preceding processor if not processor 0 and to the next processor if not M 1 The communication associated with this operation is proportional to 2N M 2 Sort the combined indices of the three or two processors Note that the CPU time associated with sorting is now 3N M log 3N M 3 On each processor the indices belonging to 1t s slab can be determined from the order of the arr
238. rder 4 Highest order in the expansion of the constraint coupling matrix lincs_order is also used for the number of Lincs iterations during energy minimization only one iteration is used in MD lincs_warnangle 30 degrees maximum angle that a bond can rotate before Lincs will complain nstlincsout 1000 steps frequency to output constraint accuracy in log file morse no bonds are represented by a harmonic potential yes bonds are represented by a Morse potential 7 3 15 NMR refinement disre none no distance restraints ignore distance restraints information in topology file simple simple per molecule distance restraints ensemble distance restraints over an ensemble of molecules disre_weighting equal divide the restraint force equally over all atom pairs in the restraint conservative the forces are the derivative of the restraint potential this results in an r7 weighting of the atom pairs T disre_mixed no the violation used in the calculation of the restraint force is the time averaged violation yes the violation used in the calculation of the restraint force is the square root of the time averaged violation times the instantaneous violation 7 3 Run Parameters 121 disre_fe 1000 kJ mol nm force constant for distance restraints which is multiplied by a possibly different factor for each restraint disre_tau 0 ps time constant for distance restraints running average
239. reflect the upper right triangle of interactions to the lower left triangle of the matrix we still cover all possible interac tions but now every row in the matrix has almost the same number of points or possible interactions We can now assign a preferably equal number of rows to each processor to compute the forces and at the same time a number of particles to do the update on the home particles The number of interactions per particle is dependent on the total number N of particles see Fig 3 10 and on the particle number i The exact formulae are given in Table 3 1 A flow chart of the algorithm is given in Fig 3 11 It is the same as the sequential algorithm except for two communication steps After the particles have been reset in the box each processor sends its coordinates left and then starts computation of the forces After this step each processor holds the partial forces for the available particles e g processor 0 holds forces acting on home particles from processor 0 1 2 and 3 These forces must be accumulated and sent back right to the home processor Finally the update of the velocity and coordinates is done on the home processor The communicate r routine is given below in the full C code 3 11 Parallelization 35 01234567 8 0123456758 o 000000001 0 0 0 0 toi KEKEE E JEES 000o 2 e 2 e o 3 e 3 e 4 4 5 5 e 6 ee 6 00 o 7 O 70 0 o O 8 g 0000
240. rformance 152 periodic boundary conditions 13 69 149 planar groups 53 pme 70 114 poisson solver 49 polymer convention 80 position restraints 56 111 potential energy 20 potential function 43 160 potentials of mean force 97 pppm 40 71 114 pressure 21 pressure coupling 23 117 principal component analysis 138 processor topology 33 program options 122 programs by topic 123 proper dihedral 54 80 protonate 209 pvm 33 38 106 146 qsar 1 quadrupole TT reaction field 46 63 161 reaction field 114 repulsion 44 run parameters 109 ryckaert bellemans 80 sampling 28 schr dinger equation 1 settle 26 153 shake 24 119 153 shared memory 40 41 shell see particles shift function 20 simulated annealing 29 118 single precision solvent optimization space decomposition statistical mechanics steepest descent stochastic dynamics surface tension coupling tabulated functions temperature temperature coupling termini database third neighbors time lag topology topology file tpbconv trajectory file tree trjcat trjconv umbrella sampling united atoms virial virtual site viscosity wheel xdr xmer xpm2ps xrama 30 15 22 28 21 66 223 145 152 34 111 23 159 20 116 84 65 131 75 86 210 112 33 210 211 97 TT 149 TT 133 212 109 169 213 213
241. ritten as h2 id r 2 h 3 h2 n n ylz yi e ven MS 2y via e Su RET u u B 61 Note that the x dependence is completely in e This can abbreviated to y t yi eF e Gi eH B 62 From this we can calculate the derivative in order to determine the forces quay UNE Ss A Re yn B 63 dx de dz If we store in the table y F G and H we need a table of length 4n The number of points per nanometer should be on the order of 500 to 1000 for accurate representation relative error lt 107 when n 500 points nm The force routines get a scaling factor s as a parameter that is equal to the number of points per nm Note that h is s71 The algorithm goes a little something like this 1 Calculate distance vector r j and distance rij Multiply r by s and truncate to an integer value no to get a table index Calculate fractional component e sr no and e Do the interpolation to calculate the potential V and the the scalar force f oe FF WO N Calculate the vector force F by multiplying f with rij The tables are stored as y F G H in the order coulomb dispersion repulsion In total there are 12 values in each table entry Note that table lookup is significantly slower than computation of the most simple Lennard Jones and Coulomb interaction However it is much faster than the shifted coulomb function used in conjunction with the PPPM method Finally it is much easier to modify a tabl
242. rmined from a trajectory or read from an XPM matrix file with the dm option RMS deviation after fitting or RMS deviation of atom pair distances can be used to define the distance between structures full linkage add a structure to a cluster when its distance to any element of the cluster is less than cutoff Jarvis Patrick add a structure to a cluster when this structure and a structure in the cluster have each other as neighbors and they have a least P neighbors in common The neighbors of a structure are the M closest structures or all structures within cutoff Monte Carlo reorder the RMSD matrix using Monte Carlo diagonalization diagonalize the RMSD matrix When unique cluster assignments can be determined full linkage and Jarvis Patrick and a trajec tory file is supplied the structure with the smallest average distance to the others or the average structure for each cluster will be written to a trajectory file Files f traj xtc Input Opt Generic trajectory xtc trr trj gro g96 pdb s topol tpr Input Opt Structure mass db tpr tpb tpa gro g96 pdb n index ndx Input Opt Index file dm rmsd xpm Input Opt X PixMap compatible matrix file o rmsd clust xpm Output X PixMap compatible matrix file g cluster log Output Log file dist rmsd dist xvg Output xvgr xmer file ev rmsd eig xvg Output Opt xvgr xmgr file cl clusters pdb Output Opt Generic trajectory xtc trr trj gro g96 pdb Other options h bool no Print he
243. rocal space when using Ewald Grid size when using PPPM or PME These values override fourierspacing per direction The best choice is powers of 2 3 5 and 7 Avoid large primes pme_order 4 Interpolation order for PME 4 equals cubic interpolation You might try 6 8 10 when running in parallel and simultaneously decrease grid dimension ewald_rtol 1e 5 The relative strength of the Ewald shifted direct potential at the cutoff is given by ewald_rtol Decreasing this will give a more accurate direct sum but then you need more wave vectors for the reciprocal sum optimize_fft no Don t calculate the optimal FFT plan for the grid at startup yes Calculate the optimal FFT plan for the grid at startup This saves a few percent for long simulations but takes a couple of minutes at start 7 3 9 Temperature coupling tcoupl no No temperature coupling yes Temperature coupling with a Berendsen thermostat to a bath with tempera ture reft K with time constant tau_t ps Several groups can be coupled separately these are specified in the tc_grps field separated by spaces tc_grps groups to couple separately to temperature bath 7 3 Run Parameters 117 taut ps time constant for coupling one for each group in tc_grps ref_t K reference temperature for coupling one for each group in tc_grps 7 3 10 Pressure coupling pcoupl no No pressure coupling This means a fixed box size isotropic Pressure coupling w
244. rocesses in membranes the dynamics of phase changes reaction kinetics or the dynamics of defects in crystals The choice of technique depends on the question asked and on the feasibility of the method to yield reliable results at the present state of the art Ideally the relativistic time dependent Schr dinger equation describes the properties of molecular systems with high accuracy but anything more complex than the equilibrium state of a few atoms cannot be handled at this ab initio level Thus approximations are mandatory the higher the complexity of a system and the longer the time span of the processes of interest is the more severe approximations are required At a certain point reached very much earlier than one would wish the ab initio approach must be augmented or replaced by empirical parameterization of the model used Where simulations based on physical principles of atomic interactions still fail due to the complexity of the system as is unfortunately still the case for the prediction of protein folding but there is hope molecular modeling is based entirely on a similarity analysis of known structural and chemical data The QSAR methods Quantitative Structure Activity Relations and many homology based protein structure predictions belong to the latter category 2 Introduction Macroscopic properties are always ensemble averages over a representative statistical en semble either equilibrium or non equilibrium of molecula
245. s pdb2gmx automatically generates all angles this means that the angles field is only useful for overriding itp parameters pdb2gmx automatically generates one proper dihedral for every rotatable bond preferably on heavy atoms When the dihedrals field is used no other dihedrals will be gen erated for the bonds corresponding to the specified dihedrals It is possible to put more than one dihedral on a rotatable bond 5 3 6 Hydrogen database The hydrogen database is stored in ff hdb It contains information for the pdb2gmx program on how to connect hydrogen atoms to existing atoms Hydrogen atoms are named after the atom they are connected to the first letter of the atom name is replaced by an H If more then one hydrogen atom is connected to the same atom a number will be added to the end of the hydrogen atom name For example adding two hydrogen atoms to ND2 in asparagine the hydrogen atoms will be named HD21 and HD22 This is important since atom naming in the rtp file see 5 3 5 must be the same The format of the hydrogen database is as follows res additions H add type i j k ALA 1 1 1 N C CA ARG 4 1 2 N CA C 1 1 NE CD CZ 2 3 NH1 CZ NE 2 3 NH2 CZ NE On the first line we see the residue name ALA or ARG and the number of additions After that follows one line for each addition on which we see e The number of H atoms added 84 Topologies e The way of adding H atoms can be any of
246. s pid processor id 0 nprocs 1 vecs vectors start starting index in vecs for each processor homenr number of home particles for each processor 1 int i processor counter int shift the amount of processors to communicate with int cur current processor to send data from int next next processor on a ring using modulo cur pid shift nprocs 2 for i 0 i lt shift i next cur 1 4 nprocs send left vecs start cur homenr cur receive right vecs start next homenr next cur next The data flow around the ring is visualised in Fig 3 12 Note that because of the ring topology each processor automatically gets the proper particles to interact with 3 12 Parallel Molecular Dynamics In this chapter we describe some details of the parallel MD algorithm used in GROMACS This also includes some other information on neighbor searching and a side excursion to parallel sorting Please note the following which we use throughout this chapter definition N Number of particles M number of processors GROMACS employs two different grids the neighbor searching grid NS grid and the 38 Algorithms charge potential grid FFT grid as will be described below To maximize the confusion these two grids are mapped onto a grid of processors when GROMACS runs on a parallel computer 3 12 1 Domain decomposition Modern day parallel computers such as an IBM SP
247. s to read from trajectory w bool no View output using xvgr or ghostview dt real O Only analyze a frame each dt picoseconds sss string HEBT Secondary structures for structure count 172 Manual Pages Diagnostics e The program is very slow FE 2 editconf editconf converts generic structure format to gro or pdb A number of options is present to modify the coordinates and box d dc and box modify the box and center the coordinates relative to the new box dc takes precedent over d box takes precedent over dc and d rotate rotates the coordinates and velocities princ aligns the principal axes of the system along the coordinate axes this may allow you to decrease the box volume but beware that molecules can rotate significantly in a nanosecond Scaling is applied before any of the other operations are performed Boxes can be scaled to give a certain density option density A special feature of the scaling option when the factor 1 is given in one dimension one obtains a mirror image mirrored in one of the plains when one uses 1 in three dimensions a point mirror image is obtained Groups are selected after all operations have been applied Periodicity can be removed in a crude manner It is important that the box sizes at the bottom of your input file are correct when the periodicity is to be removed The program can optionally rotate the solute molecule to align the molecule along its principal axes rotat
248. s and Programs 7 3 11 Simulated annealing annealing no yes No simulated annealing Simulated annealing to 0 K at time zero_temp_time ps Reference temper ature for the Berendsen thermostat is reft x 1 time zero_temp _time time constant is tau_t ps Note that the reference temperature will not go below 0 K i e after zero_temp time if it is positive the reference temper ature will be 0 K Negative zero_temp _time results in heating which will go on indefinitely zero_temp _time 0 ps time at which temperature will be zero can be negative Temperature during the run can be seen as a straight line going through T ref_t K at t 0 ps and T 0 K at t zero_temp _time ps Look in our FAQ for a schematic graph of temperature versus time 7 3 12 gen_vel no yes Velocity generation Do not generate velocities at startup The velocities are set to zero when there are no velocities in the input structure file Generate velocities according to a Maxwell distribution at temperature gen_temp K with random seed gen_seed This is only meaningful with integrator md gen_temp 300 K temperature for Maxwell distribution gen_seed 173529 integer used to initialize random generator for random velocities 7 3 13 Solvent optimization solvent_optimization lt empty gt Do not use water specific non bonded optimizations 7 3 Run Parameters 119 lt solvent molecule name gt
249. s can greatly reduce the fluctuations in a molecule This problem can be overcome by restraining to a time averaged distance 45 The forces with time averaging are 7 Ci kar fij ro 0 for for kar fij a ri FE for PO ri T2 A IA IA Tij Tij Tij Tij lt ro lt ry 4 61 lt Ya kar ra r for Tij 4 2 Bonded interactions 59 where fi is given by i aS 4 62 Because of the time averaging we can no longer speak of a distance restraint potential This way an atom can satisfy two incompatible distance restraints on average by moving between two positions An example would be an amino acid side chain which is rotating around its y dihedral angle thereby coming close to various other groups Such a mobile side chain may give rise to multiple NOEs which can not be fulfilled in a single structure The computation of the time averaged distance in the mdrun program is done in the following fashion 3 ww S o ma 3 ij 0 rig 0 E l At exp 42 ese 1 exp 42 4 63 When a pair is within the bounds it can still feel a force because the time averaged distance can still be beyond a bound To prevent the protons from being pulled too close together a mixed approach can be used In this approach the penalty is zero when the instantaneous distance is within the bounds otherwise the violation is the square root of the product of the in
250. s not the case the program will crash Files f traj xtc Input Generic trajectory xtc trr trj gro g96 pdb 176 s topol tpr n angle ndx od angdist xvg ov angaver xvg of dihfrac xvg ot dihtrans xvg oh trhisto xvg oc dihcorr xvg Other options h bool no nice int 19 b real gt i e real 1 w bool no type enum angle all bool no binwidth real 1 chandler bool no avercorr bool no acflen int si normalize bool yes P enum 0 nparm enum 1 beginfit real 0 endfit real 0 Diagnostics Manual Pages Input Generic run input tpr tpb tpa Input Index file Output xvgr xmgr file Output Opt xvgr xmer file Output Opt xvgr xmer file Output Opt xvgr xmer file Output Opt xvgr xmgr file Output Opt xvgr xmgr file Print help info and quit Set the nicelevel First frame ps to read from trajectory Last frame ps to read from trajectory View output using xvgr or ghostview Type of angle to analyse angle dihedral improper or ryckaert bellemans i i Plot all angles separately in the averages file in the order of appear ance in the index file binwidth degrees for calculating the distribution Use Chandler correlation function Nftrans 1 N gauche 0 rather than cosine correlation function Trans is defined as phi lt 60 or phi gt 60 Average the correlation functions for the individual angles dihedrals Length of the ACF default is half the number of frames Normali
251. sgdisti xvg Output xvgr xmer file od2 sgdist2 xvg Output xvgr xmer file Other options h bool no Print help info and quit nice int 19 Set the nicelevel b real 1 First frame ps to read from trajectory e real 1 Last frame ps to read from trajectory w bool no View output using xvgr or ghostview E 42 g_velacc g_velacc computes the velocity autocorrelation function Files f traj trr Input Full precision trajectory trr trj n index ndx Input Index file 0 vac xvg Output xvgr xmer file Other options h bool no Print help info and quit nice int 19 Set the nicelevel b real 1 First frame ps to read from trajectory e real 1 Last frame ps to read from trajectory w bool no View output using xvgr or ghostview acflen int 1 Length of the ACF default is half the number of frames 200 Manual Pages normalize bool yes Normalize ACF P enum O Order of Legendre polynomial for ACF 0 indicates none 0 1 2 or nparm enum 1 Number of parameters in exponential fit 1 or 2 beginfit real O Time where to begin the exponential fit of the correlation function endfit real 0 Time where to end the exponential fit of the correlation function E 43 genbox Genbox can do one of 3 things 1 Generate a box of solvent Specify cs and box 2 Solvate a solute configuration eg a protein in a bath of solvent molecules Specify cp solute and cs solvent The box specified in the solute coordinate file cp is used unless box
252. solute value of a hydrophobic atom skip int 1 Do only every nth frame E 41 g_sgangle 199 E 41 g _sgangle Compute the angle and distance between two groups The groups are defined by a number of atoms given in an index file and may be two or three atoms in size The angles calculated depend on the order in which the atoms are given Giving for instance 5 6 will rotate the vector 5 6 with 180 degrees compared to giving 6 5 If three atoms are given the normal on the plane spanned by those three atoms will be calculated using the formula P1P2 x P1P3 The cos of the angle is calculated using the inproduct of the two normalized vectors Here is what some of the file options do oa Angle between the two groups specified in the index file If a group contains three atoms the normal to the plane defined by those three atoms will be used If a group contains two atoms the vector defined by those two atoms will be used od Distance between two groups Distance is taken from the center of one group to the center of the other group od1 If one plane and one vector is given the distances for each of the atoms from the center of the plane is given seperately od2 For two planes this option has no meaning Files f traj xtc Input Generic trajectory xtc trr trj gro g96 pdb n index ndx Input Index file s topol tpr Input Generic run input tpr tpb tpa oa sg angle xvg Output xvgr xmgr file od sg dist xvg Output xvgr xmgr file od1
253. son iteration scheme The inverse function is 1 AW F B 26 y So instead of calculating Y a q B 27 the equation X q a 0 B 28 B 3 Computation of the 1 0 sqrt function 155 31 23 0 Value 1 24 12 1 F Figure B 1 IEEE single precision floating point format can now be solved using Newton Raphson An iteration is performed by calculating f Yn Yn 1 Yn B 29 fe Era ai The absolute error e in this approximation is defined by E m q B 30 using Taylor series expansion to estimate the error results in 2 fil En f Yn Ent B 31 ay 2 f Yn according to 68 equation 3 2 This is an estimation of the absolute error B 3 3 Applied to floating point numbers Floating point numbers in IEEE 32 bit single precision format have a nearly constant relative error of Ax x 27 As seen earlier in the Taylor series expansion equation eqn B 31 the error in every iteration step is absolute and in general dependent of y If the error is expressed as a relative error e the following holds En 1 y B 32 Erm 1 and so ie Yap B 33 Etny e for the function f y y the term yf 2f is constant equal to 3 2 so the relative error is independent of y 3 Erny 5 ern B 34 The conclusion of this is that the function 1 z can be calculated with a specified accuracy 156 Some implementation details B 3 4 Specification of the lookup table
254. sor include directories to include in your topology format I home john my_lib I more_lib define defines to pass to the preprocessor default is no defines You can use any defines to control options in your customized topology files Options that are already available by default are DFLEX_SPC Will tell grompp to include FLEX_SPC in stead of SPC into your topology this is necessary to make conjugate gradient work and will allow steepest descent to minimize further DPOSRE Will tell grompp to include posre itp into your topology used for position re straints 7 3 3 Run control integrator md A leap frog algorithm for integrating Newton s equations steep A steepest descent algorithm for energy minimization The maximum step size is emstep nm the tolerance is emtol kJ mol nm cg A conjugate gradient algorithm for energy minimization the tolerance is emtol kJ mol nm7 CG is more efficient when a steepest descent step is done every once in a while this is determined by nstcgsteep ld An Euler integrator for position Langevin dynamics the velocity is the force divided by a friction coefficient 1d_fric amu ps plus random thermal noise Id_temp K The random generator is initialized with 1d_seed 112 Run parameters and Programs tinit 0 ps starting time for your run only makes sense for integrators md and ld dt 0 001 ps time step for integration only makes sense for in
255. ssian distributed noise with y 0 1 Because the system is assumed to be over damped large time steps can be used LINCS should be used for the constraints since SHAKE will not converge for large atomic displacements LD is an option of the mdrun program 3 7 Energy Minimization Energy minimization in GROMACS can be done using a steepest descent or conjugate gradient method EM is just an option of the mdrun program 30 Algorithms 3 7 1 Steepest Descent Although steepest descent is certainly not the most efficient algorithm for searching it is robust and easy to implement We define the vector r as the vector of all 3N coordinates Initially a maximum displace ment ho e g 0 01 nm must be given First the forces F and potential energy are calculated New positions are calculated by F max Fn ped Prot Tn where hy is the maximum displacement and F is the force or the negative gradient of the potential V The notation max F means the largest of the absolute values of the force components The forces and energy are again computed for the new positions If Vnii lt Vn the new positions are accepted and h 1 1 2h If Vn 1 gt Vn the new positions are rejected and hn 0 2hn The algorithm stops when either a user specified number of force evaluations has been performed e g 100 or when the maximum of the absolute values of the force gradient components is smaller than a specified val
256. stant bonded interactions with dummies Number of warnings after which input processing stops e shuffling is sometimes buggy when used on systems when the number of molecules of a certain type is smaller than the number of processors E 51 highway highway is the gromacs highway simulator It is an X windows gadget that shows a periodic autobahn with a user defined number of cars Fog can be turned on or off to increase the number of crashes Nice for a background CPU eater Files f highway dat Input Generic data file a auto dat Input Generic data file Other options h bool no nice int 0 b real 1 e real 1 E 52 make_ndx Print help info and quit Set the nicelevel First frame ps to read from trajectory Last frame ps to read from trajectory Index groups are necessary for almost every gromacs program All these programs can generate default index groups You ONLY have to use make ndx when you need SPECIAL index groups There is a default index group for the whole system 9 default index groups are generated for proteins a default index group is generated for every other residue name When no index file is supplied also make ndx will generate the default groups With the index editor you can select on atom residue and chain names and numbers you can use NOT AND and OR you can split groups into chains residues or atoms You can delete and rename groups The atom numbering in the editor and the index file starts
257. stantaneous violation and the time averaged violation Averaging over multiple pairs Sometimes it is unclear from experimental data which atom pair gives rise to a single NOE in other occasions it can be obvious that more than one pair contributes due to the symmetry of the system e g a methyl group with three protons For such a group it is not possible to distinguish between the protons therefore they should all be taken into account when calculating the distance between this methyl group and another proton or group of protons Due to the physical nature of magnetic resonance the intensity of the NOE signal is proportional to the distance between atoms to the power of 6 Thus when combining atom pairs a fixed list of N restraints may be taken together where the apparent distance is given by 1 6 ry t Y rat 4 64 where we use rj or eqn 4 62 for the 7 The ry of the instantaneous and time averaged distances can be combined to do a mixed restraining as indicated above As more pairs of protons contribute to the same NOE signal the intensity will increase and the summed distance will be shorter than any of its components due to the reciprocal summation There are two options for distributing the forces over the atom pairs In the conservative option the force is defined as the derivate of the restraint potential with respect to the coordinates This results in a conservative potential when no time averaging is used
258. straining will then maintain the integrity of the inner part For spherical shells it is a wise procedure to make the force constant depend on the radius increasing from zero at the inner boundary to a large value at the outer boundary This application has not been implemented in GROMACS however The following form is used 1 Vor mi Skprlri Ral 4 54 The potential is plotted in Fig 4 12 The potential form can be rewritten without loss of generality as 1 k R E Vetri 5 Kalos Xe 24 lo YO S Hki Z 2 455 Now the forces are Fe kg a Xi F kp yi Yi 4 56 F kr 2 Zi 4 2 Bonded interactions 57 8 0 Vocero KJ mole 20 r R nm Figure 4 12 Position restraint potential Using three different force constants the position restraints can be turned on or off in each spatial dimension this means that atoms can be harmonically restrained to a plane or a line Position restraints are applied to a special fixed list of atoms Such a list is usually generated by the pdb2gmx program 4 2 8 Angle restraints These are used to restrain the angle between two pairs of particles or between one pair of particles and the Z axis The functional form is similar to that of a proper dihedral For two pairs of atoms Ti Ti Tr i Tk Var Ti ri Pki r1 kar 1 cos n 0 69 where O arccos 2 anl 2 J k 1 apt 0 E EE 4 57 For one pair of
259. structed your own top please send a copy plus description to gromacs chem rug nl so we can extend our topology database and prevent GROMACS users from inventing the wheel twice This also applies for new force field parameters that were originally not included in the GROMACS force field The files are grouped per forcefield type named e g gmx for the GROMACS forcefield or G43a1 for the GROMOS96 forcefield All files for one forcefield have names beginning with ff where stands for the forcefield name 5 2 Particle type In GROMACS there are 5 types of particles see Table 5 1 Only regular atoms and dummy particles are used in GROMACS nuclei shells and bond shells are necessary for polarizable forcefields which we don t yet have 76 5 2 1 Atom types Topologies atom nucleus shell bond shell dummy Table 5 1 Particle types in GROMACS GROMACS uses 47 different atom types as listed below with their corresponding masses in a m u This is the same listing as in the file ff atp atp atom type parameter file therefore in this file you can change and or add an atom type OM OA OW NT NL NR5 NR5x NP CH1 CH2 CH3 CR51 CR61 CB HO HW HS FE ZN NZ NE Os csi NR6 NR6 CS2 SI NA CL 15 15 15 15 14 14 14 14 14 14 12 13 14 15 13 13 12 99940 99940 99940 99940 00670 00670 00670 00670 00670 00670 011
260. t on most hardware platforms Most interactions in molecular dynamics have in principle a short ranged character Bonds angles and dihedrals are guaranteed to have the corresponding particles close in space 3 12 2 Domain decomposition for non bonded forces For large parallel computers domain decomposition is preferable over particle decomposi tion since it is easier to do load balancing Without load balancing the scaling of the code is rather poor For this purpose the computational box is divided in M slabs where M is equal to the number of processors There are multiple ways of dividing the box over processors but since the GROMACS code assumes a ring topology for the processors it is logical to cut the system in slabs in just one dimension the X dimension The algorithm for neighbor searching then becomes 1 Make a list of charge group indices sorted on increasing X coordinate Fig 3 13 Note that care must be taken to parallelize the sorting algorithm as well See sec 3 12 4 3 12 Parallel Molecular Dynamics 39 CPU number index Ma A a es X coord Y Z 012 N 1 atom number Figure 3 13 Index in the coordinate array The division in slabs is indicated by dashed lines 2 Divide this list into slabs such that each slab has the same number of charge groups 3 Put the particles corresponding to the local slab on a 3D NS grid as described above sec
261. t case you should use an index file with molecule numbers The program can also be used for calculating diffusion in one or two dimensions This is useful for studying lateral diffusion on interfaces An example of the mean square displacement of SPC water is given in Fig 8 4 8 6 Bonds angles and dihedrals g_bond g_angle g_sgangle 134 Analysis Mean Square Displacement D 3 5027 10 cm s 4000 0 3000 0 E 2000 0 a MSD 10 cm s 1000 0 0 0 50 0 100 0 150 0 Time ps Figure 8 4 Mean Square Displacement of SPC water To monitor specific bonds in your molecules during time the program g bond calculates the distribution of the bond length in time The index file consists of pairs of atom numbers for example bonds_1 1 2 4 9 10 bonds_2 1 12 13 The program g_angle calculates the distribution of angles and dihedrals in time It also gives the average angle or dihedral The index file consists of triplets or quadruples of atom numbers angles 1 2 3 2 3 4 3 4 5 dihedrals 1 2 3 4 2 3 5 5 For the dihedral angles you can use either the biochemical convention 0 cis or polymer convention 0 trans see Fig 8 5 To follow specific angles in time between two vectors a vector and a plane or two planes defined by 2 resp 3 atoms inside your molecule see Fig 8 6A B C use the program g sgangle 8 6 Bonds angles and dihedr
262. t for Phi dihedral angles psi bool no Output for Psi dihedral angles omega bool no Output for Omega dihedrals peptide bonds rama bool no Generate Phi Psi and Chil Chi2 ramachandran plots viol bool no Write a file that gives 0 or 1 for violated Ramachandran angles all bool no Output separate files for every dihedral shift bool no Compute chemical shifts from Phi Psi angles run int 1 perform running average over ndeg degrees for histograms 178 Manual Pages maxchi enum O calculate first ndih Chi dihedrals 0 1 2 3 4 5 or 6 ramomega bool no compute average omega as a function of phi psi and plot it in an xpm plot bfact real 1 bfactor value for pdb file for atoms with no calculated dihedral order parameter acflen int 1 Length of the ACF default is half the number of frames normalize bool yes Normalize ACF P enum O Order of Legendre polynomial for ACF 0 indicates none 0 1 2 or nparm enum 1 Number of parameters in exponential fit 1 or 2 beginfit real O Time where to begin the exponential fit of the correlation function endfit real O Time where to end the exponential fit of the correlation function Diagnostics e Produces MANY output files up to about 4 times the number of residues in the protein twice that if autocorrelation functions are calculated Typically several hundred files are output E 9 g_cluster g cluster can cluster structures with several different methods Distances between structures can be dete
263. tain second derivatives for most systems of interest this is beyond the available capacity There are intermediate methods building up the Hessian matrix on the fly but they also suffer from excessive storage requirements So GROMACS will shy away from 1 3 Energy Minimization and Search Methods 7 this class of methods The steepest descent method available in GROMACS is of the second class It simply takes a step in the direction of the negative gradient hence in the direction of the force without any consideration of the history built up in previous steps The step size is adjusted such that the search is fast but the motion is always downhill This is a simple and sturdy but somewhat stupid method its convergence can be quite slow especially in the vicinity of the local minimum The faster converging conjugate gradient method see e g 10 uses gradient information from previous steps In general steepest descents will bring you close to the nearest local minimum very quickly while conjugate gradients brings you very close to the local minimum but performs worse far away from the minimum Introduction Chapter 2 Definitions and Units 2 1 Notation The following conventions for mathematical typesetting are used throughout this docu ment Item Notation Example Vector Bold italic Ti Vector Length Italic r We define the lowercase subscripts 2 j k and L to denote particles r is the position vector of particl
264. tance restraints kz ky kz kJ mol nm type index low up1 up2 nm factor bo deg fe kJ mol7 mult bo deg fe kJ mol7 mult one or more atom indices 3 3 4 4 4 2 2 3 2 3 3 3 3 4 1 2 Bee PP RW NYRR REF NFWNH NH A angle res angle_restraints angle res z angle_restraints z exclusions exclusions N E System syetan system name molecules molecule name number of molecules at is the number of atom indices f tp is function type pert indicates if this interaction type can be modified during free energy perturbation 2 multiplicities can not be modified 0 only the atom type charge and mass can be modified For free energy perturbation the parameters for topology B lambda 1 should be added on the same line after the normal parameters in the same order as the normal parameters Table 5 4 The topology top file part 2 92 Topologies molecules this defines the total number of sub molecules in your system that are defined in this top In this example file it stands for 1 urea molecules dissolved in 1000 water molecules The molecule type SOL is defined in the spc itp file 5 4 2 Molecule itp file If you construct a topology file you will use more often like a water molecule spc itp it is better to make a molecule itp file which only lists the information of the molecule moleculetype name nrexcl Urea 3 atoms nr type r
265. tatic interac tion between partial charges Thus the simulations will exaggerate the long range Coulomb terms Luckily the next item compensates this effect a bit Long range interactions are cut off In this version GROMACS always uses a cut off radius for the Lennard Jones in teractions and sometimes also for Coulomb Due to the minimum image convention only one image of each particle in the periodic boundary conditions is considered for a pair interaction the cut off range can not exceed half the box size That is still pretty big for large systems and trouble is only expected for systems contain ing charged particles But then real bad things may happen like accumulation of charges at the cut off boundary or very wrong energies For such systems you should consider using one of the implemented long range electrostatic algorithms Boundary conditions are unnatural Since system size is small even 10 000 particles is small a cluster of particles will have a lot of unwanted boundary with its environment vacuum This we must avoid if we wish to simulate a bulk system So we use periodic boundary conditions to avoid real phase boundaries But liquids are not crystals so something unnatural remains This item is mentioned in the last place because it is the least evil of all For large systems the errors are small but for small systems with a lot of internal spatial correlation the periodic boundaries may enhance internal correlation
266. tc Input Generic trajectory xtc trr trj gro g96 pdb n index ndx Input Index file nm index ndx Input Opt Index file s topol tpr Input Generic run input tpr tpb tpa 0 order xvg Output xvgr xmgr file Other options h bool no Print help info and quit nice int 19 Set the nicelevel b real 1 First frame ps to read from trajectory e real 1 Last frame ps to read from trajectory w bool no View output using xvgr or ghostview d string Z Take the normal on the membrane in direction X Y or Z s1 int O Calculate order parameter as function of boxlength dividing the box in nr slices Diagnostics e The program assigns whole water molecules to a slice based on the firstatom of three in the index file group It assumes an order O H H Name is not important but the order is If this demand is not met assigning molecules to slices is different E 23 g_hbond g hbond computes and analyzes hydrogen bonds Hydrogen bonds are determined based on cutoffs for the angle Donor Hydrogen Acceptor zero is extended and the distance Hydrogen Acceptor OH and NH groups are regarded as donors O is an acceptor always N is an acceptor by default but this can be switched using nitacc Dummy hydrogen atoms are assumed to be connected to the first preceding non hydrogen atom 188 Manual Pages You need to specify two groups for analysis which must be either identical or non overlapping All hydrogen bonds between the two groups are analyzed
267. tc trr trj gro g96 pdb Other options h bool no Print help info and quit nice int 19 Set the nicelevel b real 1 First time to use e real 1 Last time to use prec int 3 Precision for xtc and gro writing in number of decimal places vel bool yes Read and write velocities if possible settime bool no Change starting time interactively sort bool yes Sort trajectory files not frames E 61 trjconv 211 E 61 trjconv trjconv can convert trajectory files in many ways from one format to another select a subset of atoms remove periodicity from molecules keep multimeric molecules together center atoms in the box fit atoms to reference structure remove duplicate frames reduce the number of frames change the timestamps of the frames e g t0 and delta t CONaATIhKWN a The program trjcat can concatenate multiple trajectory files Currently seven formats are supported for input and output xtc trr trj gro g96 pdb and g87 The file formats are detected from the file extension For gro and xtc files the output precision can be given as a number of decimal places Note that velocities are only supported in trr trj gro and g96 files The option app can be used to append output to an existing trajectory file No checks are performed to ensure integrity of the resulting combined trajectory file pdb files with all frames concatenated can be viewed with rasmol nmrpdb It is possible to se
268. tegrators md and ld nsteps 1 maximum number of steps to integrate nstcomm 1 steps if positive frequency for center of mass motion removal if negative frequency for center of mass motion and rotational motion removal should only be used for vac uum simulations 7 3 4 Langevin dynamics Id_temp 300 K temperature in ld run controls thermal noise level ld_fric 0 amu ps ld friction coefficient Id_seed 1993 integer used to initialize random generator for thermal noise when 1d_seed is set to 1 the seed is calculated as time getpid 65536 7 3 5 Energy minimization emtol 100 0 kJ mol nm the minimization is converged when the maximum force is smaller than this value emstep 0 01 nm initial step size nstcgsteep 1000 steps frequency of performing 1 steepest descent step while doing conjugate gradient en ergy minimization 7 3 6 Output control nstxout 100 steps frequency to write coordinates to output trajectory file the last coordinates are always written nstvout 100 steps frequency to write velocities to output trajectory the last velocities are always writ ten 7 3 Run Parameters 113 nstfout 0 steps frequency to write forces to output trajectory nstlog 100 steps frequency to write energies to log file the last energies are always written nstenergy 100 steps frequency to write energies to energy file the last energies are a
269. ters and Programs 7 3 18 Electric fields Ex E_y Ez If you want to use an electric field in a direction enter 3 numbers after the appro priate E_ the first number the number of cosines only 1 is implemented with frequency 0 so enter 1 the second number the strength of the electric field in V nm the third number the phase of the cosine you can enter any number here since a cosine of frequency zero has no phase Ext E yt Ezt not implemented yet 7 3 19 User defined thingies userl_grps user2_grps user3_grps userint1 0 userint2 0 userint3 0 userint4 0 userreall 0 userreal2 0 userreal3 0 userreal4 0 These you can use if you hack out code You can pass integers and reals to your subroutine Check the inputrec definition in src include types inputrec h 7 4 Program Options Optional files are not used unless the option is set in contrast to non optional files where the default file name is used when the option is not set All GROMACS programs will accept file options without a file extension or filename being specified In such cases the default filenames will be used With multiple input file types such as generic structure format the directory will be searched for files of each type with the supplied or default name When no such file is found or with output files the first file type will be used All GROMACS programs with the exception of mdrun nmrun and eneconv check if the comma
270. that terms with i j should be omitted when nz ny nz 0 0 0 The distance rijn is the real distance between the charges and not the minimum image This sum is conditionally convergent but very slow Ewald summation was first introduced as a method to calculate long range interactions of the periodic images in crystals 49 The idea is to convert the single slowly converging 70 Force fields sum eqn 4 108 into two fast converging terms and a constant term V Vair F Vrec Vo 4 109 esis EEEE gy Ean 4 110 ijn r ij Ne Ny Nex a fp Law Dy y weenie cem PY Prim aa m Mz My Mz FP 2 va a 4 112 Ei where is a parameter that determines the relative weight of the direct and reciprocal sums and m Mgr My Mz In this way we can use a short cut off of the order of 1 nm in the direct space sum and a short cut off in the reciprocal space sum e g 10 wave vectors in each direction Unfortunately the computational cost of the reciprocal part of the sum increases as N or N 3 2 with a slightly better algorithm and it is therefore not realistic to use for any large systems Using Ewald Don t use Ewald unless you are absolutely sure this is what you want for almost all cases the PME method below will perform much better If you still want to employ classical Ewald summation enter this in your mdp file if the side of your box is about 3 nm eeltype Ewald rvdw 0 9 rlist 0 9 rcoulomb 0 9 fo
271. the main group This only works for distances defined in 1 dimension and the cylinder is oriented with its long axis along this 1 dimension A second cylinder can be defined with rc with a linear switch function that weighs the contribution of atoms between r and rc with distance This smoothes the effects of atoms moving in and out of the cylinder which causes jumps in the constraint forces dynamic_t0O 100 Special Topics The same as dynamic but using the coordinates corrected for boxcrossings like in com_t0 Note that strictly speaking this is not correct if the reference group is not the whole system including the groups defined with group 1 and group 2 To further smooth rapidly fluctuating distances between the reference group and the other groups the average distance can be constrained instead of the instanteneous distance This is defined by setting reflag to the number of steps to average over However using this option is not strictly correct for calculating potentials of mean force from the average constraint force The parameter file verbose no If this is set to yes a large amount of detailed information is sent to stderr which is only useful for diagnostic purposes The pdo file also becomes more detailed which is not necessary for normal use runtype constraint Options are start afm constraint umbrella This selects the type of cal culation making starting structures AFM pulling constraint force calculat
272. thm is described in sec 3 4 first a global form of the algorithm is given which is refined in subsequent subsections The simple EM Energy Minimization algorithm is described in sec 3 7 Some other algorithms for special purpose dynamics are described after this In the final sec 3 11 of this chapter a few principles are given on which parallelization of GROMACS is based The parallelization is hardly visible for the user and is therefore not treated in detail A few issues are of general interest In all cases the system must be defined consisting of molecules Molecules again consist of particles with defined interaction functions The detailed description of the topology of the molecules and of the force field and the calcu lation of forces is given in chapter 4 In the present chapter we describe other aspects of the algorithm such as pair list generation update of velocities and positions coupling to external temperature and pressure conservation of constraints The analysis of the data generated by an MD simulation is treated in chapter 8 3 2 Periodic boundary conditions The classical way to minimize edge effects in a finite system is to apply periodic boundary conditions The atoms of the system to be simulated are put into a space filling box which is surrounded by translated copies of itself Fig 3 1 Thus there are no boundaries of the system the artifact caused by unwanted boundaries in an isolated cluster is now replace
273. tial differentiation with respect to the atomic positions The force constants in this function are related to the force constants in the harmonic form k sec 4 2 3 by K sin 0 ke 4 48 4 2 4 Improper dihedrals Improper Dihedrals are meant to keep planar groups planar e g aromatic rings or to prevent molecules from flipping over to their mirror images see Fig 4 8 VialEsjti ke Eagar amp 0 4 49 This is also a harmonic potential it is plotted in Fig 4 9 Note that since it is harmonic periodicity is not taken into account so it is best to define improper dihedrals to have a o as far away from 180 as you can manage 54 Force fields Y 2 o V kJ mole 2 o 0 0 20 0 10 0 0 0 10 0 20 0 Figure 4 9 Improper dihedral potential e 60 0 j g k 40 0 20 0 V kJ mole i 90 0 iio 270 0 360 Figure 4 10 Principle of proper dihedral angle left in trans form and the dihedral angle potential right 4 2 5 Proper dihedrals For the normal dihedral interaction there is a choice of either the GROMOS periodic function or a function based on expansion in powers of cos the so called Ryckaert Bellemans potential This choice has consequences for the inclusion of special interactions between the first and the fourth atom of the dihedral quadruple With the periodic GROMOS potential a special 1 4 LJ interaction must be included with the Ryck
274. ticular image can always be identified by an index pointing to one of 27 translation vectors and constructed by applying a translation with the indexed vector see 3 4 2 3 3 The group concept In the GROMACS MD and analysis programs one uses groups of atoms to perform certain actions on The maximum number of groups is 256 but every atom can only belong to four different groups one of each of the following kinds T coupling group The temperature coupling parameters reference temperature time constant number of degrees of freedom see 3 4 3 can be defined for each T coupling group separately For example in a solvated macromolecule the solvent that tends to produce more heating by force and integration errors can be coupled with a shorter time constant to a bath than a macromolecule or a surface can be kept cooler than an adsorbing molecule Many different T coupling groups may be defined Freeze group Atoms that belong to a freeze group are kept stationary in the dynamics This is useful during equilibration e g to avoid that badly placed solvent molecules will give unreasonable kicks to protein atoms although the same effect can also be obtained by putting a restraining potential on the atoms that must be protected The freeze option can be used on one or two coordinates of an atom thereby freezing the atoms in a plane or on a line Many freeze groups can be defined Accelerate group On each atom in an accelerate group an acc
275. tion 400 700 stretch 50 200 Table 1 1 Typical vibrational frequencies wavenumbers in molecules and hydrogen bonded liquids Compare kT h 200 cm at 300 K The equations are solved simultaneously in small time steps The system is followed for some time taking care that the temperature and pressure remain at the required values and the coordinates are written to an output file at regular intervals The coordinates as a function of time represent a trajectory of the system After initial changes the system will usually reach an equilibrium state By averaging over an equilibrium trajectory many macroscopic properties can be extracted from the output file It is useful at this point to consider the limitations of MD simulations The user should be aware of those limitations and always perform checks on known experimental properties to assess the accuracy of the simulation We list the approximations below The simulations are classical Using Newton s equation of motion automatically implies the use of classical me chanics to describe the motion of atoms This is all right for most atoms at normal temperatures but there are exceptions Hydrogen atoms are quite light and the motion of protons is sometimes of essential quantum mechanical character For example a proton may tunnel through a potential barrier in the course of a trans fer over a hydrogen bond Such processes cannot be properly treated by classical dynamics Helium liqu
276. tions mult int 1 mulitiplicity for dihedral angles by default read from topology E 16 g_dipoles g dipoles computes the total dipole plus fluctuations of a simulation system From this you can compute e g the dielectric constant for low dielectric media The file dip xvg contains the total dipole moment of a frame the components as well as the norm of the vector The file aver xvg contains lt orMuor gt and lt orMuor gt during the simulation The file dip xvg contains the distribution of dipole moments during the simulation The mu_max is used as the highest value in the distribution graph E 16 g dipoles 183 Furthermore the dipole autocorrelation function will be computed when option c is used It can be averaged over all molecules or with option avercorr it can be computed as the autocorrelation of the total dipole moment of the simulation box At the moment the dielectric constant is calculated only correct if a rectangular or cubic simulation box is used EXAMPLES g dipoles P1 n mols o dip_sqr mu 2 273 mumax 5 0 nframes 1001 nofft This will calculate the autocorrelation function of the molecular dipoles using a first order Legendre polynomial of the angle of the dipole vector and itself a time t later For this calculation 1001 frames will be used Further the dielectric constant will be calculated using an epsilonRF of infinity default temperature of 300 K default and an average dipole moment of the molec
277. tions a cyclodextrin complexes as a case study J Am Chem Soc 116 6293 6302 1994 Jorgensen W L Chandrasekhar J Madura J D Impey R W Klein M L Comparison of simple potential functions for simulating liquid water J Chem Phys 79 926 935 1983 van Buuren A R Berendsen H J C Molecular dynamics simulation of the stability of a 22 residue alpha helix in water and 30 trifluoroethanol Biopolymers 33 1159 1166 1993 Liu H Milller Plathe F van Gunsteren W F A force field for liquid dimethyl sulfoxide and liquid proporties of liquid dimethyl sulfoxide calculated using molecular dynamics simulation J Am Chem Soc 117 4363 4366 1995 Tironi I G Sperb R Smith P E van Gunsteren W F A generalized reaction field method for molecular dynamics simulations J Chem Phys 102 5451 5459 1995 van Gunsteren W F Billeter S R Fising A A H nenberger P H Kriiger P Mark A E Scott W R P Tironi I G Biomolecular Simulation The GROMOS96 manual and user guide Z rich Switzerland Hochschulverlag AG an der ETH Z rich 1996 Morse P M Diatomic molecules according to the wave mechanics II vibrational levels Phys Rev 34 57 64 1929 218 44 45 146 47 148 149 1501 151 159 153 BIBLIOGRAPHY Jorgensen W L Tirado Rives J The OPLS potential functions for proteins en ergy minimizations for crystals of cy
278. tions in structure a 137 8 9 Covariance analysis e 138 8 10 Hydrogen bonds e 139 8 11 Protein related items e 141 8 12 Interface related items e 143 S 13 Chemical shifts 2 E Da 144 A Technical Details 145 ACL Wnstallations ta A ds 145 A 2 Single or Double precision e e 145 A 3 Porting GROMACS e 146 A 3 1 Multi processor Porting tata tdo sd 146 A 4 Environment Variables o e 147 B Some implementation details 149 B 1 Single Sum Virial in GROMACS o e 149 A A RN 149 B 1 2 Virial from non bonded forces o e 150 B 1 3 The intramolecular shift mol shift 150 B 1 4 Virial from Covalent Bonds 151 CONTENTS B 1 9 Vinal from Shake sets apea oee ee Sek Ee a 152 B2 Optimizationsien moto he ew ee ee ee ee we ee we a 152 B 2 1 Inner Loop for Water o e e 152 B 2 2 Shake for Water SETTLE 153 B 2 3 Fortran Code og aor sic e dt We sd 153 B 3 Computation of the 1 0 sqrt function oia dra ae oe Ro ae Fe 154 Bial Antroductions see ha ee Sa es AA Ee Roe Bat See A 154 B 3 2 General smc ee wa Pe a Pe al A 154 B 3 3 Applied to floating point numbers 155 B 3 4 Specification of the lookup table o 156 B 3 5 Separate exponent and f
279. total heat capacity of the system k is Boltzmann s constant and Naf is the total number of degrees of freedom The reason that r Tr is that the kinetic energy change caused by scaling the velocities is partly redistributed between kinetic and potential energy and hence the change in temperature is less than the scaling energy In practice the ratio T rr ranges from 1 gas to 2 harmonic solid to 3 water When we use the term temperature coupling time constant we mean the parameter Tr Note that in practice the scaling factor A is limited to the range of 0 8 lt A lt 1 25 to avoid scaling by very large numbers which may crash the simulation In normal use A will always be much closer to 1 0 3 4 Molecular Dynamics 23 Strictly for computing the scaling factor the temperature T is needed at time t but this is not available in the algorithm In practice the temperature at the previous time step is used as indicated in eqn 3 20 which is perfectly all right since the coupling time constant is much longer than one time step The algorithm is stable up to tr At Pressure coupling In the same spirit as the temperature coupling the system can also be coupled to a pressure bath This is accomplished 17 by scaling coordinates and box size every step with a parameter u which has the effect of a first order kinetic relaxation of the pressure towards a given reference pressure Pp dP P P 3 22 dt Tp The sc
280. tructure from a trajectory with respect to a reference structure from a run input file by LSQ fitting the structures on top of each other The reference structure is taken from the structure file s Option prev produces the RMSD with a previous frame Option m produces a matrix in xpm format of RMSD s of each structure in the trajectory with respect to each other structure This file can be visualized with for instance xv and can be converted to postscript with xpm2ps All the structures are fitted on the structure in the structure file With fitall all the structures are fitted pairwise With f2 the other structures are taken from a second trajectory Option bin does a binary dump of the RMSD matrix Option bm produces a matrix of average bond angle deviations analogously to the m option Only bonds between atoms in the RMSD group are considered Files s topol tpr Input Structure mass db tpr tpb tpa gro g96 pdb f traj xtc Input Generic trajectory xtc trr trj gro g96 pdb f2 traj xtc Input Opt Generic trajectory xtc trr trj gro g96 pdb n index ndx Input Opt Index file 0 rmsd xvg Output xvgr xmgr file a avgrp xvg Output Opt xvgr xmgr file dist rmsd dist xvg Output Opt xvgr xmer file m rmsd xpm Output Opt X PixMap compatible matrix file bin rmsd dat Output Opt Generic data file bm bond xpm Output Opt X PixMap compatible matrix file Other options h bool no Print help info and quit nice int 19 Set the
281. ts correlation coulomb covariance analysis cut off data parallel degrees of freedom dielectric constant 22 46 54 81 15 97 73 33 57 52 see particles 76 131 see particles 50 79 4 45 78 82 18 20 114 ii 81 145 1 30 111 97 81 4 24 26 119 131 46 62 138 47 65 115 33 102 46 115 diffusion coefficient dihedral dispersion dispersion correction distance restraints do_dssp do shift double precision dummy dummy atom editconf electric field electrostatic force electrostatics eneconv energy file energy minimization energy monitor group ensemble average equations of motion equilibration essential dynamics ewald sum exclusions file types force field fortran free energy calculation free energy perturbation freeze group g anaelg g_analyze g_angle g_bond g_chi e cluster 133 54 44 116 57 120 148 171 148 145 see particles 67 77 103 172 122 20 114 173 166 112 15 2 2 22 166 31 138 49 69 114 65 81 109 4 43 77 153 97 31 61 121 15 139 173 174 175 176 177 178 222 g com g_confrms g_covar g_density g dielectric g dih g_dipoles g_disre g_dist g enemat g_energy g_gyrate g h2order g hbond g helix g mdmat g_mindist g msd g nmeig g nmens g order g potential grama g rdens g rdf g rms g rmsdist g rmsf g rotacf g saltbr g sas g sgangle g velacc genbox gencon
282. ttice sum for long range electrostatics The actual neighbor search is performed on a grid The details of the algorithm are not relevant for the user and are not given here Potential energy When forces are computed the potential energy of each interaction term is computed as well The total potential energy is summed for various contributions such as Lennard Jones Coulomb and bonded terms It is also possible to compute these contributions for groups of atoms that are separately defined see sec 3 3 Kinetic energy and temperature The temperature is given by the total kinetic energy of the N particle system ix Ekin a So ma 3 9 i l From this the absolute temperature T can be computed using 1 NakT Erin 3 10 where k is Boltzmann s constant and Nas is the number of degrees of freedom which can be computed from Ng 3N N 3 3 11 3 4 Molecular Dynamics 21 Figure 3 5 The Leap Frog integration method The algorithm is called Leap Frog Haasje Over because r and v are leaping like frogs over each others back Here Ne is the number of constraints imposed on the system The additional 3 degrees of freedom must be removed because the three center of mass velocities are constants of the motion which are usually set to zero This correction is small in the current version of GROMACS it is ignored The kinetic energy can also be written as a tensor which is necessary for pressure calcu lation in a triclin
283. ue e Since force truncation produces some noise in the energy evaluation the stopping criterion should not be made too tight to avoid endless iterations A reasonable value for e can be estimated from the root mean square force f a harmonic oscillator would exhibit at a temperature T This value is f 2rvV2mkT 3 45 where v is the oscillator frequency m the reduced mass and k Boltzmann s constant For a weak oscillator with a wave number of 100 cm and a mass of 10 atomic units at a temperature of 1 K f 7 7 kJ mol nm A value for e between 1 and 10 is acceptable 3 7 2 Conjugate Gradient Cojugate gradient is slower than steepest descent in the early stages of the minimization but becomes more efficient closer to the energy minimum The parameters and stop criterion are the same as for steepest descent Cojugate gradient can not be used with constraints or freeze groups 3 8 Normal Mode Analysis Normal mode analysis 24 26 can be performed using GROMACS by diagonalization of the mass weighted Hessian M PHM Q wQ 3 46 where M contains the atomic masses Q contains eigenvectors and w contains the corre sponding eigenvalues frequencies 3 9 Free energy perturbation 31 First the Hessian matrix which is a 3N x 3N matrix where N is the number of atoms has to be calculated OPV 0x 0x 5 where x and x denote the atomic x y or z coordinates In practice these equations have not been developed analytica
284. uence the slower motions in the system while enabling you to increase the time step by a factor of 3 or 4 You can also modify the potential energy function during the search procedure e g by removing barriers remove dihedral angle functions or replace repulsive potentials by soft core potentials 8 but always take care to restore the correct functions slowly The best search method that allows rather drastic structural changes is to allow excursions into four dimensional space 9 but this requires some extra programming beyond the standard capabilities of GROMACS Three possible energy minimization methods are e Those that require only function evaluations Examples are the simplex method and its variants A step is made on the basis of the results of previous evaluations If derivative information is available such methods are inferior to those that use this information Those that use derivative information Since the partial derivatives of the potential energy with respect to all coordinates are known in MD programs these are equal to minus the forces this class of methods is very suitable as modification of MD programs Those that use second derivative information as well These methods are superior in their convergence properties near the minimum a quadratic potential function is minimized in one step The problem is that for N particles a 3N x 3N matrix must be computed stored and inverted Apart from the extra programming to ob
285. ule of 2 273 SPC For the distribution function a maximum of 5 0 will be used Files enx ener edr Input Opt Generic energy edr ene f traj xtc Input Generic trajectory xtc trr trj gro g96 pdb s topol tpr Input Generic run input tpr tpb tpa n index ndx Input Opt Index file 0 Mtot xvg Output xvgr xmgr file a aver xvg Output xvgr xmgr file d dipdist xvg Output xvgr xmer file c dipcorr xvg Output Opt xvgr xmer file g gkr xvg Output Opt xvgr xmer file fa fitacf xvg Output Opt xvgr xmgr file q quadrupole xvg Output Opt xvgr xmer file Other options h bool no Print help info and quit nice int 19 Set the nicelevel b real 1 First frame ps to read from trajectory e real 1 Last frame ps to read from trajectory w bool no View output using xvgr or ghostview nframes int 10 Number of frames in trajectory overestimating is OK mu real 2 5 dipole of a single molecule in Debye mumax real 5 max dipole in Debye for histrogram epsilonRF real O epsilon of the reaction field used during the simulation needed for dieclectric constant calculation WARNING 0 0 means infinity de fault temp real 300 R temperature of the simulation needed for dielectric constant calculation avercorr bool no calculate AC function of average dipole moment of the simulation box rather than average of AC function per molecule firstatom bool no Use the first atom of a molecule water to calculate the distance between molecu
286. urierspacing 0 6 ewald_rtol le 5 The fourierspacing parameter times the box dimensions determines the highest mag nitude of wave vectors Mg My Mz to use in each direction With a 3 nm cubic box this example would use 11 wave vectors from 5 to 5 in each direction The ewald_rtol parameter is the relative strength of the electrostatic interaction at the cut off Decreasing this gives you a more accurate direct sum but a less accurate reciprocal sum 4 6 2 PME Particle mesh Ewald is a method proposed by Tom Darden 50 51 to improve the perfor mance of the reciprocal sum Instead of directly summing wave vectors the charges are assigned to a grid using cardinal B spline interpolation This grid is then Fourier trans formed with a 3D FFT algorithm and the reciprocal energy term obtained by a single sum over the grid in k space 4 6 Long Range Electrostatics 71 The potential at the grid points is calculated by inverse transformation and by using the interpolation factors we get the forces on each atom The PME algorithm scales as N log N and is substantially faster than ordinary Ewald summation on medium to large systems On very small systems it might still be better to use Ewald to avoid the overhead in setting up grids and transforms Using PME To use Particle mesh Ewald summation in GROMACS specify the following lines in your mdp file eeltype PME rvdw 0 9 rlist 0 9 rcoulomb 0 9 fourierspacing 0 12 pme
287. use their own preferred programming language Appendix C Long range corrections C 1 Dispersion In this section we derive long range corrections due to the use of a cut off for Lennard Jones interactions We assume that the cut off is so long that the repulsion term can safely be neglected and therefore only the dispersion term is taken into account Due to the nature of the dispersion interaction energy and pressure corrections both are negative While the energy correction is usually small it may be important for free energy calculations The pressure correction in contrast is very large and can not be neglected Although it is in principle possible to parameterize a force field such that the pressure is close to 1 bar even without correction such a method makes the parameterization dependent on the cut off and is therefore undesirable Please note that it is not consistent to use the long range correction to the dispersion without using either a reaction field method or a proper long range electrostatics method such as Ewald summation or PPPM C 1 1 Energy The long range contribution of the dispersion interaction to the virial can be derived analytically if we assume a homogeneous system beyond the cut off distance re The dispersion energy between two particles is written as V rg Corj C 1 and the corresponding force is Fi CG Ti C 2 The long range contribution to the dispersion energy in a system with N particles and
288. vent insertion into hydrogen bonds Files f traj xtc Input Generic trajectory xtc trr trj gro g96 pdb s topol tpr Input Generic run input tpr tpb tpa n index ndx Input Opt Index file sel select ndx Input Opt Index file num hbnum xvg Output xvgr xmgr file ac hbac xvg Output Opt xvgr xmer file dist hbdist xvg Output Opt xvgr xmer file ang hbang xvg Output Opt xvgr xmer file hx hbhelix xvg Output Opt xvgr xmgr file hbn hbond ndx Output Opt Index file hbm hbmap xpm Output Opt X PixMap compatible matrix file Other options h bool no Print help info and quit nice int 19 Set the nicelevel b real 1 First frame ps to read from trajectory e real 1 Last frame ps to read from trajectory ins bool no analyze solvent insertion a real 60 cutoff angle degrees Donor Hydrogen Acceptor r real 0 25 cutoff radius nm Hydrogen Acceptor E 24 g_helix 189 abin real 1 binwidth angle distribution degrees rbin real 0 005 binwidth distance distribution nm nitacc bool yes regard nitrogen atoms as acceptors E 24 g_helix g helix computes all kind of helix properties First the peptide is checked to find the longest helical part This is determined by Hydrogen bonds and Phi Psi angles That bit is fitted to an ideal helix around the Z axis and centered around the origin Then the following properties are computed 1 Helix radius file radius xvg This is merely the RMS deviation in two dimensions for
289. viscosity of spc and spc e water Comp Phys Comm 215 315 318 1993 Balasubramanian S Mundy C J Klein M L Shear viscosity of polar fluids Miolecular dynamics calculations of water J Chem Phys 105 11190 11195 1996 Kabsch W Sander C Dictionary of protein secondary structure Pattern recogni tion of hydrogen bonded and geometrical features Biopolymers 22 2577 2637 1983 Williamson M P Asakura T Empirical comparisons of models for chemical shift calculation in proteins J Magn Reson Ser B 101 63 71 1993 Berendsen H J C Grigera J R Straatsma T P The missing term in effective pair potentials J Phys Chem 91 6269 6271 1987 Bekker H Ontwerp van een special purpose computer voor moleculaire dynamica simulaties Master s thesis RuG 1987 van Gunsteren W F Berendsen H J C Molecular dynamics of simple systems Practicum Handleiding voor MD Practicum Nijenborgh 4 9747 AG Groningen The Netherlands 1994 220 BIBLIOGRAPHY Index Tt Er 1 4 interactions accelerate group afm pulling all hydrogen forcefield amdahl s law angle restraints angle vibration atom atom types autocorrelation function bond shell bond stretching bonded parameters born oppenheimer buckingham building block center of mass velocity charge group citing combination rules commercial use computational chemistry conjugate gradient constraint force constraint no connect constrain
290. y atomiss ao e e a Re E do A 4 6 Long Range Electrostatics o o 4 6 1 Ewald summation 2 000000 0005s 46 22 PME e A AE E a di MES PPPM ei r a a o dia y da 4 6 4 Optimizing Fourier transforms 4 7 All hydrogen forcefield 2 2 0 00 2 ee ee 4 8 GROMOS 96 notes 2 eae ee 4 8 1 The GROMOS 96 force field o o 4 8 2 GROMOS 96 files o 0 0000 o 5 Topologies pid nitro duction e A hte Bg is Bae A AAA es 524 Particle type id ais Ss ea TE E ERPS A MES 52a gt ATOM types der A Ee ek ae ee e ta Da2 Dummy atoms ii ia Be A A ee Bones Mik a AY Sle Hp het AE 5 3 Parameter files ac e tee Boe Fe ee ee Ea aR oe A aS DS AOS Gate NA a ate aT do aE age Be A te 5 3 2 Bonded parameters 2 0 a 5 3 3 Non bonded parameters 0 00 eee ee eee 5 3 4 Exclusions and 1 4 interaction o e 5 3 5 Residue database e 0 e o 5 3 6 Hydrogen database 2 2 0 0 00 0200008 5 3 7 Termini database e eee ee ee ee 5 4 Eile formats ase A E A RN 54I Topolosy file yns 4 eh Ma ia a MO ee oi aaa 5 4 2 Molec leitp file 2 A a a a a A 5 4 3 dekopo sorie 4s and pow EO Ge hee Be 5 4 4 Coordinate file 0 0 02 0200 eee ee eee 6 Special Topics 6 1 Calculating potentials of mean force the pull code 6 1 1 Overview ecu ok we aa oR Pe ee Ea eae A 6 1
291. ze ACF Order of Legendre polynomial for ACF 0 indicates none 0 1 2 or Number of parameters in exponential fit 1 or 2 Time where to begin the exponential fit of the correlation function Time where to end the exponential fit of the correlation function e Counting transitions only works for dihedrals with multiplicity 3 E 7 g bond g bond makes a distribution of bond lengths If all is well a gaussian distribution should be made when using a harmonic potential bonds are read from a single group in the index file in order il j1 i2 j2 thru in jn tol gives the half width of the distribution as a fraction of the bondlength blen That means for a bond of 0 2 a tol of 0 1 gives a distribution from 0 18 to 0 22 Files f traj xtc Input Generic trajectory xtc trr trj gro g96 pdb n index ndx Input Index file 0 bonds xvg Output xvgr xmgr file 1 bonds log Output Opt Log file Other options h bool no Print help info and quit E 8 g chi 177 nice int 19 Set the nicelevel b real 1 First frame ps to read from trajectory e real 1 Last frame ps to read from trajectory w bool no View output using xvgr or ghostview blen real 1 Bond length By default length of first bond tol real 0 1 Half width of distribution as fraction of blen aver bool yes Sum up distributions Diagnostics e It should be possible to get bond information from the topology E 8 g chi g chi computes phi psi omega and chi dihedrals for all your am

GROMACS USER MANUAL Version 2.0

Contents

Download Pdf Manuals

Related Search

Related Contents