BD BOX version 2.2 user`s manual – bd flex
Contents
1. 5 HYDRODYNAMICS AND BROWNIAN MOTION 13 AC alternate current field E E cos wt g 9 RF rotate field gt E E cos wt sin wt 0 y 10 where Ep 6 or Ep y or Ep z E is the magnitude of the external field and w its frequency Except for the rotate field all other fields act along the space fixed direction 4 4 Bounding Sphere A spherical surface impenetrable for molecules that encloses simulated system can be included in bd_flex simu lations The influence of such a containing sphere on the studied system is modeled by applying a central force of form gt A F Ep 11 Rsphere r where Rsphere is the radius of a spherical surface n is a nonnegative integer A is the amplitude of the force and r is the distance between a particular subunit and the system s centre of geometry The above force is applied to each of the studied subunits outside a predefined cutoff 5 Hydrodynamics and Brownian motion Brownian dynamics trajectories are generated using either the Ermak McCammon algorithm E M 10 or the two step predictor corrector algorithm developed by Iniesta and de la Torre IG T 11 5 1 Equations of Motions E M and I GT Algorithms An initial position of the it bead is described by r The position vector r after a time step At is computed using the following scheme 5 HYDRODYNAMICS AND BROWNIAN MOTION 14 predictor step iets s F ur PL2. aj STNYij 3r 5 T ri ksT_ 16rij as aj ai ay ar 30 ay 73 Fuh D J J T j j 7 PZA gs La Y Grasa 3213 U 321 E Sanem kgT ij 6rnas Tig lt a gt a lt where kp the Boltzmann constant T temperature I unit matrix 3x3 Dj 3x3 element of the 3Nx3N configuration dependent diffusion tensor a the hydrodynamic radius of a bead a gt the hydrodynamic radius of the larger bead 5 HYDRODYNAMICS AND BROWNIAN MOTION 16 a lt the hydrodynamic radius of the smaller bead Tij rij the distance between beads n solvent viscosity In case of finite size simulation cells containing the studied system when periodic boundary conditions are being used the form of the diffusion tensor presented above is not directly applicable We implemented in the bd_flex module of BD_BOX the direct Ewald summation procedure that leads to a periodic form of the diffusion tensor as proposed by Smith 8 Let s consider a cubic box with side L containing N spherical particles some of them may be connected with bonds with radii a Particle has position 7 With the center of the primary box at 0 0 0 we construct an array of its copies having centers at Lm with m being a vector of integer components Mm m1 mo m3 mi oo 00 im y m m m3 21 The magnitude of m is defined as m ma mal ms 22 In a given copy of the primary simulation box there ar
3. This can be done in one of the three ways One option is that the current step of a simulation is rejected positions of all subunits are reseted to initial ones and a new step is attempted with different random vector until there are no cases of overlap The second option is similar to the first however each of the subsequent attempts is made with a smaller time step After successful removal of overlaps the time step is restored to its initial value As a third option we also implemented the elastic collision method 16 in which all the collisions between subunits are considered explicitly as the elastic collision A numerical procedure applied at each step of a simulation locates time collision partners and parameters for every collision occurring in the system in chronological order and corrects positions of spherical subunits accordingly using laws of classical mechanics 7 RUNNING SIMULATIONS WITH BD_FLEX 19 OUTPUT restart E do trajectory PQR formatted structure a f control file simulation pqr debug info verification bd flex structure file out err 5777777707 INPUT Figure 2 bd_flex schematics 7 Running Simulations with bd flex Two input files are needed to perform BD simulations with the bd_flex module of BD_BOX Figure 2 The structure file str contains the definition of the molecular system to be simulated initial positions of beads Cartesian coordinates th
4. id 2 id 3 id 4 k Mm cos 6 where angle defines the form of the potential to be used Equation cos defines the form of the potential to be used Equation 5 kg the force constant 0 the equilibrium angle value cos 0 the phase m multiplicity 7 1 2 Simulation Control File The control file contains a number of keywords that allow the user to specify simulations conditions Only these lines in the control file that begin with a particular keyword are recognized by the program Each line of the prm file should contain only one keyword and its value keyword value The complete list of available keywords is given in the next section 8 Control File Keywords and Command Line Parameters Below a complete list of recognized keywords and their possible values is given Values of all keywords relevant to a simulation must be specified by the user default values that are given below are these at which program variables are initialized 8 CONTROL FILE KEYWORDS AND COMMAND LINE PARAMETERS 23 8 1 Input Output Control restart string this keyword indicates that a continuation run should be performed using the string restart file input restarts should be specified using command line out_filename string the name of the plain text output file save _xyz_freq integer value the frequency for writing to the XYZ trajectory file default 1 save_dcd_freq integer value the frequency for writing to the DCD traj
5. using a simple harmonic function 1 with kg being the force constant and 6 the equilibrium angle or more elaborate Vo ko 1 COS n COS mn n 5 where 6 0 or 6 m and m 1 2 6 4 POTENTIALS AND FIELDS 12 4 2 Nonbonded Potentials Nonbonded interactions implemented in BD_BOX bd_flex include electrostatics and repulsive attractive Lennard Jones interactions 4 2 1 Electrostatics The Debye Hiickel approximation 3 is used to model screened electrostatic interactions Two spherical subunits with central charges Q and Q interact via a pairwise additive potential of a form Q Q Vij EsTij exp kr 6 where s is the dielectric constant of the immersing medium k is the inverse of the Debye screening length and rij is the separation of charges 4 2 2 Lennard Jones Potentials Nonspecific interactions between subunits repulsive at small separations and attractive at large separations are evaluated using standard 6 12 Lennard Jones potentials ij 12 ij 8 OLJ oT Vij QELJ 7 Tij Tij where eL eL eL is the well depth and oj R R where R and R are hard core radii of interactin ij i og LJ j j 5 subunits It is also possible to model only purely repulsive interactions without the long range 4 term 4 3 Electric Fields It is possible to simulate with bd_flex the interactions of charged molecules with external electric fields DC direct current field
6. ER 1j 1 N 12 with lt i gt 0 i 1 N 13 and 28h P 2D A N 14 The above equations describe the E M algorithm 10 which is equivalent to the first order Euler algorithm except for the Brownian drift term In the IG T algorithm an additional corrector step is taken corrector step N 1 At gt hat Spr gt D Fe DE R 49 Sta 15 with lt RM gt 0 i 1 N 16 and R 1 u lt BYT gt 2 5 DI D At ij l N 17 where prime denotes that forces and diffusion tensors are evaluated for subunits in a configuration given with r in equations given above kp the Boltzmann constant T temperature Dj 3x3 element of the 3Nx3N configuration dependent diffusion tensor R random vector F total force acting on the it subunit 5 HYDRODYNAMICS AND BROWNIAN MOTION 15 The vector R representing random movement of all beads can be obtained from R SX 18 where the 3Nx3N tensor S is derived from tensor D by the relation D ss 19 and X is a 3Nx1 column vector the elements of which are random Gaussian numbers with zero mean and 2At variance bd_flex uses Cholesky decomposition of D to obtain matrices S 5 2 Diffusion Tensors For a system consisting of N spherical subunits with hydrodynamic radii a the following form of the 3Nx3N diffusion tensor is used 5 6 7 83 kgT D I 20 6mna 20 and kpT a a ET RT E A a Tig gt ai
7. and J A McCammon Flap opening dynamics in hiv 1 protease explored with a coarse grained model J Struct Biol 157 606 615 2007 A Arkhipov P L Freddolino and K Schulten Stability and dynamics of virus capsids described by coarse grained modeling Structure 14 1767 1777 2006 T Frembgen Kesner and A H Elcock Striking effects of hydrodynamic interactions on the simulated diffusion and folding of proteins J Chem Theory Comput 5 242 256 2009 G D R Echenique R R Schmidt J J Freire J G H Cifre and J G de la Torre A multiscale scheme for the simulation of conformational and solution properties of different dendrimer molecules J Am Chem Soc 131 8548 8556 2009 REFERENCES 33 27 28 29 30 31 32 33 34 N C Horton and J J Perona Crystallographic snapshots along a protein induced dna bending pathway Proc Natl Acad Sci USA 97 5729 5734 2000 W Humphrey A Dalke and K Schulten VMD Visual Molecular Dynamics J Mol Graphics 14 33 38 1996 J G de la Torre M L Huertas and B Carrasco Calculation of hydrodynamic properties of globular proteins from their atomic level structure Biophys J 78 719 730 2000 S Ludvigsen H Y Shen M Kjaer J C Madsen and F M Poulsen Refinement of the three dimensional solution structure of barley serine proteinase inhibitor 2 and comparison with the structures in crystals J Mol Biol 222 621 1991 Y Wang C Li and G J Pielak Eff
8. files are periodically updated during a BD run with frequencies defined by the user Having prepared control and structure files the user may run the simulation with the command bd_flex file prm It is also possible not to use the control file at all or to override all options specified in the control file us ing command line parameters that correspond to appropriate control file keywords bd_flex parameter value or bd_flex file prm parameter value 7 1 Input Files Both input str prm files are loosely formatted text files Below we describe their structure and some rules that must be followed upon their construction 7 1 1 Structure File The BD_BOX structure file contains the definition of the studied system initial positions of subunits beads their parameters such as charges and radii their bonded and nonbonded interactions parameters Meaningful lines in the structure file are these that begin with one of the words sub bond angle or dihe e sub lines each line describes a single spherical subunit and its parameters LJ sub name id x y z o Q 2R e m where 7 RUNNING SIMULATIONS WITH BD_FLEX 21 name the name of the subunit id an unique identifier assigned to the subunit integer x y z Cartesian coordinates of the subunit o the hydrodynamic radius of the subunit Q the central charge R the hard core Lennard Jones radius note that the value of R should be doubled i
9. shared memory machines using OpenMP and MPI libraries or on architectures with distributed memory using the MPI library GPU versions of BD_BOX binaries require the CUDA Toolkit obtainable freely at http developer nvidia com Both CPU and GPU versions can be compiled with the support for either single or double precision floating point arithmetic For the generation of random Gaussian numbers BD_BOX uses functions implemented in the GNU Scientific Library GSL http www gnu org software gsl that are based on the Mersenne Twister algorithm of Mat sumoto and Nishimura 19 We also implemented a function that uses the standard system routine drand48 and the polar Box Muller transformation 20 A generic sequential algorithm implemented in BD_BOX for the Cholesky factorization follows the choldc subroutine described in 21 However it is better to compile BD_BOX with the implemented support for the LAPACK or SCALAPACK library http www netlib org lapack that offers efficient highly memory optimized routines for the Cholesky factorization LAPACK performs the vast amount of operations by exploiting BLAS Machine specific implementations of BLAS are available and such implementations can be crucial for the per formance of BD_BOX The Cholesky factorization on GPU relays on the implemented support for the MAGMA dense linear algebra library http icl cs utk edu magma which provides functionality of LAPACK 2 Installation The con
10. BD BOX version 2 2 users manual bd flex Pawe Zieli ski Maciej D ugosz Copyright C 2010 2011 2012 2013 2014 University of Warsaw Pawe Zieli ski Maciej D ugosz This program is free software you can redistribute it and or modify it under the terms of the GNU General Public License as published by the Free Software Foundation either version 3 of the License or at your option any later version This program is distributed in the hope that it will be useful but WITHOUT ANY WARRANTY without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE See the GNU General Public License for more details You should have received a copy of the GNU General Public License along with this program If not see http www gnu org licenses Contact authors Pawe Zieli ski pzielinsOcent uw edu pl Maciej D ugosz mdlugoszOcent uw edu pl Work on the BD_BOX package is supported by National Science Centre grant number N N519 646640 BD_BOX is a scalable Brownian dynamics package for UNIX LINUX platforms BD_BOX is written in C and uses modern computer architectures and technologies e MPI technology for distributed memory architectures e OpenMP technology for shared memory systems e NVIDIA CUDA framework for GPGPU e SSE vectorization for CPU Within the BD_BOX framework macromolecules can be represented either with flexible bead models the bd_flex module of the BD_BOX package or as rigid
11. Lennard Jones potentials and hydrodynamic interactions evaluated based on the Cholesky decom position of the diffusion tensor Bonded interactions include flexible bonds and deformable planar angles DNA_BSPHERE 20 DNA like polymers see above enclosed inside of a bounding sphere Hydrodynamic interactions are evaluated based on the TEA HI approach HARD_SPHERES HARD_SPHERES_CUDA the periodic system of hard spheres 512 beads Overlaps are corrected using the elastic collision method Hydrodynamic interactions are evaluated based on the Cholesky 10 FINAL NOTES 30 decomposition of the Ewald summed diffusion tensor GPU and CPU simulation setup files are included DBELLS_EXT_E a periodic system containing 256 spring bead dimers with oppositely charged beads Non bonded interactions between dimers are evaluated using screened electrostatics and Lennard Jones potentials Dimers move under the influence of an external electric rotate field Hydrodynamic interactions are evaluated based on the Cholesky decomposition of the Ewald summed diffusion tensor A GPU simulation setup file is included CI2_CHOLESKY CI2_TEA_HI a hydrodynamic model of the chymotrypsin inhibitor 2 protein see Fig ure 1 Reduced representation of the protein with beads positioned on atoms Ca Beads within the distance of 15A are connected with harmonic springs 10 Final Notes We did our best to ensure that the BD_BOX code is bug free We have tested i
12. athods for computing hydrodynamic interactions in Brownian dynamics simulations J Chem Phys 137 064106 2012 REFERENCES 32 15 16 17 18 19 20 21 22 23 24 25 26 M X Fernandes and J G de la Torre Brownian dynamics simulations of rigid particles of arbitrary shape in external fields Biophys J 83 3039 3048 2002 P Strating Brownian dynamics simulations of hard sphere suspension Phys Rev E 59 2157 2187 1999 J Sun and H Weinstein Toward realistic modeling of dynamic processes in cell signaling Quantification of macromolecular crowding effects J Chem Phys 127 155105 155115 2007 S R McGuffee and A H Elcock Atomically detailed simulations of concentrated protein solutions the effects of salt pH point mutations and protein concentration in simulations of 1000 molecule systems J Am Chem Soc 128 12098 2006 M Matsumoto and T Nishimura Mersenne twister A 623 dimensionally equidistributed uniform pseudo random number generator ACM Transactions on Modeling and Computer Simulation 8 330 1998 G E P Box and M E Muller A note on the generation of random normal deviates Annals Math Stat 29 610 611 1958 W Press B Flannery S Teukolsky and W Vetterling Numerical recipes in C the art of scientific computing Cambridge University Press 1992 V Tozzini Multiscale modeling of proteins Acc Chem Res 43 220 230 2010 V Tozzini J Trylska C E Chang
13. bodies the bd_rigid module of the BD_BOX package When flexible models are employed each molecule consists of a various number of spherical subunits beads connected with deformable bonds 1 2 Bonded interactions that result in deformations of planar and dihedral angles can be also modeled Direct nonbonded interactions between molecules are evaluated using pairwise functions describing screened electrostatics in dielectric media 3 with effective charges assigned to spherical subunits 4 and Lennard Jones potential types The far field hydrodynamic effects are modeled using the config uration dependent Rotne Prager Yamakawa mobility tensor 5 6 7 or its Ewald summed form in case of periodic systems 9 Equations of motions are propagated using either the Ermak McCammon scheme or the predictor corrector IG T algorithm by Iniesta and Garcia de la Torre 11 Hydrodynamically correlated random displacements are generated either via the Cholesky factorization of the configuration dependent mobility tensor matrix 10 using the TEA HI approach proposed by Geyer and Winter 12 13 or with an approach described by Ando and Skolnick that utilizes Krylov subspaces With BD_BOX one can simulate flexible molecules in homogeneous flows 2 or external electric fields direct alternate or rotating fields With BD_BOX one can also simulate rigid bodies described with fully anisotropic diffusion tensors 15 Molecules treated as rigid bodies can b
14. cules such as amino or nucleic acids 23 Various levels of resolution are possible and different modeling approaches can be applied 24 BD_BOX does not offer a separate tool dedicated to build and parametrize molecular models based on atomic structures of molecules However most of the coarse grained models share the concept of a reduced representation with pseudo atoms beads that represent groups of atoms and such models can be easily incorporated in BD_BOX bd_flex simulations 25 2 26 Spherical subunits are assigned hydrodynamic radii so that the overall diffusive properties of a coarse grained model correspond to the measured or computed properties of real molecules Subunits hydrodynamic radii values can be parametrized for example using the rigid body hydrodynamic calculations 29 Additionally each subunit is assigned a hard core radius Figure 1 used to evaluate Lennard Jones interac tions The hydrodynamic and the hard core radius of a given subunit can be different 4 Potentials and Fields Below we present bonded and nonbonded interactions potentials currently implemented in the bd_flex module of the BD_BOX package 4 1 Bonded Potentials 4 1 1 Bonds The following potential is considered to model connections between spherical subunits beads i and j 2 2 1 Tmax Vij 1 Tra Ti AIC To V H z l J A 5 l 1 ij 5 Tmax N Es 72 5 Tmax o In rg Tman za ro where ro the equ
15. e N particles with particle at Lm r The array consists of those copies for which Lm lt R with R oo In the system defined above the diffusion tensor is given by kgT 3a Tij a o Dij 651 O 2 j wer j pic FE za Qeno 7 23 where I is 3x3 identity matrix and d is the Kronecker s delta Following the notation introduced in the work Bl of Smith et al 8 we introduce SIS O r I 67 Q 1 3 f 24 and o BJ lt 25 z 25 5 HYDRODYNAMICS AND BROWNIAN MOTION 17 Now for 6 4 m interactions between different particles within the primary cell or between a particular particle in the primary cell with an image of other particle we have the following Ewald formulas 8 zj 2a a02 m m G m a Orca 5 lerfFelalii DO i a The ee 2 _ 22 kije T2 m ae a2 sa k 1 a jas 26 0 T m Y ra A A VT m o 22 EE 4n je a Tia 27 fi40 gt Additionally for m interactions between a particular particle in the primary cell with its self images across the array we have 8 gt 2 OpBc m gt gt er fe a O m Op m0 304 I 27L 2 n n nen NE S dae zo ar ca 4m ee Ant 29 In the equations given above erfc is the complementary error function Vectors m and ri have integer components Summations over the vectors ri and m give reciprocal and real space co
16. e described either using a coarse grained representation or with fully atomistic details ln the latter case intermolecular interactions may include electrostatic hydrophobic and Lennard Jones potentials External electric fields can also be applied to simulated systems Hydrodynamic interactions between molecules modeled within the rigid body framework are currently not supported BD_BOX simulations can be performed without or with boundaries in the latter case containing or periodic boundary conditions can be used With BD_BOX one can effectively simulate either single molecules or multi molecular systems composed of large numbers of different species For efficient simulations of dense systems we implemented algorithms preventing the overlapping of diffusing molecules 16 17 18 This manual describes the usage of the bd_flex module of the BD_BOX package The bd_rigid module for rigid body BD simulations is described separately CONTENTS 4 Contents 6 2 Installation 6 Bead Models 9 4 Potentials and Fields 9 4 1 Bonded Potentiala a a a a a 9 AV ll BONAS E ed iria e e nie o elo Ba ae oe She es ea do 9 41 2 ANGIE wew a pon Baw ee A A a a a Be ee iD oki aao 11 ALS bihedrals ini e a godne wi b w e o a ee eae y A a G 11 4 2 _Nonbonded Potentials LL a a aa a a a a 12 4 2 1 Electrostaticsl 12 4 2 2 Lennard Jones Potentials 2 12 4 3 Electric Fi lds escorias a zadba be mara RS ee h
17. eal 331 842 elec yes no whether electrostatic interactions should be evaluated default yes bond_Ij_scale float the scaling factor for Lennard Jones interactions between bonded 1 2 pseudoatoms default 1 0 bond_c_scale float the scaling factor for electrostatic interactions between bonded 1 2 pseudoatoms de fault 1 0 nb_list string this keyword specifies the algorithm used to create nonbonded interactions lists brute de fault brute force spatial grid based verlet explicit creation of Verlet lists verlet_count integer frequency of re creation of nonbonded interactions Verlet lists default 1 8 CONTROL FILE KEYWORDS AND COMMAND LINE PARAMETERS 25 verlet_roff float outer cutoff for creation of nonbonded interactions Verlet lists default 10 0 8 3 Boundaries xbox float the primary simulation cell size in the x direction default 0 0 ybox float the primary simulation cell size in the y direction default 0 0 zbox float the primary simulation cell size in the z direction default 0 0 NOTE Currently only cubical boxes are supported in case of Ewald summed diffusion tensors bc string boundary conditions to be used either none pbc in case of periodic boundary conditions or sphere default none sboundary yes no whether to use the bounding sphere potential Equation 11 default no Note that this keyword has nothing to do with the bc keyword if bc sphere is used molecu
18. ectory file default 1 save_rst_freq integer value the frequency for writing to the restart file default 1 save_enr_freq integer value the frequency for writing to the energy file default 1 str_filename string the name of the input structure file xyz_filename string the name of the XYZ trajectory file output dcd_filename string the name of the DCD trajectory file output enr_filename string the name of the energy file output rst_filename string the name of the restart file to be written pqr_filename string the name of the PQR structure file output 8 CONTROL FILE KEYWORDS AND COMMAND LINE PARAMETERS 24 8 2 Nonbonded Interactions alpha_lj float the a Equation 7 parameter for Lennard Jones interactions scaling typically 4 0 default 4 0 cutoff_lj float the cutoff radius for Lennard Jones interactions default 0 0 Setting the cutoff_lj to 1 re sults in cutoffs defined for each pair of the subunits as 26 R Rj lj_6_term yes no whether to use the 4 term in the Lennard Jones potential Equation 17 default yes r epsilon_c float the dielectric constant of the immersing medium water default 78 54 kappa_c float the inverse of the Debye screening length the x parameter in Equation 6 default 0 1 cutoff_c float the cutoff radius for electrostatic interactions default 0 0 gamma_c float unit conversion factor the y parameter in the Equation 6 default conversion to g
19. ects of proteins on protein diffusion J Am Chem Soc 132 9392 2010 B Carrasco and J G de la Torre Hydrodynamic properties of rigid particles comparison of different modeling and computational procedures Biophys J 76 3044 3057 1999 P J Zuk E Wajnryb K A Mizerski and P Szymczak Rotne Prager Yamakawa approximation for different sized particles in application to macromolecular bead models J Fluid Mech 741 R5 2014 T Zhou and B Chen Computer simulations of diffusion and dynamics of short chain polyelectrolytes J Chem Phys 124 034904 2006
20. ee DR eR ik mdli BA sa DRE ES 12 4 4 Bounding Sphere 2 aa e 13 5 Hydrodynamics and Brownian motion 13 5 1 Equations of Motions E M and I GT Algorithms 20 00008 13 5 2 Diffusion Tensor 15 6 Overlaps 18 f Running Simulations with bd_flex 19 TA Input Files 244 544 244 e mese be ba Bed be ed ee BREE EEE EEE ta 20 7 1 1 tr ct re Eilef s lt x e249 2 005 GMa Bach Bo Boke BA SI Sos SE rk OE AE ga 20 1 12 imulation Control File 0 a a a a 22 8 Control File Keywords and Command Line Parameters 22 8 1 Input Output Control a 5 obs howe oe ee ee ee ee eee oe RKA 23 8 2 Nonbonded Interactions 2 2 a a a a a 24 CONTENTS 8 amp 3 BOU JAKIE a as Ww m ZR bw e ARE dee RE Ee aa RA SS 8 4 External Electric Fields 2 a a 9 5 IFIOWSJE eo 006 aa a a Gab wie oai ws go m GM a A Oe ae Oe lt a l Boi de e 9 BoE R W Wg ACK 8 6 Devices Controll LL LL Loo 8 1 AlgorithMS 4 4 934245 445 64844464 64 646 44546 G4 oma do 5 244 04 8 8 Physical Conditions a saa aa oe maa a pag PR CE Sar HGR PE RG bee eR 4 a 6 EK 9 Examples distributed with BD_BOX 0 Final Notes 25 26 27 27 28 29 29 30 1 REQUIREMENTS 6 1 Requirements The BD_BOX package is distributed as source code A UNIX LINUX make tool is needed to build a working binary from source code see below CPU versions of BD_BOX binaries can be run either in a serial mode or in parallel either on
21. eir identifiers name and index their parameters such as radii charges masses well depths of Lennard Jones interactions and their connectivities bonds planar angles and dihedrals Simulation parameters are stored in the text control file prm Figure 2 These include for example the type of the propagation algorithm and its time step temperature viscosity ionic strength definition of boundaries the treatment of hydrodynamic interactions values of cutoffs for nonbonded interactions specifications of the output names and types of files write frequency path to the input structure file and many others The output from bd_flex consists of a few files Figure 2 The output file out err contains the track of the BD run error messages if any and debugging information Another file in the PQR format pqr contains the definition names coordinates charges and radii of beads of the molecular system under study it can be used to verify the starting configuration of molecules and also together with a trajectory file to visualize results The trajectory file either in the binary DCD or text XYZ format dcd xyz defines the behavior of 7 RUNNING SIMULATIONS WITH BD_FLEX 20 the studied system along time The energy file enr registers different contributions to the total energy of the system during a simulation The binary restart file rst contains all the information needed to continue an interrupted BD run All
22. electric field Equations 9 and 10 possible values are AC DC or RF default DC E_freq float the frequency where applicable of the external electric field units FH default 0 0 E_dirl string the direction of the external electric field x y or z default x E_dir2 string the second direction of the external electric field RF x y or z default y E_factor float the unit conversion factor for the external electric field to keal e 1 4 1 default 1 0 8 CONTROL FILE KEYWORDS AND COMMAND LINE PARAMETERS 27 8 5 Flows vel_grad_tensor float float float float float float float float float the velocity gradient tensor G i j where i runs over rows and j runs over columns G 1 1 G 1 2 G 1 3 G 2 1 G 2 2 G 3 3 default 9x 0 0 8 6 Devices Control MPLnprow integer the number of rows in the processor grid default 0 MPLnpcol integer the number of columns in the processor grid default 0 MPL block integer the size of a block in the processor grid default O this value should be less than the rank of the diffusion tensor matrix cuda_devices integer integers this keyword specifies CUDA devices to use their number followed by their system identifiers cuda_block integer this is the dimension of the thread block possible values are 32 64 128 256 512 1024 The value of the cuda_block parameter depends on the hardware device and the number of beads in the simulated system default 256
23. figure shell script written by GNU Autoconf is used to build the BD_BOX binaries After unpacking the compressed BD_BOX archive gzip d bd_box ver tar gz tar xvf bd_box ver tar the user should execute the configure script from within the BD_BOX directory 2 INSTALLATION 7 cd bd_box ver configure configure takes instructions from Makefile in and builds Makefile and some other files that work on the user s system We provide the INSTALL file and some other files consult the README file in the bd_box ver directory with flags and options that can be passed to the configure script to tune the compilation on particular systems Next the make command followed optionally by the make install should be executed As a result of the compilation process two binaries bd_flex and bd_rigid should be created either within the bd_box ver src directory or in the directory passed by the user to the configure script with the prefix option It is possible to prevent compilation of either one of binaries using disable flex or disable rigid flags 2 INSTALLATION Units charge e length A time ps temperature K kcal energy o viscosity Poise 3 BEAD MODELS 9 3 Bead Models The bd_flex module of BD_BOX utilizes coarse grained models of molecules see for example Figure i Each model consists of a number of spherical subunits beads Beads can be placed for example on repeating units of biomole
24. ilibrium bond length Tmax the maximum bond length 4 POTENTIALS AND FIELDS 10 Figure 1 Exemplary bead models hydrodynamic subunits are shown as transparent spheres Top DNA double helix taken from 2 Middle EcoRV endonuclease PDB ID 1EOOJ 2 radii of opaque beads define excluded volume interactions in multicomponent systems The presented coarse grained model of the EcoRV molecule was created using the CG Builder module from the VMD 28 package Hydrodynamic radii of beads were computed using the HYDROPRO suite 29 Bottom Chymotrypsin inhibitor 2 PDB ID 3CI2 30 Hydrodynamic radii of beads were parametrized based on BD simulations with experimental data 31 and HYDROPRO 29 calculations as a reference 4 POTENTIALS AND FIELDS 11 H the force constant rij the distance between beads centers With an appropriate choice of parameters H and rmazx 26 2 this potential can describe either harmonic or FENE finite extensible nonlinear elastic bonds The number of bonds originating from a given subunit is unlimited 4 1 2 Angles Potential associated with the deformation of a planar angle n can be either of form 1 o 2 Vin z cos bn cos 6 2 or 1 O Vin H nl n Pn 3 with ky being the force constant and the value of a given angle at the equilibrium 4 1 3 Dihedrals Rotation around a bond connecting beads the deformation of a dihedral angle 0 is currently modeled either
25. les are not allow to cross a spherical surface around the studied system but no potential is used for that rather BD moves leading outside the spherical surface are simply rejected an repeated with different random vectors sphere_radius float the radius of the bounding sphere default 0 0 This keyword applies either when bc sphere or sboundary yes is specified sboundary_A float the magnitude of the bounding sphere force the A parameter in Equation default 0 0 sboundary_n integer the power of the radial distance dependence of the bounding sphere force the n pa rameter in Equation 11 default 0 0 8 CONTROL FILE KEYWORDS AND COMMAND LINE PARAMETERS 26 sboundary_cutoff float the bounding sphere force is applied outside this cutoff radius default 0 0 ewald_real integer the magnitude of the real lattice vectors Equation Equations 26429 default 0 ewald_recip integer the magnitude of the reciprocal lattice vectors Equation 22 Equations 26429 default 0 ewald_alpha float this parameter controls the convergence of the Ewald summation a in Equations 26429 default 7 ewald_method string the method used to build the Ewald summed diffusion tensor default smith as in 8 4 External Electric Fields E_ext yes no whether to switch on off the external electric field default no E_magn float the magnitude of the external electric field default 0 0 E_type string a choice between different types of the
26. mplemented features using rather simple and thus predictable models such as single spheres dumbbells chains but also more elaborate models of proteins Properties of these models derived from BD simulations such as for example translational and rotational diffusion coefficients at different conditions of temperature and viscosity chains end to end distances and their radii of gyration were validated using theoretical analytical predictions and available literature data Additionally we have also cross examined BD_BOX using various hardware platforms We invite users to send comments and questions regarding their own applications of BD_BOX Reports on possible bugs are also welcomed References 1 K Kremer and G S Grest Dynamics of entangled linear polymer melts A molecular dynamics simulation J Chem Phys 92 5057 5087 1990 2 J G de la Torre J G H Cifre A Ortega R R Schmidt M X Fernandes H E P S nchez and R Pamies Simuflex algorithms and tools for simulation of the conformation and dynamics of flexible molecules and REFERENCES 31 3 4 5 6 7 8 9 10 11 12 13 14 nanoparticles in dilute solution J Chem Theory Comput 5 2606 2618 2009 G M Bell S Levine and McCartney L N Approximate methods of determining the double layer free energy of interaction between two charged colloidal spheres J of Colloid Int Sci 33 335 359 1970 M Aubouy E Trizac a
27. n the structure file e J Lennard Jones well depth m mass mass is only needed when the elastic collision method is to be used during the simulation However this column is obligatory As only the ratio of masses of different subunits is important during evaluation of collisions within pairs of particles one does not need to care about units and particular values e bond lines each line define a single bond and its parameters Equation 1 bond id 1 id 2 to ma H where id 1 and id 2 identifiers of subunits to be connected fo the equilibrium bond length Fmax the maximum bond length H the force constant e angle lines each line defines a single planar angle between bonds connecting subunits id 1 id 2 and id 2 id 3 Currently two types of the planar angle potential are supported angle angle id 1 id 2 id 3 ky angle cos id 1 id 2 id 3 9 k where angle defines the form of the potential to be used Equation cos defines the form of the potential to be used Equation 2 id 1 id 2 id 3 identifiers of subunits in the planar angle the equilibrium angle value k the force constant 8 CONTROL FILE KEYWORDS AND COMMAND LINE PARAMETERS 22 e dihe lines each line defines a single dihedral angle subunits id 1 id 2 id 3 id 4 rotation around the id 2 id 3 bond Two types of the dihedral angle potential are supported dihe angle id 1 id 2 id 3 idf4 0 ko dihe cos id 1
28. nd L Bocquet Effective charge versus bare charge an analytical estimate for colloids in the infinite dilution limit J Phys A Math Gen 36 58355840 2003 J Rotne and S Prager Variational treatment of hydrodynamic interaction in polymers J Chem Phys 50 4831 4838 1969 H Yamakawa Transport properties of polymer chains in dilute solution hydrodynamic interaction J Chem Phys 53 436 444 1970 J G de la Torre and V A Bloomfield Hydrodynamic properties of macromolecular complexes i translation Biopolymers 16 1747 1763 1977 E R Smith K Snook and W van Megen Hydrodynamic interactions in brownian dynamics simulations i periodic boundary conditions for computer simulations Physica A 143 441 467 1987 C W J Beenakker Ewald sum of the rotne prager tensor J Chem Phys 85 1581 1582 1986 D L Ermak and J A McCammon Brownian dynamics with hydrodynamic interactions J Chem Phys 69 1352 1360 1978 A Iniesta and J G de la Torre A second order algorithm for the simulation of the brownian dynamics of macromolecular models J Chem Phys 92 2015 2019 1990 U Winter and T Geyer Coarse grained simulations of a small peptide Effects of finite damping and hydrodynamic interactions J Chem Phys 131 104102 104107 2009 T Geyer and U Winter An o n2 approximation for hydrodynamic interactions in brownian dynamics simulations J Chem Phys 130 114905 114913 2009 T Ando and J Skolnick Krylov subspace m
29. ntributions to the diffusion tensor The above equations can be extended to a system of spherical particles with different radii a One need 6 OVERLAPS 16 only replace in each of the above equations the radius a to the first power by a and the radius a to the third power by za a a 9 An additional modification of the original formulation of Smith et al is a correction to the final form of the periodic form of the diffusion tensor that allows for overlaps between spherical particles overlap __ a Dig Dig Aig Bi _ ABT 16r as aj a aj ri 3 a az ro ryt a gt a lt lt ry lt a as 2 Grasa 32r3 3213 r2 eS tay AE e kgT a Grands Tig lt a gt a lt kgT Tij gt ai aj a aj a a Tyt 1 2 T 1 2 2 Sri fij Tj where Dj is the Ewald summed 3 x 3 diffusion tensor for the two overlapping particles or particle and an image 30 of another particle and j given with Equation 23 6 Overlaps The presence of a Gaussian random displacement vector in the BD integration scheme Equations 12 may lead to nonphysical overlaps between beads Overlaps occur when the distance between any two subunits is smaller than the sum of their hard core radii bd_flex can check whether a particular simulation step leads to an overlap between subunits Next positions of subunits are corrected to remove all cases of overlaps
30. teger the number of attempts of repeating a particular simulation step with a different random vector when overlaps between beads are detected in the system When this number is exhausted and there still are overlaps the program will stop default 10000 geyer_on_the_fly yes no whether to compute hydrodynamically correlated random displacements within the TEA HI framework using the whole diffusion tensor matrix no or to save memory using 3x3 submatrices yes default yes lanczos_m number of steps in both of the Lanczos approaches 14 default 4 9 EXAMPLES DISTRIBUTED WITH BD_BOX 29 lanczos_s size of the normal vector block in the block variant of the Lanczos approach 14 default 4 e_collision float the restitution parameter used in the elastic collision approach falls between 0 0 perfectly inelastic collisions and 1 0 perfectly elastic collisions default 1 0 8 8 Physical Conditions T float temperature K default 298 15 visc float viscosity Poise default 0 01 vfactor float factor for conversion of viscosity units default 14 4 to convert from Poise to kcal ps AB should be set to 14 4 9 Examples distributed with BD_BOX Below we present a list of examples that are distributed along with the BD_BOX source code Examples are located in examples flex name directories DNA a single DNA like polymer composed of touching beads 52 beads with excluded volume interactions modeled via
31. this keyword is relevant in case of devices with compute capability less than 2 0 NOTE MPI_nprow x MPI_npcol should be equal or lesser than the number of computational nodes used Keywords MPI_nprow MPI_npcol and MPI_block are relevant only when SCALAPACK is being used 8 CONTROL FILE KEYWORDS AND COMMAND LINE PARAMETERS 28 8 7 Algorithms dt float the time step in ps default 0 0 bdsteps integer the total number of simulation s steps default 0 hydro string the method used to evaluate hydrodynamic interactions can be set to none a diagonal form of the diffusion tensor will be used throughout the simulation cholesky Cholesky decomposition of the diffusion tensor matrix 10 geyer the TEA HI method of Geyer and Winter 13 lanczos the Krylov subspace approach or blocklanczos the block variant of the Krylov subspace approach 14 algorithm string algorithm for the trajectory generation Possible values are igt_const igt_var ermak_const ermak_var ermak_newton igt ermak means that either the Ermak algorithm or the IG T algorithm will be used either with a constant or variable time step const var The elastic collision method can be switched on by setting algorithm to ermak_newton rand_seed integer a seed for the random number generator default 12345 check_overlap yes no whether to check for overlaps in the studied system after each simulation s step de fault yes move _attempts in
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