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1. integer serial data file containing integers swap serial data file containing integers with reversed byte ordering text data fle that can be read with F ORTRAN 77 list directed input easy or xeasy submatrix 8 or 16 bit data fle of the program XEASY Bartels et al 1995 vnmr data fle in the format of the Varian VNMR program Varian Associates Inc 1993 flename Name of the input data fle In the case of the format easy two fles will be read a XEASY parameter fle called flename 3D param and the data fle flename 3D 8 or flename 3D 16 respectively and the system variables for calibration will be set according to the XEASY 27 Commands Np fa f2 real parameter fle Number of real or complex data points to read in dimension amp If a c follows the number n complex data are read otherwise real data are read n has to be specifed with the formats real integer swap text and optionally vnmr If the number of points is not given for a fle in vnmr format the program assumes a two dimen sional data set with complex data in both dimensions and one FID per trace and extracts the number of data points from the fle head er In the case of the format easy the corresponding numbers are read from the XEASY parameter fle and real data are read from the data fle In its present version the program can handle 2D 3D and 4D data sets A one dimensional data set is formally treated as a two dimensi
2. PROSA Version 3 4 User s Manual Peter G ntert Institut f r Molekularbiologie und Biophysik Eidgen ssische Technische Hochschule CH 8093 Z rich Switzerland December 1994 1994 Institut f r Molekularbiologie und Biophysik Eidgen ssische Technische Hochschule CH 8093 Z rich Switzerland Contents Introduction 5 Installation 7 Command Interpreter 11 Commands 21 Variables 33 Macros 37 Examples 41 Algorithms 49 References 57 Introduction The program package Prosa Processing algorithms allows to perform the pro cessing steps that lead from the time domain data furnished by the NMR spectrometer to the multi dimensional spectrum Its functions include linear prediction apodiza tion Fourier transformation automatic phase correction baseline correction and for matting of the output for easy use with spectrum analysis programs The design of the program is simple both because it does not use computer graph ics and the complete multi dimensional data matrix is kept in memory throughout the processing Therefore the implementation of the program on a variety of different computers is straightforward and time consuming data processing can be executed in batch mode The fully processed spectra can then be displayed on a conventional graphics station In the present implementation the output of PROSA is compatible with the program package XraAsy Bartels et al 1994 Eccles et al 1991 Since PROS
3. amp Withric h K 1992 A new procedure for high quality baseline correction of two and higher dimensional NMR spectra J Magn Reson 96 403 407 Gintert P D tsch V Wider G amp Withric h K 1992 Processing of multi dimensional NMR data with the new software PROSA J Biomol NMR 2 619 629 KieBling I amp Lowes M 1987 Programmierung mit FORTRAN 77 Teubner Stuttgart Kumaresan R amp Tufts D W 1982 Estimating the parameters of exponentially damped si nusoids and pole zero modeling in noise IEEE Transactions on Acoustics Speech and Sig nal Processing ASSP 30 833 840 Marion D amp Bax A 1989 Baseline correction of 2D FT NMR spectra using a simple linear prediction extrapolation of the time domain data J Magn Reson 83 205 211 Olejniczak E T amp Eaton H L 1990 Extrapolation of time domain data with linear predic tion increases resolution and sensitivity J Magn Reson 87 628 632 Otting G Widmer H Wagner G amp Withric h K 1986 Origin oft and ts ridges in 2D NMR spectra and procedures for suppression J Magn Reson 66 187 193 Pearson G A 1977 A general baseline recognition and baseline fhttening algorithm J Magn Reson 27 265 272 Press W H Flannery B P Teukolsky S A Vetterling W T 1986 Numerical Recipes The art of scientife computing Cambridge University Press Cambridge Qian Y Q Otting G Billeter M Miller M Ge
4. eject ejects the plot noeject does not eject the plot The options grid margin and except for the HP 7596A plotter eject are set by default 25 Commands EE 26 100 200 300 1 f 1 1 r 200 NS 5 acs Contour plot produced with the PROSA com mand plot of part of a SC 1H COSY spec trum of a complex be tween the Antenna 1100 pedia C39S homeo domain and a DNA 14 mer Qian et al 1993 The spectrum shows correlations be tween 1 C and H at ee oms of aromatic rings co ve The default values were used for all pa rameters of the plot command 13C data points Pr T T r T r T T r T 100 200 300 H data points The default values for the parameters o size o offset a margin o label and a tics depend on the format and are chosen such that the plot makes good use of the available paper size To use the default value for a parameter an asterisk may be specifed power replaces the data in the active dimension by its squared absolute value power spectrum s gt Is predict method m n k k l calculates complex data points in the active dimension using linear prediction see p 52 with the following parameters method must be lpsvd in the present version of PROSA i e the linear pre diction coefftients are calculated with singular value decomposi tion Number of linear prediction coefftients in Eq 16 n Number of
5. FORTRAN 77 format Use of substrings Assignment to a substring Use of The evaluation of the values of variables in the command line goes from right to left This allows for example the use of indexed variables in a loop assuming ndim 2 ndata 2048 512 print Dimension i ndata i points end do Dimension 1 2048 points Dimension 2 512 points System variables are variables that are set and used by the program not exclu sively by the user with eval set etc The following section gives an alphabetical list The form variable is preferable for variables that occur in UNIx shellscripts because it avoids the evaluation by the UNIX shell 17 Command Interpreter DS 18 of all system variables Write protected variables cannot be changed explicitly by the user Only system variables may be write protected Global variables are always visible except when they are hidden by local variables with the same name Variables that are not declared in a var statement or passed as parameters to a macro are global In particular all system variables are global vari ables Local variables exist only within the macro where they are declared and in mac ros called from this macro Local variables must be declared in a var statement or passed as parameters to a macro see p 37 The following variables are used by the command interpreter echo determines which commands are echoed i e copied t
6. and n denote integer expressions n denotes the data point n m n includes the data points m m 1 n m includes the data points m m 1 up to the last data point n includes the data points 1 2 n stands for all data points On the command line a minus sign separates the last region from 23 Commands the frst base function function denotes a base function that is used to represent the baseline distor tions Any integer or real FORTRAN 77 expression can be used to specify these functions a lowercase k denotes the data point k ft IN In ne 0o 6 1 option executes a Fourier transformation in the active dimension With real input data a real Fourier transformation is performed with complex input data a complex Fou rier transformation is performed After Fourier transformation the data are al ways complex Prior to Fourier transformation the data are zero flled to N complex data points N must be a power of 2 If N is not specifed the program zero flls up to the next power of 2 if necessary Upon request i e if n and n are given the program retains only the strip consisting of the frequency domain data points ny Ne If phase correction parameters 6 and are given the program performs a phase correction according to Eq 23 and discards the imaginary parts of the data Given the option full the phase correction parameters 6 and 6 refer to the full spectral width otherwise with the de
7. are printed in bold and comments are printed in Helvetica set timing 1 Show the CPU time for commands that take more thanis of CPU time read swap fles nmr vd ser 1024c 100c The time domain data consist of 1024 complex data points in the first aquisition dimension and 100 complex data points in the second in direct dimension The data are stored as integer numbers with inverted byte ordering in a serial file called files nmr vd ser see p 27 status Show the size and organization ofthe data suppress cos 30 The residual water signal that has frequency zero in the aquisition di mension is suppressed using the macro suppress see p 39 print print Dimension 1 2 Processing of the aquisition dimension print multiply 0 5 1 Scale the first data point by 1 2 window cos Cosine window see p 40 ft 1024 Fourier transformation with zero filling to 1024 complex data points status Show the size and organization of the data print print Dimension 2 2 Processing of the second dimension print dimension 2 Transposition that activates the second dimension Examples BSS multiply 1 2 n 2 Change sign of every second data point States TPPI window cos Cosine window see p 40 ft 256 Fourier transformation with zero filling to 256 complex data points print print Phase correction print dimension 1 Re activate the aquisition dimension autophase 10 2 0 10 0 10 0 Automat
8. computer with one real data point per 32 bit word Data fles written with real format contain the data with full accuracy but are machine dependent In the format integer the data are stored in the binary integer number format of the giv en computer with one real data point per 32 bit word In principle integer format fies are also machine dependent but because most computers use the same binary rep resentation of integer numbers such fies can in general be used on various computers In the format swap the data are stored with inverse byte ordering in the binary inte ger number format of the given computer with one real data point per 32 bit word i e the 4 bytes 1 2 3 4 of an integer number are stored in the order 4 3 2 1 This for mat is useful to read integer data from a computer that uses inverse byte ordering with respect to the given machine but otherwise identical representation of integers For example Bruker X32 computers use inverse byte ordering when compared to Sun Convex and NEC SX3 computers Text is a simple ASCII format using the FORTRAN 77 format 1PE12 4 for output and list directed free format FORTRAN 77 input This format is primarily designed to store small 1D data sets for use with simple sim ulation programs or graphics programs such as GNUPLOT The format xeasy8 uses a logarithmic representation of the data with 1 byte per real data point Bartels et al 1995 Xia amp Bartels 1993 For a given data po
9. is ob tained by suitable transpositions of the data set Examples dimension 2 transposes the data set such that dimension 2 becomes active dimension 1 2 3 restores the original order of dimensions of a 3D data set flatten flatt n t function function flatten derivative n t function function flatten iterative region function function flatten manual region function function flattens the baseline of the real frequency domain data in the active dimension see p 54 The parameters have the following meaning method can be flatt or derivative and specifes the method for the determi nation of pure baseline regions either the FLATT method Gintert amp Withric h 1992 see p 54 or the method of Dietrich et al 1991 that relies on a smoothed derivative of the spectrum n When using the FLATT method n indicates the half width of the line segments that are fited to the data see Eq 24 on p 54 When using the derivative method n indicates the half width of the smoothing of the spectrum Gintert et al 1992 T is a threshold for the determination of pure baseline regions With t 1 the program recognizes about one third of the data points as pure baseline regions higher values of t yield larger regions of pure baseline see p 55 Gintert et al 1992 region When using the iterative method or the manual selection of pure baseline regions a region can be given in one of the following for mats m
10. obtained from the original spectrum s s by k 5 s ei 00 918 with t 23 Ss The method can be used for spectra containing both positive and negative peaks but of course not for anti phase multiplets In practice to determine peak positions in 1D cross sections of the power spec trum the program frst identifes all local maxima that are more than x times above 53 Algorithms E 54 the noise level of the power spectrum typically x 10 For each maximum the corre sponding boundaries for peak integration are set at the frst data points on either side that are lower than either 10 of the maximal peak intensity or twice the noise level To decide which of the maxima correspond to suitable peaks for use in the automatic phase correction the following criteria are checked i The width of the integration area must be smaller than a predetermined value u ii To exclude overlapping peaks the average intensity in the regions of width u 4 adjoining the integration area to the left and to the right must be either below 10 of the maximal peak intensity or below twice the noise level iii An upper limit v is imposed on the number of peaks that may have the same coordinates along one frequency axis typically v 20 50 If v is exceeded the program will only retain the v highest peaks so that the phasing cannot be dominated by one or several small spectral regions The results of the automatic phase correc
11. parameter fie 35 Variables EE 36 Macros This chapter gives an alphabetical list of the standard macros that are provided with the program Prosa The general initialization macro init is explained in the chapter on the command line interpreter see p 19 dummycal sets the system variables delta k ppmmax k and w0 k see p 33 35 to de fault values delta k wO k 1000 0 and ppmmax k number of data points in dimension k It thus avoids that XEASY treats the spectrum as uncalibrated cflatt flatt n t baseset m In n 116 cflatt derivative n t baseset m no n 1 6 1 cflatt iterative region baseset m In n 11 6 cflatt manual region baseset m In n 1 6 1 convenient FLATT flattens the baseline in the frequency domain of the active di mension see p 23 using standard base function sets It thus provides a conve nient interface to the fatten command see p 23 The parameters n t and region have the same meaning as for the fatten command The other parameters defne the base function set baseset denotes the set of base functions used to represent baseline distor tions The following choices are possible baseset Base functions t k n 2 ny k 1 n cft 1 cos 2rt sin2nt cos27t m 1 sin 2nt m 1 rft 1 cos n sint cosnt m 1 sinni m 1 cftw same as cft plus Lorentzian functions to account for contributions from the water line rftw sa
12. played System variables that must not be changed by the user are marked as read only Global variables that are hidden by local variables with the same name are marked as hidden subroutine name sequence of statements end defne a new user defned command within a macro i e a macro within a macro User defned commands defned by subroutine statements are called by their name possibly followed by parameters in exactly the same way as macros User defned commands defned by a subroutine statement are local to the current macro or macros called through it Within a macro a user defned command can only be called after it was defned type name displays the macro or user defned command with the given name Macros in the current path see the variable path on p 19 can be listed without giving a path otherwise the path has to be specifed var variable variable declares variables as local variables of the current macro In contrast to normal global variables local variables are only visible within the macro where they are declared and within macros that are called via that macro except when such a macro declares itself a local variable with the same name The var command must precede any other commands in a macro except the parameter command and cannot be used interactively Variables The command line interpreter allows the use of variables that are similar to shell variables in the UNIX operating system A variab
13. predicted complex data points For positive n n addition DEN Commands al data points are appended at the end for negative n the n frst data points are replaced with data points obtained from linear pre diction The latter possibility is used for the correction of baseline distortions that are caused by errors in the frst time domain data points see p 52 ki ko specify the range of data points used for the determination of linear prediction coefftients in Eq 16 If k and k are not specifed the program uses all available data points for the determination of lin ear prediction coefftients project n projects the data along the last dimension If n 0 the projection is given by the data point with the largest absolute value skyline projection For a natural number n the projection p of the data points s along the last dimension is com puted according to p n D sgns IS 2 8 k replaces complex data in the active dimension by its real part Real data remain unchanged re read format flename n lel read format flename combine f f reads a fle with time or frequency domain data In the frst form data in memory are overwritten in the second form a linear combination of the data in memory and in the input fle is formed The second form of the read statement is not al lowed for fles in vnmr format The parameters have the following meaning format real serial data file containing real numbers
14. straight line a bl toa stretch of 2n 1 data points centered about the data point k For the data points near the boundaries of the 1D cross section where p is not defned by Eq 24 p has the same value as the nearest data point inside the defnition range A minimal width for pure baseline re gions Gintert and W hric h 1992 is ensured by smoothing p FLATT Dp Min Pz_p 3 sees Ppin 3 26 Ds Algorithms Derivative method p max min p max p _ Pz 1 min p _1 Pp 41 27 The defnition of p for the derivative method implies that any point of which both neighbors belong to pure baseline regions will also belong to it and that there is no point in a pure baseline region for which both neighboring points do not belong to it Dietrich et al 1991 A cutoff p is then defned such that p lt p for one third of the data points and p gt p for two thirds of the data points and all data points k that sat isfy the relation p lt tp are considered as pure baseline where qt is a user defned pa rameter typically t 4 Any linear combination of functions that can be written as FORTRAN 77 arithmetic expressions may be used to represent the baseline distortions Usually we use the constant and the trigonometric functions corresponding to the frst m time domain data points see Eq 4 in Gintert and Withric h 1992 The linear least squares ft to the pure baseline regions is solved by standard techniques using si
15. the data processing which may improve the results of other processing steps that rely on having a fht baseline Automatic phase correction The automatic phase correction routine developed for PROSA determines the con stant and linear phase correction parameters 6 and 0 by frst searching the 1D cross sections of the power spectrum for strong well separated peaks Then in the phase sensitive spectrum the sum S 6 of the difference between the squared real and imaginary parts of the normalized integral over the peak region in the phase corrected spectrum I p So Y L Re p mip 19 P with Is i 0 0 To oP e o pap 20 NE is maximized I denotes the integral over the region of the peak p in the spectrum be fore phase correction and denotes the normalized position of peak p 0 lt lt 1 The summation runs over all the peaks that were found to be acceptable for the pur pose of the phase correction see below The maximum of S 6 is obtained by se lecting the linear phase correction 6 such that the function 21 I 2 _2i o s B Er te 21 has its maximum absolute value at 6 The constant phase correction is given by 1 do zarg s 22 where arg s is the argument of the complex number s Because s has in general mul tiple local maxima PROSA determines 6 by a one dimensional grid search with a step size AB usually AB 1 The phase corrected spectrum 8 is
16. user defned command can only be called after it was defned The statement command without parameters gives a list of all user de fned commands and indicates where they are defned EEE Command Interpreter do variable start end step sequence of statements end do executes a loop within a macro The loop is executed unconditionally if do stands without parameters i e until one of the statements break exit quit or return is encountered or as a FoRTRAN 77 do loop where the loop counter variable and the integer expressions start end and step have the usual meaning Examples do if flename eq break end do doi110 print Iteration i end do error flename text option writes the text to standard output or into the fle with the given flename and calls the error handler that is specifed with the system variable erract see p 18 This statement is suitable to treat errors that occur during the execution of a macro If the text contains blanks it must be enclosed in double quotes The default option append indicates that the text is to be appended to an existing output fle flena me Anew fle flename will be opened if necessary The option close indicates that the fle will be c losed after writing the text eval variable expression variable expression evaluates the arithmetic or string expression according to the rules of FORTRAN 77 and assigns the result to the variable In the short form variabl
17. write protected perm 1 is equiv alent to dim and denotes the active dimension 34 Variables phi0 and phil denote the constant 6 and linear 6 phase correction parameters see Eq 23 phi0 and phil are calculated and assigned with the statement autophase but can also be set by the user pi has the value 8 141593 and is write protected ppmmax k denotes the chemical shift in ppm of the frst data point in dimension k If a data fle in the format of the program XEasy Bartels et al 1994 see p 27 is read the system variables ppmmax k are set according to the values in the XEASY param eter fie timing is a system variable to control the reporting of CPU times CPU times are given for all commands except those that are built into the command line interpreter that need more seconds of CPU time than the value of timing indicates usedsize and usedwork denote the used memory and workspace sizes in words At the beginning of a PROSA session both variables have the value 0 The execution of every subsequent state ment increases these variables according to the necessary memory and workspace sizes The variables usedsize and usedwork can also be altered explicitly by the user wO0 k denotes the spectrometer frequency in MHz in dimension amp If a data fle in the format of the program XEasy Bartels et al 1994 see p 27 is read the system variables w0 k are set according to the values in the XEASY
18. 0 1 ndata 1 Maximum chemical shift in wl 10 0 ppmax 2 Maximum chemical shift in w2 10 0 ppmax 1 Size of spectrum in wl 256 ndata 2 Size of spectrum in w2 301 ndata 1 Submatrix size in wl 32 see above Submatrix size in w2 38 see above Permutation for wl 2 dimension Permutation for w2 1 dimension Folding in wl RSH always RSH in PROSA Folding in w2 RSH always RSH in PROSA Type of spectrum always in PROSA Given in parentheses are the corresponding PROSA system variables see p 33 35 The parameter fles for three and four dimensional data sets contain similar entries for the additional dimensions Data fles in vnmr format start with a 32 byte fle header followed by blocks con sisting of a block header and sequentially stored data Varian Associates 1993 The organization of the data is extracted from the fle header block headers are simply skipped by the program PROSA Noise level Several PROSA statements for example autophase and plot use a noise level to automatically adapt parameters to the scaling of data The program PROSA uses an ap proximation of the median Press et al 1986 of the absolute value of the real data points to estimate the noise level To improve the efftiency of the noise level calcula tion only about 10 or 1 of the data points are taken in
19. 0E 02 1 k cos 2 454370E 02 1 k sin 4 908740E 02 1 k cos 4 908740E 02 1 k Average size of baseline regions 84 0 Minimal size of baseline regions 55 5 Baseline corrected CPU time 17 3 s total CPU time 87 4 s noesy dimension 1 2 New order of dimensions 1 2 noesy dummycal noesy scale noise 100 scale status full Occupied memory E 262400 words 6 Dimension 1 1024 real points Dimension 2 256 real points Order of dimensions 1 2 Maximal magnitude 1 64E 07 Noise magnitude 3 40E 03 CPU time 1 0 s total CPU time scale multiply 100 3404 98 Data multiplied noesy status full Occupied memory Dimension 1 262400 1024 Dimension 2 256 Order of dimensions 12 Maximal magnitude 4 81E 05 Noise magnitude 1 00E 02 CPU time 1 1 s total CPU time noesy write easyl6 home vd noesy EN Examples 89 3 s words 6 real points real points 90 7 s File home vd noesy 3D 16 written CPU time 4 9 s total CPU time Ready The resulting spectrum is shown in the Figure 500 95 7 s Contour plot produced with the PROSA com mand plot of part of a NOESY spectrum of BPTI The data set was processed as described above 1000 45 Examples BSS As an example for the processing of higher dimensional datas sets the following shows the data processing of a three dimensional N correlated H H NOESY data set read swap tmp
20. A completely avoids disk storage of intermediate results i e at the out set the time domain data are read into the computer memory and only the fully pro cessed frequency domain data are written back onto disk the computer memory must be sufficiently large to hold the complete data set On vectorizing computers the program achieves high efficiency because of the complete vectorization of all time con suming routines which is facilitated by the fact that identical operations are applied independently to all 1D cross sections of a data set PROSA is written in standard For TRAN 77 and was implemented on a variety of computers A description of the program PROSA is given in the following publication Gintert P D tsch V Wider G amp W hric h K 1992 Processing of multi di mensional NMR data with the new software PROSA J Biomol NMR 2 619 629 In this manual literal input is printed in bold other input is printed in italics Op tional input is given in square brackets and optional input that may be repeated zero or more times is given in curly braces In examples output from the program Prosa is printed in typewriter font Comments suggestions and reports on bugs are welcome Please send them to Peter Gintert Institut f r Molekularbiologie und Biophysik HPM G21 Eidgen ssische Technische Hochschule CH 8093 Z rich Switzerland electronic mail guentert mol biol ethz ch Installation Configurat
21. RTRAN 77 KieBling amp Lowes 1987 the record length should be given in words but some compilers assume that it is specifed in bytes Ds Installation builds a PROSA executable with the given memory and workspace size in words in the current working directory The makeprosa command can be used to temporarily cre ate a PROSA executable with optimal memory and workspace usage for the execution of a particular macro the minimally required memory and workspace sizes for the ex ecution of a macro can be determined with the standard macro job see p 38 The Makefle the script makeprosa and the initialization macro macro init pro are generated from the prototype fles Makefle def src makeprosa def and src init pro def respectively Permanent changes to these fles should be made in the corresponding prototype fles because they will otherwise be overwritten by confgure or make Memory and workspace Because PROSA does not store intermediate results on disk the computer memory must be suffriently large to hold the complete data set throughout the calculation The memory size in words must always be at least as big as the total number of real data points of the current data set In addition some processing steps require addi tional temporary workspace For example transpositions of the data set see the com mand dimension on p 23 need a workspace of at least the size of the transposed plane s Thus for the processing of two dimensi
22. SFS angio 3d 1024c 150c 16c The time domain data consist of 1024 complex data points in the first aquisition dimension 150 complex data points in the second dimen sion and 16 complex data points in the third dimension The data are stored as integer numbers with inverted byte ordering in a serial file called tmp SFS angio 3d see p 27 suppress cos 30 The residual water signal that has frequency zero in the aquisition di mension is suppressed using the macro suppress see p 39 print print Dimension 1 Processing of the aquisition dimension print multiply 0 5 1 Scale the first data point by 1 2 window cos Cosine window see p 40 ft 2048 1 1024 The data are zero filled to 2048 complex data points prior to Fourier transformation and only the left half of the resulting spectrum is re tained see p 24 print print Dimension 2 Processing of the second dimension print dimension 2 Transposition that activates the second dimension multiply 1 2 n 2 Change sign of every second data point States TPPI window cos Cosine window see p 40 ft 256 1 256 90 180 The data are zero filled to 256 complex data points prior to Fourier transformation a constant phase correction of 90 and a linear phase correction of 180 are applied and only the real part of the spectrum is retained see p 24 dimension 1 Re activate the aquisition dimension autophase 14 2 0 8 0 8 0 Automatic
23. all system variables specift to the program Prosa System variables as sociated with the command line interpreter are explained on p 16 19 check determines whether Prosa statements that change the data matrix are only checked for errors or actually executed Statements are executed if check is not set or equal to NULL otherwise i e if one or several check options are set state ments are checked for different types of errors without doing the calculation The following options are possible memory Insufftient memory or workspace size is an error fle Input data fles that do not exist or output data fles that cannot be opened or created result in an error command All other errors syntax errors for instance are reported The option command is always active To determine the memory and workspace size required for the execution of a macro it is useful not to set the option memory and to examine after the test the system variables usedsize and usedwork If during the execution of a macro a new data fle is written and later read again the option fle should not be set because the attempt to test the existence of the fle results in an error that would not occur if the macro is really executed not just tested The most convenient way to test macros before execution is to use the stan dard macro job see p 38 delta k denotes the time or frequency increment between two data points in dimension k in seconds for the tim
24. arameter checks for errors in the macro without executing the actual calculation and pro vided that there is no error executes the macro afterwards The value of the sys tem variable check see p 33 determines the type errors that are detected By default i e if check has the value NULL when the macro is called check will be set to command fie If no error is detected the memory and workspace sizes necessary for the execution of the macro are displayed and the execution of the macro is started if sufftient memory and workspace is available In case of an er ror the values of all global variables are listed and the program is stopped The macro must not contain statements such as quit that stop the program job is par ticularly useful to execute macros in batch jobs Ds Macros phase 6 6 1 applies a phase correction according to Eq 23 and the given constant 6 and linear 6 phase correction parameters The values of 6 and d must be given in degrees If the phase correction parameters are known it is in general more effi cient to use them together with the Fourier transformation see p 24 than to call the macro phase reduceppm region region works as the statement reduce see p 28 except that the regions must be speci fed in ppm units instead of points This macro can only be used if the system vari ables delta k ppmmax k and wO k see p 33 35 are set savequit flename displays the values of al
25. e expression without the keyword eval the equal sign must be surrounded by blanks In con trast to FoRTRAN 77 function names must be given in lowercase letters Examples i 7 sentence A flexible program j mod i 4 2 1 len sentence show i sentence j Variables i 7 sentence A flexible program j 9 1 19 13 Command Interpreter EE 14 exit returns from a macro to interactive input Given interactively it exits from the program goto label continues execution of a macro at the frst line that begins with the label Jumps into loops do end do or conditionally executed statements if else end if are not allowed and can lead to unpredictable results A label may consist of let ters digits and underscore characters _ A label must be followed by a colon Example goto cont cont print Now at label cont help topic gives on line help for a given topic With no topic given a list of all available help topics is displayed On line help for macros can be included in the macro help macro shows all lines of the macro that start with if condition statement executes a logical if statement as in FORTRAN 77 i e the statement is executed if the logical expression condition is true A line with a logical if statement must not end with the word then In addition to the possibilities of FORTRAN 77 there are three logical functions exis
26. e domain in Hertz for the frequency domain If a data fle in the format of the program XEASY Bartels et al 1994 see p 27 is read the sys tem variables delta k are set according to the values in the XEASY parameter fle and updated during Fourier transformation dim denotes the active dimension and is write protected 33 Variables DD icmplx k equals 1 if the data in dimension k are real and 2 if the data in dimension k are complex This variable is write protected denotes the product of the numbers of real data points in the passive dimensions and is write protected max denotes the maximal absolute value of the data and is write protected max is only calculated and assigned with the statement status full maxsize and maxwork denote the available memory and workspace sizes in words see p 9 respectively and are write protected denotes the number of real or complex data points in the active dimension and is write protected ndata k denotes the number of real or complex data points in dimension amp and is write pro tected ndata dim is equivalent to n ndim denotes the number of dimensions and is write protected noise denotes the noise level and is write protected noise is only calculated and as signed with the statement status full An estimate of the median of the absolute values of the data points is used for the noise level perm denotes the current order of dimensions and is
27. easy8 easy16 xeasy16 easy and xeasy two fles will be writ ten a XEASY parameter fle called flename 3D param and the data fle flename 3D 8 or flename 3D 16 respectively The calibration entries of the parameter fle are set to the corresponding values of the system variables for calibration delta w0 and ppmmax see p 33 35 if possible Otherwise the spectrum will be treated as un calibrated by X EASY Regions of the data set that are written into the output fle The frst region corresponds to the active dimension the second region corre sponds to the second dimension etc If the number of regions is less than the number of dimensions of the data set all data points will be used from the remaining dimensions A region can be given in one of the following formats n denotes the data point n m n includes the data points m m 1 n m includes the data points m m 1 up to the last data point n includes the data points 1 2 n 7 stands for all data points Ga Ge 1 Optionally a region may be followed by r or i to indicate that in the given dimension only the real or imaginary part respectively of a complex data set should be written into the output fie 31 Commands EE 32 variables Variables The command line interpreter of the program Prosa allows the use of variables that are similar to shell variables in the UNIX operating system see p 16 The follow ing is a list of
28. ename base factor n n_ Q size a offset G margin a labels a tics option Plot fles can be written in the following formats format Language Plotter Printer Paper size hp7550a HP GL HP 7550A A3 hp7550a a4 HP GL HP 7550A AA hp7596a a0 HP GL HP 7596A AO hp7596a al HP GL HP 7596A Al hp7596a a2 HP GL HP 7596A A2 hp7596a a3 HP GL HP 7596 A A3 postscript Postscript Postscript printer A4 Name of the output plot fie For a spectrum with several planes a separate plot fie called flename k is written for every plane k Height of the lowest contour line Default value 5 times the noise lev el Factor between the heights of adjacent contour lines Default value ne Maximal number of positive contour levels Default value 12 Maximal number of negative contour levels Default value 12 Size of the plot excluding margins in the dimension in cm Offset in cm from the reference point in a dimension Margin width in a dimension in cm Label spacing in a dimension given in spectral units ppm if the spectrum is calibrated otherwise data points This parameter also determines the grid size if the option grid is set Spacing for tics in a dimension given in spectral units ppm if the spectrum is calibrated otherwise data points grid overlays the spectrum with a grid nogrid does not draw a grid margin surround the spectrum with a labelled margin nomargin does not draw a margin
29. equentially Next the data are ordered by the second dimen sion etc For example the data points s k 1 m 1 1 n of a two dimen sional data set with m points in the frst dimension and n points in the second dimension are stored in the following order Sipe Be gy Sy sou Sy CR Bee Say 12 For complex data the real part is stored followed by the imaginary part In a submatrix data fle formats xeasy8 and xeasy16 the data set is split into submatrices with sizes as given in the accompanying parameter fle Bartels et al 49 Algorithms E 50 1995 Xia amp Bartels 1993 Within each individual submatrix the data are ordered as in a serial fle and the submatrices as a whole are ordered in the same way as the data points of a serial fie On output the program PROSA uses for a data set with n real data points in a given dimension a submatrix size of n 8 but at least 1 in the corre sponding dimension If necessary the submatrix size in the active dimension is in creased to the next integer multiple of 4 or 2 for the formats xeasy8 or xeasy16 respectively in order to align the submatrices at word boundaries On input the sub matrix size in the active dimension must be an integer multiple of 2 or 4 for the for mats xeasy8 or xeasyl6 respectively For the submatrix sizes in the other dimensions there is no such condition In the format real the data are stored in the binary floating point number format of the given
30. esy ft 256 Complex Fourier transform performed CPU time 8 7 s total CPU time 36 4 s Phase correction noesy dimension 1 New order of dimensions 1 2 43 Examples 44 CPU time 2 7 s total CPU time 39 1 s noesy autophase 10 2 0 10 0 10 0 R Noise standard deviation 2 249E 04 Number of peaks used 199 Constant phase correction 25 2 deg Standard deviation 28 5 deg Automatic phase correction applied CPU time 2 5 s total CPU time 41 7 s noesy re Real part kept imaginary part discarded noesy dimension 2 New order of dimensions 2 1 noesy autophase 6 2 0 6 0 10 z Noise standard deviation 1 875E 04 Number of peaks used 414 Constant phase correction 63 3 deg Linear phase correction 129 0 deg Standard deviation 8 2 deg Automatic phase correction applied CPU time 5 1 s total CPU time 47 9 s noesy re Real part kept imaginary part discarded nn Baseline correction noesy dimension 1 New order of dimensions 1 2 noesy cflatt cft 10 6 0 3 cflatt flatten flatt 10 6 0 1 sin 6 135924E 03 1 k cos 6 135924E 03 1 k sin 1 227185E 02 1 k cos 1 227185E 02 1 k Average size of baseline regions 63 2 Minimal size of baseline regions 48 2 Baseline corrected CPU time 19 9 s total CPU time 69 0 s noesy dimension 2 New order of dimensions 2 1 noesy cflatt cft 6 6 0 3 cflatt flatten flatt 6 6 0 1 sin 2 45437
31. fault option strip they refer to the strip of data points n n ift IN In 1 ne executes a complex inverse Fourier transformation Before the inverse Fourier transformation the data are symmetrically zero filed to N complex data points If N is not specifed the program zero fils up to the next power of 2 if necessary Upon request i e if n and n are given the program retains only the strip con sisting of the time domain data points nj n multiply factor start end step multiplies the data in the active dimension with a constant or variable factor The factor may contain a lowercase k that denotes an index that runs over the data points in the active dimension from start to end with the given step Factor must be a integer real or in the case of complex data complex FORTRAN 77 expression All data points are multiplied if start end and step are omitted If only start is specifed the data point start will be multiplied The default step is 1 Examples multiply 0 05 scale data multiply 0 5 1 multiply frst data point by 1 2 multiply 1 2 n 2 change sign of every second point multiply cos pi 2 n k 1 cosine window function plot format flename base factor n n_ 24 x size x offset x margin x labels x tics y size y offset y margin y labels y tics option DEN Commands creates a contour plot of the spectrum The parameters have the following mean ing a x y format fl
32. fnes the search path for macro fles 19 Command Interpreter EE 20 Commands There are two kinds of commands in the program Prosa general built in com mands of the command line interpreter comparable to a shell in the UNIX operating system that are not specife to the program Prosa and Prosa specife commands This chapter gives an alphabetical list of the PROSA specift commands Many commands are applied to the active dimension of the data set When a data set is read the frst dimension i e the dimension along which the data are stored se quentially in the data fie becomes the active dimension Later on the user can change the active dimension by suitable transpositions with the command dimension see p 23 The non active dimensions are referrred to as passive dimensions abs replaces the data in the active dimension by its absolute value s s autophase width threshold height overlap o option determines constant and linear phase correction parameters and performs an au tomatic phase correction see p 53 The parameters have the following meaning width Maximal half width in data points of peaks in the power spectrum default 10 data points threshold Threshold to determine the extent of peak regions In a peak region intensities must exceed threshold times the noise level and 10 of the maximal height default 2 height Minimal intensity of acceptable signal maxima with respect to the noise le
33. gions are used for the phase determination Signal regions are symmetrized such that the absolute value spectrum becomes symmetric with respect to the peak maximum Information about every peak used for the phase determination is displayed All signals have the same weight Signals are weighted with the square root of their intensity proportional Signals are weighted with their intensity The options apply complex global and equal are set by default The values determined for the constant and linear phase correction parameter are assigned to the system variables phi0 und phil see p 35 converts 2n real data points in the active dimension into n complex data points by considering subsequent real data points r _ and r as the real and imaginary parts respectively of complex numbers z r _ i r k 1 n If the number of real data points is odd the imaginary part of the last complex data point will be set to zero Complex data remain unchanged converts n real data points r in the active dimension into n complex data points Z r with vanishing imaginary parts Complex data remain unchanged DEN Commands conjugate takes the complex conjugate of the complex data in the active dimension Real data remain unchanged dimension active dimension dimension transposes the data matrix such that active dimension becomes the active dimen sion If additional dimensions are given the requested order of dimensions
34. hring W amp Withric h K 1993 NMR spec troscopy of a DNA complex with the uniformly C labeled Antennapedia homeodomain and structure determination of the DNA bound homeodomain J Mol Biol 234 1070 1083 57 References MS 58 Stephenson D S 1988 Linear prediction and maximum entropy methods in NMR spectros copy Prog NMR Spectrosc 20 515 626 Varian Associates Inc 1993 User programming VNMR 4 3 Palo Alto California Withric h K 1986 NMR of Proteins and Nucleic Acids Wiley New York Xia T H amp Bartels C 1993 XEASY ETH Automated Spectroscopy for X Window Systems User Manual Institut f r Molekularbiologie und Biophysik ETH Ziric h Zhu G amp Bax A 1990 Improved linear prediction for truncated signals of known phase J Magn Reson 90 405 410
35. ic phase correction see p 21 re Discard imaginary part of the aquisition dimension dimension 2 Transposition that activates the second dimension autophase 6 2 0 6 0 10 Automatic phase correction see p 21 re Discard imaginary part print print Baseline correction print dimension 1 Transposition that activates the first dimension cfatt cft 10 6 0 3 Baseline correction using the FLATT method see p 23 37 54 with a half width of 10 data points and a threshold parameter 6 for the de termination of pure baseline regions The basis functions that are used to represent the baseline distortions are the 5 trigonometric functions that correspond to the first 3 time domain data points dimension 2 Transposition that activates the second dimension cfhtt cft 6 6 0 3 Baseline correction in the second dimension dimension 1 2 Restore original order of dimensions dummycal scale noise 100 Scale data to a noise level of 100 status full Show the size noise level and maximal intensity of the data write easy16 home vd noesy Write an output spectrum file home vd noesy 3D 16 and a parameter file home vd noesy 3D param for XEASY Assuming that the above sequence of PROSA commands is stored in a macro fle called noesy pro the data processing is executed as follows the statements are dis played before execution in the form macro statement informative output of the pro gram starts with and is indented pr
36. int s the program frst determines the integer that minimizes the expression Isa v2 113 i e l nlogl s and then stores in one byte min l 1 47 if s 2 0 95 min l 47 ifs lt 0 4 14 This format can represent numbers approximately in the range ah lt s lt pe i e 1 2 10 lt s lt 8 4 10 with a relative error of less than 20 The format xeasy16 uses a 16 bit floating point format with the exponent e given by Eq 14 in the lower valued byte and the mantissa a mais 615 if l 0 15 2 DEN Algorithms a 0 ifl 0 in the higher valued byte Bartels et al 1995 Eccles et al 1991 Xia amp Bartels 1993 This format can represent numbers in the same range as the format xeasy8 but with a relative error of less than 1 A xeasy8 or xeasy16 format data set consists of a data fle fle 3D 8 or fle 3D 16 respectively and a parameter fle fle 3D param that contains information about the type size and organization of the data fle A parameter fle written by PROSA for a two dimensional data set has the following entries Version sbk oid etd bh sus 1 always 1 in PROSA Number of dimensions 2 ndim 16 or 8 bit file type 16 8 for xeasy8 16 for xeasy16 Spectrometer frequency in wl 600 0 w0 2 Spectrometer frequency in w2 600 0 w0 1 Spectral sweep width in w1 10 0 delta 2 w0 2 ndata 2 Spectral sweep width in w2 10 0 delta 1 w
37. ion The program PROSA is delivered either on tape cartridge as a UNIX tar archive or via electronic mail as a uuencoded compressed tar archive fle To extract the indi vidual fles from the tape cartridge use the UNIX command tar xvf tape device 1 which creates in the current directory a subdirectory called prosa 3 4 that contains the prototype makefle Makefile def the installation help fle README the confg uration shell script configure and the subdirectories help macro and sre for help fies macro fies and source fies respectively To extract the individual fies from the electronic mail fle use the following se quence of UNIX commands uudecode mail file uncompress prosa 3 4 tar Z tar xvf prosa 3 4 tar 2 The Makefile is created from the prototype makefle Makefile def by the shell script configure using the UNIX command configure system 31 that recognizes the following UNIX computer systems convex hp ibm nec sgi sun and generic If no system is specifed the script tries to determine the correct system type using the uname command or the HOSTTYPE environment variable The script configure assumes that the name of the directory where the program PRO SA resides is of the form prosa version The system dependent parameters set by the confguration script are shown when the script is executed The following example is from a Sun 4 computer where the program resides in the directory home guentert pr
38. ion in the second dimension dimension 3 Activate the third dimension cfhtt cft 3 6 0 3 Baseline correction in the third dimension dimension 123 Restore original order of dimensions dummycal Set dummy calibration parameters for XEASY write easy16 tmp SFS vd hxnoe3d Write an output spectrum file tmp SFS vd hxnoe3d 3D 16 and a pa rameter file tmp SFS vd hxnoe3d 3D param for XEASY 47 Examples MM 48 Algorithms Spectrum fle f ormats The program PROSA supports various formats for the storage of time or frequency domain data The formats are summarized in the following table format order bits point coding number format real serial 32 binary real integer serial 32 binary integer swap serial 32 binary integer text serial 13x8P ASCII real xeasy8 submatrix 8 binary logarithmic xeasy16 submatrix 16 binary real vnmr serial 16 or 324 binary integer or real a With inverted byte ordering bOn output On input the number of bits point is variable Only for input Depending on the status bit S_32 in the file header Depending on the status bit S_FLOAT in the file header For all formats except vnmr the data fle contains only the data points themselves without any headers or other information For the formats xeasy8 and xeasy16 a sep arate parameter fle accompanies the data fle see below In a serial data fie the data points of the frst dimension usually the acquisition dimension are stored s
39. l global variables writes the current data in real format into the fle called fename by default savequit out and stops the program This macro is a useful error handler for long calculations Example set erract savequit sets savequit as error handling routine scale method intensity scales the data such that in the case method max the maximal absolute intensity and in the case method noise the noise level is set to the given intensity The de fault intensity is 500 000 for the maximal absolute intensity and 100 for the noise level respectively selectppm region works as the statement select see p 29 except that the regions must be specifed in ppm units instead of points This macro can only be used ifthe system variables delta k ppmmax k and wO k see p 33 35 are set suppress weight n suppresses signals of zero frequency the water line for instance by subtracting smoothed time domain data from the original time domain data using the state ment smooth see p 30 The smoothed data are calculated from the original data according to Eq 11 The following weights are possible weight weighting function name cos f cos tk 2 n 1 cosine weighting gauss f eee Gaussian weighting equal al equal weighting 39 Macros DD window type parameter applies commonly used window functions DeMarco amp W hric h 1976 Ernst et al 1987 type parameter window f
40. l water signal The data are extrapolated in the border regions over more data points than used in the smoothing in order to avoid us ing the frst two data points which are often corrupted This method is conveniently implemented in the macro suppress see p 39 status max full silent data displays information about the size and organization of the current data set With the option max also the maximum absolute value is calculated and assigned to the system variable max With the option full also the maximum absolute value and the noise level are calculated and assigned to the system variables max and noise respectively The option silent suppresses the display which is useful ifthe system variables max and noise should be updated silently With the option data the data are written to standard output if less than 2048 numbers write format flename region 30 writes part or all of the data into the output fle called fename The parameters have the following meaning format real serial data file containing real numbers integer serial data file containing integers swap serial data file containing integers with reversed flename region DEN Commands byte ordering text text fle written with FORTRAN 77 format 1PE12 4 easy8 or xeasy8 submatrix 8 bit data fie for the program X EASY easy16 or xeasy16 submatrix 16 bit data fle for X EASY Name of the output data fle In the case of the formats easy8 x
41. lation The maximal available memory and workspace sizes are given by the functions maxsize and maxwork see p 34 The minimally required memory and workspace sizes required so far in a PROSA calculation are stored in the system variables used size and usedwork see p 35 It should be noted that some processing steps for ex ample linear prediction see the command predict on p 26 may be inefftient if only the minimally required workspace is available Command Interpreter The program PROSA provides a powerful command line interpreter comparable to a shell in the UNIX operating system that allows the use of macros variables For TRAN 77 mathematical and character expressions control statements conditionals loops and jumps error handling etc When reading an input command line the com mand line interpreter executes the following steps Comments i e text following a comment sign are discarded The values of variables are substituted from right to left see p 16 The command line is split in elements defned as sequences of non blank char acters separated by blank characters The frst element becomes the command name and the following elements become command parameters e Ifthe command name corresponds to a built in command of the command in terpreter see p 12 it is executed by the command line interpreter itself e Otherwise if the command name identifes a specift command see p 21 un ambigu
42. le name consists of up to 20 letters 16 set x 4 6 set y 2 0 eval sum x y set t a sum set x y sum t Variables x 4 6 y 2 0 sum 6 60000 t a sum print This is t x y sum This is a sum 4 6 2 0 6 60000 print This is t x y sum F4 1 This is a sum 4 6 2 0 6 6 print A second t 3 5 A third t 2 A second sum A third sum set t 3 program print t or t me a program or a programme doilndim E Command Interpreter digits or underscore characters _ The value of a variable is always a character string also the results of arithmetic expressions are converted to strings upon assignment to a variable and is denoted by variable or variable in the command line As in For TRAN 77 parts of character strings may be denoted by variable begin end where be gin and end are integer expressions that denote the frst and last character of the substring respectively Numerical values of variables may be formatted according to a given FORTRAN 77 format by variable format The k th element elements are sep arated by commas of a variable is denoted by variable k where k is a non negative integer expression variable name that is immediately followed by a letter digit or underscore character must be enclosed in curly braces variable Examples Set the variable x Set the variable y Evaluate an expression Set the variable t Display values Use values Use
43. me as rft plus Lorentzian functions to account for contributions from the water line polynom polynomial of order m The methods cft and rft use trigonometric functions that corre spond to the frst m data points after complex and real Fourier Macros 38 transformation respectively The additional Lorentzian functions used in the basesets cftw and rftw assume that the water signal is located in the middle of the spectrum before a possible strip trans form m determines the number of base functions used to represent baseline distortions There will 2m 1 base functions with the methods cft and rft 2m 1 base functions with the methods eftw and rftw and m base functions with the method polynom Noy Ny specifes that the present data in the active dimension represent a strip out of a total of n data points starting at data point n By default the values n n and n 1 are used n denotes the number of data points in the active dimension 6 denotes the linear phase correction parameter used for phase cor rection The parameters n n and 6 are not allowed when using the baseset polynom hilbert performs a Hilbert transformation Ernst 1969 in the active dimension Real data are converted to complex data such that the real part remains unchanged and the Kramers Kroning relations are fulfiled im replaces complex data in the active dimension by its imaginary part Real data re main unchanged job macro p
44. ngular value decomposition Press et al 1986 55 Algorithms DD 56 References Barkhuijsen H De Beer R amp van Ormondt D 1987 Improved algorithm for noniterative time domain model fiting to exponentially damped magnetic resonance signals J Magn Reson 73 553 557 Bartels C Xia T Gintert P Billeter M amp W hric h K 1995 The program XEASY for com puter supported NMR spectral analysis J Biomol NMR in preparation DeMarco A amp W hric h K 1976 Digital fitering with a sinusodial window function An al ternative technique for resolution enhancement in FT NMR J Magn Reson 24 201 204 Dietrich W Ridel C H amp Neumann M 1991 Fast and precise automatic baseline correc tion of one and two dimensional NMR spectra J Magn Reson 91 1 11 Eccles C Gintert P Billeter M amp Withric h K 1991 Effeient analysis of protein 2D NMR spectra using the software package EASY J Biomol NMR 1 111 130 Ernst R R 1969 Numerical Hilbert transform and automatic phase correction in magnetic resomance spectroscopy J Magn Reson 1 7 26 Ernst R R Bodenhausen G amp Wokaun A 1987 The principles of nuclear magnetic reso nance in one and two dimensions Clarendon Oxford Friedrichs M S Metzler W J amp Mueller L 1991 Removal of diagonal peaks in two dimen sional NMR spectra by means of digital filtering J Magn Reson 95 178 183 Gintert P
45. o standard output before ex ecution The possible settings are NULL or not set at all In macros commands that are not built into the command line interpreter see p 21 are echoed interactively com mands are not echoed on Commands that are not built into the command line interpreter are echoed regardless of whether they occur in macros or interactively full All commands are echoed and the corresponding line numbers in macros are given off Commands are not echoed Labels are not included in the echo variable substitutions are included in the echo Statements that are preceded by will only be echoed if the system variable echo has the value full erract is a variable for error handling If an error occurs within a macro the value of er ract is executed as command By default the exit command is executed i e the program returns to interactive input Errors that occur interactively are displayed and the program continues with the execution of the next statement Example set erract chain show quit With this setting of erract in case of an error a listing of all global variables is given and the program is stopped Such error handling can be useful if the program is used non interactively nparam denotes the number of command line parameters passed to a macro see p 19 1 Errors that occur interactively are displayed and the program continues with the execution of the next statement EEE Command In
46. onal data set with a single row i e by setting n 1 Linear combination coefftient for data in memory Default value 1 Linear combination coefftient for data read from input fie Default value 1 i e by default the difference between the data in memory and in the input fie is formed converts n complex data points z in the active dimension into 2n real data points r according to r _ Rez and r Im z k 1 n Real data remain unchanged reduce region region reverse 28 reduces the data matrix to the specifed regions The frst region corresponds to the active dimension the second region corresponds to the second dimension etc Ifthe number of regions is less than the number of dimensions of the data set all data points will be used from the remaining dimensions Data points outside the spec ifed regions are discarded A region can be given in one of the following formats denotes the data point n n includes the data points m m 1 n includes the data points m m 1 up to the last data point n includes the data points 1 2 n stands for all data points reverses the order of real or complex data points in the active dimension es eS et S 9 n denotes the number of data points in the active dimension DEN Commands select region selects the specifed regions from the complete the data matrix The frst region corresponds to the active dimension the second region co
47. onal data sets it is usually advisable to choose equal memory and workspace sizes For the processing of three and four di mensional data sets the workspace size can be signiftantly smaller than the memory size On computers with moderate physical memory size the overall performance of the system can be signifrantly degraded if the PROSA memory and workspace sizes are chosen much larger than actually necessary It can therefore be advisable for a given PROSA calculation to temporarily create a PROSA executable with adapted memory and workspace sizes For the execution of a given macro see p 37 this can be done as follows e Determine the required memory and workspace sizes using the standard macro job see p 38 and a PROSA executable called prosasmall with small memory and workspace size prosasmall PROSA version 3 4 Sun Memory size 300000 words 1171 kbytes Workspace size 300000 words 1171 kbytes job macro Macro macro checked The execution of this macro requires memory words of memory Installation Un 10 and workspace words of workspace xxx Error There are only 300000 words of memory and 300000 words of workspace available e Create atemporary executable with the memory and workspace size indicated by job makeprosa memory workspace prosatmp 7 Note that only the main program source fle prosa F has to be recompiled not the whole program e Use the PROSA executable prosatmp for the actual calcu
48. osa PROSA version 2 4 Sun Memory size 4456448 words 17408 kbytes Workspace size 4202496 words 16416 kbytes Ready job noesy Checking the macro noesy 42 Ds Examples job noesy Output from the check phase is omitted noesy checked The execution of the macro requires 1052672 words of memory and 1049088 words of workspace job noesy noesy read swap files nmr vd ser 1024c 100c File files nmr vd ser read CPU time 3 8 s total CPU time 4 3 s noesy status Occupied memory 410000 words 9 3 Dimension 1 1024 complex points Dimension 2 100 complex points Order of dimensions 1 2 noesy suppress cos 30 suppress smooth 30 cos 0 5 3 141593 30 1 k 30 3 extrapolate subtract Smoothed data with extrapolated border regions subtracted CPU time 16 2 s total CPU time 20 8 s Dimension 1 noesy multiply 0 5 1 Data multiplied noesy window cos window multiply cos 3 141593 2 1024 k 1 Data multiplied noesy ft 1024 Complex Fourier transform performed CPU time 4 0 s total CPU time 25 8 s noesy status Occupied memory 410000 words 9 Dimension 1 1024 complex points Dimension 2 100 complex points Order of dimensions 12 RD Dimension 2 noesy dimension 2 New order of dimensions 2 1 noesy multiply 1 2 100 2 Data multiplied noesy window cos window multiply cos 3 141593 2 100 k 1 Data multiplied no
49. osa 3 4 Installation DS Configuration System type sun Program prosa Makeprogram makeprosa Version 3 4 Macro extension pro Base directory home guentert prosa 3 4 RECL unit 4 per word Time routine etime tarray Integer length 1 per real Complex data type complex Precompiler lib cpp Fortran compiler 77 Compiler options c O Linker options Libraries RECL unit denotes the record length unit in units per word used in record length speciftations in FORTRAN 77 OPEN statements for direct access fles The present version of the program PROSA assumes a word length of 32 bit On computers with variable word length for example the NEC SX 3 it is essential to choose the correct word length of 32 bit Compilation The executable program prosa the script makeprosa the links for help fies and the default initialization macro init are created by make 4 By default a standard memory and workspace size will be used This and several other parameters may be changed on the make command line see the Makefle for further details For example make MAXS memory MAXW workspace PROG myprosa 5 builds a PROSA executable called myprosa with the given memory and workspace sizes in words The script makeprosa can be used to build additional PROSA execut ables in other directories The command makeprosa memory workspace executable 6 1 According to the rules of FO
50. ote an index that runs over all data points in the passive dimensions Example shift n 2 nint real n 1 ndata perm 2 1 k 1 1 In a two dimensional spectrum with a diagonal through the lower left and upper right corners this command shifts the diagonal to the cen tre of the spectrum Subsequently the diagonal may be removed using the smooth command Friedrichs et al 1991 29 Commands smooth n function m option smooths the data in the active dimension by computing the moving average s over the n preceding and n following data points s that are weighted with the given function In the function f alowercase k stands for the index that runs from n ton en Taster Ts De re ee ae a The following options are possible option extrapolate computes the m gt n data points in the border regions by quadratic extrapolation ofthe smoothed data circular assumes periodic data to smooth the border regions linear uses only the available data points for smoothing in the border regions e g for the smoothed data point 2 the data points 1 2 3 2 n replace replaces the data by the smoothed data subtract subtracts the smoothed from the original data The parameter m has only ameaning with the option extrapolate By default the options extrapolate and replace are set Example smooth 20 cos 0 5 pi 19 k 22 extrapolate subtract is a method to suppress signals with zero frequency for example the residua
51. ously the specift command is executed by the program e Otherwise the command line interpreter looks for a macro with the given com mand name see p 19 and if it is found in the current macro search path see p 19 executes it If no such macro is found an error occurs Special characters The characters have special meaning in the command line vari able or variable denote the value of the variable see p 16 The curly braces in variable or variable separate the variable name variable from immediately following text label denotes a label that can be used as address in a goto statement see p 14 c treats the character c literally and allows the use of special characters in normal text V at the end of a line indicates that the statement continues on the following line text treats text as a single parameter even if it contains spaces tex also treats text as a single parameter but the apostrophes remain part of the text Apostrophes are used to specify FORTRAN 77 string constants Text between a comment sign and the end of the line is treated as a comment and skipped by the program Commands that are preceded by will only be echoed if the system variable echo has the value full see p 18 has a special meaning only if it occurs as the frst character of a command 11 Command Interpreter MS 12 Built in commands There are t
52. phase correction see p 21 re Discard imaginary part of the aquisition dimension print print Dimension 8 Processing of the third dimension print dimension 3 Transposition that activates the third dimension multiply 1 2 n 2 Change sign of every second data point States TPPI predict Ipsvd 5 16 Append 16 complex data points by linear prediction with 5 coefficients see p 26 46 Ds Examples window cos2 Cosine squared window see p 40 ft 32 Fourier transformation with zero filling to 32 complex data points autophase 4 2 0 6 0 5 Automatic phase correction see p 21 re Discard imaginary part print print Baseline correction print dimension 1 Activate the aquisition dimension cfhtt cft 10 6 0 3 2048 1 Baseline correction using the FLATT method see p 23 37 54 with a half width of 10 data points and a threshold parameter t 6 for the de termination of pure baseline regions The basis functions that are used to represent the baseline distortions are the 5 trigonometric functions that correspond to the first 3 time domain data points To correctly gen erate these basis functions the command must be provided with the in formation that the present data constitutes a strip taken out of the complete size of 2048 complex points starting at data point 1 cf the command ft 2048 1 1024 above see p 37 dimension 2 Activate the second dimension cfhtt cft 4 6 0 3 Baseline correct
53. rresponds to the second dimension etc If the number of regions is less than the number of dimensions of the data set all data points will be used from the remaining dimensions Data points outside the specifed regions remain in memory and the complete data set can be restored by a select statement without parameters provided that the size of the selected data was not changed All PRosA statements can be applied to the selected portion of the data in exactly the same way as for the complete data set A region can be given in one of the following formats n denotes the data point n m n includes the data points m m 1 n m includes the data points m m 1 up to the last data point n includes the data points 1 2 n S stands for all data points n and m always refer to the complete data set the select statement cannot be used recursively Examples select 100 200 50 80 selects the points 100 200 in the active and the points 50 80 inthe second dimension select 20 selects plane 20 of a 3D spectrum select uses again all data shift m shifts the data in the active dimension circularly by m points to the right Er ee ae s 10 Sp Sps Sh n m 9n m X On m n denotes the number of data points in the active dimension A circular shift by m data points to the left is achieved with m m or m n m m is an integer expression that is interpreted modulo n and in which a lowercase k may den
54. t variable is true if and only if the variable exists def variable is true if and only if the variable exists and has a value different from NULL fie flename is true if and only if a fle called flename exists Example set i 56 if i 1t 0 print i is negative 56 is negative if condition then sequence of statements else if condition then sequence of statements else sequence of statements end if executes a block if statement as in FORTRAN 77 In addition to the possibilities of FORTRAN 77 there are three logical functions exist variable is true if and only if the variable exists def variable is true if and only if the variable exists and has a value different from NULL fle flename is true if and only if a fle called fle name exists A Command Interpreter Example if mod i 2 eq 1 then print i is an odd number else if def x and exist y then print The variable x is defned and the variable y exists else if s eq then print The variable s is blank end if parameter variable variable changes the names of the parameters that are passed to a macro i e the param eters pl p2 get the names given in the parameter statement The parame ter statement must precede all other statements in a macro except var and cannot be used interactively print flename text option writes the text to standard output or into the fle with the given flename If
55. terpreter pl p2 denote by default the command line parameters of a macro see p 19 The names of the command line parameters may be changed at the beginning of the macro with the parameter statement see p 15 path denotes the current search path for macro fles Usually this variable is initialized in the initialization macro init see p 19 Macros Macros are fies containing statements A macro is called by its name that is iden tical to its flename except for the extension pro that is required for macro fies Mac ro fies are searched in the directories given in the system variable path see p 19 or in the explicitly given directory Command line parameters may be passed into a mac ro Within the macro they are available as local variables that are by default called pl p2 These variable names can be changed with the parameter statement see p 15 The local variable nparam denotes the number of command line parameters Macros can be called from within other macros On line help information may be in cluded into a macro as lines that start with two comment signs Such lines are copied to standard output when one requests help about a macro with the command help macro The special macro init created during installation from the fie src init pro def is an initialization macro that is automatically executed when the program starts Typically this macro sets the system variable path see p 19 that de
56. the text contains blanks it must be enclosed in double quotes The default option append indicates that the text is to be appended to an existing output fle fename Anew fle flename will be opened if necessary The option close indicates that the fle will be closed after writing the text quit exits the program return exits from the current macro and returns to the calling macro or if the macro was called interactively to interactive input Given interactively return exits from the program set variable set variable value variable value displays or sets values of variables If no variable is specifed all variables that have values different from NULL are displayed If the names of one or several variables are given the values of these variables are displayed System variables that must not be changed by the user are marked as read only In the form set variable value the given value i e a string is assigned to the variable In the short form variable value without the keyword set the sign must be sur rounded by blanks Examples set i 456 j 2 i 15 Command Interpreter EE setij Variables i 456 j 2 456 show variable displays the values of all or selected global variables If no variable is specifed all global variables that have values different from NULL are displayed If the names of one or several global variables are given the values of these variables are dis
57. tion do not depend critically on the selection of the three parameters x u and v We found that the value of should be decreased for spectra with low signal to noise ratio that the maximal peak width u should account for the increased line widths in power spectra and that v can be reduced when a spectrum contains a large number of peaks Usually the number of one dimensional peaks included for the phase correction of a 3D spectrum is of the order 1000 which renders the method robust against instabilities that might arise if only a small number of peaks were used be it because of low signal to noise ratio poor digital resolution peak overlap or occasional inclusion of artifactual peaks Baseline correction Baseline correction in the frequency domain is performed for each 1D cross section by frst identifying regions of pure baseline Gintert and Withric h 1992 and then subtracting a function which is best fited to the pure baseline regions The pure base line regions are identifed either with modifed versions of the FLATT procedure Gin tert and Withric h 1992 or with the derivative method of Dietrich et al 1991 For a data point k with intensity s both methods yield a parameter p which becomes small if the data point k is located in a pure baseline region and large otherwise n FLATT Pr min gt s a bl n21 24 a n Derivative method p ae n20 25 In Eq 24 p is determined by fiting a
58. to account for the noise level calculation if the data set includes more than 10 or 106 data points respectively 51 Algorithms E 52 Linear prediction In PROSA linear prediction Olejniczak and Eaton 1990 Stephenson 1988 Zhu and Bax 1990 is used to reduce effects caused by discrete Fourier transformation of truncated time domain signals i e primarily line broadening and the appearance of sidelobes The linear prediction method is based on the assumption that a data point s can be written as a linear combination of the m preceding data points Sk _m gt Sk 1 m Sk gt Q55 1 16 l 1 For a superposition of at most m damped oscillations with amplitudes A phases 6 frequencies and dampings T that is sampled in time steps At id Ta i y RAt e Be Ave 17 this assumption is fulfiled and the zeros z 2 of the polynomial m 1 a 12 18 l 1 T i0 At are related to the frequencies and damping factors by z J He The linear pre diction coefftients a a are determined by application of Eq 16 to the mea sured data using singular value decomposition Barkhuijsen et al 1987 Kumaresan and Tufts 1982 Press et al 1986 Since each individual coefftient represents one frequency component it is necessary to have an approximate estimate of the number of frequencies included in the time domain signal and additional coefftients are need ed to account for the noise Singular val
59. ue decomposition uses an overdetermined sys tem of equations and the maximal number of coefftients can be as high as one half of the number of complex data points To ensure that the predicted signal is stable the roots of the characteristic polynomial 18 of the linear prediction coefftients are cal culated Following conventional use of linear prediction PROSA takes all roots into ac count and guarantees a stable predicted signal by reftcting the roots z about the unit circle z gt z lz if necessary Press et al 1986 Although this procedure incorpo rates noise into the predicted data the results do usually not differ signifeantly from those obtained when putative noise roots are eliminated because the noise roots usu ally lead to rapidly decaying components of small intensity in the predicted data Stephenson 1988 Since baseline distortions are primarily caused by errors in the measurement of the frst few time domain data points Otting et al 1986 the backward linear predic tion implemented in PROSA can be used to restore this corrupted part of the signal and is thus also a suitable method for baseline correction Marion and Bax 1989 When compared with baseline correction procedures that work in the frequency domain Di etrich et al 1991 Gintert and Withric h 1992 Pearson 1977 an advantage of this method is that the baseline correction is performed at the beginning rather than at the DEN Algorithms end of
60. unction name cos _ cos nt 2 cosine window cos2 cos nt 2 cosine squared window exp L en exponential line broadening gauss LG gna Lorentz Gauss transformation hamming 0 54 0 46 cos Tt Hamming window hanning 0 5 0 5cosnt Hanning window sin 0 sin d 1 t shifted sine bell sin2 0 sin 4 0 nt shifted squared sine bell The symbols in the table have the following meaning t k 1 n where k 1 n runs over alln data points in the active dimen sion L denotes the line broadening in Hertz G denotes the maximum of the Lorentz Gauss window function at t G A denotes the time increment in seconds i e the value of the system variable delta active see p 33 6 denotes the shift of the sine bell or squared sine bell in degrees for example window sin 90 is equivalent to window cos 40 Examples This chapter illustrates the use of PROSA with some practical examples of the pro cessing of 2D and 3D data sets The program can be used in three different ways e The user may enter statements interactively The program can execute a sequence of statements contained in a macro fle This strategy is shown in two examples see p 41 45 and 46 47 A customized user interface may be created with the help of macros and the ask command The frst example shows the data processing of a 2D H H NOESY data set of the basic pancreatic trypsin inhibitor BPTI The PROSA commands
61. vel acceptable signal maxima in the absolute value spec trum must exceed the product of height times the noise intensity parameter x on p 53 overlap Maximal number of acceptable signals that involve a common fre quency coordinate parameter v on p 53 maximal absolute value of the linear phase correction parameter i e gt will be chosen such that d lt 6 6 0 indicates that only a constant phase correction will be determined max 7 1 These are the commands ask break do error eval exit goto help if parameter print quit return set show type and var see p 12 21 Commands complex complexify 22 option apply determine complex real global local symmetrize info equal sqrt The phase correction will be determined and applied The phase correction will be determined but not applied Signals will be searched in the real and imaginary parts of the passive dimensions Signals will only be searched in the real parts of the passive dimensions This option is useful if the phases in the passive dimensions are already approximately correct The global maximum of the target function in the range 0 lt 6 lt 6 will be used to determine the linear phase correction parameter 6 The local maximum of the target function with the smallest absolute value will be used to determine the linear phase correction parameter by Symmetrized signal re
62. wo kinds of commands in the program general built in commands of the command line interpreter and specife commands see p 21 The following is an alphabetical list of all built in commands of the command line interpreter alias name statement defnes a new alias name i e an abbreviation for the given statement The state ment may contain an asterisk to indicate where the command line parameters are to be inserted Without parameters alias gives a list of all currently defned aliases Example alias print 5 7 35 ask prompt variable variable writes the string prompt to standard output reads one line from standard input and assigns from this line strings separated by blanks to the given variables The command is usually used for interactive input within macros A prompt that con tains blanks must be enclosed in double quotes Example ask First and last point begin end First and last point 12 45 print range begin end range 12 45 break breaks a do loop and is only allowed in macros The execution of the macro is con tinued with the frst statement following the loop command name sequence of statements end command defne a new globally visible user defned command within a macro i e a macro within a macro User defned commands defned by command statements are called by their name possibly followed by parameters in exactly the same way as macros Within a macro a

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