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MOLREP (CCP4: Supported Program)

NAME

molrep - automated program for molecular replacement

SYNOPSIS

molrep [HKLIN in.mtz] [MAPIN EM_map.ccp4] [MODEL in.pdb ( or EM_mod_map.ccp4)] [MODEL2 in2.pdb] [PATH_OUT path_out] [PATH_SCR path_scr]
[Keyworded input]

DESCRIPTION

Version 7.2 /26.02.2002/

FEATURES

CONTENTS

REFERENCES

      
   Author:  A.A.Vagin
                email: alexei@ysbl.york.ac.uk

   References:     A.A.Vagin, New translation and packing functions.,
                   Newsletter on protein crystallography., Daresbury
                   Laboratory, (1989) 24, pp 117-121.

                   Alexei Vagin and Alexei Teplyakov.
                   An approach to multi-copy search in molecular replacement., 
                   Acta Cryst.D,(2000) 56, pp 1622-1624 

                   A.A.Vagin and M.N.Isupov
                   Spherically averaged phased translation function and 
                   its application to the search for molecules and fragments 
                   in electron-density maps
                   Acta Cryst.D,(2001) 57, pp 1451-1456


            main:  A.Vagin,A.Teplyakov, MOLREP: an automated program for
                   molecular replacement.,
                   J. Appl. Cryst. (1997) 30, 1022-1025.

INPUT/OUTPUT FILES

Input file

HKLIN
Input MTZ file or CIFile structure factors
in the case of fitting two atomic models, leave this option out.
CIF file contains indices, structure factors (and phases if you need them): h,k,l,|F|,sig(F),Phi or h,k,l,|F|,sig(F),Phi,Fom
  • MTZ file must have extension "mtz".
    • MAPIN
    MAPIN can be used instead of HKLIN
    Input file with CCP4 map.
    EM or electron density file in CCP4 format (File must have extension "ccp4").
    This file will be converted to files of !F! and phases.
    In the case of fitting two atomic models, leave this option out.
    MODEL
    Input PDB file with the coordinates or CCP4 map.
    (CCP4 map file must have extension "ccp4").

    Without this file the program computes a Self Rotation Function and plots RF(theta,phi,chi) for

    chi = 180, 90, 120, 60
    You can change the fourth value of chi (60) by keyword CHI
    You can change the scale of these plots of RF by keyword SCALE

    MODEL2
    Input PDB file with second fixed model
    PATH_SCR
    You can use this variable to redirect all scratch files to special directory.
    Default is value of TEMP1 or CCP4_SCR variable.
    If 'PATH_SCR .' all scratch files will be in current directory.
    PATH_OUT
    You can use this variable to redirect output files to special directory.

    Space group and unit cell parameters of the unknown structure will be taken from the file of structure factors. You can change the space group of the structure factor file by using keyword NOSG.

    Output files

    molrep.pdb
    new PDB coordinate file of model (plus model_2) corresponding to the best solution of Cross Rotation and Translation Function.
    molrep_fcalc.cif
    formatted CIFile of molrep solution (plus from model_2) with Fobs, Fcalc, Phcalc (this files will be created if your model is EM or density in CCP4 format).
    molrep.doc
    additional protocol (like log file in CCP4). This file will be created if keyword DOC is 'Y' or 'A'.
    molrep_rf.tab
    List of peaks of rotation function, created as soon as the program calculates a Rotation Function.
    molrep_rf.tab is default name, you can use another name using keyword FILE_T.
    You can edit this file and use it for subsequent calculations without computing the rotation function again (keyword FUN=T). The program then reads (in free format!): "Sol_", peak number and Polar angles (theta,phi,chi), e.g.: 
    "Sol_  23  10.0    22.2 40.0"
    In 'Rotation and Position the model' (keyword FUN=S), the program reads "Sol_", peak number,Polar angles and shift (sx,sy,sz) e.g.: 
    "Sol_  23  10.0    22.2 40.0  .564 .443 .032"
    If you like to use Eiler angles use "Sol_A" instead "Sol_"
    In 'Search model orientation by PRF' (keyword PRF=P), the program reads "Sol_", peak number,Polar angles and shift (sx,sy,sz) e.g.: 
    "Sol_  23  10.0    22.2 40.0  .564 .443 .032"
    But program will use only the shift (sx,sy,sz).
    molrep_srf.tab
    List of peaks of Self Rotation Function.
    molrep_srf.tab is default name, you can use another name using keyword FILE_TSR.
    molrep_rf.ps
    PostScript file of Self Rotation Function

    also (if you used keyword FILE_S):

    align.pdb
    input model corrected by sequence alignment

    WHAT MOLREP CAN DO

    
                          +-- Self RF  (FUN=R, without any model)
                          !
         +-- Standard MR -+-- Cross RF (FUN=A or FUN=R )
         !                !
         !                +-- Locked Cross RF ( FUN=A or R and LOCK=Y )
         !                !
         !                +-- TF       (FUN=A or FUN=T )
         !
         !
         !                                       +- two identical models
         !                                       !
         !                      +-- Dyad search -+
         !                      !   (DYAD=D)     !
         +-- Multi-copy search -+                +- two different
         !      for MR          !                   models 
         !                      !
MOLREP --+                      +-- Multy-copy for one model
         !                          (DYAD=Y)
         !                        
         !                        
         !                       +-- RF and PTF
         !                       !   (PRF=N)
         !                       !
         +-- Fitting two models -+-- SAPTF, RF and PTF
         !                       !   (PRF=S)
         !                       !
         !                       +-- SAPTF, PRF and PTF
         !                           (PRF=Y)
         !
         !
         !                        +-- RF and PTF
         !                        !   (PRF=N)
         !                        !
         +-- Searching in ED map -+-- SAPTF, RF and PTF 
         !                        !   (PRF=S)
         !                        !
         !                        +-- SAPTF, PRF and PTF
         !                            (PRF=Y)
         !
         +-- Rotate and position the model (FUN=S)
         !
         !
         !
         +-- Search model orientation in electron density map 
             for particular position by phased RF (PRF=P)



   where: FUN, DYAD, PRF, LOCK - keywords
          MR    - Molecular Replacement
          RF    - Rotation function
          TF    - Translation function     
          PRF   - Phased Rotation function
          PTF   - Phased Translation function
          SAPTF - Spherically Averaged Phased Translation function
          ED    - Electron density

    * Standard molecular replacement method

    The program performs molecular replacement in two steps:

    1. Rotation function (RF)
      search orientation of model
    2. Cross Translation function (TF) and Packing function (PF)
      search position of oriented model

    The result of the Rotation function depends on the radius of a spherical domain in the centre of the Patterson function (the so-called cut-off radius). This radius must be chosen so as to maximize the ratio between the number of inter- and intramolecular vectors. The program chooses the value of this radius as twice the radius of gyration, but can also use an input value.

    Instead of computing RF, the program can use a list of orientations from a Rotation function which was prepared before. Anisotropic correction of data before computing RF can be useful for data with high anisotropy.

    With a second fixed model, the use of modified stucture factors instead of |Fobs| for RF (keyword DIFF) may make RF clearer. The modified stucture factor is:

    ||Fobs|-|Fmod2|*(P2/100)|

    where P2 is the percentage of model_2 in the whole structure.

    The Translation function can check several peaks of the rotation function by computing a correlation coefficient for each peak and sorting the result. For scaling observed and calculated structure factors, the program uses the scaling by the origin peak of Patterson, but for data with high anisotropy the program can use anisotropic scaling. The Translation function can take into account the second fixed model and also, if the number of monomers is known, MOLREP can position the input number of monomers in a simple run. Also in this case the possibility to choose from symmetry-related models closest to which was found before is useful.

    The program can detect and use pseudo-translation vectors. In this case the pseudo-translation related copy will be added to the final model.

    The Packing function is very important in removing wrong solutions which correspond to overlapping symmetry-related or different models.

    Use keywords:

    COMPL, DIFF, FUN, NMON, NP, NPT, P2, PACK, PST, RAD, RESMAX, SIM, STICK, SURF, VPST, NREF, NREFP, FILE_T, FILE_TSR, NSRF

    * Self Rotation Function only

    If you define only a file of structure factors (Fobs), the program will compute a Self Rotation function with cut-off radius RAD = 30 as default. Use keyword RAD if you want another value. Other useful keywords: RESMAX, RES_R, COMPL, SIM.

    Resulting output:

    molrep_srf.tab
    List of peaks of Self Rotation Function.
    molrep_srf.tab is default name, you can use another name using keyword FILE_TSR.
    molrep_rf.ps
    PostScript file of Self Rotation Function which contains four plots RF (theta,phi,chi) for
    chi = 180, 90, 120, 60.
    You can change the fourth value of chi (60) by keyword CHI
    You can change the scale of these plots of RF by keyword SCALE

    * Search model in electron density map

    In some cases it is difficult to solve an X-ray structure by molecular replacement even when a structure for a homologous molecule is khown. If prior phase information either from SIR/MAD or from a partial structure is known, this could be used in a six-dimensional search. The program divides the six-dimensional search with phases into three steps:

    1. a spherically averaged phased translation function (SAPTF) is used to locate the position of the molecule or its fragment. It compares locally spherically avaraged experimental electron density with that calculated from the model and tabulates highest scoring positions.
    2. then for each such position a local phased rotation function (PRF) is used to find the orientation of the molecule.
      Another possibility is to use usual rotation function (RF) for modified map, i.e program sets 0 the density outside of sphere with radius = twice radius of model and with the centre in current point.
    3. the phased translation function (PTF) for found orientation which checks and refines the found position.

    You need to have the phases in a CIF file of structure factors or to use corresponding keywords for MTZ file or use EM map as input instead of Fobs file.

    • with keyword PRF = 'N' (default value):
      usual Rotation function and Phased Translation function will be used.
    • with keyword PRF = 'Y':
      SAPTF (Spherically averaged phased translation function), Phased Rotation function and Phased Translation functions will be used.
    • with keyword PRF = 'S':
      1.SAPTF (Spherically averaged phased translation function). 2.For current point of SAPTF solution input map is modified, i.e program sets 0 the density outside of sphere with radius = twice radius of model and with the centre in current point. 3.usual Rotation function for this modified map. 4.Phased Translation functions

    Other useful keywords:

    COMPL, NMON, NP, NPT, RAD, RESMAX, SIM, SURF, INVER

    * Search model orientation in electron density map for particular position by PRF

    You can use this possibility (keywords PRF=P and FUN=R or A) if you want to find the model orientation in ED map by rotating model around the defined point in ED map. Program puts the origin of model coordinate sysytem to the defined point and performs phased rotation function (PRF). Use keyword RAD to define the radius of sphere for PRF.

    You must define the list of defined points of ED map using file FILE_T , wich must contain lines with "Sol_", peak number,Polar angles and shift (sx,sy,sz) e.g.: 

    "Sol_  23  10.0    22.2 40.0  .564 .443 .032"
    But program will use only the shift (sx,sy,sz).

    Model is rotated around the origin of model coordinate sysytem. If keyword SURF= Y,A,2,O program puts the centre of model to the origin of model coordinate sysytem automatically. If you want, for example, to rotate the model around some atom, shift the origin to this atom and use SURF=N

    Other useful keywords:

    COMPL, NMON, NP, NPT, RESMAX, SIM, INVER

    * Fitting two models (FM)

    The idea is to fit the electron densities instead of the atomic models, trying to find the best overlap. Advantages are:

    • can be used for cases with very low homology;
    • can be used when amino acid sequence is absent;
    • no need to use the list of equivalent atoms.

    If you define only two files of models (searching model and model_2), without a file of structure factors (HKLIN), the program will fit the search model (MODEL) to the second model (MODEL2). The search model must be smaller or equal to the second model.

    • with keyword PRF = 'N' (default value):
      usual Rotation function (RF) to search the orientation and Phased Translation function (PTF) to search position will be used.
    • with keyword PRF = 'Y':
      Spherically averaged phased translation function (SAPTF) gives the expected position for model. Phased Rotation function (PRF) for expected position gives orientation. Phased Translation function (PTF) checks and refines the translation vector.
    • with keyword PRF = 'S':
      see above Search model in electron density map

    Other useful keywords:

    COMPL, NP, NPT, RAD, RESMAX, SIM, SURF

    The result is file molrep.pdb - model fitted to second model.

    * Just rotate and position the model

    This possibility may be useful if you want to place the model to a particular orientation and position, or to compare several solutions.

    Use keyword FUN=S and define three files: a model (MODEL), a file of structure factors (HKLIN) and file with polar angles and shifts (keyword FILE_T). The program will shift the model to the origin, rotate (by polar angles) and the position it (in fractional unis). The new model will be written to an output coordinate file. Also the program will compute an R-factor and a Correlation Coefficient.

    Other useful keywords:

    COMPL, RESMAX, RES_T, SIM

    * Multi-copy search

    There are two modes: "dyad_search" and "Multi-copy search".

    Dyad_search - Search two copies of a model simultaneously (keyword DYAD=D).

    Sometimes you can not find a solution starting with one molecule if you have several copies of the molecule in the asymmetrical part of the unit cell. In this case a search with two independent molecules may give a solution. The central point of method is the construction of a multi-copy search model from properly oriented monomers using a special TF (STF), which gives the intermolrecular verctor between properly oriented monomers (dyad). This dyad can then be used for a positional search with a conventional TF.

    1. the program checks all pairs of NP peaks of the Rotation Function (RF). For each pair the program uses the first rotation to prepare model-1. Model-2 will be prepared by using the second rotation and one rotation from the crystallographical symmetry operators. The total number of pairs to be checked is ((NP+1)*NP*Nsym)/2
    2. next, for model-1 and model-2: the program computes the Special Translation Function ( STF) to find the inter-molecular vector of the dyad.
    3. for NPT peaks (i.e. inter-molecular vectors) of the STF, the program computes the standard Translation Function (TF) using the current dyad as a model, and it calculates a Correlation Coefficient for the firstNPTD peaks of the TF.

    Solution and output file: molrep.pdb will be the dyad with the best Correlation Coefficient (or several dyads if keyword NMON > 1).

    WARNING: the procedure takes quite some time, because the total number of Translation Functions to be calculated is NMON*NPT*((NP+1)*NP*Nsym)/2.

    In the output .log (.doc) file you can find the following information:

    
Sol_      R1  R2  Rs Rslf STF TF        Shift_1     PFmax PFmin    Rfac   Corr
Sol_       1   1   1   0   2   1  0.059 0.000 0.201  1.01  0.99   0.569  0.379

and

Sol_best   1   1   1   0   2   1  0.059 0.000 0.201  1.01  0.99   0.569  0.379
Sol_best         Rot1-->2               Dyad_vector       dist d_ort d_par
Sol_best    0.0    0.0    0.0    -0.210  0.000 -0.487    39.2  19.6  33.9

    These lines means:

    R1
    peak number of rotation for model-1
    R2
    peak number of rotation for model-2
    Rs
    CS operator number which applyed before rotation for model-2
    Rslf
    peak number of self rotation function
    STF
    peak number of special translation function
    TF
    peak number of translation function
    Shift_1
    position of model-1
    PFmax PFmin
    min, max values of Packing function
    Rfac Corr
    R-factor and Correlation Coefficient
    Rot1->2
    polar angles of rotation from model-1 to model-2.
    Dyad_vector
    vector (in fractional) from model-1 to model-2.
    dist d_ort d_part
    first number - distance between models (in Angstrom)
    second number - distance orthogonal to rotation 1->2
    third number - distance parallel to rotation, i.e. for pure dimer this is 0.

    With keyword LIST=L you can find additional information:

    Sol_              angles_1             angles_2        shift_2
Sol_      90.63   98.70  118.12   90.63   98.70  118.12  0.189  0.256 -0.415
 
       +---------------------------------------------------------+ 
       !                                                         !
       !                                                         !
       !                                                         !
       !                                                         !
       !                                                         !
       !      -----------------            -----------------     !
       !     /                 \          /                 \    !
       !    /                   \        /                   \   !
       !    ! rotated (angles_1) !       ! rotated (angles_2) !  !
       !    !     monomer_1      !       !     monomer_2      !  !
       !    !                    ! dyad  !                    !  !
       !    !         +----------!-----------------+          !  !
       !    !        /           ! vector!       '            !  !
       !    !       /           /         \  '               /   !
       !    \      /           /           \                /    ! 
       !     \    /           /          '  \              /     !
       !      ---/------------        '      --------------      !
       !        /shift_1           ' shift_2                     !
       !       /                '                                !
       !      /              '                                   !
       !     /            '                                      !
       !    /          '                                         !
       !   /        '                                            !
       !  /      '                                               !
       ! /    '                                                  !
       !/  '                                                     !
       +---------------------------------------------------------+
         origin

    If you believe the Self-RF, you can try to find a dyad which has the rotation between monomers corresponding to the rotation of the Self-RF (use keywords NSRF,FILE_TSR).

    Model-2 can be different from model-1. Use keywords FILE_M2 to define file of searching model-2, FILE_T2 with list of peaks rotation function for this model (this RF have to be computed before) and NP2 number of peacks which will be used.

    Multi-copy search - Search many copies of a model (not only dyad) (keyword DYAD=Y). Program starts to search a single monomer, after that produces the dyad search, repeates dyad search for next dyad with the first being fixed and ,finaly, tryes add a single monomer.

    Use keywords:

    DYAD, DIST, NP, NSRF, NPT, NPTD, NP2, AXIS, FILE_M2, FILE_T2, FILE_T, FILE_TSR, NMON, ALL, PACK

    and also:

    COMPL, SIM, RESMAX, SURF, STICK

    * Model correction

    You can improve your model beforehand by using keyword SURF.

    * Using sequence alignment

    Another way to improve your model is to use the sequence of the unknown structure.

    Use keyword FILE_S to define a file containing a sequence. This sequence file must be ASCII:

    ! 
!
!# sequence 
!SVIGSDDRTRVTNTTAYPYRAIVHISSSIGSCTGWMIGPKTVATAGHCIY
!# this is comment
!    DTSSG--SFAGTATVSP   GRNGTSYPYG
!NRGTRITKEVFDNLTNWKNSAQ
    !

    If the first symbol in the line is "#", it means the line contains comments. Blancs are ignored.

    The program will perform sequence alignment and create a new corrected model with the atoms corresponding to the alignment. The output file with the corrected model is align.pdb. The results of the alignment are written to the DOC-file, if this was defined. Without an Fobs file, the program only performs model correction.

    * NMR Model

    You can use PDB file with NMR models or pseudo-NMR file with several homologous structures which were superimposed before. Algorithm is equivalent to sum RF or/and TF for individual structures. Program can find the best model in NMR file or use all models (see keyword NMR) .

    In the PDB file different models must be separated by MODEL record. For example: 

    HEADER    HYDROLASE (ENDORIBONUCLEASE)         
CRYST1   64.900   78.320   38.790  90.00  90.00 ...
MODEL        1 
ATOM      1  N   ASP A   1      45.161  12.836 ... 
ATOM      2  CA  ASP A   1      45.220  12.435 ...   
 ... 
ATOM    745  SG  CYS A  96      58.398   6.673 ... 
ATOM    746  OXT CYS A  96      62.238   7.178 ...  
ENDMDL                                        
MODEL        2   
ATOM      1  N   ASP B   1      44.487  11.386 ...  
ATOM      2  CA  ASP B   1      44.559  11.129 ... 
 ...

    Use keyword NMR

    * EM or electron density model

    Searching model can be Electron Microscopic model (EM) or electron density map. Only values higher the limit (if keyword ROLIM is defined) will be used. Map must have space group P1 and contains whole model. Vector ORIGIN defines the centre of model and the rotation will be performed around this point. If parameter DRAD (radius of model) is defined program will use the density only inside the sphere with radius = DRAD and with centre in vector ORIGIN. 

    
        +--------------------------------+ nz
   !    !                                !
   !    .                                .
   !
   !    !                                !
   !    .                                .
   !
   !    !                                !
   !    +--------------------------------+ izmax
   !    !                                !
   !    !                                !
   !    !                                !
   !    !      ----------------          !
   !    !     /                \         !
   !    !    /                  \        !
   !    !   /                    \       !
 C_cell !  /                      \      !
   !    !  !                       !     !
   !    !  !   DRAD                !     !
   !    !  !---------- +           !     !
   !    !  !          / centre     !     !
   !    !  !         /             /     !
   !    !  \        /             /      !
   !    !   \      /             /       !
   !    !    \    /             /        !
   !    !     \  /             /         !
   !    !      -/--------------          !
   !    !      /                         !
   !    !     /                          !
   !    !    / ORIGIN                    !
   !    !   /                            !
   !    !  /                             !
   !    ! /                              !
   !    !/                               !
   !    +--------------------------------+
        0                                nx
        ----------- A_cell --------------

    Program will get vector ORIGIN from file automatically. If it is not possible to get correct vector, program will use ORIGIN = ( 0.5, 0.5, izmax/nz). If you want you can define ORIGIN yourself.

    Use keywords:

    DSCALEM, INVERM, ROLIM, DRAD, ORIGIN

    Also you can use EM or electron density map instead of file of Fobs. In this case map will be converted into !F! and phases and Search model in electron density map will be performed as usual.

    Use keywords:

    DSCALE, INVER, DLIM

    * Locked Cross Rrotation Function

    Locked Cross Rotation function (LRF) means to average the Cross Rotation function by NCS which can be determined with Self Rotation function. LRF is especially useful when NCS forms a group.

    Use keywords:

    LOCK, NSRF, FILE_TSR,

    * Rigid body refinement

    If keyword MODE = S program produces Rigid Body refinement for each peak of TF. Number of cycles is controled by keyword NREF (default 10). Also program can refine the orientation given by RF before TF. In this case program produces Rigid Body refinement (in space group P1) for each peak of RF. Number of cycles is controled by keyword NREFP. Default value is 0, i.e. without this refinement.

    Use keywords:

    MODE, NREF, NREFP

    HOW TO USE MOLREP

    A simple way to use MOLREP is to define files for Fobs (HKLIN) and the model (MODEL), number of model to search (keyword NMON), and use default values for all parameters (i.e. without using any keywords). There is always a chance of solving the structure automatically. If this does not work, use a common strategy of molecular replacement.

    Planning ahead

    Success of the molecular replacement method depends on:

    • quality of experimental data
    • scaling |F|_obs and |F|_calc
    • low resolution limit
    • high resolution limit
    • quality of the model, homology, conformation

    Things to look out for:

    data
    Look at your data quality. Completeness is very important. Absence of low resolution reflections may cause problems, especially if the model is some part of a whole structure. Look at anisotropy and twinning.
    Think carefully: can you 'safely' use the high resolution reflections? If not, use keyword SIM to remove the potentially bad effect of this part of the data. It might be a good idea to use some program to check the data, for example SFCHECK
    model
    Look at the model regarding the shape. The automatic choice of the cut-off radius for RF is twice the radius of gyration. This is good enough if the shape is approximately spherical. If the model is very asymmetrical, it is better to make a choice yourself.
    Remove from your model the heavy atoms and some terminal residues if they lie 'outside' the model.
    Make a choice for SIM,COMPL. If you have not any idea about similarity, SIM=0.5 is a good approximation.
    If you have a dimer use it, but use RAD corresponding to a monomer.
    It is very useful to shift the model to the origin of coordinates. Use keyword SURF = O or Y (Y is default).
    Self-RF
    Compute Self-RF. It may give you some idea about NCS or about the number of copies in the asymmetrical part of unit cell.
    Choose the radius of integration carefully. The program can not make any informed choice about it without a model (default is 30Å).
    Cross-RF only
    Compute Cross-RF with LIST=L and DOC = Y. In the DOC_file you can find the list of expected orientations of the model and also the rotations between them. Compare this with the Self-RF. This is an additional check of correctness of the expected orientation. But sometimes we can not find corresponding peaks in Self-RF for correct orientation.
    If you have high anisotropy in the data, use anisotropic correction.
    Translation function
    If there are several copies of the model in the asymmetrical part of unit cell, use keyword NMON or multi-copy or dyad search. You can not use the option of Pseudo-translation for a dyad search, since this can recognize Pseudo-translation itself.
    If you have high anisotropy in the data, use anisotropic scaling.

    Pseudo-translation

    MOLREP can detect pseudo-translation, and define a pseudo-translation vector.

    If keyword PST = Y, the program applies pseudo-translation with a pseudo-translation vector which was defined by the program or the user. When calculating a Translation Function, the program will use this vector to modify structure factors. Pseudo-translation copy will be added to the final model at the end program running.

    If FUN=R and LIST=L MOLREP computes a list of Patterson peaks and writes these to molrep.doc. This may be helpful in the detection of pseudo-translation.

    Use keywords:

    PST, VPST

    Flexible model

    If your model is flexible, for example, consists of two domains, you can try to solve this problem by two ways:

    1. Create two files for each domain and use dyad search (DYAD = D)

    2. Combine these two domain files to single file with line "MODEL" between domains (like NMR file). Use usual Molecular Replacement methods with keyword NREFP or MODE = S and NREFP.

    The use many homologous models

    If you have several homologous models you can create a pseudo NMR file with these models and use its together (see NMR model). But these models must be superimposed before, for example, by MOLREP (see fitting two models).

    Keep in mind

    • If you want to play with parameters, use also Keywords for special cases.
    • Without a model file, the program only computes a Self Rotation Function.
    • Model correction can be performed by using keyword SURF, or by including FILE_S, a file with a sequence for sequence alignment.
    • If FUN=R, the program computes and writes to molrep.doc all symmetry-related peaks of the Rotation Function. If also keywords NSRF and FILT_TSR are used you can fine the pairs of peaks of cross RF which corresponds to NCsymmetry.
    • If you want to change the space group of the structure factor file, use keyword NOSG, i.e. new space group number.
    • The Packing Function (PF) is very important to remove wrong solutions which correspond to overlapping symmetry-related or different models. But you can remove this option (PACK = N ), for example, if you want to find the model in a special position. Value of PF = 1 corresponds to non-overlapping, value = -1 corresponds to completely overlapping two models.
    • When MOLREP is trying to find several models (NMON > 1) it is useful to use keyword STICK = Y. Then for each additional molecule the program will choose a symmetry-related molecule closest to which was/were found before. This option does not work with pseudo-translation.
    • Do not use MODE = S without serious consideration.
    • For the PRF and the SAPTF, the default cut-off radius is once the radius of gyration, whereas for a Patterson calculation the cut-off radius would be twice the radius of gyration.

    KEYWORDED INPUT

    The available keywords are:

    General keywords

    Common:

    DOC, LABIN, FILE_T, FUN, NMON, NP, NPT, RAD PATH_SCR

    And for structure factors control:

    COMPL, RESMAX, SIM

    And for model control:

    SURF

    And for multi-copy search:

    DYAD, FILE_M2, FILE_T2, NP2, NPTD, NSRF

    And for search in ED:

    PRF, INVER

    And for fitting two models:

    PRF

    And for EM or electron density model:

    DSCALEM, INVERM, ROLIM, DRAD, ORIGIN

    And for EM or electron density instead of Fobs:

    DSCALE, INVER, DLIM

    Keywords for special cases

    Common:

    ANISO, BADD, LIST, LMAX, LMIN, MODE, PACK, RES_R, RES_T

    And for standard MR:

    DIFF, FILE_S, NMR, NOSG, P2, PST, STICK, VPST, LOCK, NREF, NREFP

    And for Self RF:

    CHI, PST, SCALE, FILE_TSR

    And for multi-copy search:

    AXIS, DIFF, DIST, P2, ALL, STICK

    And for search in ED:

    DIFF, P2, NPTD

    And for fitting two models:

    NPTD

    General keywords

    LABIN <program label>=<file label>...

    Specify input column lables.

    The program labels defined are: F, SIGF, F(-), SIGF(-), I,SIGI, I(-), SIGI(-), PHIC, FOM

    Flabel of F or F(+)
    SIGFlabel of sigma F or sigma F(+)
    F(-)label of F(-)
    SIGF(-)label of sigma F(-)
    IStructure Intensity of hkl
    SIGIStandard deviation of the above
    I(-)Structure Intensity of -h -k -l
    SIGI(-)Standard deviation of the above
    PHIClabel of phases
    FOMlabel of figure of merit

    DOC < N | Y | A >

    Default: <N>

    use the additional file with the protocol of the running of the program: DOC-file molrep.doc

    N
    without this file
    y
    produce DOC-file with new contents
    A
    keep old contents and add new information

    The DOC-file contains the protocol of the running of the program.

    NP <np>

    Default: <10>

    <np> is the number of peaks from the rotation function to be used/checked (maximum: 50).

    In special cases (e.g. for a dyad search), the use of keywords FUN (with option 'T') and FILE_T is closely linked to NP.

    NPT <npt>

    Default: <20>

    <npt> is the number of peaks from the translation function to be used/checked (maximum: 50).

    For use in dyad search, see NPT for dyad search.

    NMON <nmon>

    Default: <1>

    <nmon> is the number of monomers. The program will try to create a full model, which will consist of NMON initial models plus model_2.

    COMPL <compl>

    Default: automatic choice

    <compl> is the completeness of the model: from 0.1 to 1.0. It corresponds to Boff: from RESMAX*2 to RESMAX*6. If COMPL is used, keywords RES_R and RES_T are ignored.

    For example: if you have a dimer in the asymmetric part of the unit cell, COMPL=0.5.

    SIM <sim>

    Default: automatic choice

    Similarity of the model: from 0.1 to 1.0. It corresponds to Badd: from Boverall to -Boverall. SIM=1 means normalized F will be used. When no knowledge of similarity is available, the use of SIM=0.5 as a starting value is recommended. If SIM is used, the keyword BADD is ignored.

    SIM (Badd)
    controls high resolution data
    COMPL (Boff)
    controls low resolution data

    The use of Boff and Badd means to change Fobs and Fmodel:

    |F|new = |F|input *EXP(-Badd*RSQ)*(1-EXP(-Boff*RSQ)

    FUN < A | R | T | S >

    Default: <A>

    R
    calculate only Rotation Function
    T
    calculate only Translation Function, reading list of peaks of RF from file (molrep_rf.tab) or from TAB_file
    A
    calculate both: RF and TF
    S
    rotate and position the model and compute R-factor and Correlation Coefficient

    FILE_T <filename>

    Default: <molrep_rf.tab>

    Input or output TAB_file (see also molrep_rf.tab)

    SURF < N | Y | A | O | 2 >

    Default: <Y>

    Perform model correction.

    N
    do not perform any model correction. For FUN=S (just_rotate_and_position) program changes N to O
    O
    only shift to the origin
    A
    make the protein into a polyalanine model (i.e. remove from the model: water molecules, H atoms, atoms with alternative conformation (except the first), atoms with occupacy = 0), make all B = 20, and shift to the origin
    Y
    remove various atoms from the model (water molecules, H atoms, atoms with alternative conformation (except the first), atoms atoms with occupacy = 0), shift to the origin, compute atomic accessible surface area and replace atomic B with B = 15.0 + SURFACE_AREA*10.0
    2
    set all B = 20 and shift to the origin

    RAD <rad>

    Default: automatically calculated from the model, unless:

    • in case of Self-RF calculations: 30Å
    • for Rotation Function calculations: twice the radius of gyration
    • for PRF and SAPTF: radius of gyration

    Cut-off radius for Patterson search or for electron density search.

    RESMAX <resmax>

    Default: <3>

    High resolution limit.

    Keywords for special cases

    PST < N | Y | C >

    Default: <N>

    How to deal with pseudo-translation.

    N
    ignore pseudo-translation altogether
    C
    check only, but do not use pseudo-translation
    Y
    use pseudo-translation. For the Translation Function, the program will add to the model a copy of the model which is translated by the pseudo-translation vector. If FUN=R and LIST=L, the program computes a list of Patterson peaks and writes these to 'molrep.doc'. It may be useful to detect pseudo-translation.

    VPST <vpst1,vpst2,vpst3>

    Default: automatically from Patterson

    Pseudo-translation vector (in fractional units), used when PST = Y.

    MODE <F | S | M>

    Default: <F>

    S
    advanced rotation and translation functions and rigid body refinement are used
    F
    standard rotation and translation functions are used without rigid body refinement
    M
    standard rotation and translation functions are used. Rigid body refinement is possible. Rather slow then MODE=F, but correlation coefficient is calculated more correctly.

    RES_R <res_r>

    Default: automatic choice

    Low resolution limit for Rotation Function. Instead of applying RES_R directly, the program uses all data and applies Boff=4*(RES_R)2.

    RES_T <res_t>

    Default: automatic choice

    Low resolution limit for Translation Function. Instead of applying RES_T directly, the program uses all data and applies Boff=4*(RES_T)2.

    BADD <badd>

    Default: <0>

    BOFF and BADD mean:

    |F|new = |F|input *EXP(-BADD*RSQ)*(1-EXP(-BOFF*RSQ)

    ANISO < N | Y | C | S | K >

    Default: <N>

    N
    do not use anisotropic correction and/or scaling
    Y
    use anisotropic correction and scaling
    C
    use anisotropic correction of Fobs for RF only
    S
    use anisotropic scaling for TF only
    K
    use scaling without B-factor

    PACK < Y | N >

    Default: <Y>

    Y
    use Packing Function with Translation Function
    N
    do not use Packing Function with Translation Function

    LMIN <lmin>

    Default: <4>

    Minimum L-index of spherical coefficients. The program does not use coefficients with L=0. Possible values are 2,4,6,... L = 2 means to use all coefficients up to Lmax.

    LMAX <lmax>

    Default: automatic choice

    Maximum L-index of spherical coefficients. Possible values are 2,4,6,8,...,58,60.

    PRF < N | Y | S | P >

    Default: <N>

    N
    standard RF and Phased Translation Function is calculated
    Y
    SAPTF (Spherically averaged phased translation function), Phased Rotation Function (PRF) and Phased Translation Function will be used.
    S
    SAPTF (Spherically averaged phased translation function), Usual Rotation Function (RF) for modified map and Phased Translation Function will be used.
    P
    Search the model orientation in ED map by rotating model around the defined points in ED map. List of points must be in the file FILE_T.

    Program wiil use the phases from MTZ file or from EM map.

    If keyword FUN=T, rather than computing the Rotation Function, the program reads rotation function results from file FILE_T ( or "molrep_rf.tab"): "Sol_ peak number, polar angles (theta,phi,chi) and shift (sx,sy,sz)"

    NOSG <nosg>

    Default: <0>

    Number of new space group if you want to change the space group for the file of structure factors. Program just changes space group name, group number and cryst. symmetry operators, but not cell and data.

    LIST < S | L >

    Default: <S>

    S
    short DOC-file
    L
    long DOC-file

    DIFF < N | P | F >

    Default: <N>

    N
    use unmodified structure factors
    P
    use modified stucture factors instead of Fobs for RF, as follows:
    use ||Fobs|-|Fmod2|*(P2/100)|
    F
    use modified stucture factors instead of Fobs for RF, as follows:
    use vector difference (Fobs - Fmod2*(P2/100))

    P2 <p2>

    Default: <0>

    Percentage of model_2 in the structure.

    NREF <ncycle>

    Default: <10>

    number of cycles of rigid body refinement for each TF solution. (working only with MODE = S)

    see keyword:MODE

    NREFP <ncycle>

    Default: <0>

    number of cycles of rigid body refinement before TF for each peak RF.

    Default is without this refinement

    STICK < N | Y >

    Default: <N>

    Choose from symmetry-related models closest to which found before (this option does not work with pseudo-translation possibility).

    FILE_S <filename>

    File with sequence for model correction by sequence alignment.

    NMR < 0 | 1 | 2 | 3 >

    Default: <0>

    0
    use PDB file with NMR structures as single model
    1
    use NMR possibility only for RF
    2
    use NMR possibility for RF and TF. Best NMR model will be found and used as solution.
    3
    use NMR possibility for RF and TF. Averaged TF will be used. All NMR models will be used as solution.

    LOCK < Y | N >

    Default: <N>

    Locked Cross Rotation function will be performed. Use also keywords: FILE_TSR and NSRF

    Keywords specific for multi-copy search

    DYAD < N | Y | D >

    Default: <N>

    Y
    multi-copy search
    D
    dyad search

    DIST <Dmin,Dmax,Dpar>

    Three distances for dyad search.

    Dmin
    Default: radius of gyration
    minimal distance between molecules
    Dmax
    Default: 1000
    maximal distance between molecules
    Dpar
    Default: 1000
    maximal shift along rotation axis

    AXIS <Chi,Delta>

    Default: <0,0>

    Chi
    check only rotation by Chi (in degrees). 0 means to check all orientations.
    Delta
    delta for Chi (in degrees)

    NSRF <nsrf>

    Default: <0>

    Number of peaks of Self-RF which will be used. 0 means not to use Self-RF. A list of Self-RF peaks will be taken from file defined by keyword FILE_TSR which must be prepared in advance (see Self Rotation Function).

    NPT <npt>

    This meaning only in conjuction with keyword DYAD: number of peaks in the STF (Special Translation Function) to be checked through Translation Function calculations, for inter-molecular vector search. If keyword DYAD is not given, the standard meaning of keyword NPT is used.

    NPTD <nptd>

    Number of peaks in TF to be checked through Correlation Coefficient calculations, for dyad search.

    NP2 <np2>

    Number of peaks in RF for second searching model to be checked for dyad search.

    FILE_M2 <filename>

    file of second searching model

    FILE_T2 <filename>

    file with list of peaks of RF for second searching model

    ALL < N | Y >

    Default: <N>

    if ALL = Y , program will use all Crystallographical Symmetry Operators

    Keywords for Self Rotation Function

    Without a file of the model, the program computes a Self Rotation Function.

    CHI <chi>

    Default: <60>

    Angle chi of additional fourth section of RF(theta,phi,chi).

    SCALE <scale>

    Default: <6>

    Maximum value of RF is SCALE * SIGMA(RF).

    FILE_TSR <filename>

    Default: <molrep_srf.tab>

    Input or output TAB_file with peaks of Self_RF.

    Keywords for EM or electron density as model:

    DSCALEM <scale>

    Default: <1>

    scale factor of correction of density cell

    INVERM < N | Y >

    Default: <N>

    If Y , inverted phases will be used

    ROLIM <limit>

    Default: <not used>

    minimal value of density which will be used

    DRAD <radius>

    Default: <0>

    radius of the model (in A). If parameter DRAD is defined program will use the density only inside the sphere with radius = DRAD and with centre in vector ORIGIN.

    ORIGIN <vector>

    Default: <0,0,0>

    center of the model in the cell (in fract.units)

    Keywords for EM or electron density instead of Fobs:

    DSCALE <scale>

    Default: <1>

    scale factor of correction of density cell

    INVER < N | Y >

    Default: <N>

    If Y , inverted phases will be used

    DLIM <limit>

    Default: <not used>

    minimal value of density which will be used

    MOLECULAR REPLACEMENT METHOD - THEORY

    Molecular replacement method (MR)

    There are two major steps in the Molecular replacement method: orientation and translation search. They are performed by Rotation and Translation function. Both of them are correlation functions (or overlapping functions) between observed and calculated from model Patterson.

    Rotation function (RF):

                  ROT(R) = I Pobs(r) * Pcalc(R,r) dr
                      rad

    where

    R
    operator of rotation
     I
    rad
    integral inside a sphere in the centre of patterson with radius=rad (i.e. the cut-off radius)
    Pobs
    observed Patterson
    Pcalc
    calculated Patterson for rotated (R) model

    Translation function (TF):

                TR(s)  = I Pobs(r) * Pcalc(s,r) dr  =
                    cell

                   = Sum ( I Pobs(r) * Pcalc_ij(s,r) dr) = Sum TRij(s)  
                     i#j                                    i#j

    where

    s
    vector of translation
    I
    integral
    i,j
    cryst. symmetry operator numbers
    Pcalc_ij(s,r)
    calculated Patterson for model corresponding to ith operator and model corresponding to jth operator
    TRij(s)
    translation function of Pattersons Pobs(r) and Pcalc_ij(s,r).
    The Translation Function is the sum of translation functions for each pair of different cryst. symmetry operators.

    The best rotation function algorithm is the Crowther Fast Rotation Function which we use here. It utilizes FFT. MOLREP can compute the Rotation Function for three different orientations of the model and average them. That reduces the noise of Rotation function.

    Translation function algorithm was developed by the author and performs calculations in the reciprocal space using FFT.

    There are two major differences from other translation functions.

    1. Instead of summation of the translation functions for two operators TRij, we use their multiplication which makes the resulting map far more contrast-rich.
    2. Finally we can multiply the translation function with the Packing Function to remove peaks corresponding to incorrect solutions with bad packing.
      Packing function (PF) is overlapping function: 
          
              P(s) = Sum ( I  Ro_i(r) * Ro_j(r) dr )
                     i#j  cell

      where Ro_i(r) is the electron density of the model which corresponds to the ith cryst. symmetry operator.

      The algorithm of calculation of the Packing Function is similar to the one for the Translation Function and performed by the same program.

      Finally the 'advanced' Translation function is: 

                  TR(s)  = [  M  TRij(s) ] * P(s)
                       i#j

      where M means multiplication of different TRij.

    Scaling by Patterson

    For scaling we use a completely new strategy based on the Patterson origin peak which is approximated by a Gaussian. This peak is computed for both the observed and calculated amplitudes, and each case the B_overall is computed. The difference

    B_diff_overall = B_obs_overall - B_calc_overall

    is then added to calculated B_overall so as to make the width of the calculated Patterson origin peak equal to the observed peak. This method makes it possible to have a good approximation for the scaling problem even if only low resolution data is available where other methods do not work. Scaling by Patterson is also useful for the Cross Rotation Function where we have different cells for the model and the unknown structure.

    Low resolution cut-off (Boff)

    Low resolution cut-off introduces systematical errors in the electron density especially near the surface of the model. This is known as the series termination effect. Instead of using the usual low resolution cut-off, MOLREP multiplies the modules of the structure factors by a special coefficient:

    Fnew = Fold (1-exp(-Boff*s2)), where Boff= 4resmin2

    Boff is called the "soft low resolution cut-off", which allows removal of structure factors in this resolution range without inroducing the series termination effect.

    The use of a priori knowledge of similarity and completeness of the model

    For low similarity the high resolution reflections are weighted down. For this, MOLREP uses an additional overall factor Badd:

    Fnew = Fold exp(-Badd*s2)

    Value of similarity 'SIM' can be: from 0.1 to 1.0. It corresponds to Badd: from (B_limit-Boverall) to -Boverall, where B_limit + 80.

    SIM=1 means normalized F will be used.

    For low completeness, e.g. when there are several molecules in the a.u., the contribution of low resolution reflections is weighted down. To manage the completeness of the model, MOLREP uses a low resolution cut-off (Boff). Completeness of model 'COMPL' can be : from 0.2 to 1.0. It corresponds to Boff: from 400 to 1600.

    Functions of electron density searching (SM)

    We suggest a new approach to divide a phased six-dimensional search into three steps:

    1. A spherically averaged translation function is used to locate the position of a molcule or its fragment. It compares locally spherically averaged experimental electron density with that calculated from the model and tabulates highly probable positions accordingly.
    2. Then for each position a local phased rotation function is used to find the orientation of the molecule.
    3. The third step is the phased translation function, used to check and refine the found position.

    Spherically averaged phased translation function (SAPTF)

    SAPTF gives the expected position of a model in an electron density map by the comparison of spherically averaged density of the model with locally spherically averaged observed density.

    SAPTF(s) = I Robs(r,s) * Rcalc(r) dr
         rad(s)

    where

      I
    rad(s)
    integral inside a sphere centred in point s of electron density with radius=rad (i.e. the cut-off radius)
    Robs
    spherically averaged around point s observed electron density
    Rcalc
    spherically averaged around origin of coordinate system calculated electron density for model

    Phased Rotation function (PRF)

    PRF gives the orientation of model placed in some point of electron density.

    PROT(O) = I Robs(r) * Rcalc(O,r) dr
        rad(s)

    where

    O
    operator of rotation
      I
    rad(s)
    integral inside a sphere centred in point s of electron density with radius=rad
    Robs
    observed electron density
    Rcalc
    calculated electron density for rotated (O) model

    Phased Translation function (PTF)

    Translation search in electron density map.

    PTR(s)  = I Robs(r) * Rcalc(s,r) dr
        cell

    where

    s
    vector of translation
    I
    integral
    Robs
    observed electron density
    Rcalc(s,r)
    calculated electron density for model placed in the vector s

    Fitting two models (FM)

    Fitting through electron density. Second model (MODEL_2) is the target model which converted to electron density. To search the best overlapping of electron densities of models there are two algorithms:

    1. Rotation Function (Patterson) and Phased Translation Function (electron density).
    2. All functions for electron density. Spherically Averaged Phased Translation Function gives expected position for model. Phased Rotation Function for expected position gives orientation. Phased Translation Function checks and refines the translation vector.

    Special Translation Function (STF) for dyad search

    Multi-copy search

    Search two copies of a model simultaneously. There are three stages to this:

    1. Rotation function. The program checks all pairs of first NP peaks of Rotation Function (RF). For each pair the program uses the first rotation to prepare model-1. Model-2 will be prepared by using the second rotation and one rotation from the crystallographical symmetry operatators.
    2. Next, for the current pair (model-1 and model-2): MOLREP computes the Special Translation Function (STF) to find the inter-molecular vector of this dyad.
    3. For NPT peaks of the previous Special Translation Function (STF) (i.e. for NPT inter-molecular vectors) the program computes a standard Translation Function (TF) using the current dyad as model and calculates a Correlation Coefficient for first NPTD peaks of TF.

    Special Translation Function (STF)

    Imagine two models in the asymm. part of the unit cell:

    F1(h)
    structure factor of model_1 with the centre of gravity in the origin of the coord. system
    F2(h)
    structure factor of model_2

    Let

    S1
    vector in unit cell from the origin of the coord. system to the centre of gravity of model_1
    S2
    vector for model_2

    When F(h) is the total structure factor (for the whole crystal structure):

    F(h) = F1(h)exp(-2pihS1) + F2(h)exp(-2pihS2)

    Then the Patterson is:

    P(h) = F(h)*F'(h)

       = F1(h)*F1'(h)
        + F1'(h)*F2(h)*exp(-2pih(S2-S1))
        + F2'(h)*F2(h)
        + F1(h)*F2'(h)*exp(-2pih(S1-S2))

       = P0(0) + P1(S2-S1) + P1(S1-S2)

    The Special Translation Function is a Phased TF with a Patterson function as electron density and P1 = F1'(h)*F2(h) as structure factors of the model. Solution of this function is the dyad vector S1-S2.

    Anisotropic correction and scaling

    Aniso correction:

  For Structure Factors we can estimate:
           
     1.  isotropic B_overal:

           F(s) ~ Scale_overall * exp (-B_overall*s^2) 

     2.  anisotropic B_overall (tensor) : 

           F(s) ~ Scale_overall * exp(-(B11a*a*hh +2B12a*b*hk+..)

    
     Aniso correction means to make data isotropic with B_overall:


   F_new(s) = F_old(s) * exp(+(B11a*a*hh +2B12a*b*hk+..) * exp(-B_overall*s^2) 
        

Aniso scaling:

       Fnew = Scale*Fold*exp(-(B11a*a*hh +2B12a*b*hk+..)

       Scale ans aniso B are taken by mimimization: sum(!Fobs-Fnew!)

    COMMAND FILE EXAMPLES

    example of Cross Rotation and Translation functions:

    # --------------------------------
molrep HKLIN test.mtz MODEL 2sar.pdb << eor
# --------------------------------
#
LABIN F=F SIGF=SIGF
NP   8
RAD 27
ANISO C
sim   .1
compl .5
eor

    example of Self Rotation function:

    
# --------------------------------
molrep HKLIN test.mtz << eor
# --------------------------------
#
LABIN F=F SIGF=SIGF
#
_RAD 27
_END
eor

    example using phases

    For searching in the electron density map for some model (standard Rotation Function will be used):

    # --------------------------------
molrep HKLIN test.mtz MODEL mod.pdb << eor
# --------------------------------
#
LABIN F=F SIGF=SIGF PHIC=PH_FO FOM=FOM
#
NP    8
END
eor

    example of fitting two models:

    # --------------------------------
molrep MODEL mod.pdb MODEL2 mod2.pdb << eor
# --------------------------------
#
PRF Y
eor

    example of dyad search:

    # --------------------------------
molrep HKLIN test.mtz MODEL mod.pdb << eor
# --------------------------------
#
LABIN F=F SIGF=SIGF 
#
dyad y
axis 0,10
dist 0,300,300
NPT  3
NPTD 3
eor

    example of dimer search:

    # --------------------------------
molrep HKLIN test.mtz MODEL mod.pdb << eor
# --------------------------------
#
LABIN F=F SIGF=SIGF 
#
dyad y
axis 180,10
dist 0,300,1
NPT  3
NPTD 3
eor

    example dimer search for Self-RF orientations:

    # --------------------------------
molrep HKLIN test.mtz MODEL mod.pdb << eor
# --------------------------------
#
LABIN F=F SIGF=SIGF
#
dyad y
axis 180,10
dist 0,300,1
NSRF 20
NPT  3
NPTD 3
FILE_SRF srf.tab
eor

    example of using file of sequence

    # --------------------------------
molrep HKLIN test.mtz MODEL mod.pdb << eor
# --------------------------------
#
LABIN F=F SIGF=SIGF 
#
NP   8
NMON 2
FILE_S new.seq
sim   .1
compl .5
eor

    Convention for rotation

    
  Rotation by Euleran angles Alpha, Beta, Gamma:

     euleran angles : 1. A( Z ) - alpha around axis Z
                      2. B( Y') - beta  around new axis Y
                      3. G( Z') - gamma around new axis Z

  Rotation by Polar angles Theta, Phi, Chi:

                    polar coordinates Theta, Phi of rotate axis:
 
       Theta     -  angle between  rotate axis and Z
       Phi       -  angle in plan XY between X and projection rotate axis

       Chi       -  rotation angle arount rotate axis

    Convention for Orthonormal coordinate system

           Orthonormal axes are defined to have:
 
       A parallel to X , Cstar parallel to Z

    MEMORY CONTROL PARAMETERS

    In main_molrep_mtz.f:

     
CC --- MEMORY - common memory for maps and coordinates
       PARAMETER ( MEMORY  =4000000 )
CC --- NCRDMAX - maximal number of coordinates
       PARAMETER ( NCRDMAX = 100000  )
CC --- IPRSYM - maximal number of symmetry operators
       PARAMETER ( IPRSYM=96        )
       INTEGER*2 ISYM(5,3,IPRSYM)
       PARAMETER ( MEM = MEMORY/2 )
       REAL*8    POOL(MEM)
C ----

    If program stops with message:

                   ERROR: not memory enough ...

    change parameter MEMORY in main_molrep_mtz.f