Crystallographic and Coordinate Transformation Section

This section describes the geometry of the crystallographic experiment and the coordinate system transformations.

CRYST1

Overview

The CRYST1 record presents the unit cell parameters, space group, and Z value. If the structure was not determined by crystallographic means, CRYST1 simply provides the unitary values, with an appropriate REMARK.

Record Format

COLUMNS       DATA  TYPE    FIELD          DEFINITION
-------------------------------------------------------------
 1 -  6       Record name   "CRYST1"
 7 - 15       Real(9.3)     a              a (Angstroms).
16 - 24       Real(9.3)     b              b (Angstroms).
25 - 33       Real(9.3)     c              c (Angstroms).
34 - 40       Real(7.2)     alpha          alpha (degrees).
41 - 47       Real(7.2)     beta           beta (degrees).
48 - 54       Real(7.2)     gamma          gamma (degrees).
56 - 66       LString       sGroup         Space  group.
67 - 70       Integer       z              Z value.

Details

If the entry describes a structure determined by a technique other than X-ray crystallography, CRYST1 contains a = b = c = 1.0, alpha = beta = gamma = 90 degrees, space group = P 1, and Z = 1.
The Hermann-Mauguin space group symbol is given without parenthesis, e.g., P 43 21 2. Please note that the screw axis is described as a two digit number.
The full International Table’s Hermann-Mauguin symbol is used, e.g., P 1 21 1 instead of P 21.
For a rhombohedral space group in the hexagonal setting, the lattice type symbol used is H.
The Z value is the number of polymeric chains in a unit cell. In the case of heteropolymers, Z is the number of occurrences of the most populous chain.

As an example, given two chains A and B, each with a different sequence, and the space group P 2 that has two equipoints in the standard unit cell, the following table gives the correct Z value.

         Asymmetric  Unit Content                      Z value
--------------------------------------------------------------------------------
--------------------------------------------------------------------------------
             A                                            2
             AA                                           4
             AB                                           2
             AAB                                          4
             AABB                                         4

In the case of a polycrystalline fiber diffraction study, CRYST1 and SCALE contain the normal unit cell data.

Verification/Validation/Value Authority Control

The given space group and Z values are checked during processing for correctness and internal consistency. The calculated SCALE factor is compared to that supplied by the depositor. Packing is also computed, and close contacts of symmetry-related molecules are diagnosed.

Relationships to Other Record Types
The unit cell parameters are used to calculate SCALE. If the EXPDTA record is NMR, Electron microscopy, or Fiber Diffraction, the CRYST1 record is predefined as in the last example (see below). In these cases, an explanatory REMARK must also appear in the entry. Some fiber diffraction structures will be done this way, while others will have a CRYST1 record containing measured values.

Examples

         1         2         3         4         5         6         7         8
12345678901234567890123456789012345678901234567890123456789012345678901234567890
CRYST1   52.000   58.600   61.900  90.00  90.00  90.00 P 21 21 21    8 
CRYST1   42.544   69.085   50.950  90.00  95.55  90.00 P 1 21 1      2

Example of experimental method other than X-ray crystallography or fiber diffraction

CRYST1    1.000    1.000    1.000  90.00  90.00  90.00 P 1           1

Known Problems

No standard deviations are given.

ORIGXn

Overview

The ORIGXn (n = 1, 2, or 3) records present the transformation from the orthogonal coordinates contained in the entry to the submitted coordinates.

Record Format

COLUMNS        DATA  TYPE     FIELD         DEFINITION
----------------------------------------------------------------
 1 -  6         Record name   "ORIGXn"      n=1, 2, or 3
11 - 20         Real(10.6)    o[n][1]       On1
21 - 30         Real(10.6)    o[n][2]       On2
31 - 40         Real(10.6)    o[n][3]       On3
46 - 55         Real(10.5)    t[n]          Tn

Details

This information is included in the file even if the transformation is an identity transformation (unitary matrix, null translation vector). See the SCALE section of this document for a definition of the default orthogonal Angstroms system.
If the original submitted coordinates are Xsub, Ysub, Zsub and the orthogonal Angstroms coordinates contained in the data entry are X, Y, Z, then:

        Xsub = O11X +  O12Y + O13Z + T1
        Ysub = O21X +  O22Y + O23Z + T2
        Zsub = O31X +  O32Y + O33Z + T3

Verification/Validation/Value Authority Control

If the coordinates are submitted in the same orthogonal Angstrom coordinate frame as they appear in the entry (the usual case), then ORIGX is an identity matrix with a null translation vector. If the transformation is not an identity matrix with a null translation vector, then applying this transformation to the coordinates in the entry yields the coordinates of the original deposited file.

Relationships to Other Record Types

ORIGX relates the coordinates in the ATOM and HETATM records to the coordinates in the file.

Example

         1         2         3         4         5         6         7         8
12345678901234567890123456789012345678901234567890123456789012345678901234567890
ORIGX1      0.963457  0.136613  0.230424       16.61000               
ORIGX2     -0.158977  0.983924  0.081383       13.72000               
ORIGX3     -0.215598 -0.115048  0.969683       37.65000

SCALEn

Overview

The SCALEn (n = 1, 2, or 3) records present the transformation from the orthogonal coordinates as contained in the entry to fractional crystallographic coordinates. Non-standard coordinate systems should be explained in the remarks.

Record Format

COLUMNS         DATA  TYPE    FIELD              DEFINITION
------------------------------------------------------------------
 1 -  6         Record name   "SCALEn" n=1,  2, or 3
11 - 20         Real(10.6)    s[n][1]            Sn1
21 - 30         Real(10.6)    s[n][2]            Sn2
31 - 40         Real(10.6)    s[n][3]            Sn3
46 - 55         Real(10.5)    u[n]               Un

Details

The standard orthogonal Angstroms coordinate system used is related to the axial system of the unit cell supplied (CRYST1 record) by the following definition:

If vector a, vector b, vector c describe the crystallographic cell edges, and vector A, vector B, vector C are unit cell vectors in the default orthogonal Angstroms system, then vector A, vector B, vector C and vector a, vector b, vector c have the same origin; vector A is parallel to vector a, vector B is parallel to vector C times vector A, and vector C is parallel to vector a times vector b (i.e., vector c*). * If the orthogonal Angstroms coordinates are X, Y, Z, and the fractional cell coordinates are xfrac, yfrac, zfrac, then:

            xfrac =  S11X + S12Y + S13Z + U1
            yfrac =  S21X + S22Y + S23Z + U2
            zfrac =  S31X + S32Y + S33Z + U3

For NMR, fiber diffraction, and EM entries, SCALE is given as an identity matrix with no translation.

Verification/Validation/Value Authority Control

The inverse of the determinant of the SCALE matrix equals the volume of the cell. This volume is calculated and compared to the SCALE matrix supplied by the depositor.

Relationships to Other Record Types

The SCALE transformation is related to the CRYST1 record, as the inverse of the determinant of the SCALE matrix equals the cell volume.

Example

         1         2         3         4         5         6         7         8
12345678901234567890123456789012345678901234567890123456789012345678901234567890
SCALE1      0.019231  0.000000  0.000000        0.00000               
SCALE2      0.000000  0.017065  0.000000        0.00000               
SCALE3      0.000000  0.000000  0.016155        0.00000

MTRIXn

Overview

The MTRIXn (n = 1, 2, or 3) records present transformations expressing non-crystallographic symmetry. MTRIXn will appear only when such transformations are required to generate an entire asymmetric unit, such as a large viral structure.

Record Format

COLUMNS        DATA  TYPE    FIELD         DEFINITION
-------------------------------------------------------------------------------
 1 -  6        Record name   "MTRIXn"      n=1, 2, or 3
 8 - 10        Integer       serial        Serial number.
11 - 20        Real(10.6)    m[n][1]       Mn1
21 - 30        Real(10.6)    m[n][2]       Mn2
31 - 40        Real(10.6)    m[n][3]       Mn3
46 - 55        Real(10.5)    v[n]          Vn
60             Integer       iGiven        1 if coordinates for the  representations
                                           which  are approximately related by the 
                                           transformations  of the molecule are
                                           contained in the entry. Otherwise, blank.

Details

The MTRIX transformations operate on the coordinates in the entry to yield equivalent representations of the molecule in the same coordinate frame. One trio of MTRIX records with a constant serial number is given for each non-crystallographic symmetry operation defined. If coordinates for the representations which are approximately related by the given transformation are present in the file, the last “iGiven” field is set to 1. Otherwise, this field is blank.

Verification/Validation/Value Authority Control

All MTRIX records are verified using records from the author and review.

Relationships to Other Record Types

None.

Example

         1         2         3         4         5         6         7         8
12345678901234567890123456789012345678901234567890123456789012345678901234567890
MTRIX1   1 -1.000000  0.000000  0.000000        0.00000    1          
MTRIX2   1  0.000000  1.000000  0.000000        0.00000    1          
MTRIX3   1  0.000000  0.000000 -1.000000        0.00000    1