Crystallographic and Coordinate Transformation Section

The Crystallographic 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 defines a unit cube.

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 coordinate entry describes a structure determined by a technique other than 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 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 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, THEORETICAL MODEL, or FIBER DIFFRACTION, FIBER, the CRYST1 record is predefined as

a = b = c = 1.0, alpha = beta = gamma = 90 degrees, space group = P 1 and Z = 1.

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.

Example

         1         2         3         4         5         6         7 
1234567890123456789012345678901234567890123456789012345678901234567890 
CRYST1   52.000   58.600   61.900  90.00  90.00  90.00 P 21 21 21    8 
CRYST1    1.000    1.000    1.000  90.00  90.00  90.00 P 1           1 
CRYST1   42.544   69.085   50.950  90.00  95.55  90.00 P 1 21 1      2

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

The PDB supplies this information even if the transformation is an identity transformation (unit matrix, null 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 in the original deposited file.

Relationships to Other Record Types

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

Example

         1         2         3         4         5         6         7
1234567890123456789012345678901234567890123456789012345678901234567890
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 by the PDB 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 - fiber sample, and theoretical model 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
1234567890123456789012345678901234567890123456789012345678901234567890
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.

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 contained in the file, the iGiven field is set to 1. Otherwise, this field is blank.

A corresponding REMARK must appear which describes the transformation.

Verification/Validation/Value Authority Control

The PDB verifies all MTRIX records using records from the author and review.

Relationships to Other Record Types

A corresponding REMARK must appear which describes the transformation.

Example

         1         2         3         4         5         6         7
1234567890123456789012345678901234567890123456789012345678901234567890
MTRIX1   1 -1.000000  0.000000 -0.000000        0.00001    1          
MTRIX2   1 -0.000000  1.000000  0.000000        0.00002    1          
MTRIX3   1  0.000000 -0.000000 -1.000000        0.00002    1

TVECT

Overview

The TVECT records present the translation vector for infinite covalently connected structures.

Record Format

COLUMNS     DATA TYPE       FIELD       DEFINITION
---------------------------------------------------
 1 -  6     Record name     "TVECT "
 8 - 10     Integer         serial      Serial number.
11 - 20     Real(10.5)      t[1]        Components of translation vector.
21 - 30     Real(10.5)      t[2]        Components of translation vector.
31 - 40     Real(10.5)      t[3]        Components of translation vector.
41 - 70     String          text        Comment.

Details

For structures not comprised of discrete molecules (e.g., infinite polysaccharide chains), the entry contains a fragment which can be built into the full structure by the simple translation vectors of TVECT records.

A corresponding REMARK describing the structure must appear.

Verification/Validation/Value Authority Control

PDB applies the translation and checks the generated molecule.

Relationships to Other Record Types

A corresponding REMARK describing the structure must appear.

Example

         1         2         3         4         5         6         7
1234567890123456789012345678901234567890123456789012345678901234567890
TVECT    1   0.00000   0.00000  28.30000

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