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.
* Appendix 2 details the derivation of the SCALE coordinate transformation.
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