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According to the PDB guide there are some coordinate translation matrices found in PDB file:

ORIGXn                  Transformation from orthogonal  coordinates to the
                        submitted coordinates (n = 1, 2, or 3).
SCALEn                  Transformation from orthogonal coordinates to fractional
                        crystallographic coordinates  (n = 1, 2, or 3).
MTRIXn                  Transformations expressing non-crystallographic symmetry
                        (n = 1, 2, or 3). There may be multiple sets of these records.

For example, in 10gs complex from RCSB I see:

ORIGX1      1.000000  0.000000  0.000000        0.00000                         
ORIGX2      0.000000  1.000000  0.000000        0.00000                         
ORIGX3      0.000000  0.000000  1.000000        0.00000                         
SCALE1      0.012543  0.000000  0.001805        0.00000                         
SCALE2      0.000000  0.011055  0.000000        0.00000                         
SCALE3      0.000000  0.000000  0.014557        0.00000                         
MTRIX1   1  0.945333  0.099229  0.310644       -5.48795    1                    
MTRIX2   1  0.099832 -0.994906  0.013998       21.83043    1                    
MTRIX3   1  0.310451  0.017779 -0.950423       27.67516    1 

I want to do 3D voxel reconstruction of some part of the complex stored in PDB. What is the purpose of those matrices, do I need to apply any of those translations to the coordinates stored in PDB to "standartize" the data and obtain the same coordinate system and same grid for different PDBs? Or they are just related to the data which was submitted by authors and are needed for inverse translation? Or something else? Thank you very much!

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1 Answer 1

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The purpose of these matrices is to reconstruct the crystal lattice from the coordinates, which only contain one copy of the repeating structural unit found in the crystal. In other words, they represent the affine transformations required to convert one copy of the repeating unit to its neighbors.

To a biologist (as opposed to a crystallographer), these are not useful except if one of the crystallographic symmetry axes happens to also be a biological dimer (or other multimer) axis. However, in this case, the PDB usually gives an option to download the "biological unit", which includes the coordinates for all neighboring copies that associate in the cell with the copy specified by the original coordinates. I should point out that sometimes the biological unit is in fact smaller than the crystallographic unit, if multiple copies of a monomer or dimer or whatever occur in non-equivalent spatial contexts within the crystal. There is no substitute for biological knowledge to know what the relevant structural unit in the cell is.

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  • $\begingroup$ Thanks! So, it means that generally I can forget about them and treat different PDBs from RCSB as represented in the same coordinate system and use spatial representation of those different proteins as data points for training a machine learning model (e,g, classifier) without any recalculation? $\endgroup$
    – Slowpoke
    Aug 2, 2020 at 22:57
  • $\begingroup$ Different PDBs from RCSB? There is no way to relate the coordinates frames of entirely different proteins that are not bound to each other in the same crystal, their rotational and translational positions are arbitrary because they aren't relative to anything. There is no such thing as the "top", "bottom", "back", or "front" of a protein. Only distances and angles, i.e. measures within the internal coordinate system of a molecule, are meaningful. If you mean the length scale, then yes that's the same across all PDB files (it's always in units of Angstroms). $\endgroup$
    – biohacker
    Aug 3, 2020 at 1:48
  • $\begingroup$ Okay, so we may consider that coordinate system across PDBs is the same up to orthogonal transformation (rotation, swap of axes, etc). Scale is always the same and is represented in angstroms, angles are preserved. Thank you! $\endgroup$
    – Slowpoke
    Aug 3, 2020 at 10:54

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