Python Programming for Biology: Bioinformatics and Beyond

Coordinate superimposition

In accordance with earlier examples that show how sequences can be aligned, this section

describes  how  coordinates  in  three-dimensional  space  may  be  aligned  by  superimposing

atom  positions.  Naturally  this  is  a  geometric  operation  that  allows  us  to  compare  the

shapes  of  structures,  rather  than  a  per-residue  analysis.  Essentially  the  coordinate

alignment  involves  moving  the  centres  of  the  structures  to  the  same  point  (translation  to

the  centre)  and  then  finding  the  optimal  rotation  which  gives  the  minimal  deviation

between  corresponding  pairs  of  coordinates;  we  superimpose  equivalent  atoms  to  place

them  as  close  together  as  possible  without  distorting  the  shape  of  the  structures.  Overall

this  procedure  is  commonly  used  to  superimpose  structures  with  identical  atoms,  i.e.

different structural conformations (models). However, we can also attempt to superimpose

structures of molecules with different atoms (different residue sequences). Below there is

an example of this, where we find a common set of equivalent atoms, which can be used

to  guide  two  different  molecules.  There  may  be  better  ways  to  do  this,  but  it  illustrates

how it can be done with relatively simple Python.

Note  that  similar  functionality  is  also  available  via  BioPython,  by  use  of  the

Bio.PDB.Superimposer object. However, we define our own functionality here to explain

the basics of what is happening and to give experience with Python. The following Python

examples work with the structure data model we have described and are split into several

separate  functions,  so  that  we  can  more  clearly  explain  what  is  going  on  at  each  step.

Although these procedures are usually applied to structures of proteins, it is possible to do

the same thing to other kinds of molecule, including RNA and DNA.