Description of protein structure in PDB format

The PDB file for a protein structure is a text description of the 3D-coordinates of the atoms/residues with the protein is comprised of. The file consists of a linear list $L_{pdb}$ list of atoms which are part of the protein and corresponding 3-D coordinates of each atom, these atoms are part of the residues which correspond to the 20 Amino-acids. $L_{pdb} = (a_{1,1},a_{1,2},a_{1,3}{\ldots}a_{i,j}{\ldots}$ ), and $a_{i,j}$ is the $j^{th}$ atom in residue $i$ , a very important fact to be noticed at this point is that the list $L_{pdb}$ is partially ordered with respect to the residue numbers, $a_{p,q} < a_{m,n} \iff (p<m)$ , although there is an ordering in the residues the atoms within each of these residues may not follow any order. Thus given two instances of a same protein PDB structure ${L^{1}}_{pdb}$ and ${L^{2}}_{pdb}$ , the ordering of the atoms within each residue(residue's will be in same order) may be different, as an example the atoms in $1^{st}$ residue of ${L^{1}}_{pdb}$ may be ordered as $(a_{1,2},a_{1,1},a_{1,5},a_{1,4},a_{1,3},\ldots)$ but the atoms in the same residue of ${L^{2}}_{pdb}$ can be ordered as $(a_{1,5},a_{1,1},a_{1,2},a_{1,4},a_{1,3}\ldots)$ . The reason for this variation is mainly due to different frames of reference during X-ray crystallography. The variation of the ordering of the atoms within the same residue makes structural alignment algorithms which consider the sidechain conformations non-trivial. In the next few sections we will see how our algorithm overcomes this ordering issue when side-chain conformations are considered.