# RMSD calculation in AWK

## 1. Overview

The RMSD (root-mean-square deviation) is a common way to compare structures of biomolecules or solid bodies^{[3]}. The basic idea is a least square optimization to superimpose the models. The AWK script performs the optimal alignment and prints out the RMSD of two PDB files. The program can be used as follows:

./pdbalign.awk file1.pdb file2.pdb

The implementation of the RMSD is based on Coutsias et al^{[1]}, who presented a method based on quaternions to align rotations. The entire algorithm is based on first centering the structures to the center of geometry (COG), then performing a rotational alignment based on quaternions^{[4]}. To compute the eigenvectors the Householder transform is used to get a tridiagonal matrix and the QL decomposition is used to calculate the eigenvalues^{[2]}.

## 2. Downloads

pdbalign.awk## 3. References

^{[1]}Coutsias E.A., Seok C., Dill K.A.,

*Using quaternions to calculate RMSD.*J Comput Chem.(2004) 25(15):1849-1857.

^{[2]}Press W.H.,

*Numerical Recipes in C: The Art of Scientific Computing*. Cambridge University Press(1992).

^{[3]}RMSD http://en.wikipedia.org/wiki/Root-mean-square_deviation_(bioinformatics)

^{[4]}Quaternions http://en.wikipedia.org/wiki/Quaternions_and_spatial_rotation