Rapid calculation of RMSDs using a quaternion-based characteristic polynomial

Abstract

A common measure of conformational similarity in structural bioinformatics is the minimum root mean square deviation (RMSD) between the coordinates of two macromolecules. In many applications, the rotations relating the structures are not needed. Several common algorithms for calculating RMSDs require the computationally costly procedures of determining either the eigen decomposition or matrix inversion of a 3 x 3 or 4 x 4 matrix. Using a quaternion-based method, here a simple algorithm is developed that rapidly and stably determines RMSDs by circumventing the decomposition and inversion problems. © 2005 International Union of Crystallography - all rights reserved.