Determining Geometrically Stable Domains in Molecular Conformation Sets

Detecting significant conformational changes occurring in biomolecules is a challenging task, especially when considering tens to hundreds of thousands of conformations. Conformational variability can be described by dividing a biomolecule into dynamic domains, i.e., by finding compact fragments that move as coherent units. Typical approaches, based on calculating a dynamical cross-correlation matrix, are limited by their inability to reveal correlated rotations and anticorrelated motions. We propose a geometric approach for finding dynamic domains, where we compare traces of atomic movements in a pairwise manner, and search for their best superposition. A quaternion representation of rotation is used to simplify the complex. calculations The algorithm was implemented in a Java graphical program: Geometrically Stable Substructures (GeoStaS). The program processes PDB and DCD binary files with large structural sets for proteins, nucleic acids, and their complexes. We demonstrate its efficiency in analyzing (a) ensembles of structures generated by NMR experiments and (b) conformation sets from biomolecular simulations, such as molecular dynamics. The results provide a clear description of the molecular movements even for large biomolecules. Compared to a standard dynamic cross-correlation matrix, our algorithm detects the correlations in both translational and rotational motions.