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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.

A quantum-classical molecular dynamics model (QCMD), applying explicit integration of the time-dependent Schrödinger equation (QD) and Newtonian equations of motion (MD), is presented. The model is capable of describing quantum dynamical processes in complex biomolecular systems. It has been applied in simulations of a multistep catalytic process carried out by phospholipase A(2) in its active site. The process includes quantum-dynamical proton transfer from a water molecule to histidine localized in the active site, followed by a nucleophilic attack of the resulting OH(-) group on a carbonyl carbon atom of a phospholipid substrate, leading to cleavage of an adjacent ester bond. The process has been simulated using a parallel version of the QCMD code. The potential energy function for the active site is computed using an approximate valence bond (AVB) method. The dynamics of the key proton is described either by QD or classical MD. The coupling between the quantum proton and the classical atoms is accomplished via Hellmann-Feynman forces, as well as the time dependence of the potential energy function in the Schrödinger equation (QCMD/AVB model). Analysis of the simulation results with an Advanced Visualization System revealed a correlated rather than a stepwise picture of the enzymatic process. It is shown that an sp(2)--> sp(3) configurational change at the substrate carbonyl carbon is mostly responsible for triggering the activation process.

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