Dynamic Combinatorial Analysis of Local Configurations in Molecular Dynamics Simulation: Frequent Itemset Mining and Hierarchical Hidden Markov Model

Abstract

An automatic, multi-scale, and three-dimensional (3D) summary of local configurations of the dynamics of proteins can help to discover and describe the relationships between different parts of proteins across spatial scales, including the overall conformation and 3D configurations of side chains and domains. These discoveries can improve understanding of the function and allosteric mechanism of proteins. Current methods are unable to effectively summarize 3D shapes or dynamics of local configurations across multiple spatial scales. We propose Frequent Substructure Clustering (FSC) and Subconformational Hierarchical Hidden Markov Model (SHHMM) to fill this gap. FSC of the Cβ atoms of the GB3 protein identifies six clusters of co-occurring local configurations. The clusters localize at different regions, contribute to the overall conformation, and form two anti-correlating groups. The results suggest FSC could describe dynamical relationships between different parts of proteins through 3D descriptions of the frequently occurring local configurations at different spatial resolutions. SHHMM consists of three layers describing transition between conformations, conformations as combinations of sub-conformations, and sub-conformations as pairwise distances. Each sub-conformation describes the 3D configurations of part of a molecular system. Two sub-conformations may describe distinct shapes formed by the same set of atoms. SHHMM extracts clusters of sub-conformations and their general 3D shapes, transition probabilities, and equilibrium probabilities. When a protein is rigid except for two loops transiting between opened and closed states, SHHMM would describe each state of each loop as a cluster of sub-conformations. The transition probabilities describe the correlation between the current state of one loop to the future state of another or the same loop. Both methods can augment other techniques for studying the function of sub-cellular processes and highlight the role of local configurations in biomolecular systems.