Statistical properties of liquid protein-water molecular system dynamics

Abstract

It is considered an established fact that water plays the major role in protein motion, there is a close connection between the water dynamics and the protein conformational dynamics. We report on statistical analysis of such conformational dynamics obtained using classical molecular dynamics simulations with explicit water. We investigate specific moments in time when one of the dihedral angles of a simulated protein (a peptide dialanine) makes a large amplitude change causing a conformational transition in the peptide. We are interested in finding statistical correlations between the values of the angle at the moment of transition and several moments in advance of the transition (between 0.0 and 50.1ps). We also investigate how these correlations change when conditioned on the presence of water at different locations in space around the peptide. The challenge is in a large number of parameters that influence the conformational dynamics, which leads to multivariate probabilities. As statistical tools, we use pair-copulas and the Kendall's tau correlation. Copulas are a special way of representing multivariate probabilities. Paircopulas construction (PCC) decomposes a multivariate probability density into bivariate copulas, so-called pair-copulas. D-vine is one of graphical models that give a specific way of decomposing the probability density. The dependency structure is determined by the bivariate copulas and a nested set of trees using pair-copula. For this research, we apply the D-vine to study the statistical correlations between variables describing molecular conformation of a peptide and the properties of water molecules surrounding the peptide. We have found that the dynamics of peptides conformation possesses temporal correlations well in advance of the moments of conformational transitions. Moreover, when conditioned on the presence of water molecules at a few very specific locations in the first hydration shell of the peptide, these correlations become stronger and longer in time. This quantifies the influence of water on the conformational transitions and specifies water molecules that appear critical for the peptide to make successful conformational transition.