Information theoretics for the machine learning detection of functionally conserved and coordinated protein motions

Traditional information theoretic analysis of functionally conserved binding interactions described by multiple sequence alignments are unable to provide direct insights into the underlying strength, spatial distribution, and coordination of the biophysical motions that govern protein binding interactions during signaling and regulatory function. However, molecular dynamic (MD) simulations of proteins in bound vs. unbound conformational states can allow for the combined application of machine learning classification and information theory towards many problems posed by comparative protein dynamics. After both bound and unbound protein dynamic states are adequately sampled in MD software, they can be employed as a comparative training set for a binary classifier capable of discerning the complex dynamical consequences of protein binding interactions with DNA or other proteins. The statistical validation of the learner on MD simulations of homologs can be used to assess its ability to recognize functional protein motions that are conserved over evolutionary time scales. Regions of proteins with functionally conserved dynamics are identifiable by their ability to induce significant correlations in local learning performance across homologous MD simulations. Through case studies of Rbp subunit 4/7 interaction in RNA Pol II and DNA-protein interactions of TATA binding protein, we demonstrate this method of detecting functionally conserved protein dynamics. We also demonstrate how the concepts of relative entropy (i.e. information gain) and mutual information applied to the binary classification states of MD simulations can be used to compare the impacts of molecular variation on conserved dynamics and to identify coordinated motions involved in dynamic interactions across sites.