Abstract
Elastic network (EN) models have been widely used in recent years for describing protein dynamics, based on the premise that the motions naturally accessible to native structures are relevant to biological function. We posit that equilibrium motions also determine communication mechanisms inherent to the network architecture. To this end, we explore the stochastics of a discrete-time, discrete-state Markov process of information transfer across the network of residues. We measure the communication abilities of residue pairs in terms of hit and commute times, i.e., the number of steps it takes on an average to send and receive signals. Functionally active residues are found to possess enhanced communication propensities, evidenced by their short hit times. Furthermore, secondary structural elements emerge as efficient mediators of communication. The present findings provide us with insights on the topological basis of communication in proteins and design principles for efficient signal transduction. While hit/commute times are information-theoretic concepts, a central contribution of this work is to rigorously show that they have physical origins directly relevant to the equilibrium fluctuations of residues predicted by EN models.
Highlights
Proteins function neither as static entities nor in isolation, under physiological conditions
A major goal in this study is to relate the hitting times derived from the Markovian stochastics model to the equilibrium fluctuations of residues predicted by elastic network (EN) models, bridging the gap between two disciplines, information theory and statistical mechanics. To this end, using the theory of generalized matrix inverses [12,13,14], we show that hitting/commute times can be expressed in terms of the Kirchhoff matrix of inter-residue contacts that underlie the Gaussian Network Model (GNM) methodology
There has been a surge in the number of studies using network models for understanding biomolecular systems dynamics
Summary
Proteins function neither as static entities nor in isolation, under physiological conditions They are instead subject to constant motions and interactions, both within and between molecules. Elastic network (EN) models in conjunction with modal analysis, and in particular the Gaussian Network Model (GNM) [1,2,3], have been widely used for elucidating the collective dynamics of proteins and exploring their relevance to biological function [4,5,6,7,8,9] We posit that these collective motions determine communication patterns that are inherent to the native architecture.
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