Active Gaussian Network Model: a non-equilibrium description of protein fluctuations and allosteric behavior

Abstract

Understanding the link between structure and function in proteins is fundamental in molecular biology and proteomics. A central question in this context is whether allostery - where the binding of a molecule at one site affects the activity of a distant site - emerges as a further manifestation of the intricate interplay between structure, function, and intrinsic dynamics. This study explores how allosteric regulation is modified when intrinsic protein dynamics operate under out-of-equilibrium conditions. To this purpose, we introduce a simple nonequilibrium model of protein dynamics, inspired by active matter systems, by generalizing the widely employed Gaussian Network Model (GNM) to incorporate non-thermal effects. Our approach underscores the advantage of framing allostery as a causal process by using, as a benchmark system, the second PDZ domain of the human phosphatase hPT1E that mediates protein-protein interactions. We employ causal indicators, such as response functions and transfer entropy, to identify the network of PDZ2 residues through which the allosteric signal propagates across the protein structure. These indicators reveal specific regions that align well with experimental observations. Furthermore, our results suggest that deviations from purely thermal fluctuations can significantly influence allosteric communication by introducing distinct timescales and memory effects. This influence is particularly relevant when the allosteric response unfolds on timescales incompatible with relaxation to equilibrium. Accordingly, non-thermal fluctuations may become essential for accurately describing protein responses to ligand binding and developing a comprehensive understanding of allosteric regulation.