Entropy Transfer between Residue Pairs Shows that Allostery is an Intrinsic Property of Proteins: Quantifying Allosteric Communication in Ubiquitin

Abstract

AbstractIt has recently been proposed by Gunasakaran et al. that allostery may be an intrinsic property of all proteins. Here, we apply Schreiber’s transfer entropy formulation to the non-allosteric protein Ubiquitin and show that there are indeed systematic pathways of entropy and information transfer between residues that correlate well with the activities of the protein. We use 600 nanosecond molecular dynamics trajectories for Ubiquitin and its complex with human polymerase iota and evaluate entropy transfer between all pairs of residues of Ubiquitin and quantify the binding susceptibility changes upon complex formation. Calculations show that specific residues act as entropy reservoirs in Ubiquitin and others as entropy sinks. Using the plausible conjecture that extracting entropy from a residue makes it more susceptible for interaction with a partner, we explain the ternary complex formation of Ubiquitin in terms of entropy transfer. Finally, we show that time delayed correlation of fluctuations of two interacting residues possesses an intrinsic causality that tells which residue controls the interaction and which one is controlled. Our work shows that time delayed correlations, entropy transfer and causality are the required new concepts for explaining allosteric communication in proteins.Author SummaryAllosteric communication is essential for the function of proteins. Recent work shows that allostery results from dynamic processes in the protein associated with atomic fluctuations leading to entropic interactions that involve ensemble of pathways rather than discrete two state transitions. Based on this new picture of allostery, it was proposed that allostery may indeed be an intrinsic property of all proteins. In order to test this hypothesis, we derive the computational tools for quantifying allosteric communication, and explain allostery in terms of entropy transfer, a new concept based on information theory. We use long molecular dynamics simulations of proteins from which we calculate the transfer of entropy between pairs of residues. Results of simulations show that certain residues act as entropy sources while others as entropy sinks. Evaluation of time delayed correlations shows the presence of causality of interactions that allow us to differentiate between residues that are drivers in allosteric activity and those that are driven. Identification of driver-driven relations is important for drug design. Using the example of Ubiquitin, a protein that is not known to be allosteric, we identify paths of information transfer that control its binding to diverse partners in the Ubiquitin-Proteasome System. We conclude that allosteric communication resulting from entropy transfer between residues is an intrinsic property of all proteins.