Stepwise as Opposed to Concerted Conformational Changes Optimize Signal Transmission in Allosteric Dimers

Abstract

Quantifying how assemblies of molecules coordinate their motions is key to understanding the operation of biological machines and other modular nanosystems. We explore the question of how tightly coupled the motions of adjacent units should be to optimize the transmission of signals, in an environment beset by thermal fluctuations. In this paper, we consider an allosteric dimer consisting of two ligand-binding domains and study how variations of ligand binding at one site are translated to similar variations in ligand affinity at the adjacent site. We compute the dynamics using a simple energy landscape model, and using mathematical methods used to study phenomenon of stochastic resonance, quantify the fraction of signal that propagates through the allosteric system as a transmission coefficient. We find that the transmission coefficient is optimized for an intermediate coupling between domains. The intermediate coupling is a compromise—when it is too low, the motion of the domains become uncorrelated, and fidelity suffers, but when it is too high, the system must surmount multiple transition barriers to change conformation, and communication slows down. There are two consequences. First, for a wide range of energy landscape parameters, the intermediate coupling corresponds to stepwise switching of domains via high energy (1.4 kcal/mol) lowly populated (<10% occupancy) intermediates. Second, the compromise between fidelity and rate caps the transmission coefficient at 40%, so that the majority of signal is degraded, even at the most perfectly formed allosteric interface. We propose that the stepwise switching observed in many allosteric proteins does not arise from an inherent limit in the mechanical couplings within the protein, but is a consequence of optimizing signal transmission; and that in general, if signals are to be communicated between domains via conformational change, a certain looseness of coupling is preferred, to provide a useful freedom of motion.