Stochastically pumped adaptation and directional motion of molecular machines

Abstract

Recent developments in synthetic molecular motors and pumps have sprung from a remarkable confluence of experiment and theory. Synthetic accomplishments have facilitated the ability to design and create molecules, many of them featuring mechanically bonded components, to carry out specific functions in their environment—walking along a polymeric track, unidirectional circling of one ring about another, synthesizing stereoisomers according to an external protocol, or pumping rings onto a long rod-like molecule to form and maintain high-energy, complex, nonequilibrium structures from simpler antecedents. Progress in the theory of nanoscale stochastic thermodynamics, specifically the generalization and extension of the principle of microscopic reversibility to the single-molecule regime, has enhanced the understanding of the design requirements for achieving strong unidirectional motion and high efficiency of these synthetic molecular machines for harnessing energy from external fluctuations to carry out mechanical and/or chemical functions in their environment. A key insight is that the interaction between the fluctuations and the transition state energies plays a central role in determining the steady-state concentrations. Kinetic asymmetry, a requirement for stochastic adaptation, occurs when there is an imbalance in the effect of the fluctuations on the forward and reverse rate constants. Because of strong viscosity, the motions of the machine can be viewed as mechanical equilibrium processes where mechanical resonances are simply impossible but where the probability distributions for the state occupancies and trajectories are very different from those that would be expected at thermodynamic equilibrium.