Non-equilibrium kinetics and trajectory thermodynamics of synthetic molecular pumps

Abstract

A major goal in the design of synthetic molecular machines is the creation of pumps that can use the input of energy to transport material from a reservoir at low chemical potential to a different reservoir at higher chemical potential, thereby forming and maintaining a chemical potential gradient. Such pumps are ubiquitous in biology. Some, including the Ca⁺²-ATPase of the sarcoplasmic reticulum, and the (Na⁺,K⁺)-ATPase found in the membranes of almost all cells, use energy from ATP hydrolysis to accomplish this task. Others, such as bacteriorhodopsin, use energy from light. Here, we examine in the context of recent artificial molecular pumps, the kinetics and thermodynamics of both light or externally driven pumps on the one hand and pumps driven by chemical catalysis on the other. We show that even for formally similar mechanisms there is a tremendous difference in the design principles for these two classes of pumps, where the former can function as energy ratchets, and the latter must operate as information ratchets. This difference arises because, unlike optically or externally driven pumps, the transition constants for pumps in which the required energy is provided by catalysis of a chemical reaction obey the principle of microscopic reversibility. We use cycle kinetics developed by Terrell Hill in the analysis of energy driven pumping. This approach is based on the trajectory thermodynamics of Onsager and Machlup. The recent “stochastic thermodynamic” approach is shown to be fundamentally flawed and to lead to incorrect predictions regarding the behavior of molecular machines driven by catalysis of an exergonic chemical reaction.