Non-equilibrium kinetics and trajectory thermodynamics of synthetic molecular pumps

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Abstract

Hypothetical transmembrane rotaxane as a model for trajectory thermodynamic theory 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.

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Stochastic thermodynamics, fluctuation theorems and molecular machines.

Udo Seifert (2012)

Stochastic thermodynamics as reviewed here systematically provides a framework for extending the notions of classical thermodynamics such as work, heat and entropy production to the level of individual trajectories of well-defined non-equilibrium ensembles. It applies whenever a non-equilibrium process is still coupled to one (or several) heat bath(s) of constant temperature. Paradigmatic systems are single colloidal particles in time-dependent laser traps, polymers in external flow, enzymes and molecular motors in single molecule assays, small biochemical networks and thermoelectric devices involving single electron transport. For such systems, a first-law like energy balance can be identified along fluctuating trajectories. For a basic Markovian dynamics implemented either on the continuum level with Langevin equations or on a discrete set of states as a master equation, thermodynamic consistency imposes a local-detailed balance constraint on noise and rates, respectively. Various integral and detailed fluctuation theorems, which are derived here in a unifying approach from one master theorem, constrain the probability distributions for work, heat and entropy production depending on the nature of the system and the choice of non-equilibrium conditions. For non-equilibrium steady states, particularly strong results hold like a generalized fluctuation-dissipation theorem involving entropy production. Ramifications and applications of these concepts include optimal driving between specified states in finite time, the role of measurement-based feedback processes and the relation between dissipation and irreversibility. Efficiency and, in particular, efficiency at maximum power can be discussed systematically beyond the linear response regime for two classes of molecular machines, isothermal ones such as molecular motors, and heat engines such as thermoelectric devices, using a common framework based on a cycle decomposition of entropy production.