Optimal Control of Rotary Motors

Abstract

Single-molecule experiments have found near-perfect thermodynamic efficiency in the rotary motor F1-ATP synthase. To help elucidate the principles underlying nonequilibrium energetic efficiency in such stochastic machines, we investigate driving protocols that minimize dissipation near equilibrium in a simple model rotary mechanochemical motor, as determined by a generalized friction coefficient. Our simple model has a periodic friction coefficient that peaks near system energy barriers. This implies a minimum-dissipation protocol that proceeds rapidly when the system is overwhelmingly in a single macrostate, but slows significantly near energy barriers, thereby harnessing thermal fluctuations to kick the system over energy barriers with minimal work input. This model also manifests a phenomenon not seen in otherwise similar non-periodic systems: sufficiently fast protocols can effectively lap the system. While this leads to a non-trivial tradeoff between accuracy of driving and energetic cost, we find that our designed protocols out-perform naive protocols.

arXiv comment12 pages, 11 figures

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• Optimal Control of the F${}_1$-ATPase Molecular Motor
• Performance of optimal linear-response processes in driven Brownian motion far from equilibrium
• Beyond Linear Response: Equivalence between Thermodynamic Geometry and Optimal Transport
• Energy Landscape Design Principle for Optimal Energy Harnessing by Catalytic Molecular Machines
• Stochastic thermodynamic bounds on logical circuit operation
• Optimal control with a strong harmonic trap
• Optimal control of protein copy number
• Failure of the geometric approach prediction of excess work scaling for open and isolated quantum systems
• Assembly of heteropolymers via a network of reaction coordinates
• Modeling work-speed-accuracy trade-offs in a stochastic rotary machine
• Hidden energy flows in strongly coupled nonequilibrium systems
• Multiparameter optimal control of F1-ATPase
• Optimal finite-time processes in weakly driven overdamped Brownian motion
• Global thermodynamic manifold for conservative control of stochastic systems