Optimal nonequilibrium driving of a rotary mechanochemical motor

Prompted by current experiments on mechanically driven F1 ATP synthase, we investigate optimal (minimum-dissipation) driving protocols of rotary mechanochemical motors. We propose a simple model system coupling chemical reactions to mechanical motion under periodic boundary conditions, driven by a periodic time-dependent force. Under linear response approximations near equilibrium and near nonequilibrium steady states, optimal driving protocols are determined by a generalized friction coefficient. Such a model has a periodic generalized friction coefficient that peaks near system energy barriers, implying optimal protocols that proceed rapidly when the system is overwhelmingly in a single macrostate, but slow significantly near energy barriers, harnessing thermal fluctuations to kick the system over the energy barriers for free.