Energy and information flows in strongly coupled rotary machines

Living systems at the molecular scale are composed of many coupled components with interactions varying in nature and strength. Microscopic biological systems operate far from equilibrium and are subject to strong fluctuations. These conditions pose significant challenges to efficient, precise, and rapid free-energy transduction, yet nature has evolved numerous molecular machines that do just this. We present a model of strongly coupled stochastic rotary motors inspired by FoF1-ATP synthase and study its behavior. Rather than aiming for the most accurate model of ATP synthase, the model is meant to be a starting point to explore the effect of less-than-tight coupling between components. To this end, we aim to give the model a minimum level of complexity while keeping biological considerations in mind. Energy and information flows are studied numerically and through analytically tractable limiting cases. The limiting cases provide bounds on the system's performance. We find that the output power of a work-to-work converter consisting of two coupled subsystems in the presence of energy barriers can be maximized at intermediate-strength coupling rather than at tight coupling. This phenomenon is backed up by a simple theory that predicts the power maximizing coupling strength, and agrees well with numerical results. We observe several characteristics that show up at the coupling strength that maximizes output power: a maximum in power transmitted from Fo to F1, a maximum in information flow, and equal subsystem entropy production rates. Finally, we derive a bound on the machine's input and output power, which accounts for the energy and information passed between subsystems. We conclude that intermediate-strength coupling is a realistic option for biological systems passing on energy and information to downstream processes.