General efficiency relation for dissipative molecular machines

Abstract

Living systems use chemical fuel to process information, assemble structures and maintain fluxes. Many of these processes are dissipative: energy is consumed purely to maintain non-equilibrium steady-state outputs. How efficiently the input energy is transduced toward the output dissipation as opposed to being lost during intermediate steps, and whether the efficiency is constrained by general principles or specific fine-tuning, are open questions. Here, applying a recent mapping from non-equilibrium systems to battery-resistor circuits, an analytic expression for the efficiency of any dissipative molecular machine driven by a chemical potential difference is derived. This expression disentangles the chemical potential from the machine’s details, whose effect on the efficiency is fully specified by a constant called the load resistance. The efficiency passes through an inflection point separating totally inefficient machines from efficient machines if the balance between chemical potential difference and load resistance exceeds thermal noise. This explains all-or-none dynein stepping with increasing ATP concentration observed in single-molecule experiments. These results indicate that energy transduction in living systems is efficient not because of idiosyncratic optimization of biomolecules, but rather because the concentration of chemical fuel is kept above a threshold level.