Energy-speed-accuracy tradeoffs in a driven, stochastic, rotary machine

Molecular machines are stochastic systems capable of converting between different forms of energy such as chemical potential energy and mechanical work. The F1 subunit of ATP synthase couples the rotation of its central crankshaft with the synthesis or hydrolysis of ATP. This machine can reach maximal speeds of hundreds of rotations per second, and is believed to be capable of nearly 100% efficiency in near-equilibrium conditions, although a biased cycling machine is a nonequilibrium system and therefore must waste some energy in the form of dissipation. We explore the fundamental relationships among the accuracy, speed, and dissipated energy of such driven rotary molecular machines, in a simple model of F1. Simulations using Fokker-Planck dynamics are used to explore the parameter space of driving strength, internal energetics of the system, and rotation rate. A tradeoff between accuracy and work as speed increases is found to occur over the range of biologically rele- vant timescales. We search for a way to improve this tradeoff by applying approximations of dissipation minimizing protocols and find a reduction in both work and accuracy, yet accuracy drops less than the work does, leading to an overall decrease in the ratio of work to accuracy.