The effects of external torque on the F 1-ATPase rotary molecular motor are studied from the viewpoint of recent advances in stochastic thermodynamics. This motor is modeled in terms of discrete-state and continuous-state stochastic processes. The dependence of the discrete-state description on external torque and friction is obtained by fitting its transition rates to a continuous-angle model based on Newtonian mechanics with Langevin fluctuating forces and reproducing experimental data on this motor. In this approach, the continuous-angle model is coarse-grained into discrete states separated by both mechanical and chemical transitions. The resulting discrete-state model allows us to identify the regime of tight chemomechanical coupling of the F 1 motor and to infer that its chemical and mechanical efficiencies may reach values close to the thermodynamically allowed maxima near the stalling torque. We also show that, under physiological conditions, the F 1 motor is functioning in a highly-nonlinear-response regime, providing a rotation rate a million times faster than would be possible in the linear-response regime of nonequilibrium thermodynamics. Furthermore, the counting statistics of fluctuations can be obtained in the tight-coupling regime thanks to the discrete-state stochastic process and we demonstrate that the so-called fluctuation theorem provides a useful method for measuring the thermodynamic forces driving the motor out of equilibrium.
A model of processive walking and slipping of kinesin-8 molecular motors