In a single-molecule assay, the motion of a molecular motor is often inferred by measuring the stochastic trajectory of a large probe particle attached to it. We discuss a simple model for this generic setup taking into account explicitly the elastic coupling between the probe and the motor. The combined dynamics consists of discrete steps of the motor and the continuous Brownian motion of the probe. Motivated by recent experiments on the F 1 -ATPase, we investigated three types of efficiencies both in simulations and in a Gaussian approximation. Overall, we obtained good quantitative agreement with the experimental data. In particular, we clarify the conditions under which one of these efficiencies becomes larger than 1.
Many single molecule experiments for molecular motors comprise not only the motor but also large probe particles coupled to it. The theoretical analysis of these assays, however, often takes into account only the degrees of freedom representing the motor. We present a coarse-graining method that maps a model comprising two coupled degrees of freedom which represent motor and probe particle to such an effective one-particle model by eliminating the dynamics of the probe particle in a thermodynamically and dynamically consistent way. The coarse-grained rates obey a local detailed balance condition and reproduce the net currents. Moreover, the average entropy production as well as the thermodynamic efficiency is invariant under this coarse-graining procedure. Our analysis reveals that only by assuming unrealistically fast probe particles, the coarse-grained transition rates coincide with the transition rates of the traditionally used one-particle motor models. Additionally, we find that for multicyclic motors the stall force can depend on the probe size. We apply this coarse-graining method to specific case studies of the F1-ATPase and the kinesin motor.
By considering sub-exponential contributions in large deviation theory, we determine the fine structure in the probability distribution of the observable displacement of a bead coupled to a molecular motor. More generally, for any stochastic motion along a periodic substrate, this approach reveals a discrete symmetry of this distribution for which hidden degrees of freedom lead to a periodic modulation of the slope typically associated with the fluctuation theorem. Contrary to previous interpretations of experimental data, the mean force exerted by a molecular motor is unrelated to the long-time asymptotics of this slope and must rather be extracted from its short-time limit.
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