Fluctuation theorem and large deviation function for a solvable model of a molecular motor

TL;DR

This paper investigates a minimal stochastic model of a molecular motor, analyzing the constraints imposed by the Fluctuation Theorem on its operation, and compares theoretical predictions with experimental data on kinesin.

Contribution

It provides an exact calculation of the large deviation function for a solvable molecular motor model and links various formulations of the Fluctuation Theorem to entropy production.

Findings

Exact large deviation function derived for the model

Good agreement with experimental data on kinesin

Unified understanding of different FT formulations through entropy production

Abstract

We study a discrete stochastic model of a molecular motor. This discrete model can be viewed as a \emph{minimal} ratchet model. We extend our previous work on this model, by further investigating the constraints imposed by the Fluctuation Theorem on the operation of a molecular motor far from equilibrium. In this work, we show the connections between different formulations of the Fluctuation Theorem. One formulation concerns the generating function of the currents while another one concerns the corresponding large deviation function, which we have calculated exactly for this model. A third formulation of FT concerns the ratio of the probability of making one forward step to the probability of making one backward step. The predictions of this last formulation of the Fluctuation Theorem adapted to our model are in very good agreement with the data of Carter and Cross [Nature, {\bf 435}, 308 (2005)] on single molecule measurements with kinesin. Finally, we show that all the formulations of FT can be understood from the notion of entropy production.