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

Abstract

We study a discrete stochastic model of a molecular motor. This discrete model can be viewed as a 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 concerns the ratio of the probability of observing a velocity v to the same probability of observing a velocity -v . Finally, we show that all the formulations of the fluctuation theorem can be understood from the notion of entropy production.

Entropy production in the nonequilibrium steady states of interacting many-body systems

“…Studying a one-dimensional system composed of a single particle driven along a periodic potential, they reformulated the problem as a time-independent eigenvalue problem [7] and showed that for this system the large deviation function of the entropy production exhibits a kink at zero entropy production. Similar kinks in the large deviation function of the entropy production or in related large deviation functions of other quantities can also be found in a range of other systems [8][9][10][11][12][13]. These are intriguing results that raise the important question whether the presence of this kink is a universal feature of systems with non-equilibrium steady states.…”

Sufficient conditions for the additivity of stall forces generated by multiple filaments or motors

“…This non-equilibrium at stall for one motor manifests itself in the form of nonadditivity of stall forces in the presence of multiple motors even though the only interaction between them is self-exclusion ( Fig.7(a)) [32,78,79]. Interestingly, a discrete version of this two-state model [102,103], shows additivity of stall forces for multiple motors with only self-inclusion interactions (see Fig. 7(b)).…”

“…Schematic of the (a) continuous [72] and (b) discrete two-state Brownian ratchet model [102,103]. (a) A spontaneous motion is expected when the ratio of transition rates ω 1 (x) ω 2 (x) is far from the equilibrium value given by the detailed balance condition.…”

Entropy production in nonequilibrium steady states: A different approach and an exactly solvable canonical model

“…This is the kind of trajectory, or path, employed in previous work on the subject (see, e.g., Refs. [4,10,13,16]). …”

“…While entropy production is a system-dependent quantity, some remarkable universal properties emerge: For example, the probability distribution of the total entropy production satisfies a detailed fluctuation theorem in large classes of systems (see, e.g., Refs. [1][2][3][4][5]), and a kink appears in its large deviation function (and in that of related currents) at zero entropy production [6][7][8][9][10][11][12]. Initially, this kink has been attributed to specific properties of the systems under investigation, but a recent study indicates that it is a generic feature, related to the detailed fluctuation theorem [13].…”