Kirone Mallick

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

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.

Nonequilibrium self-assembly of a filament coupled to ATP/GTP hydrolysis.

We study the stochastic dynamics of growth and shrinkage of single actin filaments or microtubules taking into account insertion, removal, and ATP/GTP hydrolysis of subunits. The resulting phase diagram contains three different phases: two phases of unbounded growth: a rapidly growing phase and an intermediate phase, and one bounded growth phase. We analyze all these phases, with an emphasis on the bounded growth phase. We also discuss how hydrolysis affects force-velocity curves. The bounded growth phase shows features of dynamic instability, which we characterize in terms of the time needed for the ATP/GTP cap to disappear as well as the time needed for the filament to reach a length of zero (i.e., to collapse) for the first time. We obtain exact expressions for all these quantities, which we test using Monte Carlo simulations.

Modified fluctuation-dissipation theorem for non-equilibrium steady states and applications to molecular motors

We present a theoretical framework to understand a modified fluctuation-dissipation theorem valid for systems close to non-equilibrium steady states and obeying Markovian dynamics. We discuss the interpretation of this result in terms of trajectory entropy excess. The framework is illustrated on a simple pedagogical example of a molecular motor. We also derive in this context generalized Green-Kubo relations similar to the ones obtained recently in Seifert U., Phys. Rev. Lett., 104 (2010) 138101 for more general networks of biomolecular states.

Role of ATP-Hydrolysis in the Dynamics of a Single Actin Filament

We study the stochastic dynamics of growth and shrinkage of single actin filaments taking into account insertion, removal, and ATP hydrolysis of subunits either according to the vectorial mechanism or to the random mechanism. In a previous work, we developed a model for a single actin or microtubule filament where hydrolysis occurred according to the vectorial mechanism: the filament could grow only from one end, and was in contact with a reservoir of monomers. Here we extend this approach in two ways--by including the dynamics of both ends and by comparing two possible mechanisms of ATP hydrolysis. Our emphasis is mainly on two possible limiting models for the mechanism of hydrolysis within a single filament, namely the vectorial or the random model. We propose a set of experiments to test the nature of the precise mechanism of hydrolysis within actin filaments.

Condensation of actin filaments pushing against a barrier

We develop a model to describe the force generated by the polymerization of an array of parallel biofilaments. The filaments are assumed to be coupled only through mechanical contact with a movable barrier. We calculate the filament density distribution and the force–velocity relation with a mean-field approach combined with simulations. We identify two regimes: a non-condensed regime at low force in which filaments are spread out spatially and a condensed regime at high force in which filaments accumulate near the barrier. We confirm a result previously known from other related studies, namely that the stall force is equal to N times the stall force of a single filament. In the model studied here, the approach to stalling is very slow, and the velocity is practically zero at forces significantly lower than the stall force.

Fluctuation theorem for the flashing ratchet model of molecular motors.

Molecular motors convert chemical energy derived from the hydrolysis of adenosine triphosphate (ATP) into mechanical energy. A well-studied model of a molecular motor is the flashing ratchet model. We show that this model exhibits a fluctuation relation known as the Gallavotti-Cohen symmetry. Our study highlights the fact that the symmetry is present only if the chemical and mechanical degrees of freedom are both included in the description.

Fluctuation Relations for Molecular Motors

This review is focused on the application of specific fluctuation relations, such as the Gallavotti-Cohen relation, to ratchet models of a molecular motor. A special emphasis is placed on two-state models such as the flashing ratchet model. We derive the Gallavotti-Cohen fluctuation relation for these models and we discuss some of its implications.