A modified active Brownian dynamics model using asymmetric energy conversion and its application to the molecular motor system

Abstract

We consider a modified energy depot model in the overdamped limit using an asymmetric energy conversion rate, which consists of linear and quadratic terms in an active particle's velocity. In order to analyze our model, we adopt a system of molecular motors on a microtubule and employ a flashing ratchet potential synchronized to a stochastic energy supply. By performing an active Brownian dynamics simulation, we investigate effects of the active force, thermal noise, external load, and energy-supply rate. Our model yields the stepping and stalling behaviors of the conventional molecular motor. The active force is found to facilitate the forwardly processive stepping motion, while the thermal noise reduces the stall force by enhancing relatively the backward stepping motion under external loads. The stall force in our model decreases as the energy-supply rate is decreased. Hence, assuming the Michaelis-Menten relation between the energy-supply rate and the ATP concentration, our model describes an ATP-dependent stall force in contrast to kinesin-1.

Stochastic dynamics of coupled active particles in an overdamped limit

“…Since an active Brownian particle model in an overdamped limit is a plausible candidate to describe the dynamics of a processive molecular motor in a cell, kinesin-1 was analyzed using our model. Kinesin-1 is a well-known processive cytoskeletal motor that exhibits discrete unidirectional motion, and our model successfully captured the primary features of the motor, including its forward and backward steppings and the stalling against an external load force [7,8].…”

“…In order to model the active dynamics in the overdamped limit where the velocity is not a well-defined stochastic variable, we considered the energy conversion rate to be a function of the drift velocity, up to the quadratic order [7]. Since an active Brownian particle model in an overdamped limit is a plausible candidate to describe the dynamics of a processive molecular motor in a cell, kinesin-1 was analyzed using our model.…”

“…In Section 2, we construct a model for the dynamics of active particles bound to a passive particle based on our previous model [7]. The results of the active Brownian dynamics simulation follow in Section 3.…”

Two-dimensional motion of Brownian swimmers in linear flows

“…Note that F represents a force and β = 1/k B T according to ten Hagen nomenclature. Finally, (24)- (26) show that the activity of the particle in a shear flow provides extra coefficients to its MSD that scale in time in the same way as a passive particle under shear. The only difference with the passive case relies on the component x 2 1 (t) , where a new quadratic term in time appears due to the activity of the particle.…”

“…More recently, active particles (driven by an assumed internal mechanism) have been widely studied [7,[22][23][24][25][26][27][28][29]. For example, the Brownian motion of active bodies of simple shape, one sphere [3,30], multiple spheres [5], or ellipsoids [30] have been published.…”