A Hopping Mechanism for Cargo Transport by Molecular Motors on Crowded Microtubules

Most models designed to study the bidirectional movement of cargos as they are driven by molecular motors rely on the idea that motors of different polarities can be coordinated by external agents if arranged into a motor-cargo complex to perform the necessary work Gross, Hither and yon: a review of bidirectional microtubule-based transport (Gross in Phys. Biol. 1:R1-R11, 2004). Although these models have provided us with important insights into these phenomena, there are still many unanswered questions regarding the mechanisms through which the movement of the complex takes place on crowded microtubules. For example (i) how does cargo-binding affect motor motility? and in connection with that-(ii) how does the presence of other motors (and also other cargos) on the microtubule affect the motility of the motor-cargo complex? We discuss these questions from a different perspective. The movement of a cargo is conceived here as a hopping process resulting from the transference of cargo between neighboring motors. In the light of this, we examine the conditions under which cargo might display bidirectional movement even if directed by motors of a single polarity. The global properties of the model in the long-time regime are obtained by mapping the dynamics of the collection of interacting motors and cargos into an asymmetric simple exclusion process (ASEP) which can be resolved using the matrix ansatz introduced by Derrida (Derrida and Evans in Nonequilibrium Statistical Mechanics in One Dimension, pp. 277-304, 1997; Derrida et al. in J. Phys. A 26: 1493-1517, 1993).

The dynamics of cargo driven by molecular motors in the context of asymmetric simple exclusion processes

We consider the dynamics of cargo driven by a collection of interacting molecular motors in the context of ail asymmetric simple exclusion process (ASEP). The model is formulated to account for (i) excluded-volume interactions, (ii) the observed asymmetry of the stochastic movement of individual motors and (iii) interactions between motors and cargo. Items (i) and (ii) form the basis of ASEP models and have already been considered to study the behavior of motor density profile [A. Parmeggiani. T. Franosch, E. Frey, Phase Coexistence in driven one-dimensional transport, Phys. Rev. Lett. 90 (2003) 086601-1-086601-4]. Item (iii) is new. It is introduced here as an attempt to describe explicitly the dependence of cargo movement on the dynamics of motors in this context. The steady-state Solutions Of the model indicate that the system undergoes a phase transition of condensation type as the motor density varies. We study the consequences of this transition to the behavior of the average cargo velocity. (C) 2009 Elsevier B.V. All rights reserved.

Cellular automaton model for molecular traffic jams

We consider the time evolution of an exactly solvable cellular automaton with random initial conditions both in the large-scale hydrodynamic limit and on the microscopic level. This model is a version of the totally asymmetric simple exclusion process with sublattice parallel update and thus may serve as a model for studying traffic jams in systems of self-driven particles. We study the emergence of shocks from the microscopic dynamics of the model. In particular, we introduce shock measures whose time evolution we can compute explicitly, both in the thermodynamic limit and for open boundaries where a boundary-induced phase transition driven by the motion of a shock occurs. The motion of the shock, which results from the collective dynamics of the exclusion particles, is a random walk with an internal degree of freedom that determines the jump direction. This type of hopping dynamics is reminiscent of some transport phenomena in biological systems.