Collective effects in models for interacting molecular motors and motor-microtubule mixtures

Abstract

Three problems in the statistical mechanics of models for an assembly of molecular motors interacting with cytoskeletal filaments are reviewed. First, a description of the hydrodynamical behaviour of density-density correlations in fluctuating ratchet models for interacting molecular motors is outlined. Numerical evidence indicates that the scaling properties of dynamical behavior in such models belong to the KPZ universality class. Second, the generalization of such models to include boundary injection and removal of motors is provided. In common with known results for the asymmetric exclusion processes, simulations indicate that such models exhibit sharp boundary driven phase transitions in the thermodynamic limit. In the third part of this paper, recent progress towards a continuum description of pattern formation in mixtures of motors and microtubules is described, and a non-equilibrium "phasediagram" for such systems discussed.Email address: menon@imsc.res.in (Gautam I. Menon).

Interacting particles in disordered flashing ratchets

“…2(a) as a function of the overall particle density ρ for two values of the asymmetry parameter a = 1, 2. A similar plot was obtained in [30,31], apart from an overall sign due to different orientation of V (x). The symmetry of the plot around ρ = 1/2 is due to the not so apparent particle-hole symmetry of the dynamics, as was elucidated in [30].…”

“…This has led to many interesting collective effects in models of elastically coupled motors [15,16,17,1,3,4] and excluded volume interactions [18,19,20,21,22,23,24,25,26,27,28,29]. Of particular interest to the present work is the model of a discrete flashing ratchet considered in [30,31] in which large scale properties of a system of hard-core particles moving in a ratchet potential defined on a discrete lattice was studied.…”