Collective Effects in Models for Interacting Molecular Motors and Motor-Microtubule Mixtures

TL;DR

This paper reviews statistical mechanics models of interacting molecular motors, highlighting hydrodynamical behavior, boundary effects, and pattern formation in motor-microtubule systems, with implications for understanding cellular transport.

Contribution

It provides a comprehensive analysis of hydrodynamics, boundary effects, and pattern formation in models of molecular motors, extending previous work with new continuum descriptions.

Findings

Scaling properties belong to the KPZ universality class.

Models exhibit boundary-driven phase transitions.

Progress towards a continuum description of 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 ``phase-diagram'' for such systems discussed.