Length regulation of microtubules by molecular motors: Exact solution and density profiles

TL;DR

This paper presents an exact analytical solution for microtubule length regulation by kinesin motors, revealing exponential length distributions and complex phase behavior in diverging regimes.

Contribution

It provides the first exact solution for a microtubule model with processive motors and analyzes phase diagrams for diverging lengths.

Findings

Lengths are exponentially distributed in the finite-length regime.

Diverging microtubules exhibit complex density profile phases.

Monte Carlo simulations support the analytical results.

Abstract

In this work we study a microtubule (MT) model, whose length is regulated by the action of processive kinesin motors. We treat the case of infinite processivity, i.e. particle exchange in the bulk is neglected. The exact results can be obtained for model parameters which correspond to a finite length of the MT. In contrast to the model with particle exchange we find that the lengths of the MT are exponentially distributed in this parameter regime. The remaining parameter space of the model, which corresponds to diverging MT lengths, is analyzed by means of extensive Monte Carlo simulations and a macroscopic approach. For divergent MTs we find a complex structure of the phase diagram in terms of shapes of the density profile.