Length control of microtubules by depolymerizing motor proteins

TL;DR

This paper presents a quantitative model of depolymerizing motor proteins controlling microtubule length, revealing conditions for steady-state distributions and implications for cellular length regulation.

Contribution

The study introduces a mathematical model that explains how depolymerizing motor proteins regulate microtubule length distributions, including the effects of motor concentration and processivity.

Findings

Steady-state length distribution can be non-monotonic with a single peak.

High motor density leads to exponential length distribution.

Motor proteins can precisely control microtubule lengths in cells.

Abstract

In many intracellular processes, the length distribution of microtubules is controlled by depolymerizing motor proteins. Experiments have shown that, following non-specific binding to the surface of a microtubule, depolymerizers are transported to the microtubule tip(s) by diffusion or directed walk and, then, depolymerize the microtubule from the tip(s) after accumulating there. We develop a quantitative model to study the depolymerizing action of such a generic motor protein, and its possible effects on the length distribution of microtubules. We show that, when the motor protein concentration in solution exceeds a critical value, a steady state is reached where the length distribution is, in general, non-monotonic with a single peak. However, for highly processive motors and large motor densities, this distribution effectively becomes an exponential decay. Our findings suggest that such motor proteins may be selectively used by the cell to ensure precise control of MT lengths. The model is also used to analyze experimental observations of motor-induced depolymerization.