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

Length control of microtubules by depolymerizing motor proteins