Analysis of non-processive molecular motor transport using renewal reward theory

TL;DR

This paper develops a mathematical model for cargo transport by non-processive molecular motors, using renewal reward theory and stochastic analysis to derive explicit formulas for key transport metrics and explain experimental observations.

Contribution

It introduces a novel mathematical framework combining renewal theory and stochastic differential equations to analyze non-processive motor transport.

Findings

Derived explicit formulas for cargo velocity and run length.

Predicted the importance of motor number-dependent rates for explaining data.

Highlighted the role of clustering in non-processive motor efficiency.

Abstract

We propose and analyze a mathematical model of cargo transport by non-processive molecular motors. In our model, the motors change states by random discrete events (corresponding to stepping and binding/unbinding), while the cargo position follows a stochastic differential equation (SDE) that depends on the discrete states of the motors. The resulting system for the cargo position is consequently an SDE that randomly switches according to a Markov jump process governing motor dynamics. To study this system we (1) cast the cargo position in a renewal theory framework and generalize the renewal reward theorem and (2) decompose the continuous and discrete sources of stochasticity and exploit a resulting pair of disparate timescales. With these mathematical tools, we obtain explicit formulas for experimentally measurable quantities, such as cargo velocity and run length. Analyzing these formulas then yields some predictions regarding so-called non-processive clustering, the phenomenon that a single motor cannot transport cargo, but that two or more motors can. We find that having motor stepping, binding, and unbinding rates depend on the number of bound motors, due to geometric effects, is necessary and sufficient to explain recent experimental data on non-processive motors.