On the motion of kinesin in a viscoelastic medium

TL;DR

This paper introduces a semi-Markov model for kinesin movement in viscoelastic media, showing that such environments reduce velocity and diffusion but increase randomness, differing from traditional Markovian models.

Contribution

It develops a semi-Markov kinetic model for kinesin in viscoelastic media, accounting for non-Markovian waiting times and analyzing their effects on motor dynamics.

Findings

Viscoelasticity decreases kinesin velocity.

Viscoelasticity reduces diffusion constant.

Increases the randomness or Fano-factor.

Abstract

Kinesin is a molecular motor that transports cargo along microtubules. The results of many {\it in vitro} experiments on kinesin-1 are described by kinetic models \cite{Clancy11} in which one transition corresponds to the forward motion and subsequent binding of the tethered motor head. We argue that in a viscoelastic medium like the cytosol of a cell this step is not Markov and has to be described by a non-exponential waiting time distribution. We introduce a semi-Markov kinetic model for kinesin that takes this effect into account. We calculate, for arbitrary waiting time distributions, the moment generating function of the number of steps made, and determine from this the average velocity and the diffusion constant of the motor. We illustrate our results for the case of a waiting time distribution that is Weibull. We find that for realistic parameter values, viscoelasticity decreases the velocity and the diffusion constant, but increases the randomness (or Fano-factor).