Abstract:
Motivated by the recent experimental observations on motor induced cooperative mechanism controlling the
length dynamics of microtubules (MTs), we examine how plus-end-targeted proteins of the kinesin family
regulate MT polymerization and depolymerization routines. Here, we study a stochastic mathematical model
capturing the unusual form of collective motor interaction on MT dynamics originating due to the molecular
traffic near the MT tip. We provide an extensive analysis of the joint effect of motor impelled MT polymerization
and complete depolymerization. The effect of the cooperative action is included by modifying the intrinsic
depolymerization rate. We analyze the model within the framework of continuum mean-field theory and the
resultant steady-state analytic solution is expressed in terms of Lambert W functions. Four distinct steady-state
phases including a shock phase have been reported. The significant features of the shock including its position
and height have been analyzed. Theoretical outcomes are supported by extensive Monte Carlo simulations. To
explore the system alterations between the regime of growth and shrinkage phase, we consider kymographs
of the microtubule along with the length distributions. Finally, we investigated the dependence of MT length
kinetics both on modifying factor of depolymerization rate and motor concentration. The overall extensive study
reveals that the flux of molecular traffic at the microtubule plus end initiates a cooperative mechanism, resulting
in significant change in MT growth and shrinkage regime as also observed experimentally.