Stochastic Model of Microtubule Dynamics.

We introduce a continuous time stochastic process on strings made of two types of particle, whose dynamics mimics that of microtubules in a living cell. The long term behaviour of the system is described in terms of the velocity v of the string end. We show that v is an analytic function of its parameters and study its monotonicity properties. We give a complete characterisation of the phase diagram of the model and derive several criteria of the growth ( $$v>0$$ ) and the shrinking ( $$v<0$$ ) regimes of the dynamics. [ABSTRACT FROM AUTHOR]