Regular Phase in a Model of Microtubule Growth

O. Hryniv

2012, v.18, №2, 177-200


We study a continuous-time stochastic process on strings made of two types of particles, whose dynamics mimics the behaviour of microtubules in a living cell; namely, the strings evolve via a competition between (local) growth/shrinking as well as (global) hydrolysis processes. We show that the velocity of the string end, which determines the long-term behaviour of the system, depends analytically on the growth and shrinking rates. We also identify a region in the parameter space where the velocity is a strictly monotone function of the rates. The argument is based on stochastic domination, large deviations estimates, cluster expansions and semi-martingale techniques.

Keywords: microtubules,phase transition,birth-and-death process,stochastic domination,coupling,cluster expansions


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