Regular phase in a model of microtubule growth

Hryniv, Ostap

Abstract

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.

Citation

Hryniv, O. (2012). Regular phase in a model of microtubule growth. Markov processes and related fields, 18(2), 177-200

• Journal Article Type: Article
• Publication Date: Jan 1, 2012
• Deposit Date: Mar 14, 2012
• Journal: Markov processes and related fields.
• Print ISSN: 1024-2953
• Publisher: Polymat
• Peer Reviewed: Peer Reviewed
• Volume: 18
• Issue: 2
• Pages: 177-200
• Keywords: Microtubules, Phase transition, Birth-and-death process, Stochastic domination, Coupling, Cluster expansions.
• Public URL: https://durham-repository.worktribe.com/output/1479879
• Publisher URL: http://mech.math.msu.su/~malyshev/abs12.htm