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Regular phase in a model of microtubule growth

Hryniv, Ostap

Authors



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.
Publisher URL http://mech.math.msu.su/~malyshev/abs12.htm