Long time behaviour in a model of microtubule growth

TL;DR

This paper models microtubule growth using a stochastic process with local and global dynamics, providing a full phase diagram and criteria for different long-term behaviors.

Contribution

It introduces a novel continuous-time stochastic model of microtubule dynamics and characterizes its phase diagram and recurrence properties.

Findings

Complete phase diagram of the model

Criteria for transience and recurrence

Insights into microtubule growth behavior

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 give a complete characterization of the phase diagram of the model, and derive several criteria of the transient and recurrent regimes for the underlying stochastic process.