Cooperative dynamics of microtubule ensembles: Polymerization forces and rescue-induced oscillations

TL;DR

This paper models the cooperative behavior of microtubule ensembles against elastic barriers, revealing how force generation and oscillations depend on rescue rates, with implications for cellular force regulation.

Contribution

It introduces a dynamical mean-field model for microtubule ensembles including force sharing, catastrophes, and rescues, highlighting oscillatory dynamics and force scaling laws.

Findings

Maximal polymerization force scales linearly with N for small N or stiff barriers.

Oscillatory rescue and catastrophe dynamics form a robust limit cycle.

Force growth depends on rescue rates and tubulin on-rates, relevant for cellular regulation.

Abstract

We investigate the cooperative dynamics of an ensemble of N microtubules growing against an elastic barrier. Microtubules undergo so-called catastrophes, which are abrupt stochastic transitions from a growing to a shrinking state, and rescues, which are transitions back to the growing state. Microtubules can exert pushing or polymerization forces on an obstacle, such as an elastic barrier if the growing end is in contact with the obstacle. We use dynamical mean-field theory and stochastic simulations to analyze a model where each microtubule undergoes catastrophes and rescues and where microtubules interact by force sharing. For zero rescue rate, cooperative growth terminates in a collective catastrophe. The maximal polymerization force before catastrophes grows linearly with N for small N or a stiff elastic barrier, in agreement with available experimental results, whereas it crosses over to a logarithmic dependence for larger N or a soft elastic barrier. For a nonzero rescue rate and a soft elastic barrier, the dynamics becomes oscillatory with both collective catastrophe and rescue events, which are part of a robust limit cycle. Both the average and maximal polymerization forces then grow linearly with N, and we investigate their dependence on tubulin on-rates and rescue rates, which can be involved in cellular regulation mechanisms. We further investigate the robustness of the collective catastrophe and rescue oscillations with respect to different catastrophe models.