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

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.

Minimal model for collective kinetochore–microtubule dynamics

“…Another model proposes that oscillations occur via a general mechanobiochemical feedback (25). Models of force-dependent MTs interacting with the same object also exhibit cooperative behavior (5,(26)(27)(28)(29). However, these models do not explain error correction dynamics.…”

Effects of microtubule mechanics on hydrolysis and catastrophes

“…These approaches include details of the hydrolysis mechanism into the model for the catastrophe rate [21,22,23,24]. One focus of these approaches was the explanation of the behavior of MT growth dynamics under force.…”

Sufficient conditions for the additivity of stall forces generated by multiple filaments or motors

“…Some of these theoretical studies have demonstrated that the stall force of multiple, non-interacting filaments without ATP/GTP dynamics, scales linearly with the number of filaments [26,[28][29][30]54]. In contrast, a few other recent papers quite clearly report that inclusion of ATP/GTP hydrolysis can lead to either enhanced or reduced cooperativity in the maximum force generated by multiple growing filaments; the stall forces need not always scale with the number of filaments [31,[56][57][58].…”

“…On the theoretical and computational front, there are a number of very detailed models for understanding the force-velocity dynamics of a single biofilament [50][51][52][53], as well as a few that try to model the dynamics of multiple biofilaments [26,[28][29][30][31][54][55][56]. Some of these theoretical studies have demonstrated that the stall force of multiple, non-interacting filaments without ATP/GTP dynamics, scales linearly with the number of filaments [26,[28][29][30]54].…”

“…Many dynein motors attach to molecular cargo and generate force for cellular transportation [24,25], while myosin motors primarily work together to generate forces in stress fibres and muscle tissues. Hence, study of such systems, which are involved in a wide range of biological processes, requires understanding of the generation of collective force by multiple cytoskeletal filaments or motors [26][27][28][29][30][31][32][33][34][35][36][37][38].…”