Dynamics and length distribution of microtubules under force and confinement

Abstract

We investigate the microtubule polymerization dynamics with catastrophe and rescue events for three different confinement scenarios, which mimic typical cellular environments: (i) The microtubule is confined by rigid and fixed walls, (ii) it grows under constant force, and (iii) it grows against an elastic obstacle with a linearly increasing force. We use realistic catastrophe models and analyze the microtubule dynamics, the resulting microtubule length distributions, and force generation by stochastic and mean field calculations; in addition, we perform stochastic simulations. Freely growing microtubules exhibit a phase of bounded growth with finite microtubule length and a phase of unbounded growth. The main results for the three confinement scenarios are as follows: (i) In confinement by fixed rigid walls, we find exponentially decreasing or increasing stationary microtubule length distributions instead of bounded or unbounded phases, respectively. We introduce a realistic model for wall-induced catastrophes and investigate the behavior of the average length as a function of microtubule growth parameters. (ii) Under a constant force, the boundary between bounded and unbounded growth is shifted to higher tubulin concentrations and rescue rates. The critical force f(c) for the transition from unbounded to bounded growth increases logarithmically with tubulin concentration and the rescue rate, and it is smaller than the stall force. (iii) For microtubule growth against an elastic obstacle, the microtubule length and polymerization force can be regulated by microtubule growth parameters. For zero rescue rate, we find that the average polymerization force depends logarithmically on the tubulin concentration and is always smaller than the stall force in the absence of catastrophes and rescues. For a nonzero rescue rate, we find a sharply peaked steady-state length distribution, which is tightly controlled by microtubule growth parameters. The corresponding average microtubule length self-organizes such that the average polymerization force equals the critical force f(c) for the transition from unbounded to bounded growth. We also investigate the force dynamics if growth parameters are perturbed in dilution experiments. Finally, we show the robustness of our results against changes of catastrophe models and load distribution factors.

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

“…Improved mean-field results including this effect [28] agree quantitatively with full stochastic simulations [see Fig. 5(a) and 5(c)].…”

“…Finally, we want to note that the collective dynamics for N ≫ 1 that we described here differ markedly from the dynamics of a single MT (N = 1) [7]. For a single MT rescue does not happen at a particular force level F min but after an average time 1/ω r set by the individual rescue rate.…”

Microtubule catastrophe from protofilament dynamics

“…The negative effects of polymerization force, when generated against a rigid barrier, on the growth velocity of microtubules was first shown experimentally by Dogterom and Yurke [29] and subsequently studied theoretically by other authors(see, e.g., [30][31][32][33]). Experiments have also shown that the catastrophe frequency is enhanced by the proximity of the microtubule tip to a barrier, both in vitro [28] and in vivo [34], which is consistent with a reduced binding rate in the presence of force (see [35,36], two recent theoretical studies of h ow microtubule dynamic instability is affected by force and confinement). Interestingly, the 13-protofilament model used by the authors of [30,31,33] is similar to the model studied in the second part of this paper.…”

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.…”