Dynamics and length distributions of microtubules with a multistep catastrophe mechanism

Abstract

Regarding the experimental observation that microtubule catastrophe can be described as a multistep process, we extend the Dogterom-Leibler model for dynamic instability in order to discuss the effect that such a multistep catastrophe mechanism has on the distribution of microtubule lengths in the two regimes of bounded and unbounded growth. We show that in the former case, the steady state length distribution is non-exponential and has a lighter tail if multiple steps are required to undergo a catastrophe. If rescue events are possible, we detect a maximum in the distribution, i.e., the microtubule has a most probable length greater than zero. In the regime of unbounded growth, the length distribution converges to a Gaussian distribution whose variance decreases with the number of catastrophe steps. We extend our work by applying the multistep catastrophe model to microtubules that grow against an opposing force and to microtubules that are confined between two rigid walls. We determine critical forces below which the microtubule is in the bounded regime, and show that the multistep characteristics of the length distribution are largely lost if the growth of a microtubule in the unbounded regime is restricted by a rigid wall. All results are verified by stochastic simulations.