Collision induced spatial organization of microtubules

Abstract

The dynamic behavior of microtubules in solution can be strongly modified by interactions with walls or other structures. We examine here a microtubule growth model where the increase in size of the plus-end is perturbed by collisions with other microtubules. We show that such a simple mechanism of constrained growth can induce ordered structures and patterns from an initially isotropic and homogeneous suspension. First, microtubules self-organize locally in randomly oriented domains that grow and compete with each other. By imposing even a weak orientation bias, external forces like gravity or cellular boundaries may bias the domain distribution eventually leading to a macroscopic sample orientation.

Computer simulation and mathematical models of the noncentrosomal plant cortical microtubule cytoskeleton

“…Indeed, more complex models distinguish between the relative significance of those two mechanisms as discussed below. Baulin et al [2007] simulate a CMT system where they incorporate CMT nucleation and assume simple deterministic dynamics based on average CMT velocities of both plus and minus ends. They consider stalling as the only interaction mechanism, where a CMT encountering another one remains static as long as it is blocked by the barrier CMT and resumes its growth as soon as the blocking is over.…”

“…Stalling is different from pausing that is part of the normal stochastic dynamic behavior of CMTs, where the end of a CMT appears to neither grow nor shorten for a certain duration irrespective of whether the CMT has encountered another one. The simulations of Baulin et al show that even these overly simplified CMT dynamics and interaction mechanisms are enough to achieve parallel CMT organization [Baulin et al, 2007]. However, their model is limited in the sense that only growth-prone dynamics can be studied due to exclusion of dynamic instability.…”

“…In general, the mathematical models of CMT organization complement the simulation models in terms of analysis and results. In the mathematical model of Baulin et al [2007], the impact of interactions (that result in CMT stalling) are approximated inspired by the kinetic theory of gases based on the average length, velocity, and density of CMTs in the system, and accounting for the fact that CMTs with similar angles run into each other less frequently. Hawkins et al [2010] developed a stronger mathematical model that considers CMT bundling and collision-induced depolymerization.…”

“…both mathematical and simulation models to generate a phase diagram that relates regions of CMT dynamics and density parameters to array organization, although their CMT interaction mechanism is quite simplistic, similar to Baulin et al [2007].…”

Effect of weightlessness on colloidal particle transport and segregation in self-organising microtubule preparations

“…More recently, Baulin et al [37] consider theoretically a rather more simplified situation in which the reactive shrinking and growing of individual microtubules is limited to the complete disassembly of individual microtubules accompanie d by the nucleation and formation of new ones. They also predicted the formation of aligned arrays of microtubules -though not patterns of microtubule concentration -which would self-organise under the effect of a weak external orienting factor.…”