Computational Modeling of Motor-Driven Extension of Microtubule Bundles in Axons

In addition to actin assembly at the growth cone, neuronal axons elongate via interactions between microtubules and microtubule-associated proteins including dynein motor proteins and cross-linking proteins. Dynein translocates microtubules toward the growth cone to exert extensile forces for axonal outgrowth. During this process, microtubules are most likely to experience compressive loads, which can result in bending deformation on microtubules called buckling. Such buckled microtubules are impaired in their ability to bear compressive forces and may not contribute significantly to axonal outgrowth. If microtubules are interconnected by cross-linking proteins, they are less likely to be buckled and thus able to resist larger compressive loads. Despite the importance of the buckling and connectivity of microtubules, their effects on the axonal outgrowth have not been investigated to date. In this study, using an agent-based computational model, we created a microtubule bundle to simulate the microtubule system in axons. This bundle increased its length by interactions between dynein-like motors and microtubules against a mechanical load. We found that intermediate cross-linking density resulted in maximal elongation of the bundle, because microtubules were easily buckled at low cross-linking density, whereas the displacement of microtubules was inhibited at high cross-linking density. When individual microtubules were much stiffer, the bundle showed higher elongation even with lower cross-linking density, since stiff microtubules were less likely to be buckled by compressive loads. Our study provides new insights into the mechanisms driving axonal outgrowth.