Computational modeling of motor-driven extension of microtubule bundles in axons reveals a biphasic effect of crosslinker density

In addition to actin assembly at the growth cone, neuronal axons elongate via interactions between microtubules, dynein motor proteins and cross-linking proteins. Dynein translocates microtubules toward the growth cone and exerts extensile forces for axonal outgrowth. During this process, microtubules likely experience compressive loads, which can result in bending deformation 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 can resist larger compressive loads. Despite the importance of microtubule buckling and connectivity, their effects on 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. Motor activity elongated the bundle against a mechanical load. We found that intermediate cross-linking density maximized bundle elongation, because microtubules were easily buckled at low cross-linking density, whereas their displacements were inhibited at high cross-linking density. When microtubules were stiffer, the bundle elongated longer even with lower cross-linking density, since stiff microtubules experience less buckling by compressive loads. Our study provides new insights into the mechanisms driving axonal outgrowth.