Theory of antiparallel microtubule overlap stabilization by motors and diffusible crosslinkers

Antiparallel microtubule bundles are essential structural elements of many cytoskeletal structures, for instance the mitotic spindle. In such bundles, neighbouring microtubules are bonded by specialised crosslinkers of the Ase1/PRC1/MAP65 family that can diffuse longitudinally along microtubules. Similarly, some kinesin motors implicated in bundle formation have a diffusible tail allowing them to slide passively along microtubules. We develop here a theory of two microtubules connected by motors and diffusible connectors, in different configurations that can be realized experimentally. In all cases, the microtubule sliding speed derived analytically is validated by stochastic simulations and used to discuss recent experimental results, such as force generation by kinesin-14, and overlap stabilization by Ase1. Some systems can produce steady overlaps that are determined by the density of crosslinkers on the microtubule lattice. This property naturally leads to robust coordination between sliding and growth in dynamic bundles of microtubules, an essential property in mitosis.