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. Sliding of microtubules relative to each other can lead to an overall elongation of the bundle. However, such sliding must be accompanied by microtubule growth, to maintain the overlap, which is a landmark of anaphase. Diffusive crosslinkers of the Ase1/PRC1/MAP65 family are able to form stable overlaps in combination with kinesin-14 motors. This process is thought to arise through a balance of forces between motors and crosslinkers, the latter effectively producing an entropic pressure. We provide a continuous theory to explain the formation of stable overlaps, in which steric effects caused by the finite number of binding sites available on the microtubule lattice play a leading role. We confirmed the validity of this approach using discrete stochastic simulations performed with the Open Source simulation engine Cytosim. From the densities of motors and crosslinkers, their diffusion rates, and the velocities of motors, the theory predicts the sliding speed of microtubules and explains the force production and breaking effect of crosslinkers and motors containing diffusible microtubule-binding domains. Finally, we discuss a mechanism by which sliding and microtubule growth can be coordinated without the need for fine-tuning the parameters of the system, in line with the known robustness of mitosis.