Emergent spacing and order of crosslinked microtubules in the fission yeast spindle

Crosslinked cytoskeletal filaments provide structure and generate forces in many cellular structures, including the mitotic spindle. How the organization of filaments is established is an open question. At the midzone of the fission yeast mitotic spindle, microtubules form an orderly square array in which the microtubules are significantly closer together than the length of the proteins crosslinking them. How this structure and spacing are set has remained unknown. We developed a model of lateral separation of microtubule pairs and found that motor proteins pull antiparallel microtubules together while non-motor crosslinkers push them apart. Together these interactions are sufficient to explain the microtubule separation observed in the fission yeast spindle. Further, we expanded our model to include the full number of microtubules present at the midzone and found that our model reproduced the experimentally observed square array. We also investigated how separation affects crosslinking proteins, finding that because microtubule separation considerably affects the binding of crosslinkers, strong history dependence in binding and separation can occur. Our results show that lateral microtubule separation is an underappreciated aspect of microtubule assemblies that affects forces and kinetics of crosslinking proteins.