Feedback between filament spacing, crosslinker binding, and self-organization in cytoskeletal bundles

The lateral spacing between filaments in crosslinked cytoskeletal bundles is a critical yet poorly understood physical parameter that affects force generation, transport, and bundle architecture. We develop a biophysical model of crosslinkers and crosslinking motors on filament pairs. Motor/crosslinker binding sets the filament spacing, which in turn biases which motors/crosslinkers can bind. Crosslinking motors generate pulling forces that bring antiparallel filaments closer together, while non-motor crosslinkers with a preferred binding angle exert repulsive torques that maintain larger spacing. We demonstrate these principles in a model of the fission yeast anaphase mitotic spindle midzone, where microtubules form a square array with nearest-neighbor spacing 2-5 times smaller than the length of crosslinking proteins. Our model shows that motor-crosslinker interactions alone are sufficient to drive self-organization into this experimentally observed geometry. Furthermore, the feedback between geometry and binding creates strong indirect cooperativity, because crosslinkers establish spacing that favors binding of similar-length proteins, leading to history-dependent states that persist long after individual protein binding equilibration. This feedback mechanism in which crosslinkers control geometry and geometry controls crosslinker binding should operate in any multi-crosslinker-filament system and represents a general self-organizing principle for cytoskeletal networks.