A Binding Site Competition Model for Relative Sliding of Antiparallel Microtubules Mediated by Kinesin-4 Motors and PRC1 Proteins

The dynamic behaviors of the mitotic spindle composed of antiparallel microtubules (MTs) are critical for the successful completion of cell division. Motor proteins kinesin-4 and MT cross-linking proteins PRC1 can cooperatively regulate the length of antiparallel MT overlaps. However, the physical mechanism of relative sliding of the two MTs by the two types of proteins to regulate the overlap length is unclear. Here, using both the theoretical analysis and numerical simulation, we first study the clusters at MT plus ends formed by kinesin-4s alone and those formed by kinesin-4s and PRC1s, where a kinesin-4 and a PRC1 can form an unstable complex. The forward movement of the complex is proposed to be realized via a "binding site competition" mechanism; namely, the competition of the site bound by the kinesin-4 head with the PRC1 head makes the complex move forward. Furthermore, we study MT sliding mediated by the kinesin-4s and PRC1s. The theoretical/numerical results reproduce quantitatively the published experimental results and, in particular, the puzzling results showing that the initial MT sliding velocity increases with the initial MT overlap length. The study indicates that the MT sliding by the kinesin-4s and PRC1s occurs via the "binding site competition" mechanism, which is different from the well-known "force-driving" mechanism by kinesin-5 motors, where the forces generated by the kinesin-5s drive the MT sliding.