A Mathematical Model for Force Generation at the Kinetochore-Microtubule Interface

Abstract

In this paper we construct and analyze a mathematical model for kinetochore (Kt) motors operating at the chromosome/microtubule interface. Motor dynamics are modeled using a jump-diffusion process that incorporates biased diffusion due to the binding of microtubules (MTs) by Kt binder elements and thermal ratchet forces that arise when the polymer grows against the Kt plate. The resulting force-velocity relationships are nonlinear and depend on the strength of MT binding at Kts, as well as the spatial distribution of binders and of MT rate-altering enzymes inside the Kt. In the case when Kt binders are weakly bound and spaced with the same period as the MT binding sites, the numerical results for the motor force-velocity relation and breaking loads are in complete agreement with our approximate analytic solutions. We show that in this limit motor velocity depends directly on the balance of polymer tip polymerization/depolymerization rates and is fairly insensitive to load variations. In the strong binding...