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In the mitotic spindle microtubules attach to kinetochores via catch bondsduring metaphase, and microtubule depolymerization forces give rise tostochastic chromosome oscillations. We investigate the cooperative stochasticmicrotubule dynamics in spindle models consisting of ensembles of parallelmicrotubules, which attach to a kinetochore via elastic linkers. We include thedynamic instability of microtubules and forces on microtubules and kinetochoresfrom elastic linkers. A one-sided model, where an external force acts on thekinetochore is solved analytically employing a mean-field approach based onFokker-Planck equations. The solution establishes a bistable force-velocityrelation of the microtubule ensemble in agreement with stochastic simulations.We derive constraints on linker stiffness and microtubule number forbistability. The bistable force-velocity relation of the one-sided spindlemodel gives rise to oscillations in the two-sided model, which can explainstochastic chromosome oscillations in metaphase (directional instability). Wederive constraints on linker stiffness and microtubule number for metaphasechromosome oscillations. Including poleward microtubule flux into the model wecan provide an explanation for the experimentally observed suppression ofchromosome oscillations in cells with high poleward flux velocities. Chromosomeoscillations persist in the presence of polar ejection forces, however, with areduced amplitude and a phase shift between sister kinetochores. Moreover,polar ejection forces are necessary to align the chromosomes at the spindleequator and stabilize an alternating oscillation pattern of the twokinetochores. Finally, we modify the model such that microtubules can onlyexert tensile forces on the kinetochore resulting in a tug-of-war between thetwo microtubule ensembles. Then, induced microtubule catastrophes afterreaching the...

Bistability and oscillations in cooperative microtubule and kinetochore dynamics in the mitotic spindle