  In the mitotic spindle microtubules attach to kinetochores via catch bonds
during metaphase, and microtubule depolymerization forces give rise to
stochastic chromosome oscillations. We investigate the cooperative stochastic
microtubule dynamics in spindle models consisting of ensembles of parallel
microtubules, which attach to a kinetochore via elastic linkers. We include the
dynamic instability of microtubules and forces on microtubules and kinetochores
from elastic linkers. A one-sided model, where an external force acts on the
kinetochore is solved analytically employing a mean-field approach based on
Fokker-Planck equations. The solution establishes a bistable force-velocity
relation of the microtubule ensemble in agreement with stochastic simulations.
We derive constraints on linker stiffness and microtubule number for
bistability. The bistable force-velocity relation of the one-sided spindle
model gives rise to oscillations in the two-sided model, which can explain
stochastic chromosome oscillations in metaphase (directional instability). We
derive constraints on linker stiffness and microtubule number for metaphase
chromosome oscillations. Including poleward microtubule flux into the model we
can provide an explanation for the experimentally observed suppression of
chromosome oscillations in cells with high poleward flux velocities. Chromosome
oscillations persist in the presence of polar ejection forces, however, with a
reduced amplitude and a phase shift between sister kinetochores. Moreover,
polar ejection forces are necessary to align the chromosomes at the spindle
equator and stabilize an alternating oscillation pattern of the two
kinetochores. Finally, we modify the model such that microtubules can only
exert tensile forces on the kinetochore resulting in a tug-of-war between the
two microtubule ensembles. Then, induced microtubule catastrophes after
reaching the...
