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...

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有丝分裂纺锤体协同微管和动粒动力学的双稳态和振荡

在有丝分裂纺锤体中，微管在中期通过捕获键连接到动粒，微管解聚力引起随机染色体振荡。我们研究了由平行微管集合组成的纺锤体模型中的协作随机微管动力学，这些平行微管通过弹性连接器连接到动粒。我们包括微管的动态不稳定性以及弹性接头对微管和动粒的作用力。使用基于 Fokker-Planck 方程的平均场方法解析求解单侧模型，其中外力作用在动粒上。该解决方案建立了与随机模拟一致的微管集合的双稳态力-速度关系。我们推导出对双稳态接头刚度和微管数量的约束。一侧纺锤体模型的双稳态力-速度关系引起两侧模型的振荡，这可以解释中期染色体的随机振荡（方向不稳定）。我们推导出对中期染色体振荡的接头刚度和微管数量的约束。将极地微管通量包括到模型中，我们可以解释实验观察到的对具有高极向通量速度的细胞中染色体振荡的抑制。染色体振荡在极地喷射力存在的情况下持续存在，但是，在姐妹动粒之间具有减小的振幅和相移。此外，为了使纺锤体赤道的染色体对齐并稳定两个动粒的交替振荡模式，极地喷射力是必要的。最后，我们修改了模型，使得微管只能对动粒施加张力，从而导致两个微管集合之间的拉锯战。然后，在到达...后诱导微管灾难。