Bistability and oscillations in cooperative microtubule and kinetochore dynamics in the mitotic spindle
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 m...
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| Format: | Article |
| Language: | English |
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IOP Publishing
2020-01-01
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| Series: | New Journal of Physics |
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| Online Access: | https://doi.org/10.1088/1367-2630/ab7ede |
| _version_ | 1827873037953794048 |
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| author | Felix Schwietert Jan Kierfeld |
| author_facet | Felix Schwietert Jan Kierfeld |
| author_sort | Felix Schwietert |
| collection | DOAJ |
| description | 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 kinetochore are necessary to stimulate oscillations. The model can reproduce experimental results for kinetochore oscillations in PtK1 cells quantitatively. |
| first_indexed | 2024-03-12T16:31:52Z |
| format | Article |
| id | doaj.art-ce698e39b40f468a9e73fa8254b5a4fa |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-12T16:31:52Z |
| publishDate | 2020-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | New Journal of Physics |
| spelling | doaj.art-ce698e39b40f468a9e73fa8254b5a4fa2023-08-08T15:27:26ZengIOP PublishingNew Journal of Physics1367-26302020-01-0122505300810.1088/1367-2630/ab7edeBistability and oscillations in cooperative microtubule and kinetochore dynamics in the mitotic spindleFelix Schwietert0Jan Kierfeld1Physics Department, TU Dortmund University , 44221 Dortmund, GermanyPhysics Department, TU Dortmund University , 44221 Dortmund, GermanyIn 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 kinetochore are necessary to stimulate oscillations. The model can reproduce experimental results for kinetochore oscillations in PtK1 cells quantitatively.https://doi.org/10.1088/1367-2630/ab7edemitotic spindledirectional instabilitymicrotubule dynamicskinetochore oscillationsbistabilitystochastic simulation |
| spellingShingle | Felix Schwietert Jan Kierfeld Bistability and oscillations in cooperative microtubule and kinetochore dynamics in the mitotic spindle New Journal of Physics mitotic spindle directional instability microtubule dynamics kinetochore oscillations bistability stochastic simulation |
| title | Bistability and oscillations in cooperative microtubule and kinetochore dynamics in the mitotic spindle |
| title_full | Bistability and oscillations in cooperative microtubule and kinetochore dynamics in the mitotic spindle |
| title_fullStr | Bistability and oscillations in cooperative microtubule and kinetochore dynamics in the mitotic spindle |
| title_full_unstemmed | Bistability and oscillations in cooperative microtubule and kinetochore dynamics in the mitotic spindle |
| title_short | Bistability and oscillations in cooperative microtubule and kinetochore dynamics in the mitotic spindle |
| title_sort | bistability and oscillations in cooperative microtubule and kinetochore dynamics in the mitotic spindle |
| topic | mitotic spindle directional instability microtubule dynamics kinetochore oscillations bistability stochastic simulation |
| url | https://doi.org/10.1088/1367-2630/ab7ede |
| work_keys_str_mv | AT felixschwietert bistabilityandoscillationsincooperativemicrotubuleandkinetochoredynamicsinthemitoticspindle AT jankierfeld bistabilityandoscillationsincooperativemicrotubuleandkinetochoredynamicsinthemitoticspindle |