Kinetic theory for structured populations: application to stochastic sizer-timer models of cell proliferation
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866915996210561024 |
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| author | Xia, Mingtao Chou, Tom |
| author_facet | Xia, Mingtao Chou, Tom |
| contents | We derive the full kinetic equations describing the evolution of the probability density distribution for a structured population such as cells distributed according to their ages and sizes. The kinetic equations for such a "sizer-timer" model incorporates both demographic and individual cell growth rate stochasticities. Averages taken over the densities obeying the kinetic equations can be used to generate a second order PDE that incorporates the growth rate stochasticity. On the other hand, marginalizing over the densities yields a modified birth-death process that shows how age and size influence demographic stochasticity. Our kinetic framework is thus a more complete model that subsumes both the deterministic PDE and birth-death master equation representations for structured populations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2101_03470 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Kinetic theory for structured populations: application to stochastic sizer-timer models of cell proliferation Xia, Mingtao Chou, Tom Populations and Evolution Statistical Mechanics We derive the full kinetic equations describing the evolution of the probability density distribution for a structured population such as cells distributed according to their ages and sizes. The kinetic equations for such a "sizer-timer" model incorporates both demographic and individual cell growth rate stochasticities. Averages taken over the densities obeying the kinetic equations can be used to generate a second order PDE that incorporates the growth rate stochasticity. On the other hand, marginalizing over the densities yields a modified birth-death process that shows how age and size influence demographic stochasticity. Our kinetic framework is thus a more complete model that subsumes both the deterministic PDE and birth-death master equation representations for structured populations. |
| title | Kinetic theory for structured populations: application to stochastic sizer-timer models of cell proliferation |
| topic | Populations and Evolution Statistical Mechanics |
| url | https://arxiv.org/abs/2101.03470 |