Demographic modeling of transient amplifying cell population growth
Quantitative measurement for the timings of cell division and death with the application of mathematical models is a standard way to estimate kinetic parameters of cellular proliferation. On the basis of label-based measurement data, several quantitative mathematical models describing short-term dyn...
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AIMS Press
2013-09-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2014.11.363 |
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| author | Shinji Nakaoka Hisashi Inaba |
| author_facet | Shinji Nakaoka Hisashi Inaba |
| author_sort | Shinji Nakaoka |
| collection | DOAJ |
| description | Quantitative measurement for the timings of cell division and death with the application of mathematical models is a standard way to estimate kinetic parameters of cellular proliferation. On the basis of label-based measurement data, several quantitative mathematical models describing short-term dynamics of transient cellular proliferation have been proposed and extensively studied. In the present paper, we show that existing mathematical models for cell population growth can be reformulated as a specific case of generation progression models, a variant of parity progression models developed in mathematical demography. Generation progression ratio (GPR) is defined for a generation progression model as an expected ratio of population increase or decrease via cell division. We also apply a stochastic simulation algorithm which is capable of representing the population growth dynamics of transient amplifying cells for various inter-event time distributions of cell division and death. Demographic modeling and the application of stochastic simulation algorithm presented here can be used as a unified platform to systematically investigate the short term dynamics of cell population growth. |
| format | Article |
| id | doaj-art-9b4cad8870b6429082dfe3362e051898 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2013-09-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-9b4cad8870b6429082dfe3362e0518982025-01-24T02:28:02ZengAIMS PressMathematical Biosciences and Engineering1551-00182013-09-0111236338410.3934/mbe.2014.11.363Demographic modeling of transient amplifying cell population growthShinji Nakaoka0Hisashi Inaba1Laboratory for Mathematical Modeling of Immune System, RCAI, RIKEN Center for Integrative Medical Sciences (IMS-RCAI), Suehiro-cho 1-7-22, Tsurumi-ku, Yokohama, 230-0045Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba Meguro-ku, Tokyo 153-8914Quantitative measurement for the timings of cell division and death with the application of mathematical models is a standard way to estimate kinetic parameters of cellular proliferation. On the basis of label-based measurement data, several quantitative mathematical models describing short-term dynamics of transient cellular proliferation have been proposed and extensively studied. In the present paper, we show that existing mathematical models for cell population growth can be reformulated as a specific case of generation progression models, a variant of parity progression models developed in mathematical demography. Generation progression ratio (GPR) is defined for a generation progression model as an expected ratio of population increase or decrease via cell division. We also apply a stochastic simulation algorithm which is capable of representing the population growth dynamics of transient amplifying cells for various inter-event time distributions of cell division and death. Demographic modeling and the application of stochastic simulation algorithm presented here can be used as a unified platform to systematically investigate the short term dynamics of cell population growth.https://www.aimspress.com/article/doi/10.3934/mbe.2014.11.363renewal equationsage structured population modelstransient amplifying cell population dynamicsgeneration progression modelstochastic simulation. |
| spellingShingle | Shinji Nakaoka Hisashi Inaba Demographic modeling of transient amplifying cell population growth Mathematical Biosciences and Engineering renewal equations age structured population models transient amplifying cell population dynamics generation progression model stochastic simulation. |
| title | Demographic modeling of transient amplifying cell population growth |
| title_full | Demographic modeling of transient amplifying cell population growth |
| title_fullStr | Demographic modeling of transient amplifying cell population growth |
| title_full_unstemmed | Demographic modeling of transient amplifying cell population growth |
| title_short | Demographic modeling of transient amplifying cell population growth |
| title_sort | demographic modeling of transient amplifying cell population growth |
| topic | renewal equations age structured population models transient amplifying cell population dynamics generation progression model stochastic simulation. |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2014.11.363 |
| work_keys_str_mv | AT shinjinakaoka demographicmodelingoftransientamplifyingcellpopulationgrowth AT hisashiinaba demographicmodelingoftransientamplifyingcellpopulationgrowth |