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Mathematical Biosciences and Engineering

2014, Volume 11, Issue 2: 363-384. doi: 10.3934/mbe.2014.11.363
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Demographic modeling of transient amplifying cell population growth

  • 1.
    Laboratory for Mathematical Modeling of Immune System, RCAI, RIKEN Center for Integrative Medical Sciences (IMS-RCAI), Suehiro-cho 1-7-22, Tsurumi-ku, Yokohama, 230-0045
  • 2.
    Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba Meguro-ku, Tokyo 153-8914
  • 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.

    Citation: Shinji Nakaoka, Hisashi Inaba. Demographic modeling of transient amplifying cell population growth[J]. Mathematical Biosciences and Engineering, 2014, 11(2): 363-384. doi: 10.3934/mbe.2014.11.363

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  • 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.


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  • This article has been cited by:

    1. Christian A. Yates, Matthew J. Ford, Richard L. Mort, A Multi-stage Representation of Cell Proliferation as a Markov Process, 2017, 79, 0092-8240, 2905, 10.1007/s11538-017-0356-4
    2. Hisashi Inaba, 2017, Chapter 2, 978-981-10-0187-1, 75, 10.1007/978-981-10-0188-8_2
    3. A. Golubev, Applications and implications of the exponentially modified gamma distribution as a model for time variabilities related to cell proliferation and gene expression, 2016, 393, 00225193, 203, 10.1016/j.jtbi.2015.12.027
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