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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
  • Received: 01 November 2012 Accepted: 29 June 2018 Published: 01 October 2013

  • MSC : 92B05, 92C37, 92D25, 37N25.

  • 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.


    [1] Bull. Math. Biol., 73 (2011), 116-150.
    [2] Biophys. J., 7 (1967), 329-351.
    [3] Nat. Rev. Mol. Cell. Biol., 10 (2009), 207-217.
    [4] Bull. Math. Biol., 68 (2006), 1011-1031.
    [5] Cambridge Monographs on Applied and Computational Mathematics, 15, Cambridge University Press, Cambridge, 2004.
    [6] Immunol. Rev., 216 (2007), 119-129.
    [7] J. Immunol., 170 (2003), 4963-4972.
    [8] Cell. Res., 10 (2000), 179-192.
    [9] Population Studies, 37 (1983), 75-89.
    [10] Grune and Stratton, 1959.
    [11] J. Immunol., 179 (2007), 950-957.
    [12] Nat. Immunol., 1 (2000), 239-244.
    [13] Journal of Computational Physics, 22 (1976), 403-434.
    [14] Math. Biosci., 86 (1987), 67-95.
    [15] Proc. Natl. Acad. Sci. USA, 106 (2009), 13457-13462.
    [16] Proc. Natl. Acad. Sci. USA, 104 (2007), 5032-5037.
    [17] Working Paper Series 9, Institute of Population Problems, Tokyo, 1992.
    [18] Math. Popul. Studies, 1 (1988), 49-77.
    [19] J. Math. Biol., 65 (2012), 309-348.
    [20] Math. Biosci., 216 (2008), 77-89.
    [21] J. Math. Biol., 1 (1974/75), 17-36.
    [22] J. Theor. Biol., 229 (2004), 455-476.
    [23] J. Theor. Biol., 215 (2002), 201-213.
    [24] J. Math. Biol., 54 (2007), 57-89.
    [25] Theor. Biol. Med. Model., 4 (2007).
    [26] Cambridge Studies in Mathematical Biology, 8, Cambridge University Press, Cambridge, 1989.
    [27] Proc. Edinburgh. Math. Soc., 44 (1926), 98-130.
    [28] Bull. Math. Biol., 74 (2012), 300-326.
    [29] Nature, 441 (2006), 1068-1074.
    [30] Cell, 132 (2008), 598-611.
    [31] J. Comput. Appl. Math., 177 (2005), 269-286.
    [32] 8th Edition, Immunobiology: The Immune System (Janeway), Garland Science, 2012.
    [33] J. Math. Biol., 66 (2013), 807-835.
    [34] Methods Mol. Biol., 296 (2005), 95-112.
    [35] Nat. Immunol., 2 (2001), 925-931.
    [36] in Studies in Mathematical Biology Part II: Populations and Communities (ed. S. Levin), Studies in Mathematical Biology, 16, The Mathematical Association of America, Washington, D.C., 1978, 389-410.
    [37] Acta Pathol. Microbiol. Scand., 41 (1957), 161-182.
    [38] Proc. Natl. Acad. Sci. USA, 70 (1973), 1263-1267.
    [39] Journal of Statistical Software, 33 (2010), 1-25.
    [40] Publ. Res. Inst. Math. Sci., 9 (1973/74), 721-741.
    [41] Princeton Series in Theoretical and Computational Biology, Princeton University Press, Princeton, NJ, 2003.
    [42] SIAM J. Appl. Math., 57 (1997), 1281-1310.
    [43] BMC Bioinformatics, 8 (2007).
    [44] PLoS One, 5 (2010), e12775.

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