Demographic modeling of transient amplifying cell population growth

Shinji Nakaoka; Hisashi Inaba

doi:10.3934/mbe.2014.11.363

Article Contents

2014, Volume 11, Issue 2: 363-384. Doi: 10.3934/mbe.2014.11.363 open access

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Demographic modeling of transient amplifying cell population growth

Shinji Nakaoka^1, and
Hisashi Inaba^2,

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: November 2012

Revised: August 2013

Published: October 2013

Abstract / Introduction Related Papers Cited by

Abstract

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.

Keywords:

Transient amplifying cell population dynamics,
generation progression model,
age structured population models,
renewal equations,
stochastic simulation.

Mathematics Subject Classification: 92B05, 92C37, 92D25, 37N25.

Citation:

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