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.
Highlights
The kinetic balance between inflow and outflow of cells contributes to maintain tissue homeostasis
In Appendix, we show the relation between R0 and generation progression ratio (GPR) by formulating the generation progression model as a multi-group McKendrick equation system
We demonstrate that for each generation progression model studied in subsections 2.2–2.6, the developed algorithm is applied to perform stochastic simulations by specifying incidence probability of cell division Λn(τ ) and survival probability Fn(τ )
Summary
The kinetic balance between inflow and outflow of cells contributes to maintain tissue homeostasis. Quantitative data representing cell population growth can be used to estimate growth kinetic parameters of lymphocytes (the rate for cell division and death). We define the generation progression ratio and calculate it for each specific cell population growth model.
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