Abstract
Cancer Stem Cells (CSC), a subset of cancer cells resembling normal stem cells with self-renewal and asymmetric division capabilities, are present at various but low proportions in many tumors and are thought to be responsible for tumor relapses following conventional cancer therapies. In vitro, most intriguingly, isolated CSCs rapidly regenerate the original population of stem and non-stem cells (non-CSCs) as shown by various investigators. This phenomenon still remains to be explained. We propose a mathematical model of cancer cell population dynamics, based on the main parameters of cell population growth, including the proliferation rates, the rates of cell death and the frequency of symmetric and asymmetric cell divisions both in CSCs and non-CSCs sub-populations, and taking into account the stabilization phenomenon. The analysis of the model allows determination of time-varying corridors of probabilities for different cell fates, given the particular dynamics of cancer cells populations; and determination of a cell-cell communication factors influencing these time-varying probabilities of cell behavior (division, transition) scenarios. Though the results of the model have to be experimentally confirmed, we can anticipate the development of several fundamental and practical applications based on the theoretical results of the model.
Highlights
Stem cells are undifferentiated cells present in very low numbers in most tissues
Following our previous work [53] we suggest a model accounting for 4 scenarios of cell behaviors for stem and non-stem cells, and assumed that each scenario can occur with some probability (Table 1): Though we include the scenarios D!S+S and D!S for daughter cells in Table 1 as theoretically possible, for a time being we will consider in a model only two scenarios for daughter cells, which discriminates two principal modes of their behavior: the regular one (D!D+D) and the de-differentiation of daughter cells into S cells, which requires the activation of different genetic program
We considered that cell divisions/transition occur with the rate λ1 in stem cells (S) and with the rate λ2 in daughter cells (D), and that death rates are γ1 and γ2 in S and D cells respectively
Summary
Stem cells are undifferentiated cells present in very low numbers in most tissues. Stem cells are responsible for tissue renewal and homeostasis, by giving rise to non-stem cells that proliferate and further differentiate in specialized cells. Stem cells show very specific features, notably regarding cell division: they are able to undergo asymmetrical division, dividing into a stem cell and non-stem cell; the rate of stem cells division is very low as compared to that of non-stem cells [1,2,3]. Cancer stem cells stabilization and analysis, decision to publish, or preparation of the manuscript
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