Abstract
Recent discovery of cancer stem cells in tumorigenic tissues has raised many questions about their nature, origin, function and their behavior in cell culture. Most of current experiments reporting a dynamics of cancer stem cell populations in culture show the eventual stability of the percentages of these cell populations in the whole population of cancer cells, independently of the starting conditions. In this report we present a review about a class of mathematical models of cancer stem cell population behavior, based on specific features of cancer stem cell divisions and including, as a mathematical formalization of cell-cell communications, an underlying field concept. We compare the qualitative behavior of mathematical models of stem cells evolution, without and with an underlying signal. In presence of an underlying field the model is described by a system of delay differential equations, by admitting a possibly delayed signal originated by existing cells. Under a variety of assumptions on the parameters, in all cases we show that the stability of percentages can be recovered, provided that the delay is sufficiently small. Further, for the DDE case we show the possible existence of, either damped or standing, oscillations in the cell populations. The outcomes of the analysis may offer to experimentalists a tool for addressing the issue regarding the possible non-stem to stem cells transition. Further, they may stimulate further experiments for elucidating the nature of “instructive” signals for cell divisions.
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Acknowledgements
The research contribution by Beretta and Capasso has been performed within the Italian PRIN project “Mathematical Theory of Populations: Methods, Models, Comparison with Experimental Data” (grant 2007.77BWEP-003). The research contribution by Harel-Bellan and Morozova was performed within the project “Cancérôpole”– \( \hat{I} \)le-de-France, n. 2007-1-ACI-CNRS EST-1.
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Beretta, E., Morozova, N., Capasso, V., Harel-Bellan, A. (2012). Some Results on the Population Behavior of Cancer Stem Cells. In: d’Onofrio, A., Cerrai, P., Gandolfi, A. (eds) New Challenges for Cancer Systems Biomedicine. SIMAI Springer Series. Springer, Milano. https://doi.org/10.1007/978-88-470-2571-4_8
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DOI: https://doi.org/10.1007/978-88-470-2571-4_8
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