Mathematical Modeling Reveals the Factors Involved in the Phenomena of Cancer Stem Cells Stabilization

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, when isolated, CSCs return to their original proportion level as shown by various investigators. This phenomenon still remains to be explained.\n\nWe suggest a mathematical model of cancer cell population dynamics, based on the main parameters of cell population dynamics, including the proliferation rates, the rates of cell death and the frequency of symmetric and asymmetric cell divisions both in CSCs and in non-CSCs. This model should help elucidating some important factors underlying the dynamics of the two populations, first of all, the phenomena of cancer stem cell population stabilization.\n\nAuthor SummaryCancer Stem Cells (CSC) present a subset of cancer cells which is thought to be responsible for tumor growth. That is why CSC are also named \"tumor initiation cells\". Additionally, it was shown that CSC are resistant to chemo- and radio-therapies which suggests that these cells can be responsible for tumor relapses after these treatments. Experimental data in cancer cell lines have shown the intriguing phenomena of CSC population stability, which means that isolated CSC population rapidly stabilizes at its characteristic level (the relative proportion of CSC in a whole cancer population). We suggest a mathematical model of cancer cell population dynamics, based on experimentally measured dynamics of CSC population stabilization and including main parameters of cell population growth.\n\nWe have computationally predicted probability of different scenarios of cancer cell behavior for each experimental case with measurable growth parameters. Moreover, we provide an analytical tool for elucidating important biochemical factors responsible for a particular dynamics of CSC population.\n\nThe results may have important implications in therapeutic, because the destroying of a set of factors underlying CSC stability may help to avoid tumor relapses.