Stochastic modeling of cellular colonies with quiescence: An application to drug resistance in cancer

Several cancers are thought to be driven by cells with stem cell like properties. An important characteristic of stem cells, which also applies to primitive tumor cells, is the ability to undergo quiescence, where cells can temporarily stop the cell cycle. Cellular quiescence can affect the kinetics of tumor growth, and the susceptibility of the cells to therapy. To study how quiescence affects treatment, we formulate a stochastic birth–death process with quiescence, on a combinatorial cellular mutation network, and consider the pre-treatment (growth) and treatment (decay) regimes. We find that, in the absence of mutations, treatment (if sufficiently strong) will proceed as a biphasic decline with the first (faster) phase driven by the elimination of the cycling cells and the second (slower) phase limited by the process of cell awakening. Other regimes are possible for weaker treatments. We also describe how the process of mutant generation is influenced by quiescence. Interestingly, for single-drug treatments, the probability to have resistance at start of treatment is independent of quiescence. For two or more drugs, the probability to have generated resistant mutants before treatment grows with quiescence. Finally, we study the influence of quiescence on the treatment phase. Starting from a given composition of mutants, the chances of treatment success are not influenced by the presence of quiescence.