Investigating the role of intrinsic cell heterogeneity emerging from variations in cell-cycle parameters and apoptosis is a crucial step toward better informing drug administration. Antimitotic agents, widely used in chemotherapy, target exclusively proliferative cells and commonly induce a prolonged mitotic arrest followed by cell death via apoptosis. In this paper, we developed a physiologically motivated mathematical framework for describing cancer cell growth dynamics that incorporates the intrinsic heterogeneity in the time individual cells spend in the cell-cycle and apoptosis process. More precisely, our model comprises two age-structured partial differential equations for the proliferative and apoptotic cell compartments and one ordinary differential equation for the quiescent compartment. To reflect the intrinsic cell heterogeneity that governs the growth dynamics, proliferative and apoptotic cells are structured in “age,” i.e., the amount of time remaining to be spent in each respective compartment. In our model, we considered an antimitotic drug whose effect on the cellular dynamics is to induce mitotic arrest, extending the average cell-cycle length. The prolonged mitotic arrest induced by the drug can trigger apoptosis if the time a cell will spend in the cell cycle is greater than the mitotic arrest threshold. We studied the drug's effect on the long-term cancer cell growth dynamics using different durations of prolonged mitotic arrest induced by the drug. Our numerical simulations suggest that at confluence and in the absence of the drug, quiescence is the long-term asymptotic behavior emerging from the cancer cell growth dynamics. This pattern is maintained in the presence of small increases in the average cell-cycle length. However, intermediate increases in cell-cycle length markedly decrease the total number of cells and can drive the cancer population to extinction. Intriguingly, a large “switch-on/ switch-off” increase in the average cell-cycle length maintains an active cell population in the long term, with oscillating numbers of proliferative cells and a relatively constant quiescent cell number.
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledgements: The work of AL was supported by the King Abdullah University of Science and Technology (KAUST) baseline and start-up funds (BAS/1/1648-01-01 and BAS/1/1648-01-02). The work of D-AB was partially supported by the Intramural Research Program of the National Institutes of Health, Center for Cancer Research, National Cancer Institute, as part of a seed grant from the UMD-NCI Partnership for Cancer Technology. The work of DL was supported in part by the John Simon Guggenheim Memorial Foundation, the Simons Foundation, and the Jayne Koskinas Ted Giovanis Foundation. The funders had no role in the study design, data collection and analysis, decision to publish, or preparation of the manuscript.