Lorz Alexander, Botesteanu Dana-Adriana, Levy Doron
CEMSE Division, King Abdullah University of Science and Technology (KAUST), Thuwal, Saudi Arabia.
Sorbonne Universités, UPMC Univ Paris 06, UMR 7598, Laboratoire Jacques-Louis Lions, Paris, France.
Front Oncol. 2017 Aug 30;7:189. doi: 10.3389/fonc.2017.00189. eCollection 2017.
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.
研究由细胞周期参数和凋亡变化产生的内在细胞异质性的作用，是更好地指导药物给药的关键一步。抗有丝分裂药物在化疗中广泛使用，专门针对增殖细胞，通常会诱导长时间的有丝分裂停滞，随后通过凋亡导致细胞死亡。在本文中，我们开发了一个具有生理学动机的数学框架，用于描述癌细胞生长动力学，该框架纳入了单个细胞在细胞周期和凋亡过程中所花费时间的内在异质性。更确切地说，我们的模型包括两个用于增殖细胞和凋亡细胞区室的年龄结构偏微分方程，以及一个用于静止细胞区室的常微分方程。为了反映控制生长动力学的内在细胞异质性，增殖细胞和凋亡细胞按“年龄”进行结构划分，即每个相应区室中剩余的时间量。在我们的模型中，我们考虑了一种抗有丝分裂药物，其对细胞动力学的作用是诱导有丝分裂停滞，延长平均细胞周期长度。如果细胞在细胞周期中花费的时间大于有丝分裂停滞阈值，药物诱导的长时间有丝分裂停滞可触发凋亡。我们使用药物诱导的不同时长的有丝分裂停滞，研究了该药物对长期癌细胞生长动力学的影响。我们的数值模拟表明，在汇合且无药物的情况下，静止是癌细胞生长动力学出现的长期渐近行为。在平均细胞周期长度略有增加的情况下，这种模式得以维持。然而，细胞周期长度的中度增加会显著减少细胞总数，并可能导致癌细胞群体灭绝。有趣的是，平均细胞周期长度的大幅“开启/关闭”增加会在长期内维持活跃的细胞群体，增殖细胞数量振荡，静止细胞数量相对恒定。
