Tonekaboni Seyed Ali Madani, Dhawan Andrew, Kohandel Mohammad
Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada.
School of Medicine, Queen's University, Kingston, Ontario, K7L 3N6 Canada.
Math Biosci. 2017 Jan;283:30-37. doi: 10.1016/j.mbs.2016.11.008. Epub 2016 Nov 8.
The cancer stem cell (CSC) hypothesis suggests that cancer stem cells proliferate via a hierarchical model of unidirectional differentiation. However, growing experimental evidence has advanced this hypothesis by introducing a bidirectional hierarchy, in which non-CSCs may dedifferentiate into CSCs. Various models have been developed enabling the incorporation of this plasticity within cancer cell populations, focusing on behaviour in the limit of a large number of cells. However, stochastic effects predominate in the limit of small numbers of cells, which correlates with biologically relevant assays such as the mammosphere formation assay (MFA). Here, we consider two mathematical models incorporating cellular plasticity, namely a two-compartment model and a hierarchical model, and by parameterizing these models with experimental data, we show this behavioural difference in the limits of large and small numbers of cells. Additionally, we analyse the effects of varying cellular plasticity on the survival of the cancer cell population, and show that interestingly, increased plasticity, in certain cases, may be advantageous in reducing the survival probability. Thus, this analysis highlights the necessity of experimentally studying both small and large populations of cancer cells concurrently to obtain valid model predictions, potentially aiding the design of novel therapeutics.
癌症干细胞（CSC）假说认为，癌症干细胞通过单向分化的层级模型进行增殖。然而，越来越多的实验证据通过引入双向层级对这一假说进行了拓展，即非癌症干细胞可能会逆分化为癌症干细胞。人们已经开发出各种模型，能够将这种可塑性纳入癌细胞群体中，重点关注大量细胞情况下的行为。然而，在少量细胞情况下，随机效应占主导，这与诸如乳腺球形成试验（MFA）等生物学相关试验相关。在此，我们考虑两个纳入细胞可塑性的数学模型，即双室模型和层级模型，并通过用实验数据对这些模型进行参数化，展示了在大量和少量细胞情况下的这种行为差异。此外，我们分析了细胞可塑性变化对癌细胞群体存活的影响，并表明有趣的是，在某些情况下，增加可塑性可能有利于降低存活概率。因此，该分析强调了同时对少量和大量癌细胞群体进行实验研究以获得有效模型预测的必要性，这可能有助于新型疗法的设计。
