表型异质生长细胞群的基于个体的连续体模型
Individual-based and continuum models of phenotypically heterogeneous growing cell populations
摘要：
现有的研究比较基于个体的模型的增长细胞群体和他们的连续对应物主要集中在同质群体，其中所有的细胞具有相同的表型特征。然而，在细胞系统中通常观察到显著的细胞间表型变异。因此，我们在这里开发了一个基于个体的表型异质性细胞群体生长模型。在该模型中，每个细胞的表型状态由结构变量描述，该结构变量捕获细胞增殖和迁移速率的细胞间变异性。该模型跟踪单细胞的空间演化动力学，其经历压力依赖性增殖、可遗传的表型变化和响应于压力差的定向运动。我们正式表明，该模型的连续极限包括一个非局部偏微分方程的细胞种群密度，概括早期的模型不断增长的细胞种群。基于个体的模型的结果说明了塑造单细胞进化的增殖-迁移权衡如何导致在群体水平上形成行波，其中高度移动的细胞在侵入性前沿局部占主导地位，而在后方发现更多增殖性细胞。我们证明，有一个很好的定量协议，这些结果和数值模拟和正式行波分析的连续模型的结果，当被认为是足够大的细胞数量。我们提供了数值证据的情况下，这两个模型的预测可能会有所不同，由于人口统计的随机性，这不能被连续模型捕获。这表明在对表型异质性细胞群体的生长进行建模时，整合基于个体的方法和连续体方法的重要性。
英文摘要：
Existing studies comparing individual-based models of growing cell populations and their continuum counterparts have mainly focused on homogeneous populations, in which all cells have the same phenotypic characteristics. However, significant intercellular phenotypic variability is commonly observed in cellular systems. Therefore, we develop here an individual-based model for the growth of phenotypically heterogeneous cell populations. In this model, the phenotypic state of each cell is described by a structuring variable that captures intercellular variability in cell proliferation and migration rates. The model tracks the spatial evolutionary dynamics of single cells, which undergo pressure-dependent proliferation, heritable phenotypic changes and directional movement in response to pressure differentials. We formally show that the continuum limit of this model comprises a non-local partial differential equation for the cell population density, which generalises earlier models of growing cell populations. Results of the individual-based model illustrate how proliferation-migration tradeoffs shaping the evolution of single cells can lead to the formation of travelling waves at the population level where highly-mobile cells locally dominate at the invasive front, while more-proliferative cells are found at the rear. We demonstrate that there is an excellent quantitative agreement between these results and the results of numerical simulations and formal travelling-wave analysis of the continuum model, when sufficiently large cell numbers are considered. We provide numerical evidence of scenarios in which the predictions of the two models may differ due to demographic stochasticity, which cannot be captured by the continuum model. This indicates the importance of integrating individual-based and continuum approaches when modelling the growth of phenotypically heterogeneous cell populations.
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