Jin Wang, McCue Scott W, Simpson Matthew J
School of Mathematical Sciences, Queensland University of Technology (QUT), Brisbane, Queensland, Australia.
School of Mathematical Sciences, Queensland University of Technology (QUT), Brisbane, Queensland, Australia.
J Theor Biol. 2018 May 14;445:51-61. doi: 10.1016/j.jtbi.2018.02.027. Epub 2018 Feb 23.
Cell proliferation is the most important cellular-level mechanism responsible for regulating cell population dynamics in living tissues. Modern experimental procedures show that the proliferation rates of individual cells can vary significantly within the same cell line. However, in the mathematical biology literature, cell proliferation is typically modelled using a classical logistic equation which neglects variations in the proliferation rate. In this work, we consider a discrete mathematical model of cell migration and cell proliferation, modulated by volume exclusion (crowding) effects, with variable rates of proliferation across the total population. We refer to this variability as heterogeneity. Constructing the continuum limit of the discrete model leads to a generalisation of the classical logistic growth model. Comparing numerical solutions of the model to averaged data from discrete simulations shows that the new model captures the key features of the discrete process. Applying the extended logistic model to simulate a proliferation assay using rates from recent experimental literature shows that neglecting the role of heterogeneity can, at times, lead to misleading results.
细胞增殖是调节活组织中细胞群体动态的最重要的细胞水平机制。现代实验程序表明，在同一细胞系中，单个细胞的增殖速率可能会有显著差异。然而，在数学生物学文献中，细胞增殖通常使用经典的逻辑斯蒂方程进行建模，该方程忽略了增殖速率的变化。在这项工作中，我们考虑了一个细胞迁移和细胞增殖的离散数学模型，该模型受体积排斥（拥挤）效应的调节，且整个人口中的增殖速率可变。我们将这种变异性称为异质性。构建离散模型的连续极限会导致经典逻辑斯蒂增长模型的推广。将模型的数值解与离散模拟的平均数据进行比较表明，新模型捕捉到了离散过程的关键特征。应用扩展的逻辑斯蒂模型，使用近期实验文献中的速率来模拟增殖试验，结果表明忽略异质性的作用有时可能会导致误导性结果。
