Department of Applied Mathematics, University of Washington, Seattle, WA 98195, USA.
Proc Biol Sci. 2023 Oct 25;290(2009):20231020. doi: 10.1098/rspb.2023.1020. Epub 2023 Oct 18.
The questions of how healthy colonic crypts maintain their size, and how homeostasis is disrupted by driver mutations, are central to understanding colorectal tumorigenesis. We propose a three-type stochastic branching process, which accounts for stem, transit-amplifying (TA) and fully differentiated (FD) cells, to model the dynamics of cell populations residing in colonic crypts. Our model is simple in its formulation, allowing us to estimate all but one of the model parameters from the literature. Fitting the single remaining parameter, we find that model results agree well with data from healthy human colonic crypts, capturing the considerable variance in population sizes observed experimentally. Importantly, our model predicts a steady-state population in healthy colonic crypts for relevant parameter values. We show that and mutations, the most significant early alterations leading to colorectal cancer, result in increased steady-state populations in mutated crypts, in agreement with experimental results. Finally, our model predicts a simple condition for unbounded growth of cells in a crypt, corresponding to colorectal malignancy. This is predicted to occur when the division rate of TA cells exceeds their differentiation rate, with implications for therapeutic cancer prevention strategies.
结肠隐窝中健康的隐窝如何维持其大小，以及其体内平衡如何被驱动突变所破坏，这些问题是理解结直肠肿瘤发生的核心。我们提出了一个三类型随机分支过程，它考虑了干细胞、过渡扩增（TA）和完全分化（FD）细胞，以模拟结肠隐窝中细胞群体的动力学。我们的模型在其公式中很简单，使我们能够从文献中估计除一个模型参数之外的所有参数。拟合唯一剩下的参数，我们发现模型结果与来自健康人类结肠隐窝的数据非常吻合，捕获了实验中观察到的相当大的群体大小变化。重要的是，我们的模型预测了健康结肠隐窝中的稳定群体状态。我们表明， 和 突变是导致结直肠癌的最重要的早期改变，导致突变隐窝中的稳定群体增加，这与实验结果一致。最后，我们的模型预测了隐窝中细胞无限制生长的简单条件，对应于结直肠恶性肿瘤。当 TA 细胞的分裂率超过其分化率时，就会出现这种情况，这对癌症预防策略具有重要意义。
