Here we study how the structure and growth of a cellular population vary with the distribution of maturation times from each stage. We consider two cell cycle stages. The first represents early G1. The second includes late G1, S, G2, and mitosis. Passage between the two reflects passage of an important cell cycle checkpoint known as the restriction point. We model the population as a system of partial differential equations. After establishing the existence of solutions, we characterize the maturation rates and derive the steady-state age and stage distributions as well as the asymptotic growth rates for models with exponential and inverse Gaussian maturation time distributions. We find that the stable age and stage distributions, transient dynamics, and asymptotic growth rates are substantially different for these two maturation models. We conclude that researchers modeling cellular populations should take care when choosing a maturation time distribution, as the population growth rate and stage structure can be heavily impacted by this choice. Furthermore, differences in the models' transient dynamics constitute testable predictions that can help further our understanding of the fundamental process of cellular proliferation. We hope that our numerical methods and programs will provide a scaffold for future research on cellular proliferation.

中文翻译：

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成熟时间分布对细胞群结构和生长的影响。

在这里，我们研究细胞群的结构和生长如何随着每个阶段成熟时间的分布而变化。我们考虑两个细胞周期阶段。第一个代表早期的 G1。第二个包括晚期 G1、S、G2 和有丝分裂。两者之间的通道反映了被称为限制点的重要细胞周期检查点的通过。我们将总体建模为偏微分方程组。在确定解的存在性后，我们表征成熟率并推导出稳态年龄和阶段分布以及具有指数和逆高斯成熟时间分布的模型的渐近增长率。我们发现这两个成熟模型的稳定年龄和阶段分布、瞬态动态和渐近增长率有很大不同。我们得出的结论是，在选择成熟时间分布时，对细胞群进行建模的研究人员应该小心，因为这种选择会严重影响种群增长率和阶段结构。此外，模型瞬态动力学的差异构成了可测试的预测，可以帮助我们进一步了解细胞增殖的基本过程。我们希望我们的数值方法和程序将为未来的细胞增殖研究提供一个支架。瞬态动力学构成了可测试的预测，可以帮助我们进一步了解细胞增殖的基本过程。我们希望我们的数值方法和程序将为未来的细胞增殖研究提供一个支架。瞬态动力学构成了可测试的预测，可以帮助我们进一步了解细胞增殖的基本过程。我们希望我们的数值方法和程序将为未来的细胞增殖研究提供一个支架。