SIAM Journal on Applied Dynamical Systems, Volume 19, Issue 2, Page 1540-1573, January 2020.
We study a model of the cell cycles of a large ensemble of cells that was conceived to explain the coupling between metabolism and the cell cycle observed in cell cycle related, metabolic oscillations in yeast continuous culture. An essential feature of the model is that a negative feedback mechanism robustly produces temporal clustering: cohorts of cells proceeding through the cell cycle in phase synchrony, a phenomenon that was observed in the yeast experiments. In this paper we focus on the possibility of temporal clustering in which different cohorts are of unequal sizes. We observe in numerical simulations of the model that the clusters tend very strongly toward having nearly equal numbers of cells. This is consistent with the available experimental data. We study the case of two unequal clusters analytically and conclude that solutions with two unequal clusters are locally asymptotically stable in the clustered subspace. However, local asymptotic stability of unbalanced clusters in the full phase space depends delicately on the parameters of the model. The global dynamics reveal a more robust picture. If clusters become unbalanced, the influence of the larger cluster can radically shift the basins of attraction of individual clusters, making it more likely for an unclustered cell to join a smaller cluster. We propose that this points to a general principle: systems that form temporal clusters via nonlocal coupling tend to form nearly equal clusters. Finally, we describe an exception. When the number of clusters is a composite, we observe that groups of clusters may decouple with different numbers of cells in each group.

中文翻译：

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细胞周期动力学的负反馈种群模型中的簇趋于相等大小

SIAM应用动力系统杂志，第19卷，第2期，第1540-1573页，2020年1月。
我们研究了大细胞集合的细胞周期模型，该模型旨在解释代谢与酵母连续培养中细胞周期相关，代谢振荡中观察到的细胞周期之间的耦合。该模型的一个基本特征是，负反馈机制会强有力地产生时间聚类：一群细胞以同步的方式经历细胞周期，这是在酵母实验中观察到的现象。在本文中，我们关注于时间集群的可能性，其中不同队列的大小不相等。我们在模型的数值模拟中观察到，群集趋向于具有几乎相等数量的单元格。这与可用的实验数据一致。我们通过分析研究了两个不等聚类的情况，并得出结论，具有两个不等聚类的解在聚类子空间中是局部渐近稳定的。但是，在整个相空间中，不平衡簇的局部渐近稳定性取决于模型的参数。全球动态揭示了一幅更为稳健的图景。如果群集变得不平衡，则较大群集的影响会从根本上转移单个群集的吸引盆地，从而使未群集的单元更有可能加入较小的群集。我们建议这指向一个通用原理：通过非局部耦合形成时间簇的系统趋于形成几乎相等的簇。最后，我们描述一个例外。如果簇数是复合数，