Tyson J J, Diekmann O
J Theor Biol. 1986 Feb 21;118(4):405-26. doi: 10.1016/s0022-5193(86)80162-x.
In an asynchronous, exponentially proliferating cell culture there is a great deal of variability among individual cells in size at birth, size at division and generation time (= age at division). To account for this variability we assume that individual cells grow according to some given growth law and that, after reaching a minimum size, they divide with a certain probability (per unit time) which increases with increasing cell size. This model is called sloppy size control because cell division is assumed to be a random process with size-dependent probability. We derive general equations for the distribution of cell size at division, the distribution of generation time, and the correlations between generation times of closely related cells. Our theoretical results are compared in detail with experimental results (obtained by Miyata and coworkers) for cell division in fission yeast, Schizosaccharomyces pombe. The agreement between theory and experiment is superior to that found for any other simple models of the coordination of cell growth and division.
在异步指数增殖的细胞培养物中，各个细胞在出生时的大小、分裂时的大小以及世代时间（=分裂时的年龄）存在很大差异。为了解释这种变异性，我们假设单个细胞按照某种给定的生长规律生长，并且在达到最小尺寸后，它们以一定概率（每单位时间）进行分裂，该概率随着细胞大小的增加而增加。这个模型被称为宽松大小控制，因为细胞分裂被假定为一个具有大小依赖性概率的随机过程。我们推导了关于分裂时细胞大小分布、世代时间分布以及紧密相关细胞世代时间之间相关性的一般方程。我们将理论结果与宫田及其同事获得的关于裂殖酵母（粟酒裂殖酵母）细胞分裂的实验结果进行了详细比较。理论与实验之间的一致性优于任何其他关于细胞生长和分裂协调的简单模型。
