Koppes L J, Woldringh C L, Grover N B
Department of Microbiology, University of Uppsala, Sweden.
J Theor Biol. 1987 Dec 7;129(3):325-35. doi: 10.1016/s0022-5193(87)80005-x.
The question of how an individual bacterial cell grows during its life cycle remains controversial. In 1962 Collins and Richmond derived a very general expression relating the size distributions of newborn, dividing and extant cells in steady-state growth and their growth rate; it represents the most powerful framework currently available for the analysis of bacterial growth kinetics. The Collins-Richmond equation is in effect a statement of the conservation of cell numbers for populations in steady-state exponential growth. It has usually been used to calculate the growth rate from a measured cell size distribution under various assumptions regarding the dividing and newborn cell distributions, but can also be applied in reverse--to compute the theoretical cell size distribution from a specified growth law. This has the advantage that it is not limited to models in which growth rate is a deterministic function of cell size, such as in simple exponential or linear growth, but permits evaluation of far more sophisticated hypotheses. Here we employed this reverse approach to obtain theoretical cell size distributions for two exponential and six linear growth models. The former differ as to whether there exists in each cell a minimal size that does not contribute to growth, the latter as to when the presumptive doubling of the growth rate takes place: in the linear age models, it is taken to occur at a particular cell age, at a fixed time prior to division, or at division itself; in the linear size models, the growth rate is considered to double with a constant probability from cell birth, with a constant probability but only after the cell has reached a minimal size, or after the minimal size has been attained but with a probability that increases linearly with cell size. Each model contains a small number of adjustable parameters but no assumptions other than that all cells obey the same growth law. In the present article, the various growth laws are described and rigorous mathematical expressions developed to predict the size distribution of extant cells in steady-state exponential growth; in the following paper, these predictions are tested against high-quality experimental data.
单个细菌细胞在其生命周期中的生长方式问题仍然存在争议。1962年，柯林斯和里士满推导出了一个非常通用的表达式，该表达式将稳态生长中新生细胞、分裂细胞和现存细胞的大小分布与其生长速率联系起来；它代表了目前可用于分析细菌生长动力学的最强大框架。柯林斯 - 里士满方程实际上是稳态指数生长种群细胞数量守恒的一种表述。它通常被用于在关于分裂细胞和新生细胞分布的各种假设下，根据测量的细胞大小分布来计算生长速率，但也可以反过来应用——根据指定的生长规律计算理论细胞大小分布。这样做的优点是它不限于生长速率是细胞大小的确定性函数的模型，例如简单指数或线性生长模型，而是允许评估更为复杂的假设。在这里，我们采用这种反向方法来获得两个指数生长模型和六个线性生长模型的理论细胞大小分布。前者的区别在于每个细胞中是否存在对生长无贡献的最小尺寸，后者的区别在于假定的生长速率加倍发生的时间：在线性年龄模型中，它被认为发生在特定的细胞年龄、分裂前的固定时间或分裂时；在线性大小模型中，生长速率被认为从细胞诞生起以恒定概率加倍，或以恒定概率但仅在细胞达到最小尺寸后加倍，或在达到最小尺寸后以随细胞大小线性增加的概率加倍。每个模型都包含少量可调整参数，但除了所有细胞都遵循相同生长规律外没有其他假设。在本文中，描述了各种生长规律并推导出了严格的数学表达式，以预测稳态指数生长中现存细胞的大小分布；在接下来的论文中，将根据高质量的实验数据对这些预测进行检验。
