Grover N B, Woldringh C L, Koppes L J
Hubert H. Humphrey Centre for Experimental Medicine and Cancer Research, Hebrew University-Hadassah Medical School, Jerusalem, Israel.
J Theor Biol. 1987 Dec 7;129(3):337-48. doi: 10.1016/s0022-5193(87)80006-1.
The way individual cells grow and divide uniquely determines the (time-invariant) cell size distribution of populations in steady-state exponential growth. In the preceding article, theoretical distributions were derived for two exponential and six linear models containing a small number of adjustable parameters but no assumptions other than that all cells obey the same growth law. The linear models differ from each other with respect to the timing of the presumptive doubling in their growth rate, the exponential models--according to whether there is or is not a part of the cell that does not contribute to the growth rate. Here we compared the size distributions predicted by each of these models with those of cell length and surface area measured by electron microscopy; the quality of the fit, as determined by the mean-square successive-differences test and the chi 2 goodness-of-fit test, was taken as a measure of the adequacy of the model. The actual data came from two slow-growing E. coli B/r cultures, an A strain (pi = 125 min) and a K strain (pi = 106 min), and a correction was introduced in each to account for the distortion caused by the finite size of the picture frame. The parameter estimates produced by the various models are quite reliable (cv less than 0.1%); we discuss them briefly and compare their values in the two strains. All the length extension models were rejected outright whereas most of the surface growth versions were not. When the same models were tested on A-strain data from a faster growing culture (tau = 21 min), those models that provided an adequate fit to the cell surface area data proved equally satisfactory in the case of cell length. These findings are evaluated and shown to be consistent with cell surface area rather than cell length being the dimension under active control. Three surface area models, all linear, are rejected--those in which doubling of the growth rate occurs with a constant probability from cell birth, at a particular cell age, and precisely at cell division. The evidence in the literature that appears to contradict this last result, rejection of the simple linear surface growth model, is shown to be faulty. The 16 original models are here reduced to five, two involving exponential surface growth and three linear, and possible reasons are presented for our inability to discriminate further at this stage.
单个细胞生长和分裂的方式独特地决定了处于稳态指数生长的群体的（时间不变的）细胞大小分布。在前一篇文章中，推导出了两个指数模型和六个线性模型的理论分布，这些模型包含少量可调参数，且除了所有细胞都遵循相同的生长规律外没有其他假设。线性模型在其生长速率假定加倍的时间方面彼此不同，指数模型则根据是否存在不参与生长速率的细胞部分而有所不同。在这里，我们将这些模型各自预测的大小分布与通过电子显微镜测量的细胞长度和表面积的分布进行了比较；通过均方逐差检验和卡方拟合优度检验确定的拟合质量，被用作模型充分性的度量。实际数据来自两种生长缓慢的大肠杆菌B/r培养物，一种是A菌株（代时 = 125分钟）和一种K菌株（代时 = 106分钟），并且对每种数据都进行了校正，以考虑由相框有限尺寸引起的失真。各种模型产生的参数估计相当可靠（变异系数小于0.1%）；我们简要讨论了它们，并比较了它们在两种菌株中的值。所有长度扩展模型都被直接拒绝，而大多数表面生长模型则未被拒绝。当在来自生长更快的培养物（代时 = 21分钟）的A菌株数据上测试相同模型时，那些对细胞表面积数据提供了充分拟合的模型在细胞长度的情况下同样令人满意。对这些发现进行了评估，并表明它们与细胞表面积而非细胞长度是受主动控制的维度这一观点一致。三个表面积模型，均为线性模型，被拒绝——即那些生长速率加倍以恒定概率在细胞出生时、特定细胞年龄时以及恰好细胞分裂时发生的模型。文献中似乎与最后这个结果相矛盾的证据，即简单线性表面生长模型被拒绝，被证明是有缺陷的。这里将16个原始模型简化为5个，两个涉及指数表面生长，三个是线性的，并给出了我们在此阶段无法进一步区分的可能原因。
