CELL GROWTH AND DIVISION .I. A MATHEMATICAL MODEL WITH APPLICATIONS TO CELL VOLUME DISTRIBUTIONS IN MAMMALIAN SUSPENSION CULTURES
CELL GROWTH AND DIVISION .I. A MATHEMATICAL MODEL WITH APPLICATIONS TO CELL VOLUME DISTRIBUTIONS IN MAMMALIAN SUSPENSION CULTURES
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DOI：
10.1016/s0006-3495(67)86592-5
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发表时间：
1967-01-01
影响因子：
3.4
通讯作者：
ANDERSON, EC
中科院分区：
文献类型：
--
作者：
BELL, GI;ANDERSON, EC
为细胞群的发育制定了一个数学模型，其中各个成员可以生长、分裂或死亡。给定细胞的特征在于其年龄和体积，并且假定这些参数确定体积增长率以及每单位时间分裂或死亡的概率。公式化了初始值问题，结果表明，如果细胞生长速率与细胞体积成正比，则在不添加分散机制的情况下，体积分布将不会收敛到时不变形状。详细考虑了指数期或稳态群体特殊情况下可能的数学简化，分析了指数生长悬浮培养物中哺乳动物细胞的实验体积分布，并推导出生长速率和分裂概率。结论是细胞体积增长率大约与细胞体积成正比，并且分裂概率随着体积高于临界阈值而增加。在计算机模型中检查了分裂成不等体积子细胞对体积分布的影响。
A mathematical model is formulated for the development of a population of cells in which the individual members may grow and divide or die. A given cell is characterized by its age and volume, and these parameters are assumed to determine the rate of volume growth and the probability per unit time of division or death. The initial value problem is formulated, and it is shown that if cell growth rate is proportional to cell volume, than the volume distribution will not converge to a time-invariant shape without an added dispersive mechanism. Mathematical simplications which are possible for the special case of populations in the exponential phase or in the steady state are considered in some detail,, Experimental volume distributions of mammalian cells in exponentially growing suspension cultures are analyzed, and growth rates and division probabilities are deduced. It is concluded that the cell volume growth rate is approximately proportional to cell volume and that the division probability increases with volume above a critical threshold. The effects on volume distribution of division into daughter cells of unequal volumes are examined in computer models.