Age distribution of human diploid fibroblasts. A stochastic model for in vitro aging.

Variation in the lifespan of mass cultures and clones of human diploid fibroblasts can be explained on the basis of variation in the length of the mitotic cycle. This variation is of biological significance; the intrinsic standard deviation of culture lifespan is equal to about 10% of the mean. We constructed a two-parameter stochastic model based on the following assumptions: the time between successive divisions of a given cell is of random duration; cells divide or lose the ability to divide independently of one another; the probability that a cell can undergo further division is constant up to some maximum number of divisions and zero thereafter. We determined numerically the proportion of nondividing cells and the distribution of cell generations. Samples taken by Monte Carlo means from a hypothetical in vitro population were compared with clonal survival data obtained experimentally. The fit between experimental and theoretical findings was within the range of sampling variation. If we accept our model as being applicable to human diploid cell culture, we can draw the following conclusions: the proportion of dividing cells is an inadequate index of a population's age; even in populations in which almost all cells are still capable of division, a majority of the cells have less than eight generations remaining to them. At each subcultivation the ultimate fate of a culture is determined by the disposition of a relatively small number of "young" cells.