Distribution of mutants in aggregates of cultured cells

The analysis of the distribution of mutants in an exponentially growing culture of cells that are aggregated into clumps of homogeneous size is described, given the mutation rate and a random process by which clumps divide to produce progeny. The mean and standard deviation of the proportion of clumps with a given number of mutant cells at a particular time are calculated. Since the standard deviation tends to be much smaller than the mean, the following conclusions can be drawn. Aggregation lowers the number of mutant-containing clumps in cultures grown to a standard number of cells, but raises the number of mutant-containing clumps in cultures grown to a standard number of clumps. In the absence of mutation, or at low mutation rates, clumps tend to become pure types (normal or mutant). The probability of finding pure, nonmutant-containing clumps, however, is approximately the initial fraction of nonmutant cells (given realistic forward and back mutation rates). Also, in terms of the given process, it is possible to compute the probability that all the cells in an aggregate descend from a single, common parent cell within a given number of generations, and thus to calculate the probability that all the cells in a clone grown from an aggregate descend from a single cell within a known number of generations.