Luria-Delbrück fluctuation experiments; accounting simultaneously for plating efficiency and differential growth rate.

Cells growing in culture are subject to mutation, and as mutation is a random event, the number of mutants in a culture will be a random variable. The size of the clone of mutants arising from a single mutational event depends on the timing of the mutation; the earlier the mutation the larger the corresponding clone of mutants. The frequency with which new mutations arise may be estimated from examining the number of mutants found in a number of parallel cultures, each culture arising from a single cell. An efficient estimator of mutation rate in such an experiment is a maximum likelihood estimator. The use of such an estimator presupposes knowledge of the probability distribution for the number of mutants to be detected in a culture, given the mutation rate. In turn this depends on the probability distribution for the size of the clone of detected mutants arising from any single mutation. This latter distribution depends on the relative cell cycle time, tau, of the mutants, and on the probability, s, that a mutant which exists will be detected. This paper develops the required probability distribution.