Reversibility of resistance in a fluctuation test experiment modifies the tail of the Luria-Delbrück distribution

We consider a fluctuation test experiment in which cell colonies are grown from a single cell until they reach a given population size, and then they are exposed to treatment. While they grow, the cells may, with a low probability, acquire resistance to treatment and pass it on to their offspring. Unlike the classical Luria–Delbrück fluctuation test and motivated by recent work on drug-resistance acquisition in cancer/microbial cells, we allow for the resistant cell state to switch back to a drug-sensitive state. This modification does not affect the central part of the (Luria–Delbrück) distribution of the number of resistant survivors: the previously developed approximation by the Landau probability density function applies. However, the right tail of the modified distribution deviates from the power law decay of the Landau distribution. We demonstrate that the correction factor is equal to the Landau cumulative distribution function.