Emergence of mutants in bacterial populations: a simulation-based approach for parameter inference in extended Luria & Delbrück scenarios

Bacterial mutation rates are traditionally inferred from phenotypic data using fluctuation assays. Mutation rate computation from these assays relies on a mathematical model describing the emergence of mutants during population growth. However, this standard model relies on restrictive assumptions that are often transgressed in real biological setups. Key assumptions include equal growth rate of the wild-type and the mutant population, no cell death during the growth phase, and no post-growth sampling. Although several refined mathematical models have been proposed over the last decades to circumvent some of these assumptions, none can fully account for the complex ecological scenarios frequently observed in the lab or in the wild, such as the combination of cell death and an unknown fitness effect of the mutation, or non-constant death rates. In this work, we propose to replace these standard mathematical models by a stochastic simulation framework, which can circumvent all these assumptions. We provide a fast and accurate implementation of this stochastic model, and combine it with an Approximate Bayesian Computation scheme to perform simulation-based, likelihood-free parameter inference. Our approach can simultaneously infer mutation rate and fitness effect of the mutation while accounting for death and partial plating, and could be extended to arbitrary complex conditions that can be efficiently simulated.