Estimating Mutation Rates Under Heterogeneous Stress Responses

Abstract Exposure to environmental stressors, including certain antibiotics, induces stress responses in bacteria. Some of these responses increase mutagenesis and thus potentially accelerate resistance evolution. Many studies report increased mutation rates under stress, often using the standard experimental approach of fluctuation assays. However, single-cell studies have revealed that many stress responses are heterogeneously expressed in bacterial populations, which existing estimation methods have not yet addressed. We develop a population dynamic model that considers heterogeneous stress responses (subpopulations of cells with the response off or on ) that impact both mutation rate and cell division rate, inspired by the DNA-damage response in Escherichia coli (SOS response). We derive the mutant count distribution arising in fluctuation assays under this model and then implement maximum likelihood estimation of the mutation-rate increase specifically associated with the expression of the stress response. Using simulated mutant count data, we show that our inference method allows for accurate and precise estimation of the mutation-rate increase, provided that the induction of the response also reduces the division rate. Moreover, we find that in many cases, our model of heterogeneous stress responses and the standard model with mutant fitness cost reproduce fluctuation assay data equally well, suggesting that separate experiments would be required to identify the true underlying process. In cases where stress responses are heterogeneous, current methods still correctly infer the effective increase in population mean mutation rate, but we provide a novel method to infer heterogeneity in stress-induced mutation rates. Author summary How does environmental stress, especially from antibiotics, affect mutation rates in bacteria? This question has often been examined by estimating mutation rates using fluctuation assays, a standard experiment dating back to Luria and Delbrück in the 1940s. We address a gap in currently available estimation methods: we consider cell-to-cell variation in stress responses within bacterial populations, as revealed by recent single-cell studies. Our approach involves a population dynamic model inspired by the DNA-damage response in E. coli (SOS response). It accounts for a subpopulation with high expression of the stress response, which increases the mutation rate and decreases the division rate of a cell. Notably, we find that existing models and our heterogeneous-response model reproduce simulated fluctuation assay data equally well in certain scenarios. This emphasises the need for separate experiments to uncover the true underlying processes. Nevertheless, when stress responses are known to be heterogeneous, our study offers a novel method for accurately estimating mutation rates specifically associated with the high expression of the stress response. Uncovering the heterogeneity in stress-induced mutation rates could be important for predicting the evolution of antibiotic resistance.