The evolution of antibiotic resistance is a critical challenge in the treatment of bacterial infections. Resistance first arises (e.g. by de novo mutation) in individual bacterial cells, which may either establish surviving lineages or be lost due to demographic stochasticity. Despite being a classic problem in theoretical population genetics and extensively modelled mathematically (e.g. using branching processes), the stochastic process of establishment has rarely been investigated empirically, and is largely overlooked in the antibiotic resistance literature. Indeed, a prevailing paradigm in medical microbiology is that resistance will be selected at antibiotic concentrations within the "mutant selection window" (MSW) between the standardised minimum inhibitory concentrations (MICs) of sensitive and resistant strains, assessed by absence of detectable growth in a large population of the respective strain. This view neglects stochastic loss of rare resistant cells, which we predict will depend on environmental variables and may become substantial as antibiotic concentration increases, even within the MSW. We investigated this question using high-replicate experiments with a streptomycin-resistant strain of the clinically relevant bacterium Pseudomonas aeruginosa, combined with a likelihood-based statistical framework to infer from these data the per-cell probability of establishing a surviving lineage. We found that establishment probability of resistant cells decreases with streptomycin concentration, and already approaches zero well below their MIC (i.e. the upper bound of the MSW). These results suggest that stochastic mathematical models for the emergence of resistance are needed for predicting optimal antibiotic dosing, instead of simply using the MSW as an "all-or-nothing" predictor. Furthermore, the experimental and statistical methods developed here could be transferred to other bacteria/antibiotic systems.

This is joint work with R. C. MacLean. This work was funded by a Swiss National Science Foundation fellowship (P2EZP3_165188) to HKA and a Wellcome Trust grant to RCM.