Modeling the Emergence of Antibiotic Resistance in the Environment: an Analytical Solution for the Minimum Selection Concentration

Environmental antibiotic risk management requires an understanding of how subinhibitory antibiotic concentrations contribute to the spread of resistance. We develop a simple model of competition between sensitive and resistant bacterial strains to predict the minimum selection concentration (MSC), the lowest level of antibiotic at which resistant bacteria are selected. We present an analytical solution for the MSC based on the routinely measured MIC, the selection coefficient ( sc ) that expresses fitness differences between strains, the intrinsic net growth rate, and the shape of the bacterial growth dose-response curve with antibiotic or metal exposure (the Hill coefficient [κ]). We calibrated the model by optimizing the Hill coefficient to fit previously reported experimental growth rate difference data. The model fit varied among nine compound-taxon combinations examined but predicted the experimentally observed MSC/MIC ratio well ( R 2 ≥ 0.95). The shape of the antibiotic response curve varied among compounds (0.7 ≤ κ ≤ 10.5), with the steepest curve being found for the aminoglycosides streptomycin and kanamycin. The model was sensitive to this antibiotic response curve shape and to the sc , indicating the importance of fitness differences between strains for determining the MSC. The MSC can be >1 order of magnitude lower than the MIC, typically by the factor sc κ This study provides an initial quantitative depiction and a framework for a research agenda to examine the growing evidence of selection for resistant bacterial communities at low environmental antibiotic concentrations.