In this work, we use the well-studied multiple antibiotic resistance (MAR) system in E. coli to experimentally characterize the trade-off between drug toxicity (“cost”) and drug-induced resistance (“benefit”) mediated by efflux pumps. Specifically, we show that the combined effects of a MAR-inducing drug and an antibiotic are governed by a superposition of cost and benefit functions that govern these trade-offs. We find that this superposition holds for all drug concentrations, and it therefore allows us to describe the full dose–response diagram for a drug pair using simpler cost and benefit functions. Moreover, this framework predicts the existence of optimal growth at a non- trivial concentration of inducer. We demonstrate that optimal growth does not coincide with maximum induction of the mar promoter, but instead results from the interplay between drug toxicity and mar induction. Finally, we derived and experimentally validated a general phase diagram highlighting the role of these opposing effects in shaping the interaction between two drugs.

Our analysis provides a quantitative description of the MAR system and highlights the trade-off between inducible resistance and the toxicity of the inducing agent in a multi-component environment. The results provide a predictive framework for the combined effects of drug toxicity and induction of the MAR system that are usually masked by bulk measurements of bacterial growth. The framework may also be useful for identifying optimal growth conditions in more general systems where combinations of environmental cues contribute to both transient resistance and toxicity.




Phase Diagram for Interactions Between Salicylate and Chloramphenicol.

Simple cost-benefit analysis predicts general properties of drug interactions as a function of the maximum inducible benefit betamax and the concentration of inducer, S. Solid line, phase boundary between synergistic and antagonistic drug interactions. Dashed line, phase boundary between antagonistic and suppressive interactions. In general, a higher value of the betamax increases the antagonism between drug pairs at a given concentration of drug S. Parameters characterizing individual drugs include KS and Kind, which characterize, respectively, the cost of drug S and the corresponding induction of resistance systems (e.g. efflux pumps), and KA and n, which characterize the cost of drug A. By contrast, betamax couples the individual effects of two drugs. Insets, heat maps of two-dimensional growth surfaces for 3 cell strains in the presence of Salicylate (Sal) and Chloramphenicol (Cm); top: betamax = 1.15 (WT cells; suppressive), betamax = 0.19 (mar mutant, antagonistic), and betamax = 0.15 (tolC mutant, synergistic).