Phase Diagram for Salicylate-Chloramphenicol Interactions. a. The concentration of salicylate, S* (in mM), at which growth is maximal depends on the external concentration of antibiotic. A transition occurs between the low antibiotic regime, where the presence of salicylate is harmful, to the high antibiotic where the presence of salicylate increases the growth of cells. Red, tetracylcline; Blue, chloramphenicol. Concentrations for both drugs measured in μg/mL. Curves, numerical calculation from model; circles, estimates of S* from experiments at single concentrations of A. Maxima were estimated using cubic spline interpolation between data points at different concentrations of salcilyate. Error bars, concentrations corresponding to +/− 1% of maximum. b. Apparent MIC, defined as the minimum concentration of antibiotic (red, tetracycline; blue, chloramphenicol; both in units of μg/mL) at which growth is reduced to δ = 0.5. While the quantitative results depend on the precise definition of MIC, the qualitative features do not depend on the choice of δ. c. Cost-benefit theory predicts general properties of drug interactions as a function of the maximum inducible benefit βmax 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 βmax 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, βmax 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: βmax = 1.15 (WT cells; suppressive), βmax = 0.19 (mar mutant, antagonistic), and βmax = −0.15 (tolC mutant, synergistic). See also Additional file 1: Figure S3.