Figure 3
Cost-Benefit Analysis Quantitatively Describes Multi-Drug Growth Cost Functions. a. Multi-drug growth cost curves for salicylate and tetracycline (top) and salicylate and chloramphenicol (bottom) are increasing functions of antibiotic concentration, but also depend on the concentration of salicylate. Each growth cost curve represents growth in increasing concentrations of antibiotic at a single salicylate concentration, ranging from 0 to 7 mM. Black lines, ([salicylate] = 0 mM), which correspond to the single drug growth cost functions. Data points, means of four replicates. Error bars, +/− one sample standard deviation. b. The cost-benefit model requires rescaled versions of the multi-drug cost functions to have the same mathematical form as single drug cost functions (Equation 3). To directly test this assumption, we rescaled the multi-drug cost functions in panel a by removing the contribution from salicylate toxicity (cost) to each multi-drug growth cost function. Then, we rescaled the concentration of each antibiotic (chloramphenicol or tetracycline) using the single parameter βmax, which accounts for the salicylate-induced reduction of intracellular antibiotic concentration (benefit). We trivially exploit the common Hill form of the single drug costs functions to show data from both drug pairs on a single plot, achieved by replacing drug concentration with effective toxicity, defined as ([A]/KA)n, where KA and n characterize the single drug growth cost function for the antibiotics (see Figure 1). We use the salicylate induction curve of the mar promoter (Figure 2b) as the benefit function β(S), for both drug interactions, with only the overall scale of the benefit function (βmax) specific to the two antibiotics. See also Additional file 1: Figure S2 for a direct comparison of growth rates from experiments and models.