Synergistic effects of amoxicillin and clavulanate when inhibiting growth of a β-lactamase-expressing bacterium. (a) Predicted inhibition (A) from a theoretical model of control of a β-lactamase-expressing bacterium (equation 1). The color gradient shows values as highlighted by the contours. The model is illustrated using parameters fitted to the data in panel b: a = amoxillicin/amoxicillin_max (30 μg/ml), b = clavulanate/clavulanate_max (40 μg/ml); x = y = 0.198, r = 0.952. (b) Measured inhibition of ancestral E. coli expressing β-lactamase from a plasmid. The circles represent three replicate measures, while the surface is a loess smoothed fit. For ease of comparison with the theoretical model, inhibition was calculated from growth after 22 h by subtracting growth from the maximum measured growth value (OD600 of 0.81). The gray diamonds show the 15 selection conditions used for the experimental evolution, with the darkest diamonds representing stronger inhibition. Note that in both plots, the axes have been transformed (inverse hyperbolic sine) to show the data more clearly.