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When the Most Potent Combination of Antibiotics Selects for the Greatest Bacterial Load: The Smile-Frown Transition

Figure 1

The drug interaction profile, i(θ), as defined in Materials and Methods.

The drug interaction profile is closely related to the two ‘checkerboard’ diagrams shown in (a) and (c). In a checkerboard, the concentration of both drugs is given on the x and y axes, bacterial growth inhibition (or population density or some other fitness measure) is then plotted on the z axis. The contour of all concentrations that reduce this measure by half is an isobole here denoted IC50 and figures (a) and (c) show two checkerboard plots viewed from above. Basal concentrations of both drugs that achieve the same inhibitory effect in this illustration are D50 and E50, θ then parameterises the equidosage line between these two values. The fitness measure evaluated along this line is shown in (b) and (d) and we define the degree of interaction based on this curve, this is i(θ). We say the interaction is synergistic when the drug proportion that minimises i(θ) satisfies 0<θ<1 as in (b), we denote the resulting value by θsyn. In (d) we observe θsyn = 0 or θsyn = 1, in this case the drugs are said to be antagonistic as i(θ) is maximised by some drug combination and minimised by the monotherapies.

Figure 1