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

Figure 2

Smile-frown transition: a verbal argument and a toy mathematical model.

(a) Synergistic drugs suppress drug-susceptible sub-populations (yellow cells) more than single-drug therapies however, this eliminates competitors of the drug-resistant red cells who grow more rapidly than the yellow cells would have done at weaker synergies. Thus greater synergy can increase population densities. (b) Solving Equation 1ab and plotting population density against drug proportion shows that a short-term synergistic combination (blue) can maximise densities later (red). The red dots show the path of the optimal combination, note this idealised model is symmetric about θ = 1/2 but empirical data will not be. (c and d) The densities of drug-susceptible cells (S on the vertical axis in (c)) and resistants (R on the vertical axis in (d)) are shown at different times where, again, the blue line denotes a treatment of short duration and the red line denotes a longer treatment. The arrow in (c) represents the loss of S that occurs because of the drug whereas the arrow in (d) represents the analogous gain in R. For longer treatments the latter more than compensates for the former and by summing the red and blue lines in (b) and (c), respectively, we obtain the red and blue curves showing population density, Δ = S+R, in (a).

Figure 2