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Optimal Drug Synergy in Antimicrobial Treatments

Figure 4

Prevention of multi-drug resistance by drug antagonism depends on resource competition.

(A) Heat map of instantaneous rates of double-mutant formation, , as a function of single-mutant and total population sizes: increases with the size of the single-mutant population, and decreases with total population size due to resource competition. Treatment course trajectories for synergistic (, solid line) and antagonistic (, dashed line) drug treatments begin with total initial population size and initial single-mutant population size (magenta circle), and move toward the origin as the infection is cleared (black circles indicate 20-minute intervals). The different initial slopes of these trajectories (arrows), determined by the relative fitness of the wild-type and single-drug resistant mutants in synergistic versus antagonistic treatments, lead them to different regions of the heat map: synergistic drug pairs quickly kill the wild-type, relieving resource competition before the single-mutant population is killed and leading to a region with high (solid trajectory goes through red region), while antagonistic pairs kill the single mutants before competition is relieved, leading to a region of low (dashed trajectory goes through green region). (B) The over each treatment plotted as a function of time; black circles indicate 40-minute intervals in this panel. (C) Relative ability of these strongly synergistic and antagonistic drug pairs to prevent multi-drug resistance, , for different initial population sizes (circles). For strong resource competition at the start of treatment ( close to ), antagonistic drug pairs prevent resistance better than synergistic drug pairs (). For weak competition, however ( significantly less than ), synergistic drug pairs better prevent resistance (). Artificially turning off wild-type to single-drug resistant mutation during treatment (leaving only the single-mutant population that exists at the onset of treatment) eliminates the advantage of synergy over antagonism at low (triangles). (D) When initial population size is low and synergy is advantageous, the tradeoff between treatment efficacy and prevention of multi-drug resistance is eliminated, such that maximally synergistic drug pairs yield both the greatest treatment efficacy and greatest prevention of multi-drug resistance (compare panel C to Fig. 2).

doi: https://doi.org/10.1371/journal.pcbi.1000796.g004