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Optimal Drug Synergy in Antimicrobial Treatments
Figure 3
The synergy ceiling 
is determined by clearance of the wild-type population before the single-mutant subpopulation.
(A) Population sizes of the wild-type (
, black) and single-drug resistant mutants (
, blue) over treatment courses with levels of interaction below, at or above the critical value 
(
). Populations start with sizes 
and are killed by antibiotics until they are cleared at times 
and 
respectively; the overall time of clearance of the infection is simply 
(orange markers). The interaction level 
affects the order in which the wild-type and the single-drug resistant subpopulations are eliminated: below the synergy ceiling (
, top), the wild-type is eliminated after the single-drug resistant mutant and 
; at the synergy ceiling (
, middle), the two populations die simultaneously and 
; above the synergy ceiling (
, bottom), the single-drug resistant mutant outlives the wild-type, such that 
. Because increasing 
increases the wild-type killing rate but has no effect on the single-mutant killing rate, efficacy increases with 
below the synergy ceiling (
), but plateaus at and above it (
; vertical dashed line: notice that 
is the same both at and above the synergy ceiling). (B) Increased mutation rates, 
, give rise to lower 
. Inset: treatment efficacy, 
, plateaus at lower levels of drug interaction 
for higher mutation rates (
, blue; 
, orange; 
, green; blue and green lines are shifted slightly along y-axis for clarity); 
values for each line are indicated by vertical dashed lines, and by circles in the main panel. Orange markers indicate the treatment efficacy achieved for different values of 
when 
, corresponding to the 
values in panel A.
doi: https://doi.org/10.1371/journal.pcbi.1000796.g003