Quantifying Subpopulation Synergy for Antibiotic Combinations via Mechanism-Based Modeling and a Sequential Dosing Design

Quantitative modeling of combination therapy can describe the effects of each antibiotic against multiple bacterial populations. Our aim was to develop an efficient experimental and modeling strategy that evaluates different synergy mechanisms using a rapidly killing peptide antibiotic (nisin) combined with amikacin or linezolid as probe drugs. Serial viable counts over 48 h were obtained in time-kill experiments with all three antibiotics in monotherapy against a methicillin-resistant Staphylococcus aureus USA300 strain (inoculum, 10(8) CFU/ml). A sequential design (initial dosing of 8 or 32 mg/liter nisin, switched to amikacin or linezolid at 1.5 h) assessed the rate of killing by amikacin and linezolid against nisin-intermediate and nisin-resistant populations. Simultaneous combinations were additionally studied and all viable count profiles comodeled in S-ADAPT and NONMEM. A mechanism-based model with six populations (three for nisin times two for amikacin) yielded unbiased and precise (r = 0.99, slope = 1.00; S-ADAPT) individual fits. The second-order killing rate constants for nisin against the three populations were 5.67, 0.0664, and 0.00691 liter/(mg.h). For amikacin, the maximum killing rate constants were 10.1 h(-1) against its susceptible and 0.771 h(-1) against its less-susceptible populations, with 14.7 mg/liter amikacin causing half-maximal killing. After incorporating the effects of nisin and amikacin against each population, no additional synergy function was needed. Linezolid inhibited successful bacterial replication but did not efficiently kill populations less susceptible to nisin. Nisin plus amikacin achieved sub-population synergy. The proposed sequential and simultaneous dosing design offers an efficient approach to quantitatively characterize antibiotic synergy over time and prospectively evaluate antibiotic combination dosing strategies.