Two-drug antimicrobial chemotherapy: a mathematical model and experiments with Mycobacterium marinum.

Multi-drug therapy is the standard-of-care treatment for tuberculosis. Despite this, virtually all studies of the pharmacodynamics (PD) of mycobacterial drugs employed for the design of treatment protocols are restricted to single agents. In this report, mathematical models and in vitro experiments with Mycobacterium marinum and five antimycobacterial drugs are used to quantitatively evaluate the pharmaco-, population and evolutionary dynamics of two-drug antimicrobial chemotherapy regimes. Time kill experiments with single and pairs of antibiotics are used to estimate the parameters and evaluate the fit of Hill-function-based PD models. While Hill functions provide excellent fits for the PD of each single antibiotic studied, rifampin, amikacin, clarithromycin, streptomycin and moxifloxacin, two-drug Hill functions with a unique interaction parameter cannot account for the PD of any of the 10 pairs of these drugs. If we assume two antibiotic-concentration dependent functions for the interaction parameter, one for sub-MIC and one for supra-MIC drug concentrations, the modified biphasic Hill function provides a reasonably good fit for the PD of all 10 pairs of antibiotics studied. Monte Carlo simulations of antibiotic treatment based on the experimentally-determined PD functions are used to evaluate the potential microbiological efficacy (rate of clearance) and evolutionary consequences (likelihood of generating multi-drug resistance) of these different drug combinations as well as their sensitivity to different forms of non-adherence to therapy. These two-drug treatment simulations predict varying outcomes for the different pairs of antibiotics with respect to the aforementioned measures of efficacy. In summary, Hill functions with biphasic drug-drug interaction terms provide accurate analogs for the PD of pairs of antibiotics and M. marinum. The models, experimental protocols and computer simulations used in this study can be applied to evaluate the potential microbiological and evolutionary efficacy of two-drug therapy for any bactericidal antibiotics and bacteria that can be cultured in vitro.