Multi-scale model of drug induced adaptive resistance of Gram-negative bacteria to polymyxin B

The purpose of this report is to apply multi-scale modeling using the theory of physiologically structured populations (PSP) to develop a mathematical model for antimicrobial resistance based on a heterogeneous distribution of receptors and affinities among bacterial cells. The theory has been tested on data obtained from an in vitro static time-kill infection model analyzing the pharmacodynamics of polymyxin B against Gram-negative bacteria. The drug binding parameter K(D) (dissociation equilibrium constant) is assumed to vary between the bacterial cells. The PSP model describes the time course of the density distribution of K(D) upon exposure to cytotoxic drug concentrations. The drug increases the hazard of cell death as a function of receptor occupancy. The initial distribution of K(D) is described by the Weibull function. Time-kill data were used for model qualification. In vitro static time-kill experiments to evaluate the rate and extent of killing due to polymyxin B against two Klebsiella pneumoniae clinical isolates with differing susceptibilities to polymyxin B were performed over 48 h. The time-kill kinetics data of bacterial load cfu (colony forming units)/mL was used for model qualification. The resistant bacterial population is determined by the balance between growth rate and hazard of cell death controlled by polymyxin B concentrations. There exists a critical K(D) value below which cells continue to grow. Estimates of shape parameters for distributions of K(D) yielded unimodal distributions with the modes at 0 nM and the right tails containing approximately 25% of the bacteria. Our findings support a hypothesis that resistance of Klebsiella pneumoniae to polymyxin B can be at least partially attributed to a drug-induced selection of a subpopulation due to heterogeneity of polymyxin B receptor binding in the bacterial population.