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 druginduced selection of a subpopulation due to heterogeneity of polymyxin B receptor binding in the bacterial population.