Wojciech Krzyzanski (1), Alan Forrest (1), Gauri Rao (1)
(1) University at Buffalo
Objectives: To set up a framework for application of PSP models [1] for studying resistance of cell populations to cytotoxic drugs based on heterogeneity of distribution of target binding properties among cells and to apply it to explain resistance of Gram-negative bacteria to PB.
Methods: The drug binding parameter KD (dissociation equilibrium constant) is assumed to vary between cells and is considered as individual cell state characteristics (structure). A theory of PSP offers a p-state equation describing the time course of the density distribution of KD upon exposure to cytotoxic drug concentration (environment). The drug increases the hazard of cell death as a sigmoidal function of receptor occupancy (RO). The initial distribution of KD is described by the Weibull function. In vitro time-kill studies were performed [2] to describe the pharmacodynamic effect of PB (0, 1, 2, and 4 mg/L) against an initial inoculum of 106 CFU (colony forming units)/mL of Klebsiella pneumoniae strain, BAA1705. Serial cultures obtained at 0, 1, 2, 4, 6, 8, 24, 28, 32, and 48 h were quantified. The PSP model was used to describe the PB action against the bacteria using the nlinfit function in MATLAB.
Results: Based on the balance between the cell growth and death hazard functions, the PSP model provides a criterion for eradication or survival of cells exposed to the drug depending on their KD values. For cell populations with the first-order (population size independent) growth rate there exists a critical KDcrit such that cells with KD < KDcrit become extinct over time whereas cells with KD > KDcrit continue growing. Consequently, only a fraction of the initial population grows to form a new (resistant) population. The KDcrit increases with increased drug concentrations. The PSP model with saturable (population size dependent) growth rate [3] was applied to the time-kill data. PB exposure resulted in a maximal increase in the death hazard by 22.9-fold with RO50 = 2.3. The KD distribution in the inoculated bacteria was right skewed with a median of 32.9 nM. The PSP model predicts that the bacteria regrow to reach a steady state. However, as time passes, cells with specific binding affinity to PB are eradicated and cells with weaker affinity are able to transiently persist.
Conclusions: Heterogeneous distribution of KD among cells results in emergence of a resistant population. The PSP models can adequately quantify the time course of KD distribution.
References:
[1] de Roos, A gentle introduction to physiologically 647 structured population models structured-population models in marine, terrestrial, and freshwater systems. In Tuljapurkar S, Caswell H (Eds.) Structured-population Models in Marine, Terrestial, and Fresh Water Systems. (1997) Chapman and Hall, New York.
[2] Begic D, von Eiff C, Tsuji BT. Daptomycin pharmacodynamics against Staphylococcus aureus hemB mutants displaying the small colony variant phenotype. J. Antimicrob. Chemother. (2009) 63: 977-981.
[3] Bulitta JB, Yang JC, Yohonn L, Ly NS, Brown SV, D’Hondt RE, Jusko WJ, Forrest A, Tsuji BT, Attenuation of colistin bactericidal activity by high inoculum of Pseudomonas aeruginosa characterized by a new Mechanism-based population pharmacodynamic model. Antimicrob. Agents Chemother. (2010) 54: 2051–2062.
Reference: PAGE 24 (2015) Abstr 3475 [www.page-meeting.org/?abstract=3475]
Poster: Drug/Disease modeling - Infection