Attenuation of colistin bactericidal activity by high inoculum of Pseudomonas aeruginosa characterized by a new mechanism-based population pharmacodynamic model

Abstract

Colistin is increasingly being utilized against Gram-negative pathogens, including Pseudomonas aeruginosa, resistant to all other antibiotics. Since limited data exist regarding killing by colistin at different initial inocula (CFUo), we evaluated killing of Pseudomonas aeruginosa by colistin at several CFUo and developed a mechanism-based mathematical model accommodating a range of CFUo. In vitro time-kill experiments were performed using >or=8 concentrations up to 64 x the MIC of colistin against P. aeruginosa PAO1 and two clinical P. aeruginosa isolates at CFUo of 10(6), 10(8), and 10(9) CFU/ml. Serial samples up to 24 h were simultaneously modeled in the NONMEM VI (results shown) and S-ADAPT software programs. The mathematical model was prospectively "validated" by additional time-kill studies assessing the effect of Ca(2+) and Mg(2+) on killing of PAO1 by colistin. Against PAO1, killing of the susceptible population was 23-fold slower at the 10(9) CFUo and 6-fold slower at the 10(8) CFUo than at the 10(6) CFUo. The model comprised three populations with different second-order killing rate constants (5.72, 0.369, and 0.00210 liters/h/mg). Bacteria were assumed to release signal molecules stimulating a phenotypic change that inhibits killing. The proposed mechanism-based model had a good predictive performance, could describe killing by colistin for all three studied strains and for two literature studies, and performed well in a prospective validation with various concentrations of Ca(2+) and Mg(2+). The extent and rate of killing of P. aeruginosa by colistin were markedly decreased at high CFUo compared to those at low CFUo. This was well described by a mechanism-based mathematical model, which should be further validated using dynamic in vitro models.

FIG. 1.

Structure of the pharmacodynamic model, including bacterial growth, killing, and the inoculum effect (A) and the receptor occupancy model (B). The bacterial model contains one compartment for the susceptible, intermediate, and least-susceptible (“resistant”) population and a lag compartment for the susceptible population. In the lag compartment, bacteria do not replicate and are not subject to natural death but are subject to drug-induced killing and the effect of signal molecules. For the other three bacterial compartments, loss of cells occurs via a first-order natural death and a second-order killing process by colistin. Signal molecules were assumed to inhibit bacterial killing by colistin and the rate of bacterial replication (only the arrow for the effect of signal molecules on the susceptible population is shown). Initial conditions (IC) were estimated (see Methods). The target site model comprised a competitive interaction of colistin with Mg²⁺ and Ca²⁺ at the LPS binding sites in the outer membrane. Binding sites occupied by Mg²⁺ and Ca²⁺ were assumed to decrease the colistin concentration that is available in the active conformation(s) at the site of action.

FIG. 2.

Population predicted versus observed log₁₀ (CFU/ml) for three strains of P. aeruginosa at a low (top), intermediate (middle), or high (bottom) initial inoculum (see also Table 1 and Fig. 1; based on results from S-ADAPT). A log₁₀ value of observed colony counts plotted as zero means no colony was on the plate. Given the volume of 50 μl plated, one colony is equivalent to 20 CFU/ml (approximately 1.3 on log₁₀ scale) for an undiluted sample.

FIG. 3.

Viable counts on drug-free and drug-containing plates at 24 h for P. aeruginosa PAO1 for an initial inoculum of 10⁶ (A), 10⁸ (B), or 10⁹ (C) CFU/ml (agar MIC of PAO1, 2 mg/liter). Colistin concentrations above 16 mg/liter were not studied at the 10⁶-CFU/ml inoculum. Plates with 8 mg/liter colistin showed a log₁₀ CFU/ml between 1.6 and 4.1 for 2 mg/liter at the 10⁶ inoculum and for 2, 4, and 8 mg/liter colistin in broth at the 10⁸-CFU/ml inoculum. The log₁₀ CFU/ml was 2.75 for 16 mg/liter colistin at the 10⁸-CFU/ml inoculum. All other plates with 8 or 16 mg/liter colistin showed no viable growth.

FIG. 4.

Pharmacodynamic relationship between colistin concentration/MIC and the log ratio area [log₁₀ (area under the CFU curve from 0 to 24 h for colistin/area under the CFU curve from 0 to 24 h for growth control)] at each initial inoculum for three P. aeruginosa strains (all r² values ranged between 0.978 and 0.999): PAO1 (A), URMC1 (B), and URMC2 (C).

FIG. 5.

Observed versus predicted bacterial counts on log₁₀ scale for P. aeruginosa PAO1 (based on results from NONMEM). (A) Observed versus individual fitted CFU/ml. (B) Observations versus population predictions when all data were used for estimation. (C) Observations versus population predictions from the internal cross-validation. Importantly, none of the observations at the respective inocula were used during cross-validation when data at this inoculum were predicted. A log₁₀ value of observed colony counts plotted as zero means no colony was on the plate.

FIG. 6.

Fitted and observed bacterial counts versus time for one-compartment in vitro model data from the work of Gunderson et al. (32) (A) (lower limit of detection: log₁₀ CFU/ml of 2.48; observations below this reported lower limit are plotted as 0 log₁₀ [CFU/ml]) and time-kill data from Li et al. (42) (B) (plates with zero colonies are plotted as zero).

FIG. 7.

Observed and individual fitted viable counts of P. aeruginosa PAO1 for various concentrations of Ca²⁺, Mg²⁺, or EDTA added to LB broth: 2.0 mM EDTA (A), no cations and no EDTA added (B), 10 mg/liter Ca²⁺ and 5 mg/liter Mg²⁺ (C), 20 mg/liter Ca²⁺ and 10 mg/liter Mg²⁺ (D), or 80 mg/liter Ca²⁺ and 40 mg/liter Mg²⁺ (E). Observed viable counts of zero mean no colony on the plate (using a volume of 200 μl plated manually for samples with low viable counts).