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Emerging Infections and Host Defense Theme, Ordway Research Institute, Albany, New York
San Diego Super Computer Center, University of California San Diego, La Jolla
The emergence of resistance to antibiotics is a serious problem often related to suboptimal drug dosing; such suboptimal dosing results in the preferential killing of drug-susceptible microbial subpopulations, allowing amplification of drug-resistant microbial subpopulations. We determined the effect that fluctuating concentrations of quinolone drugs have on both the total population and the resistant subpopulation of Pseudomonas aeruginosa, by employing, over a 48-h period, human pharmacokinetics and multiple regimens in an in vitroinfection model. All data were simultaneously modeled by use of 3 parallel inhomogeneous differential equations. Model parameters were used to derive the minimal, or breakpoint, drug exposure necessary to suppress amplification of the resistant subpopulation. In a prospective-validation study, we found that a drug exposure near to but below the calculated breakpoint amplified the resistant subpopulation, whereas a drug exposure at the breakpoint suppressed it. This approach allows delineation of target drug exposures (area under the concentration/time curve for 24 h : minimal inhibitory concentration [AUC24 : MIC] = 190) that will suppress amplification of the antibiotic-resistant subpopulation, thereby preserving the susceptibility of target pathogens.
Resistance of bacteria to many antimicrobial agents in the physicians' armamentarium is increasing at an alarming rate [1, 2]. Because the discovery of new antimicrobial agents is a process requiring a substantial period, it is important to preserve the utility of currently available agents and to develop strategies to preserve the activity of agents with new targets, once the latter have been developed; efforts should be focused on the judicious and optimal use of these agents [3]. Little attention has been focused on delineating the correct drug dose to suppress the amplification of less-susceptible mutant bacterial subpopulations.
In a large bacterial population, subpopulations with differing susceptibilities to the administered antimicrobial agent coexist. Under antimicrobial pressure, subpopulations with reduced susceptibilities to antimicrobial agents have a survival advantage, proliferating preferentially. Although initially the total population decreases, the antimicrobial agent's inability to eradicate the resistant subpopulations permits the latter to increase relative to the susceptible subpopulations, and regrowth is observed; such amplification of resistant subpopulations may be overcome with appropriate drug exposure. To study the change in the size of susceptible and resistant subpopulations under incremental drug-selective pressures, we used an in vitroinfection model to delineate the relationship between various exposures to a quinolonegarenoxacinand the growth kinetics of both the total population and the resistant subpopulations of Pseudomonas aeruginosa.
MATERIALS AND METHODS
Antimicrobial agent.
Garenoxacin powder (lot 807T-3(A)) was supplied by Bristol-Myers Squibb Pharmaceuticals. A stock solution of garenoxacin at a concentration of 1 mg/mL of sterile water was prepared, aliquoted, and stored at -20°C. Before each experiment, an aliquot of the drug was thawed and diluted to the desired concentrations, with cation-adjusted Mueller-Hinton II broth (ca-MHB) (Difco).
Protein-binding studies.
The extent to which garenoxacin binds to human serum protein was determined by use of an ultrafiltration method. In brief, garenoxacin was added to 100% human serum, to final concentrations of 0.2, 0.5, 1, 2, 5, 10, 15, and 20 g/mL; an aliquot was taken from each sample, the remainder of the sample was ultrafiltered by use of a Centricon 30 Amicon ultrafiltration device, and the ultrafiltrate was collected. The garenoxacin concentration in the preultrafiltrated aliquots and in the ultrafiltrates was measured by use of a validated high-performance liquid chromatography (HPLC) method, as detailed below. The percentage of garenoxacin bound to serum proteins was calculated as follows: (drug concentration in serum minus drug concentration in ultrafiltrate)/(drug concentration in serum).
Microorganism.
P. aeruginosa ATCC 27853 (American Type Culture Collection) was used in the study. The bacterium was stored at -70°C in skim milk. For each experiment, fresh isolates were grown on blood-agar plates (BBL Microbiology Systems) at 35°C for 24 h.
Susceptibility studies.
Studies of the ratio of garenoxacin's minimum inhibitory concentration (MIC) to its minimum bactericidal concentration (MBC)its MIC : MBC ratiowere conducted in Ca-MHB, by a macrobroth-dilution method described by the NCCLS [4]. The bacterial concentration in each macrobroth-dilution tube was 5 × 105 cfu/mL of either Ca-MHB or human serum (90%). Initially, serial 2-fold dilutions of drugs were used, followed by arithmetic dilutions of the drug, to more precisely determine susceptibility. The MIC was defined as the lowest concentration that resulted in no visible growth after incubation in ambient air at 35°C for 24 h. Samples (50 L) both from clear tubes and from the cloudy tube with the highest drug concentration were inoculated on tryptic soy-agar plates. The MBC was defined as the lowest drug concentration that resulted in 99.9% killing of the initial inoculum. The studies were conducted in duplicate and were repeated once on a separate day.
HPLC assay.
In brief, after the samples were spiked with trovafloxacin as an internal standard, they were extracted, by use of Waters Oasis HLB cartridges, by serial washings with methanol at various pH values and then were eluted with acetonitrile. The HPLC system that was used was a HP1100 with 1046A fluorescence detector and Supelco Hypersil BDS C18 column; 30 mmol sodium citrate/L, at pH 3.5 and 25% acetonitrile, were used in the mobile phase. Excitation was performed at 275 nm, and emission was performed at 425 nm. The lower limit of quantitation was 0.02 mg/L. The between-day coefficient of variation for the assay was 10.3% at 0.2 mg/L and 9.5% at 2.0 mg/L. The results of the assay were linear up to 5.0 mg/L.
Hollow-fiber infection model.
The hollow-fiber bioreactor system (HFS) was described first, by Blaser et al. [5], for use as a pharmacodynamic system for bacteria, and subsequently, by Bilello et al. [6], for HIV pharmacodynamic studies. Both a schematic diagram of the system and a description of its use have been presented in our study of Mycobacterium tuberculosis [7]. In the present study, garenoxacin was injected once daily, over a 1-h period, directly into the central reservoir, to achieve the peak concentration desired at 1 and 25 h (and, in the case of the validation experiment, at 49 h).
Dose-response studies.
The inoculum was prepared by growing 3 medium-sized colonies of P. aeruginosa in Ca-MHB at 35°C overnight. Hollow-fiber systems were maintained in a humidified incubator at 35°C. Samples (9 mL) of bacterial culture in late log-phase growth (2.4 × 108 cfu/mL) were infused into each of 6 cartridges, 1 for each nominal drug exposure (calculated as the area under the concentration/time curve for 24 h [AUC24 ] : MIC)0, 10, 50, 75, 100, and 200. These exposures were used to simulate steady-state pharmacokinetics, in humans, of unbound garenoxacin given once every 24 h (terminal half-life, 12.8 h; clearance, 6 L/h) [8]. The garenoxacin exposures in the experiments were determined on the basis of the drug's concentration, by use of a validated HPLC method (described above), in samples taken from the central bioreactor loop, at 1, 6, 12, 24, 25, 35, and 48 h. Preliminary studies had demonstrated that, for this drug, the central and peripheral compartments came to equilibrium in <20 min (data not shown). At 0, 3, 6, 11, 23, 35, and 48 h, samples of the bacterial cultures were obtained from the cartridges, were washed, and were resuspended in normal saline, to minimize the drug-carryover effect, and serial 10-fold dilutions were performed. The serially diluted samples were quantitatively cultured onto drug-free ca-MH agar plates, to quantify the total bacterial population; the resistant subpopulations were quantified by culturing the samples on medium-treated plates supplemented with a garenoxacin concentration at 3 times the MIC for the wild-type bacterial isolate. Because drug-susceptibility testing was performed in 2-fold dilutions and because a 1-tube difference is accepted as a reasonable interday variation, quantitative culturing on garenoxacin-supplemented (at 3 × MIC) medium-treated plates would allow reliable detection of subpopulations that have a reduced susceptibility to this drug. Medium-treated plates were incubated at 35°C for up to either 24 h (for the total population) or 72 h (for the resistant subpopulations) before readings were taken. The MICs for the resistant subpopulations at the end of the experiment were determined, to confirm the emergence of resistance.
To ascertain the mechanism of resistance, the quinolone-resistancedetermining regions (QRDRs) of either topoisomerase II (gyrA/B) or topoisomerase IV (parC/E) were amplified by polymerase chain reaction and then were sequenced, as described elsewhere [9, 10]. In addition, the susceptibility studies of the resistant isolates recovered were also performed in the presence of an efflux-pump blocker, Phe-Arg -naphthyl-amide dihydrochloride (MC-207,110; Sigma-Aldrich), as described elsewhere [11]; the present study used this blocker at a concentration that was twice that described in the original study.
Modeling.
Details of the modeling used are provided in the Appendix.
Prospective-validation study.
An experiment was performed to validate the findings of the mathematical model and to demonstrate that exposures close to but on different sides of the minimal, or breakpoint, exposure behaved differently. The bacterial inoculum was prepared as described above. Three hollow-fiber cartridges were inoculated with 9 mL of 2 × 108 cfu of bacteria/mL in late log-phase growth. The duration of the experiment was extended from 48 to 72 h, so that the future was being predicted. Nominal AUC24 : MIC values simulated were 0, 140, and 200, corresponding to the control experiment, and exposures on different sides of the calculated breakpoint exposure value derived from the mathematical analysis. At 0, 6, 11, 23, 30, 35, 48, 50, 52, 54, 59, and 72 h, samples were obtained from the hollow-fiber cartridges. The bacterial samples were processed, and both the total bacterial population and the resistant subpopulations were quantified as described above.
RESULTS
Protein binding.
The mean ± SD percentage of the binding of garenoxacin to human serum was found to be 90.2% ± 0.38%, over a concentration range of 0.220 mg/L.
Susceptibility studies.
In ca-MHB, garenoxacin's MIC : MBC with respect to P. aeruginosa was 3 : 6 mg/L.
Modeling.
A reasonable fit between the model and the data was obtained. After the Bayesian step, the r2, over time, for the observed versus the predicted garenoxacin concentration was 0.973; for the total bacterial population and the garenoxacin-resistant subpopulation, the r2 values were 0.945 and 0.800, respectively (figure 2). The final estimate of the maximum-growth-rate constant for the susceptible subpopulation was not dramatically different from that for the resistant subpopulation (0.745/h vs. 0.614/h); likewise, the maximum kill rate for the susceptible subpopulation was similar to that for the resistant subpopulation (27.85/h vs. 31.72/h); however, the garenoxacin concentration necessary to achieve a 50% maximum kill rate was 6 times higher in the resistant subpopulation compared with the susceptible subpopulation (107 mg/L vs. 17 mg/L).
Bayesian parameter estimates were incorporated into the subroutines of ADAPT II [12]. Bacterial responses to various drug exposures were calculated; the regrowth phenomenon often observed in both in vitro and animal-infection models can often be explained on the basis of disparate effects in the different bacterial subpopulations. In these simulations, the breakpoint AUC24 : MIC that, at 72 h, is necessary to suppress the preferential growth of the resistant subpopulation and to sustain the killing of the total population was estimated to be 190.
DISCUSSION
Emergence of resistance is a pressing issue; it is imperative that we preserve the utility of currently available agents, by judicious and optimal use of them. Resistance becomes a problem when there is transfer of DNA (e.g., acquisition of a plasmid/transposon, creation of mosaic chromosomes in S. pneumoniae); and, once it occurs, it is spread by horizontal transmission, among other mechanisms. However, a major mechanism of resistance is amplification of preexistent mutants already present in a large bacterial population, an example being the amplification of target-site mutants or efflux-pumpoverexpressed strains when fluoroquinolones are used.
A question arises as to whether this mechanism might have importance in the clinical arena. Chow et al., in a study of patients with Enterobacter bacteremia [13], found that resistance emerged during therapy in patients who started therapy with a susceptible isolate; the rate at which such resistance occurred was 19% and was associated mainly with therapy with third-generation cephalosporin. It is likely that this result was due to amplification of a small, stably derepressed mutant bacterial population present at the start of therapy. When drug therapy is evaluated, resistant bacterial subpopulations, in addition to the total bacterial population, should be considered.
Indeed, a number of laboratories have begun to study the issue of resistance suppression by dosing. Drlica and colleagues [14, 15] have identified the idea of an in vitro test that they have termed the "mutant prevention concentration." This simple but elegant idea allows identification of a drug concentration that prevents the amplification of preexistent mutant bacterial populations. Although this idea is powerful, its limitation is that the drug concentration is static and bears little relation to the concentration/time curve seen in humans. Drlica and colleagues have also extended this idea to the realm of the change in concentration of antimicrobial agents, as is seen in humans, through use of the mutation-prevention window. Prospective validations are required for evaluation of this innovative yet simple technique. Also, MacGowan et al. [16] have examined P. aeruginosa and the ability of moxifloxacin exposure to suppress resistance in vitro in a pharmacodynamic model; they were unable to identify an exposure that would suppress the mutant bacterial population over time, even at a final AUC : MIC ratio of >400.
Our laboratory [10] has previously examined this issue in a mouse-thigh model of P. aeruginosa infection, in which the animals were granulocyte competent; in that study, the fluoroquinolone levofloxacin was employed, and, in a prospective-validation procedure, a total-drug AUC : MIC ratio of 157 (free-drug AUC : MIC ratio, 110) was found to suppress the resistant mutant P. aeruginosa subpopulation. In the present study, we sought to extend these investigations to our in vitro pharmacodynamic model, to see whether the exposures that, in the immune-competent mouse, suppressed resistant subpopulations of P. aeruginosa would perform similarly in a system in which there is no immune function.
When all of the available data (i.e., drug concentrations, total bacterial-population size, and resistant bacterial-population size) from the initial 48-h study were comodeled simultaneously, the AUC : MIC ratio necessary for suppression of the bacterial population was found to be 190. To prospectively test this hypothesis, we performed a subsequent study for 72 h (so that the future was being predicted), with regimens resulting in AUC : MIC ratios of 140 and 200, which were calculated to amplify and suppress, respectively, the resistant subpopulations; the AUC : MIC ratios actually achieved were 137 and 200. By 36 h, the AUC : MIC ratio of 137which, although substantial, is inadequate for suppression of resistancehad mediated an 5.5-log10 (cfu/mL) decrease in total population burden; however, at that time, virtually all the remaining organisms were resistant. During the next 36 h, the colony counts returned almost to baseline levels, with the resistant subpopulation supplanting the susceptible subpopulation. The regimen calculated to suppress resistance did, indeed, perform as predictedand did so for a period longer than the original period of observation for the model building. This prospective validation demonstrates that this model system can accurately predict the disparate effects that a drug regimen has on both the susceptible subpopulation and the resistant subpopulation. The correctness of the predictionswith the use of exposures that, although not greatly different, are on both sides of the identified resistance-suppression exposureserves to validate both the microbiology and the mathematical modeling.
In the present study, an AUC : MIC ratio of 190 was the breakpoint drug exposure necessary to suppress amplification of the resistant mutant subpopulation. Using a non-neutropenic mouse-thighinfection model with a different fluoroquinolone (levofloxacin), our laboratory found that a total-drug AUC : MIC ratio of 157 was necessary to suppress emergence of resistance in the same strain of P. aeruginosa [10]. In the mouse, levofloxacin is 30% protein bound, making the free-drugtarget AUC : MIC ratio 110. Also using a mouse-thighinfection model, Andes and Craig have demonstrated that, when a fluoroquinolone is used, neutropenia increases the AUC : MIC ratio by 1.52.0 fold [17]; the free-drug target in the present study was 190, which is 1.73 times the free-drug target identified in our granulocyte-competent mouse model [10] and is therefore consistent with the results of the present study.
The results of the present study also underscore the central role that efflux pumps play in the emergence of resistance. During the first 48 h of amplification of the resistant bacterial subpopulation, none of the resistant clones had target-site mutations, and all responded with a 16-fold reduction in MIC when an efflux-pump inhibitor was added. We have seen this behavior previously in an in vitromodel evaluation of the fluoroquinolone moxifloxacin used as therapy for infection by Mycobacterium tuberculosis [7], as well as in our animal model using the fluoroquinolone levofloxacin as therapy for infection by P. aeruginosa [10]. In both models, evaluations at early time points in the study demonstrated that drug-resistant organisms had no mutations in any of the QRDRs; and, in the case of the animal model, we were able to demonstrate, as we have demonstrated in the present study, that drug resistance was due to efflux-pump overexpression. It is likely that early expression of efflux pumps will allow some escape from drug pressure and may provide the organisms with enough rounds of replication under error-prone replication (at least in the case of quinolones) to later obtain a target-site mutation.
Our data strongly suggest that suboptimal drug exposures are detrimental to efforts aimed at preventing the emergence of drug resistance. This finding gains added importance when one realizes that another major issue in drug resistance is the horizontal spread of resistant bacteria. If we can suppress amplification of the resistant bacterial subpopulation, there will be fewer resistant clones to spread horizontally. In the search for new agents to combat multidrug-resistant pathogens, the application of these techniques could enhance the efficiency of the drug-development process and optimize resources by focusing on doses with both a high probability of clinical success and the ability to suppress amplification of resistant clones.
The ability to identify a target-drug exposure that suppresses amplification of drug-resistant clones can be readily translated, through the use of Monte Carlo simulation, into a clinical dose that will achieve this end, as our laboratory has demonstrated in previous studies [18, 19]. Given the proposed clinical dose of garenoxacin (600 mg), the drug-clearance rate (6 L/h), the 90% protein binding (all of which will produce a free-drug AUC of 10.0), and the MIC distribution [20], we are highly likely to find that, when the necessity to achieve a free-drug AUC : MIC ratio of 190 is taken into account, this agent will be able to suppress drug resistance in few cases of P. aeruginosa infection in which the bacterial burden is large (e.g., in the case of nosocomial pneumonia).
In conclusion, this model can be used to predict how both the total bacterial population and the resistant subpopulation will respond to various dosing regimens of quinolones; and it can also be applied to optimize the use of other antimicrobial agents either currently available or under development. Our results suggest that pharmacodynamic-targetoriented dosing regimens may be beneficial in suppressing (or delaying) the emergence of resistance and should be investigated in clinical trials.
APPENDIX
Differential-Equations Model System
To mathematically determine the minimal, or breakpoint, drug exposure necessary to suppress the emergence of resistance, 3 simultaneous, parallel, inhomogeneous differential equations were used to describe the time course of garenoxacin concentrations over time, the total bacterial population, and the resistant subpopulation (see below).
Equation (1) describes the rate of change in garenoxacin concentration over time; equation (2) describes the rate of change in the susceptible bacterial subpopulation over time; equation (3) describes the rate of change in the resistant bacterial subpopulation over time; equation (4) is a logistic carrying function that limits the total bacterial population to a maximum number; and equation (5) is a sigmoid Emax effect function that relates drug concentration to the fraction of the maximum kill rate achieved for both the susceptible subpopulation and the resistant subpopulation.
EC50, drug concentration necessary to achieve 50% of maximum kill rate
H, sigmoidicity constant
K, maximum-growth-rate constant of resistant bacterial subpopulation
K, maximum-growth-rate constant of susceptible bacterial subpopulation
K, maximum-kill-rate constant of resistant bacterial subpopulation
K, maximum-kill-rate constant of susceptible bacterial subpopulation
M, sigmoid Emax effect function, linking garenoxacin concentration to the fraction of the maximum kill rate achieved (which, in equation [2], includes both the EC50 and the H for the susceptible bacterial subpopulation and, in equation [3], includes both the EC50 and the H for the resistant bacterial subpopulation)
NR, size of resistant bacterial subpopulation
NS, size of susceptible bacterial subpopulation
POPmax, maximum total bacterial population
R(1), time-delimited drug-infusion rate
SCL, clearance
Vc, volume of distribution
X1, amount of garenoxacin in central compartment
, garenoxacin concentration in central compartment
All data were simultaneously comodeled in a population analysis employing the Non-Parametric Adaptive Grid (NPAG) program to estimate the model parameters [21]. The parameter estimates from the overall-best-fit model were employed as prior estimates, and Bayesian parameter estimates were obtained for each regimen, by use of the "population of one" utility in NPAG. The susceptible and resistant bacterial subpopulations' biologic responses under increasing drug exposures were calculated.
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