We developed two novel pharmacodynamic models that assign mechanisms of action to fluoroquinolone antimicrobial agents (growth inhibition or death stimulation) and compared the abilities of these models and two other maximum effect models—our previously described net effect model (5
) and the MIC-based model reported by Meagher and colleagues (18
)—to describe and predict the changes in bacterial population dynamics during in vitro system experiments where S. aureus
was exposed to a series of simulated ciprofloxacin pharmacokinetic profiles (4
All four models described the growth of ciprofloxacin-susceptible and -resistant bacteria observed in the absence of ciprofloxacin, the killing of susceptible subpopulations, and, in some cases, selection and growth of resistant subpopulations in the presence of ciprofloxacin during the in vitro system experiments. Overall, the growth inhibition and net effect models afforded the best combination of a good fit with minimal bias, high precision of parameter estimates, and good predictive performance. The correlation between model-predicted and observed viable counts for the growth inhibition and net effect models was strong and the residuals were small, with the observed counts randomly scattered about the model-predicted curves in most cases. Parameter estimates for the growth inhibition and net effect models were also the most precise among the four models evaluated. The goodness-of-fit as assessed by the AICc was best for the growth inhibition and net effect models, with the growth inhibition model having the lowest AICc. Although the correlation between model-predicted and observed viable counts was also high for the death stimulation and MIC-based models, these models exhibited more bias and had higher AICc values, and the resulting parameter estimates were less precise. Furthermore, several of the parameters for the all-important resistant subpopulations were highly correlated, making these models less desirable than the growth inhibition and net effect models. Estimates of the parameter R0 were the least precise for all four models. It was set as a parameter to be estimated by the models because of an inability to precisely quantify the small numbers of resistant bacteria that spontaneously appeared in the inocula used in these experiments. The large difference in sizes of the susceptible (~107 CFU/ml) and resistant (<102 CFU/ml) subpopulations made it more difficult for the least-square minimization algorithm to arrive at a precise solution for this parameter.
When the performances of the models were examined, all except the death stimulation model correctly predicted that resistant bacteria would not emerge in the high- and low-inoculum scenarios. The death stimulation model predicted selection of resistant subpopulations of MRSA 8282 upon challenge with one of the experimental dosing regimens (Fig. ). This may have been due to the high estimate of R0 for MRSA 8282 predicted by the death stimulation model compared to that predicted by the other models that were evaluated. It may also have been the result of the larger variation of parameter estimates for the death stimulation model, perhaps because of the increased number of parameters in the model (10 instead of 8 as in the other three models).
The MIC-based model did not describe the data as well as the other models examined, perhaps because it differed in several potentially important respects. First, it did not assign unique values for the growth (VGmax
) or death (Kd
) rates of ciprofloxacin-susceptible and -resistant subpopulations as did the other models. We found in our earlier work that the net growth and fluoroquinolone killing rates of the grlA
mutant derivatives (MRSA 8043C0-1 and MRSA 8282C0-1) were slower than those of the wild-type parent strains (MRSA 8043 and MRSA 8282) (3
). Second, the term used in the MIC-based model to describe bounded growth in the in vitro system did not slow bacterial growth until the total population size exceeded VGmax
. Based on our parameter estimates for the MIC-based model and the observed maximum bacterial densities in our in vitro system experiments, the growth rate of the bacteria will not approach zero when this growth-limiting factor is used. We found in our previous work that the net growth rates of the wild-type and grlA
mutant strains started to slow as the bacterial population approached within 1 log10
of the carrying capacity of the in vitro system and that this process was adequately described using a logistic growth expression (3
). Third, the MIC-based model relates pharmacokinetics to a discrete measure of antimicrobial effect, the MIC, which does not describe the concentration- and time-dependent effects of the antimicrobial agent. Instead, the MIC represents the net effect of an antimicrobial agent at a fixed concentration over a defined incubation period. This differs from exposure to an antimicrobial in the in vitro system or in humans, where drug concentrations and the patterns of bacterial growth and killing change with time. The MIC is also not equivalent to the concentration predicted by the pharmacodynamic models to produce no net growth or killing of bacteria. This concentration, termed the Z
MIC, or stationary concentration, has been described for other net effect pharmacodynamic models (1
). Others have shown that the correlation between MIC and stationary concentration varies with the antimicrobial tested, making the MIC a poor pharmacodynamic parameter for characterization of the concentration-effect relationship of an antimicrobial agent (19
It is not clear whether the growth inhibition or death stimulation model most accurately characterizes what actually occurs when bacteria are exposed to ciprofloxacin. It is known that quinolones target DNA gyrase and topoisomerase IV in bacteria (13
). DNA gyrase relieves topological stress ahead of the replication fork by maintaining negative supercoiling, and topoisomerase IV unlinks newly replicated DNA, allowing proper chromosome and plasmid segregation (16
). Both enzymes create transient double-stranded breaks in the helix, catalyze passage of DNA strands through each other, and religate the break. Quinolones bind to single-stranded DNA within the topoisomerase-DNA complex and stop DNA synthesis by stabilizing a reversible intermediate, the cleavable complex, in which the topoisomerase is covalently bound to DNA. The ternary complex blocks passage of RNA polymerase, thereby terminating transcription (25
). In this context, quinolone activity could be described by a pharmacodynamic model in which the agent inhibits cell division. If quinolones completely inhibit bacterial cell division, it would follow that the common maximal bacterial killing rates observed in our experiments with S. aureus
and four quinolones merely represented the natural death rate of the cells that would occur without exposure to the antimicrobials (see Appendix). The ternary complex may also present a physical barrier to the replication fork. Collision of the replication fork with the ternary complex may result in formation of a nonreversible DNA lesion and ultimately the release of cytotoxic free ends of DNA (13
). In this context, quinolone activity could be described by a death stimulation model in which the antimicrobial stimulates a natural death process. If this is the case, it would follow that the common maximal bacterial killing rates observed were due not only to similar natural death rates but also to similar cell division rates and maximal stimulatory effects among all of the quinolones (see Appendix).
The interactions between antimicrobial agents and bacteria are often very complex, and it is unlikely that modeling alone can distinguish among plausible mechanisms of action. This is due, in part, to the nature of the data used for modeling, which are often limited to pharmacokinetics and an effect measure, such as viable bacterial counts. An additional complication is the often greater number of parameters required for mechanistic models than for their empirical (descriptive) counterparts. Moreover, it is possible that many mechanistic models, including ours, are interrelated and not completely unique. Additional knowledge about the mechanism of action of quinolones will help to identify a model with the most biological relevance. However, the ultimate value of any of these models will be determined by evaluating their predictions under varied experimental conditions which directly test whether quinolone antimicrobial agents inhibit cell division or stimulate cell death. At present, however, it is difficult if not impossible to discern experimentally whether the observed antibacterial effect of quinolones is due to inhibition of cell division or stimulation of a natural cell death process. Rigorously validated models that accurately characterize the mechanisms of action of antimicrobials may ultimately prove valuable for optimizing dosing of old and newly introduced agents to prevent the emergence of resistance.