Pharmacodynamic functions: a multiparameter approach to the design of antibiotic treatment regimens.

There is a complex quantitative relationship between the concentrations of antibiotics and the growth and death rates of bacteria. Despite this complexity, in most cases only a single pharmacodynamic parameter, the MIC of the drug, is employed for the rational development of antibiotic treatment regimens. In this report, we use a mathematical model based on a Hill function-which we call the pharmacodynamic function and which is related to previously published E(max) models-to describe the relationship between the bacterial net growth rates and the concentrations of antibiotics of five different classes: ampicillin, ciprofloxacin, tetracycline, streptomycin, and rifampin. Using Escherichia coli O18:K1:H7, we illustrate how precise estimates of the four parameters of the pharmacodynamic function can be obtained from in vitro time-kill data. We show that, in addition to their respective MICs, these antibiotics differ in the values of the other pharmacodynamic parameters. Using a computer simulation of antibiotic treatment in vivo, we demonstrate that, as a consequence of differences in pharmacodynamic parameters, such as the steepness of the Hill function and the minimum bacterial net growth rate attained at high antibiotic concentrations, there can be profound differences in the microbiological efficacy of antibiotics with identical MICs. We discuss the clinical implications and limitations of these results.

Fitness evolution and the rise of mutator alleles in experimental Escherichia coli populations.

We studied the evolution of high mutation rates and the evolution of fitness in three experimental populations of Escherichia coli adapting to a glucose-limited environment. We identified the mutations responsible for the high mutation rates and show that their rate of substitution in all three populations was too rapid to be accounted for simply by genetic drift. In two of the populations, large gains in fitness relative to the ancestor occurred as the mutator alleles rose to fixation, strongly supporting the conclusion that mutator alleles fixed by hitchhiking with beneficial mutations at other loci. In one population, no significant gain in fitness relative to the ancestor occurred in the population as a whole while the mutator allele rose to fixation, but a substantial and significant gain in fitness occurred in the mutator subpopulation as the mutator neared fixation. The spread of the mutator allele from rarity to fixation took >1000 generations in each population. We show that simultaneous adaptive gains in both the mutator and wild-type subpopulations (clonal interference) retarded the mutator fixation in at least one of the populations. We found little evidence that the evolution of high mutation rates accelerated adaptation in these populations.