A mathematical description of short-term effects of β-lactam antibiotics on bacterial growth in vitro

Abstract

Bacterial growth at moderately high concentrations of β-lactam antibiotics and within the first few hours of exposure cannot be described by a simple exponential equation. The quadratic function InN t=InN 0+k0t−1/2at2, in whichk 0 is the initial growth rate constant anda a rate inhibition constant, is a better approximation. Whena is used as a single parameter, the effect of a particular antibiotic can be described as a concentration-effect relation. This approach also permits comparison of antibiotics, e.g., nafcillin and cloxacillin. The relation betweenk 0 anda in the interaction between nafcillin and chloramphenicol shows that chloramphenicol antagonizes the effect of nafcillin.