Mathematical modelling of bacterial growth at subinhibitory levels of aminoglycosides

Abstract

The subinhibitory effect of antibiotics has often been studied without any clear theoretical framework; we have chosen to use mathematical bacterial growth modelling as a useful tool to analyse these biological states in a more rigorous manner. Since their mode of action and molecular target are relatively well known, aminoglycosides were well suited for this more sophisticated study of subinhibitory action. We have shown that two models (the Monod and the logistic models) regularly used in bacteriology, were adequate to describe these effects in a glucose-limited medium.

A change of model, according to antibiotic concentration, revealed the existence of two separate actions. At lower concentrations, inhibition affected mainly glucose use, the substrate remained limiting and growth mode did not change. As soon as the concentration exceeded a threshold, growth was totally disturbed, probably through a physiological ⪡catastrophe⪢. This threshold can be used to estimate bacterial susceptibility to these antibiotics.