Determining optimum carvacrol treatment as a cardinal value of a secondary model

Abstract

Predictive microbiology methods were used to study the effect of carvacrol on the bacterial resistance to antimicrobials. Our objective was to estimate the optimum dose of carvacrol at concentrations below its MIC value (Minimum Inhibitory Concentration). As a fluorescent marker, ethidium bromide (EtBr) was applied to Escherichia coli to acquire raw data. The accumulation of EtBr was measured by its fluorescence signal (Fs), in the unit of RFU (Relative Fluorescence Unit). The temporal change of the fluorescence values, at a constant concentration of carvacrol, was described by a saturation curve (primary model). The difference, within the observation interval, between the fitted initial and maximum fluorescent values was chosen as the primary parameter to be fitted in the secondary model: a convex, asymmetric, bi-linear function of the carvacrol concentration changing between 0 and 0.5 MIC. Its breakpoint is the optimum value of the carvacrol, a cardinal parameter of the secondary model, where the chosen primary parameter assumes its highest value. This optimum was estimated with high uncertainty for individual experiments, but F-test showed that, with appropriate experimental and numerical procedure, its existence and value can be claimed with confidence. Our results demonstrate that the estimation of the optimum of the secondary model can be robust even if the full secondary model is uncertain.