A model for the efficacy of combined inhibitors

Aims: The method of the sum of the fractional inhibitory concentrations (SigmaFIC) is used ubiquitously in the investigation of antimicrobial combinations. The inherent assumption of this simple equation is that in a mixture all antimicrobials have identical dose responses. The aim of this work was to analyse the outcome of removing this assumption. Methods and Results: A model to describe the efficacy of combined inhibitors was produced which removed the assumption of identical dose responses. The results of several checkerboard experiments showed that the new model, termed the fa(comb) was a more general form of the SigmaFIC method, but the features described by the SigmaFIC as either synergy or antagonism could be attributed to differences in the dose responses of antimicrobials in combination. Where the model failed to adequately describe experimental data it was suggested that these might be cases of true antagonism or synergy. Conclusions: The SigmaFIC methodology used to describe the effect of antimicrobial combinations ( preservatives and antibiotics) is valid only when it is demonstrated that individual components of the mixture have identical dose responses. Otherwise the SigmaFIC method is invalid. Descriptions of antimicrobial synergy may simply be due to the mixing of antimicrobials with differing dose responses. Significance and Impact of the Study: Studies aimed at producing synergistic mixtures of antimicrobials, which ignore the dose response of the individual antimicrobials, may waste valuable research effort looking for a physiological explanation for an apparent synergy, where none, in-fact, exists. Conversely, mixing antimicrobials with very different dose responses might lead to mixtures with an 'apparent' synergy which may themselves be very useful therapeutically.