Quantification of hurdles: Predicting the combination of effects — Interaction vs. non-interaction

Combination of disparate as well as related antimicrobial effects constitutes the concept of hurdle technology. Quantification of combined effects, including claims of synergy, can be accomplished using surface response modelling, as is frequently done and reported. The Gamma hypothesis, however, states that the relative effects of different antimicrobial factors combine independently. Studies performed using time to detection have shown that the Gamma hypothesis is an adequate foundation for the analysis of multi-factor environmental stresses placed on microorganisms, including pH, weak acids and temperature. Data from the combined action of Na acetate and pH on Aeromonas hydrophila, Na acetate/pH , K sorbate/pH and combined Na acetate/K sorbate at pH 6.5, 6.0 and 5.5 on Escherichia coli and the combined action of Na acetate/pH and temperature on Enterobacter sakazakii were examined using nominal logistic modelling, response surface modelling (RS) and by using a Gamma model. The Gamma model can be used in a predictive manner unlike the RS models and the parameters of the RS models can be approximated from the fit of the Gamma model to the observed data. The expansion of the Gamma model explains the occurrence of the statistically significant cross terms of the RS polynomials. The emphasis within the literature of seeking interactions or synergies between environmental factors should be replaced with one emphasising the falsification of the Gamma approach. This can be done by examining the relative ratios of the gamma factors when in combination, but this also requires the use of appropriate functions to do this.