Comparing Nonsynergistic Gamma Models with Interaction Models To Predict Growth of Emetic Bacillus cereus when Using Combinations of pH and Individual Undissociated Acids as Growth-Limiting Factors

A combination of multiple hurdles to limit microbial growth is frequently applied in foods to achieve an overall level of protection. Quantification of hurdle technology aims at identifying synergistic or multiplicative effects and is still being developed. The gamma hypothesis states that inhibitory environmental factors aiming at limiting microbial growth rates combine in a multiplicative manner rather than synergistically. Its validity was tested here with respect to the use of pH and various concentrations of undissociated acids, i.e., acetic, lactic, propionic, and formic acids, to control growth of Bacillus cereus in brain heart infusion broth. The key growth parameter considered was the maximum specific growth rate, μ_max, as observed by determination of optical density. A variety of models from the literature describing the effects of various pH values and undissociated acid concentrations on μ_max were fitted to experimental data sets and compared based on a predefined set of selection criteria, and the best models were selected. The cardinal model developed by Rosso (for pH dependency) and the model developed by Luong (for undissociated acid) were found to provide the best fit and were combined in a gamma model with good predictive performance. The introduction of synergy factors into the models was not able to improve the quality of the prediction. On the contrary, inclusion of synergy factors led to an overestimation of the growth boundary, with the inherent possibility of leading to underestimation of the risk under the conditions tested in this research.Consumers expect safe and sufficiently stable food within the given shelf life of a food product or component. Several growth-limiting factors, collectively referred to as hurdles, can be used to ensure food stability and safety. Examples of such hurdles are low pH, low water activity, or low temperature (12). Combining hurdles to achieve food stability and safety, known as hurdle technology, can be used to achieve an overall level of protection in food while minimizing impacts on food quality (20). When a combination of hurdles is used, generally the intensity of the hurdles may be lower, to exert a comparable preservative effect, than the intensity of those hurdles when used individually (20). Three classes of interaction can be defined when applying hurdle technology: “no interaction,” in which the effect of a combination is as expected from the response of the separate factors; “synergy,” in which the effect is greater than expected; and “antagonism,” in which the effect is less than expected (6).Though the concept of hurdle technology is rather well established, the quantification of the combined impact of hurdles on growth of microorganisms is still being developed. One significant problem is that there are two opposite views of how antimicrobial factors combine. One view states that there are interactive effects between hurdles; when they are applied together, they give a protection significantly greater than that expected on the basis of the application of the individual hurdles (synergy). The alternative view considers that the combined effect may be complex but that there are no interactive effects culminating in synergy. The latter view is called the gamma hypothesis (41) and states that inhibitory environmental factors combine in a multiplicative manner to produce the observed overall microbial inhibition. A major benefit of models based on the gamma hypothesis is a reduction in experimental work, since growth rates and, as a result, growth boundaries can be estimated upon evaluating single hurdles rather than their various combinations. This benefit can only be realized, however, when the gamma hypothesis is valid for the combination of hurdles considered. If the hypothesis is not valid and interactive effects are present, growth boundaries are estimated wrongly, which might result in fail-safe predictions.Over the years, the gamma hypothesis has been confirmed by several studies (16, 17, 26, 34, 38) that concluded that the combined effect of hurdles on growth rates is multiplicative rather than synergistic. Contrarily, Rödel and Scheuer (30) concluded that interaction occurs when various hurdles are combined, stressing the occurrence of synergy. Both Le Marc et al. (21) and Augustin and Carlier (5) developed a synergy model to take account of synergy occurring when hurdles are combined. It is prudent to conclude that the effect of combinations of hurdles is best evaluated on a case-by-case basis in order to ensure appropriate utility of hurdle technology approaches in establishing food designs that are stable and safe.This research aimed to validate or falsify the gamma hypothesis for two closely related hurdles often used in the food industry: the pH level and the undissociated acid concentration (HA]). The approach chosen was to establish an overview of models for pH and undissociated acid from the literature. Based on predefined criteria, models were then selected to construct a new gamma model without synergy factors for the various hurdle combinations. The criteria were meant to enable evaluation of the fitting performance of all individual models to select the best-performing models for inclusion in the new gamma models. Finally, the validity of the gamma hypothesis was judged by comparing the predictive performance of the newly constructed gamma models with two gamma models, including a synergy factor reported in the literature. Bacillus cereus F4810/72, relevant for both food spoilage and poisoning (14, 19), was used as the model microorganism. Maximum specific growth rates were determined by optical density measurements combined with time to detection. This method was selected after thorough investigation of three different methods to obtain parameters for growth, as recently published (8).