Comparing Nonsynergy Gamma Models and Interaction Models To Predict Growth of Emetic Bacillus cereus for Combinations of pH and Water Activity Values

Abstract

This research aims to test the absence (gamma hypothesis) or occurrence of synergy between two growth-limiting factors, i.e., pH and water activity (a w ), using a systematic approach for model selection. In this approach, preset criteria were used to evaluate the performance of models. Such a systematic approach is required to be confident in the correctness of the individual components of the combined (synergy) models. With Bacillus cereus F4810/72 as the test organism, estimated growth boundaries for the a w -lowering solutes NaCl, KCl, and glucose were 1.13 M, 1.13 M, and 1.68 M, respectively. The accompanying a w values were 0.954, 0.956, and 0.961, respectively, indicating that equal a w values result in similar effects on growth. Out of the 12 models evaluated using the preset criteria, the model of J. H. T. Luong (Biotechnol. Bioeng. 27:280-285, 1985) was the best model to describe the effect of a w on growth. This a w model and the previously selected pH model were combined into a gamma model and into two synergy models. None of the three models was able to describe the combined pH and a w conditions sufficiently well to satisfy the preset criteria. The best matches between predicted and experimental data were obtained with the No combination of models that was able to predict the impact of both individual and combined hurdles correctly could be found. Consequently, in this case we could not prove the existence of synergy nor falsify the gamma hypothesis.The microorganism Bacillus cereus is associated with food spoilage as well as food poisoning (1, 34). The spores formed by B. cereus generally will resist treatments used to prolong the shelf life of food. Viable spores present in a food product may germinate, and the vegetative cells can subsequently grow if conditions are favorable, leading to spoilage of the food product (9, 14, 18). 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 (a w ), and 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 detrimental impacts on food quality (19).Improved quantification of the combined impact of hurdles on growth of microorganisms is an ongoing endeavor, but there are different views of how antimicrobial factors combine. One view is that there are interactive effects between hurdles. When combinations of hurdles are used, they might give significantly greater protection than expected on the basis of the application of the individual hurdles, so called synergy (19). The other view follows the gamma hypothesis (39) in which there is no synergy, but inhibitory environmental factors combine in a multiplicative manner to produce the observed overall microbial inhibition. Evidently, it is important in the selection of hurdles to know whether either the gamma hypothesis is valid or synergy occurs between factors. A...

Modeling and Validation of the Ecological Behavior of Wild-Type Listeria monocytogenes and Stress-Resistant Variants

“…The gamma theory is, however, not always pertinent, and its applicability seems to depend on the organism, as well as on the combination of mild stress factors (27,39,40). Especially around the growth boundaries, the gamma model has shown poor agreement with experimental observations when no synergy factor was included (41). However, for L. monocytogenes, among other organisms, it was shown that further away from the growth boundaries, the gamma model without synergy generally performs well to describe the combined effect of water activity, pH, and temperature on growth (42).…”