Comparing nonsynergy gamma models and interaction models to predict growth of emetic Bacillus cereus for combinations of pH and water activity values

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 gamma model, followed by the synergy model of Y. Le Marc et al. (Int. J. Food Microbiol. 73:219-237, 2002). 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.