Convergence of Bigelow and Arrhenius models over a wide range of heating temperatures.

The heat resistance of the bacterial spores of Moorella thermoacetica, Clostridium sporogenes, Geobacillus stearothermophilus and Bacillus coagulans was determined over a wide range of temperatures using the capillary method and thermoresistometer Mastia. The results showed that the two experimental methods gave similar heat resistance values excepted for Geobacillus stearothermophilus. The effect of temperature on thermal resistance was evaluated using the Arrhenius and Bigelow models. The fit of the heat sensitivity parameters of the Arrhenius and Bigelow models on the heat resistance parameter values obtained over a wide temperature range was equally good. Despite the apparent mathematical incompatibility of the two equations, it is recognized that they yield the same goodness of fit. This paper finds a mathematical reason for this convergence and explains why inside a temperature range of at least 100 °C, no significant difference in the quality of fit between these two models can be found.

Sporulation boundaries and spore formation kinetics of Bacillus spp. as a function of temperature, pH and a(w).

Sporulation niches in the food chain are considered as a source of hazard and are not clearly identified. Determining the sporulation environmental boundaries could contribute to identify potential sporulation niches. Spore formation was determined in a Sporulation Mineral Buffer. The effect of incubation temperature, pH and water activity on time to one spore per mL, maximum sporulation rate and final spore concentration was investigated for a Bacillus weihenstephanensis and a Bacillus licheniformis strain. Sporulation boundaries of B. weihenstephanensis and of B. licheniformis were similar to, or included within, the range of temperatures, pH and water activities supporting growth. For instance, sporulation boundaries of B. weihenstephanensis were evaluated at 5°C, 35°C, pH 5.2 and a(w) 0.960 while growth boundaries were observed at 5°C, 37°C, pH 4.9 and a(w) 0.950. Optimum spore formation was determined at 30°C pH 7.2 for B. weihenstephanensis and at 45°C pH 7.2 for B. licheniformis. Lower temperatures and pH delayed the sporulation process. For instance, the time to one spore per mL was tenfold longer when sporulation occurred at 10°C and 20°C, for each strain respectively, than at optimum sporulation temperature. The relative effect of temperature and pH on sporulation rates and on growth rates is similar. This work suggests that the influence of environmental factors on the quantitative changes in sporulation boundaries and rates was similar to their influence on changes in growth rate.

Modeling heat resistance of Bacillus weihenstephanensis and Bacillus licheniformis spores as function of sporulation temperature and pH.

Although sporulation environmental factors are known to impact on Bacillus spore heat resistance, they are not integrated into predictive models used to calculate the efficiency of heating processes. This work reports the influence of temperature and pH encountered during sporulation on heat resistance of Bacillus weihenstephanensis KBAB4 and Bacillus licheniformis AD978 spores. A decrease in heat resistance (δ) was observed for spores produced either at low temperature, at high temperature or at acidic pH. Sporulation temperature and pH maximizing the spore heat resistance were identified. Heat sensitivity (z) was not modified whatever the sporulation environmental factors were. A resistance secondary model inspired by the Rosso model was proposed. Sporulation temperatures and pHs minimizing or maximizing the spore heat resistance (T(min(R)), T(opt(R)), T(max(R)), pH(min(R)) and pH(opt(R))) were estimated. The goodness of the model fit was assessed for both studied strains and literature data. The estimation of the sporulation temperature and pH maximizing the spore heat resistance is of great interest to produce spores assessing the spore inactivation in the heating processes applied by the food industry.

Modelling of growth, growth/no-growth interface and nonthermal inactivation areas of Listeria in foods.

Growth, growth boundary and inactivation models have been extensively developed in predictive microbiology and are commonly applied in food research nowadays. Few studies though report the development of models which encompass all three areas together. A tiered modelling approach, based on the Gamma hypothesis, is proposed here to predict the behaviour of Listeria. Datasets of Listeria spp. behaviour in laboratory media, meat, dairy, seafood products and vegetables were collected from literature, unpublished sources and from the databases ComBase and Sym'Previus. The explanatory factors were temperature, pH, water activity, lactic and sorbic acids. For the growth part, 697 growth kinetic datasets were fitted. The estimated growth rates and 2021 additional growth primary datasets were used to fit the secondary growth models. In a second step, the fitted model was used to predict the growth/no-growth boundary. For the inactivation modelling phase, 535 inactivation curves were used. Gamma models with and without interactions between the explanatory factors were used for the growth and boundary models. The correct prediction percentage (predicted growth when growth is observed+predicted inactivation when inactivation is observed) varied from 62% to 81% for the models without interactions, and from 85% to 87% for the models with interactions. The median error for the predicted population size was less than 0.34 log(10)(CFU/mL) for all models. The kinetics of inactivation were fitted with modified Weibull primary models and the estimated bacterial resistance was then modelled as a function of the explanatory factors. The error for the predicted microbial population size was less than 0.71 log(10)(CFU/mL) with a median value of less than 0.21 for all foods. The model enables the quantification of the increase or decrease in the bacterial population for a given formulation or storage condition. It might also be used to optimise a food formulation or storage condition in the case of a targeted increase or decrease of the bacterial population.

Modelling the influence of palmitic, palmitoleic, stearic and oleic acids on apparent heat resistance of spores of Bacillus cereus NTCC 11145 and Clostridium sporogenes Pasteur 79.3.

Heat resistance of spores is affected by many factors such as temperature, pH, water activity (aw) and others. Previous studies have reported that free fatty acids can affect the germination and growth of bacterial spores. In this study, we investigated the influence of free fatty acids in heating medium or in recovery medium on the heat resistance of spores of Bacillus cereus NTCC 11145 and Clostridium sporogenes Pasteur 79.3. Four free fatty acids were studied: palmitic, palmitoleic, stearic and oleic acids. During thermal treatments, the impact of these FFA in heating media was generally low, but the presence of free fatty acids in the recovery medium highly decreases bacterial spore apparent heat resistance, particularly with unsaturated fatty acids. A mathematical model was developed to describe and quantify the influence of free fatty acids in recovery media on the D-values. The z'(FFA) parameter values which quantify the impact of free fatty acids were determined. The variation of this parameter value according to the free fatty acid type was compared with MIC value variation given in the literature. The model enables the decrease in D-values in the presence of free fatty acids to be estimated. The high concentrations of free fatty acids in liver or canned duck may explain the microbial stability with low sterilization values applied.

Survival curves of heated bacterial spores: effect of environmental factors on Weibull parameters.

The classical D-value of first order inactivation kinetic is not suitable for quantifying bacterial heat resistance for non-log linear survival curves. One simple model derived from the Weibull cumulative function describes non-log linear kinetics of micro-organisms. The influences of environmental factors on Weibull model parameters, shape parameter "p" and scale parameter "delta", were studied. This paper points out structural correlation between these two parameters. The environmental heating and recovery conditions do not present clear and regular influence on the shape the parameter "p" and could not be described by any model tried. Conversely, the scale parameter "delta" depends on heating temperature and heating and recovery medium pH. The models established to quantify these influences on the classical "D" values could be applied to this parameter "delta". The slight influence of the shape parameter p variation on the goodness of fit of these models can be neglected and the simplified Weibull model with a constant p-value for given microbial population can be applied for canning process calculations.

Modelling the influence of single acid and mixture on bacterial growth.

Depending on environmental factors, the prediction of bacterial growth is made difficult by the complexity of foodstuff. Although the influence of temperature, pH, and water activity are usually taken into account, models have to be completed with the influence of acid mixture. Nine strains of Listeria spp., four Salmonella spp., one Staphylococcus aureus, one Escherichia coli, and Listeria innocua ATCC 33090 were used for this study to extend model proposed by [Le Marc, Y., Huchet, V., Bourgeois, C., Guyonnet, J., Mafart, P., Thuault, D., 2002. Modelling the growth kinetics of Listeria as a function of temperature, pH and organic acid concentration. International Journal of Food Microbiology 73, 219-237]. Derived from data of [Houtsma, P.C., Kusters, B.J., De Wit, J.C., Rombouts, F.M., Zwietering, M.H., 1994. Modelling growth rates of Listeria innocua as a function of lactate concentration. International Journal of Food Microbiology 24, 113-123] and our own data, the extended model described accurately different effects of addition of acid salts in the medium (decrease of water activity and pH, variation of undissociated weak acid form, and variation of synergetic effect between environmental factors). This previous model was implemented to describe the observed variability of behaviour of the different studied strains. alpha reflected the general behaviour of species (sensitiveness to low or high undissociated acid concentration), and MIC(U) reflected the various resistances of strains. From this simple model, a new model was built for describing the effects of concentrations of several mixed acids on bacterial growth rates. Simulations of growth were carried out from three acids mixtures by inputting parameter estimates previously obtained. Despite a very variable effect of investigated acids on growth, the new model yielded fair predictions.