Applicability of an Arrhenius Model for the Combined Effect of Temperature and CO ₂ Packaging on the Spoilage Microflora of Fish

Abstract

The temperature behavior of the natural microflora on the Mediterranean fish red mullet (Mullus barbatus) was examined as a case study. The growth of the spoilage bacteria Pseudomonas spp., Shewanella putrefaciens, Brochothrix thermosphacta, and lactic acid bacteria was modeled as a function of temperature and the concentration of carbon dioxide in modified atmosphere packaging. Combined models were developed and comparatively assessed based on polynomial, Belehradek, and Arrhenius equations. The activation energy parameter of the Arrhenius model, E A , was independent of the packaging atmosphere and ranged from 75 to 85 kJ/mol for the different bacteria, whereas the preexponential constant decreased exponentially with the packaging CO 2 concentration. We evaluated the applicability of the models developed by using experimental bacterial growth rates obtained from 42 independent experiments performed with three Mediterranean fish species and growth rates predicted from the models under the same temperature and packaging conditions. The accuracy factor and bias factor were used as statistical tools for evaluation, and the developed Arrhenius model and the Belehradek model were judged satisfactory overall.Predictive modeling is currently accepted as a useful method for describing quantitatively the effects of ecological determinants (e.g., temperature, water activity) on bacterial growth (20, 28). In particular, predictive microbiology has been used to predict the growth of specific spoilage microorganisms in order to determine the shelf life of various fish products (3,22). However, the development of specific spoilage bacteria in a fish ecosystem is a result of both environmental conditions and microbial competition (7,16). In fish packed aerobically competition occurs between members of an aerobic gramnegative flora (mainly pseudomonads and Shewanella putrefaciens). In fish packed under modified atmosphere packing (MAP) conditions competition occurs between members of a facultatively anaerobic gram-positive flora (such as Brochothrix thermosphacta and lactic acid bacteria). The bacteria mentioned above have been reported to be important specific spoilage bacteria of Mediterranean fish stored under MAP conditions or aerobically (6,13,22,23). Selection of a specific microflora eventually leads to spoilage at a rate that depends on pretreatment, packaging conditions, and temperature conditions during distribution and storage in the chill chain. Modeling the behavior of this microflora and quantitatively correlating it with shelf life can provide an effective tool for predicting chilled fish quality. To achieve this, it is necessary not only to identify the specific spoilage organisms but also to define the spoilage domain (i.e., the range of conditions, including microbial interactions, in which different groups of microorganisms are responsible for spoilage) (3). Most mathematical modeling studies have not allowed workers to predict quantitatively the growth behavior of a mixed naturally existing flora consisting...

Development of a Microbial Model for the Combined Effect of Temperature and pH on Spoilage of Ground Meat, and Validation of the Model under Dynamic Temperature Conditions

“…Activation energies for max of pseudomonads and B. thermosphacta were 69.3 and 69.5 kJ/mol, respectively. These values are in agreement with the results of other studies on the effect of temperature on the growth of these bacteria on other foods or laboratory media (18,19,46). For Enterobacteriaceae and lactic acid bacteria, max showed much higher temperature dependence, with E A values of 95.8 and 99.6, respectively.…”

“…The modification of the Arrhenius model was based on the observation that pH did not affect the temperature dependence (E A ) of the kinetic parameters. Similar results have been reported for the effect of temperature and CO 2 on growth of spoilage bacteria on fresh fish (19), where the authors used a similar modification of the Arrhenius model to describe the combined effect of these environmental factors. The parameters and statistics of equations 1 and 2 for the tested spoilage bacteria are shown in Tables 2 and 3.…”

“…It has been shown however, that the lag phase duration of the "specific specific organisms" (SSO; the fraction of the total microflora which is considered responsible for spoilage) can be a significant part of the total shelf life of foods (19,20). Ignoring lag phase may lead to underestimated shelf life predictions, with significant economic losses for the food industry.…”

A Model Based Simulation of Brewing Yeast Propagation

“…Following the principle of a master reaction for the biomass growth, an Arrhenius approach with an activation energy E a = 84.801 kJ mol -1 was used to describe the temperature dependency of the specific growth rate at the required temperatures. The activation energy E a lies in a reasonable range for microbial specific growth rates 10,14,19 . A comparison of these results to experimental data of baker's yeast propagations and industrial trials with top and bottom fermenting brewing yeasts from Manger et al 22 and Lehmann 21 showed, that the activation energy for the growth of Saccharomyces type yeasts did not seem to be dependent on the growth medium or the specific species.…”

“…In contrast to this, several authors described the temperature dependence of microbial growth in general 9,32 or for specific bacteria. The most common approaches were exponential following the Arrhenius equation 10,14,19 or parabolic Belehradek-type equations 24,31 . The latter relation, however, is better suited to the description of microorganism growth at sub-optimal temperatures.…”