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Modeling the Microbiological Shelf Life of Foods and Beverages
Abstract
From about 1985 to 2015, the subject of predictive microbiology has become a mature area of study in and of itself. The ability to predict the growth of a bacterial species within a food matrix for a given set of intrinsic and environmental conditions offers many advantages and benefits to the food industry professional, and chief among these is the ability to determine shelf life using mathematical models.
... Second, mathematical models are routinely used to inform strategies to prevent or promote biofilm formation in specific situations relevant to, e.g., 1 food and water security [27,49] or biofuel production [30,50]. 2 In this review, we give a concise summary of the current stage of application of 3 mathematical models of biofilms, providing arguments for the continuation and further 4 strengthening interdisciplinary collaboration within the field. We emphasise the applications 5 of the models rather than their mathematical intricacies which are covered by other reviews 6 [1,51,52]. Section 2 describes results obtained from mathematical models used to understand 7 key mechanisms for biofilm formation (see Table 1 for a summary of the reviewed models and 8 Figure 1 for a schematic diagram of all sections discussed).The importance of mathematical 9 modelling to address each of the selected topics is demonstrated by reviewing key findings 10 based on state-of-the-art models that represent a substantial addition to the understanding 11 gained through experimental approaches. ...
... 4 Other fundamental roles include facilitating gene transfer [98] or inducing formation of 5 complex, self-organised structures [70]. The ECM has also been reported to protect the biofilm 6 cells from desiccation, biocides, antibiotics, heavy metals, UV light, host immune responses, 7 and protozoan grazers [97]. 8 In IbM models, individual agents such as bacteria cells or EPS material are treated as 9 discrete entities, with specific properties assigned to them, such as their biomass, size and 10 interactions with the environment. ...
... Computational analysis identified the potential evolutionary advantage of EPS 5 production in terms of aiding the individual's genes propagation. The study considered two 6 species, in all other aspects equal, except that one produced EPS and the other did not. The 7 non-EPS producer grew faster, as it had more resources available to allocate for reproduction 8 compared to the other species. ...
This article reviews modern applications of mathematical descriptions of biofilm formation. The focus is on theoretically obtained results which have implications for areas including the medical sector, food industry and wastewater treatment. Examples are given as to how models have contributed to the overall knowledge on biofilms and how they are used to predict biofilm behaviour. We conclude that the use of mathematical models of biofilms has demonstrated over the years the ability to significantly contribute to the vast field of biofilm research. Among other things, they have been used to test various hypotheses on the nature of interspecies interactions, viability of biofilm treatment methods or forces behind observed biofilm pattern formations. Mathematical models can also play a key role in future biofilm research. Many models nowadays are analysed through computer simulations and continue to improve along with computational capabilities. We predict that models will keep on providing answers to important challenges involving biofilm formation. However, further strengthening of the ties between various disciplines is necessary to fully use the tools of collective knowledge in tackling the biofilm phenomenon.
... Secondary models are used to describe the influence of environmental factors on fungal growth 39 . These models are of great importance and fundamentally very useful because they can be used to predict the microbiological shelf life of a food product 35 . In particular, in the Rosso cardinal model all of the studied parameters have a physiological meaning 19 . ...
Animal feeds are characterized by low water activity values. Nevertheless, fungal contamination with Eurotium species are quite common, causing nutritional depletion, spoilage and economic losses. The aim of this work was to assess Eurotium amstelodami, E. chevalieri, E. repens and E. rubrum growth in a feed matrix at different conditions of water activity (0.71–0.97) and temperature (5, 15, 25, 30 and 37 °C). It was found that Eurotium species are able to grow in a wide range of water activity and temperature in a short period of time (7 days) and faster than in synthetic media. Rosso and probabilistic models were applied in order to determine the limiting and optimum growth conditions as well as growth probability at certain combinations of environmental factors. Both models provided an accurate fit to the cardinal parameters and good performance for growth/no growth cases. This is the first report assessing the growth parameters of Eurotium species directly in animal feed. Data obtained in the present study is useful to predict and avoid Eurotium species growth in animal feed.
Within a microbial risk assessment framework, modeling the maximum population density (MPD) of a pathogenic microorganism is important but often not considered. This paper describes a model predicting the MPD of Salmonella on alfalfa as a function of the initial contamination level, the total count of the indigenous microbial population, the maximum pathogen growth rate and the maximum population density of the indigenous microbial population. The model is parameterized by experimental data describing growth of Salmonella on sprouting alfalfa seeds at inoculum size, native microbial load and Pseudomonas fluorescens 2-79. The obtained model fits well to the experimental data, with standard errors less than ten percent of the fitted average values. The results show that the MPD of Salmonella is not only dictated by performance characteristics of Salmonella but depends on the characteristics of the indigenous microbial population like total number of cells and its growth rate. The model can improve the predictions of microbiological growth in quantitative microbial risk assessments. Using this model, the effects of preventive measures to reduce pathogenic load and a concurrent effect on the background population can be better evaluated. If competing microorganisms are more sensitive to a particular decontamination method, a pathogenic microorganism may grow faster and reach a higher level. More knowledge regarding the effect of the indigenous microbial population (size, diversity, composition) of food products on pathogen dynamics is needed in order to make adequate predictions of pathogen dynamics on various food products.
Sterile apple juice inoculated with S. cerevisiae ATCC 9763 (103 CFU/mL) was processed in a bubble column with gaseous ozone of flow rate of 0.12 L/min and concentration of 33–40 μg/mL for 8 min. The growth kinetics of S. cerevisiae as an indicator of juice spoilage was monitored at 4, 8, 12 and 16 °C for up to 30 days. The kinetics was quantitatively described by the primary model of Baranyi and Roberts, and the maximum specific growth rate was further modeled as a function of temperature by the Ratkowsky type model. The developed model was successfully validated for the microbial growth of control and ozonated samples during dynamic storage temperature of periodic changes from 4 to 16 °C. Two more characteristic parameters were also evaluated, the time of spoilage of the product under static temperature conditions and the temperature quotient, Q
10. At lower static storage temperature (4 °C), no spoilage occurred either for unprocessed or ozone-processed apple juice. In the case of ozone-processed apple juice, the shelf life was increased when compared with the controls, and the Q
10 was found to be 7.17, which appear much higher than that of the controls, indicating the effectiveness of ozonation for the extension of shelf life of apple juice.
Unlabelled:
Cronobacter sakazakii is a life-threatening bacterium, infrequently implicated in illnesses associated with the consumption of powdered infant formula (PIF). It can cause rare but invasive infections in neonatal infants who consume contaminated PIF. The objective of this research was to investigate the growth kinetics and develop mathematical models to predict the growth of heat-injured C. sakazakii in reconstituted PIF (RPIF). RPIF, inoculated with a 6-strain cocktail of non-heat-treated (uninjured) or heat-injured C. sakazakii, was incubated at different temperatures to develop growth models. Except for storage at 6 °C, C. sakazakii grew well at all test temperatures (10 to 48 °C). Uninjured C. sakazakii exhibited no observable lag phase, while a lag phase was apparent in heat-treated cells. A simple 3-parameter logistic equation was used to fit growth curves for non-heat-treated cells, while both Baranyi and Huang models were suitable for heat-treated C. sakazakii. Calculated minimum and maximum growth temperatures were 6.5 and 51.4 °C for non-heat-treated cells, and 6.9 and 50.1 °C for heat-treated cells of C. sakazakii in RPIF, respectively. There was no significant difference between growth rates of non-heat-treated and heat-injured cells in RPIF. For heat-treated cells of C. sakazakii, the lag phase was temperature-dependent and very short (between 25 °C and 48 °C). These results suggest that both non-heat-treated and heat-injured C. sakazakii cells may present a risk to infants if the pathogens are not completely destroyed by heat in RPIF and then exposed to subsequent temperature abuse.
Practical application:
C. sakazakii is a life-threatening bacterium found in powdered infant formula (PIF). This study shows that the uninjured bacterium exhibits very short or no lag phase if not refrigerated and can grow well in reconstituted PIF (RPIF), while the heat-injured cells can multiply at an equivalent rate following metabolic recovery. Temperature abuse may allow C. sakazakii to grow and endanger infants fed with RPIF. Predictive models developed in this study can be used to estimate the growth and conduct risk assessments of this pathogen.
A method is developed to combine qualitative and quantitative information for the prediction of growth of microorganisms in foods. pH, water activity, temperature and oxygen availability of foods are coupled to growth characteristics of microorganisms. For that purpose, a database with characteristics of foods and a database of kinetic parameters of microorganisms are built. The first database has a tree structure, based on physical similarity of food products. This structure makes it possible to estimate information about a food product which is not listed by comparison with similar products at the same level of the tree or the level above. A method is developed to make an estimation of the microbial growth kinetics on the basis of models. This is done by introducing a growth factor, which can be calculated on the basis of readily available data from literature. Finally, qualitative knowledge is added. Since any bit of information can be changed, the system will give better predictions when more and more accurate information is added.
The spoilage potential of Zygosaccharomyces bailii has been widely recognized within the food industry. However, few data are available on the growth characteristics of this yeast at low temperature and in the absence of chemical preservatives. In this study, the growth/no growth boundary of Z. bailii was defined at refrigeration temperature (7 °C) and at conditions relevant to high-sugar, low-pH foods (such as ketchup and salad dressing), i.e. pH 3.0–5.0 (five levels), a
w 0.93–0.97 (five levels) and acetic acid concentration 0–2.5% (v/v; six levels). Yeast growth was followed during 90 days by optical density measurements, and logistic regression models were used to describe the data. Acetic acid had a significant effect on the relation between a
w and NaCl concentration and this interaction had important consequences for the model development. When data were modelled as a function of a
w or NaCl concentration, a stimulatory effect by acetic acid was observed. In contrast, as a function of (toxic) Na+ ions, no evidence was found of such a phenomenon. These results indicate that in cases where the relationship between a
w and solute concentration is not straightforward such as in the presence of acid preservatives, one must be critical towards the interpretation of data and correspondingly, the development of predictive models. On a practical note, the developed models, especially the one incorporating Na+ ions, may be used (1) to assess the stability of shelf-stable acidified foods stored under chilled conditions after opening or (2) to formulate new additive-free products intended for storage at 7 °C.
Cabbage is the main material of coleslaw, a popular side dish in Korea as well as many other countries. In the present study, the combined effect of temperature (15, 25, and 35 °C) and relative humidity (60%, 70%, and 80%) on the growth of Escherichia coli O157:H7 on cabbage was investigated. The polynomial models for growth rate (GR), lag time (LT), and maximum population density (MPD) estimated from the Baranyi model were conducted with high coefficients of determination (R2> 0.98). Subsequently, performance and reliability of the models were assessed through external validation, employing three indices as bias factor (Bf), accuracy factor (Af), and the standard error of prediction expressed in percentage (%SEP). The Bf, Af, and %SEP values of the predictive models for GR were 1.008, 1.127 and 18.70%, while 1.033, 1.187 and 20.79% for LT and 0.960, 1.044 and 5.22% for MPD, respectively. The results demonstrated that the developed secondary models showed a good agreement between the observed and predicted values. Therefore, the established models can be suitable to estimate and control E. coli O157:H7 growth risk on cabbage at some steps from farm to table in Korea as a valuable tool.
Practical Application: The combined effect of temperature and relative humidity on the growth or survival of Escherichia coli O157:H7 on cabbage was investigated. The validated predictive models are qualified to provide good predictions for E. coli O157:H7 growth, which can help to conduct the quantitative microbiological risk assessment (QMRA) of E. coli O157:H7 on cabbage from farm to table in Korea.
Two complementary measures are proposed as simple indices of the performance of models in predictive food microbiology. The indices assess the level of confidence one can have in the predictions of the model and whether the model displays any bias which could lead to 'fail-dangerous' predictions. The use of the indices is demonstrated using data collated from independent and published literature. This analysis supports previous reports that evaluation of predictive models by comparison to published microbial growth rate data may be inappropriate because of limitations in that data. The indices may fail to reveal some forms of systematic deviation between observed and predicted behaviour. It is concluded, however, that the indices provide an objective and readily interpreted summary of model performance and may serve as a first step towards the development of an objective and useful definition of the term 'validated model' in predictive food microbiology.