Towards a novel class of predictive microbial growth models

Food safety and quality are influenced by the presence (and possible proliferation) of pathogenic and spoilage microorganisms during the life cycle of the product (i.e., from the raw ingredients at the start of the production process until the moment of consumption). In order to simulate and predict microbial evolution in foods, mathematical models are developed in the field of predictive microbiology. In general, microbial growth is a self-limiting process, principally due to either (i) the exhaustion of one of the essential nutrients, and/or (ii) the accumulation of toxic products that inhibit growth. Nowadays, most mathematical models used in predictive microbiology do not explicitly incorporate this basic microbial knowledge. In this paper, a novel class of microbial growth models is proposed. In contrast with the currently used logistic type models, e.g., the model of Baranyi and Roberts [Baranyi, J., Roberts, T.A., 1994. A dynamic approach to predicting bacterial growth in food. International Journal of Food Microbiology 23, 277–294], the novel model class explicitly incorporates nutrient exhaustion and/or metabolic waste product effects. As such, this novel model prototype constitutes an elementary building block to be extended in a natural way towards, e.g., microbial interactions in co-cultures (mediated by metabolic products) and microbial growth in structured foods (influenced by, e.g., local substrate concentrations). While under certain conditions the mathematical equivalence with classical logistic type models is clear and results in equal fitting capacities and parameter estimation quality (see Poschet et al. [Poschet, F., Vereecken, K.M., Geeraerd, A.H., Nicolaï, B.M., Van Impe, J.F., 2004. Analysis of a novel class of predictive microbial growth models and application to co-culture growth. International Journal of Food Microbiology, this issue] for a more elaborated analysis in this respect), the biological interpretability and extendability represent the main added value.     

Biological implications from an autonomous version of Baranyi and Roberts growth model

An autonomous version of Baranyi and Roberts model (Int. J. Food Microbiology, 23, 1994, pp. 277-294) is developed and analyzed to reveal some subtle points, which are difficult to observe accurately from its equivalent non-autonomous form. In particular we are able to provide a meaningful interpretation to the "physiological state of the cells at inoculation", a parameter introduced by Baranyi and Roberts [Baranyi, J., Roberts, T. A., 1994. A dynamic approach to predicting bacterial growth in food. International Journal of Food Microbiology 23, 277-294] that has a profound impact on microbial growth but is not a direct measurable quantity. In addition, the analysis shows that the transient growth depends on the initial cell concentration and the initial growth rate, but is independent of "the history of the cells" and depends only indirectly (via the initial growth rate) on the previous (pre-inoculation) environment. The stationary solution is independent of the initial conditions. A new, more natural, and biologically meaningful formulation of LAG duration is being suggested in terms of initial conditions being in the neighborhood of one of the unstable stationary points revealed by this autonomous version of the model.     

Methods to determine the growth domain in a multidimensional environmental space

Data from a database on microbial responses to the food environment (ComBase, see www.combase.cc) were used to study the boundary of growth several pathogens (Aeromonas hydrophila, Escherichia coli, Listeria monocytogenes, Yersinia enterocolitica). Two methods were used to evaluate the growth/no growth interface. The first one is an application of the Minimum Convex Polyhedron (MCP) introduced by Baranyi et al. [Baranyi, J., Ross, T., McMeekin, T., Roberts, T.A., 1996. The effect of parameterisation on the performance of empirical models used in Predictive Microbiology. Food Microbiol. 13, 83–91.]. The second method applies logistic regression to define the boundary of growth. The combination of these two different techniques can be a useful tool to handle the problem of extrapolation of predictive models at the growth limits.     

Validation of a model for growth of Lactococcus lactis and Listeria innocua in a structured gel system: effect of monopotassium phosphate

The effect of monopotassium phosphate (KH(2)PO(4)) on the chemical environment and on growth of Listeria innocua and Lactococcus lactis in coculture were investigated in a liquid and in a gelled microbiological medium at 12 degrees C and an initial pH of 6.2. As expected, addition of KH(2)PO(4) to both the liquid and gelled media resulted in an increase in buffering capacity. This effect on buffering capacity changed the profiles of lactic acid dissociation and pH evolution. At all gelatin concentrations studied, addition of KH(2)PO(4) increased the growth rate and the stationary cell concentration of L. lactis. In addition, the growth rate of L. innocua slightly increased but, in contrast, the stationary cell concentration remained unchanged. A new class of predictive models developed previously in our research team to quantify the effect of food model gel structure on microbial growth [Antwi, M., Bernaerts, K., Van Impe, J. F., Geeraerd, A. H., 2007. Modelling the combined effect of food model system and lactic acid on L. innocua and L. lactis growth in mono- and coculture. International Journal of Food Microbiology 120, 71-84] was applied. Our analysis indicate that KH(2)PO(4) influenced the parameters of the chemical and microbiological subprocesses of the model. Nonetheless, the growth model satisfactorily predicted the stationary cell concentration when (i) the undissociated lactic acid concentrations at which L. innocua and L. lactis growth cease were chosen as previously reported, and (ii) all other parameters of the chemical and microbiological subprocesses were computed for each medium. This confirms that the undissociated lactic acid concentrations at which growth ceases is a unique property of a bacterium and does not, within our case study, depend on growth medium. The study indicates that microbial growth depends on the interplay between the individual food components which affect the physicochemical properties of the food, such as the buffering capacity. Towards future research, it can be concluded that mathematical models which embody the effect of buffering capacity are needed for accurate predictions of microbial growth in food systems.     

Effect of pH, water activity and gel micro-structure, including oxygen profiles and rheological characterization, on the growth kinetics of Salmonella Typhimurium

In this study, the growth of Salmonella Typhimurium in Tryptic Soy Broth was examined at different pH (4.50-5.50), water activity a(w) (0.970-0.992) and gelatin concentration (0%, 1% and 5% ) at 20 degrees C. Experiments in TSB with 0% gelatin were carried out in shaken erlenmeyers, in the weak 1% gelatin media in petri plates and in the firm 5% gelatin media in gel cassettes. A quantification of gel strength was performed by rheological measurements and the influence of oxygen supply on the growth of S. Typhimurium was investigated. pH, as well as a(w) as well as gelatin concentration had an influence on the growth rate. Both in broth and in gelatinized media, lowering pH or water activity caused a decrease of growth rate. In media with 1% gelatin a reduction of growth rate and maximal cell density was observed compared to broth at all conditions. However, the effects of decreasing pH and a(w) were less pronounced. A further increase in gelatin concentration to 5% gelatin caused a small or no additional drop of growth rate. The final oxygen concentration dropped from 5.5 ppm in stirred broth to anoxic values in petri plates, also when 0% and 5% gelatin media were tested in this recipient. Probably, not stirring the medium, which leads to anoxic conditions, has a more pronounced effect on the growth rate of S. Typhimurium then medium solidness. Finally, growth data were fitted with the primary model of Baranyi and Roberts [Baranyi, J. and Roberts, T. A., 1994. A dynamic approach to predicting bacterial growth in food. International Journal of Food Microbiology 23, 277-294]. An additional factor was introduced into the secondary model of Ross et al. [Ross, T. and Ratkowsky, D. A. and Mellefont, L. A. and McMeekin, T. A., 2003. Modelling the effects of temperature, water activity, pH and lactic acid concentration on the growth rate of Escherichia coli. International Journal of Food Microbiology 82, 33-43.] to incorporate the effect of gelatin concentration, next to the effect of pH and a(w). A two step and a global regression procedure were applied. Both procedures were able to fit the data well, but the global regression procedure led to smaller standard errors on the parameters.     

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. 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.     

Modelling Yersinia enterocolitica inactivation in coculture experiments with Lactobacillus sakei as based on pH and lactic acid profiles

In food processing and preservation technology, models describing microbial proliferation in food products are a helpful tool to predict the microbial food safety and shelf life. In general, the available models consider microorganisms in pure culture. Thus, microbial interactions are ignored, which may lead to a discrepancy between model predictions and the actual microbial evolution, particularly for fermented and minimally processed food products in which a background flora is often present. In this study, the lactic acid mediated negative microbial interaction between the lactic acid bacterium Lactobacillus sakei and the psychrotrophic food pathogen Yersinia enterocolitica was examined. A model describing the lactic acid induced inhibition (i.e., early induction of the stationary phase) of the pathogen [Vereecken, K.M., Devlieghere, F., Bockstaele, A., Debevere, J., Van Impe, J.F., 2003. A model for lactic acid induced inhibition of Yersinia enterocolitica in mono- and coculture with Lactobacillus sakei. Food Microbiology 20, 701-713.] was extended to describe the subsequent inactivation (i.e., decrease of the cell concentration to values below the detection limit). In the development of a suitable model structure to describe the inactivation process, critical points in the variation of the specific evolution rate mu [1/h] with the dynamic (time-varying) pH and undissociated lactic acid profiles were taken into account. Thus, biological knowledge, namely, both pH and undissociated lactic acid have an influence on the microbial evolution, was incorporated. The extended model was carefully validated on new data. As a result, the newly developed model is able to accurately predict the growth, inhibition and subsequent inactivation of Y. enterocolitica in coculture as based on the dynamic pH and lactic acid profiles of the medium.     

Predictive modelling of the microbial lag phase: a review

This paper summarises recent trends in predictive modelling of microbial lag phenomena. The lag phase is approached from both a qualitative and a quantitative point of view. First, a definition of lag and an analysis of the prevailing measuring techniques for the determination of lag time is presented. Furthermore, based on experimental results presented in literature, factors influencing the lag phase are discussed. Major modelling approaches concerning lag phase estimation are critically assessed. In predictive microbiology, a two-step modelling approach is used. Primary models describe the evolution of microbial numbers with time and can be subdivided into deterministic and stochastic models. Primary deterministic models, e.g., Baranyi and Roberts [Int. J. Food Microbiol. 23 (1994) 277], Hills and Wright [J. Theor. Biol. 168 (1994) 31] and McKellar [Int. J. Food Microbiol. 36 (1997) 179], describe the evolution of microorganisms, using one single (deterministic) set of model parameters. In stochastic models, e.g., Buchanan et al. [Food Microbiol. 14 (1997) 313], Baranyi [J. Theor. Biol. 192 (1998) 403] and McKellar [J. Appl. Microbiol. 90 (2001) 407], the model parameters are distributed or random variables. Secondary models describe the relation between primary model parameters and influencing factors (e.g., environmental conditions). This survey mainly focuses on the influence of temperature and culture history on the lag phase during growth of bacteria.     

Effect of temperature, water-phase salt and phenolic contents on Listeria monocytogenes growth rates on cold-smoked salmon and evaluation of secondary models

Salting and smoking are ancient processes for fish preservation. The effects of salt and phenolic smoke compounds on the growth rate of L. monocytogenes in cold-smoked salmon were investigated through physico-chemical analyses, challenge tests on surface of cold-smoked salmon at 4 degrees C and 8 degrees C, and a survey of the literature. Estimated growth rates were compared to predictions of existing secondary models, taking into account the effects of temperature, water phase salt content, phenolic content, and additional factors (e.g. pH, lactate, dissolved CO2). The secondary model proposed by Devlieghere et al. [Devlieghere, F., Geeraerd, A.H., Versyck, K.J., Vandewaetere, B., van Impe, J., Debevere, J., 2001. Growth of Listeria monocytogenes in modified atmosphere packed cooked meat products: a predictive model. Food Microbiology 18, 53-66.] and modified by Giménez and Dalgaard [Giménez, B., Dalgaard, P., 2004. Modelling and predicting the simultaneous growth of Listeria monocytogenes and spoilage micro-organisms in cold-smoked salmon. Journal of Applied Microbiology 96, 96-109.] appears appropriate. However, further research is needed to understand all effects affecting growth of L. monocytogenes in cold-smoked salmon and to obtain fully validated predictive models for use in quantitative risk assessment.     

Exploring the performance of logistic regression model types on growth/no growth data of Listeria monocytogenes

Several model types have already been developed to describe the boundary between growth and no growth conditions. In this article two types were thoroughly studied and compared, namely (i) the ordinary (linear) logistic regression model, i.e., with a polynomial on the right-hand side of the model equation (type I) and (ii) the (nonlinear) logistic regression model derived from a square root-type kinetic model (type II). The examination was carried out on the basis of the data described in Vermeulen et al. [Vermeulen, A., Gysemans, K.P.M., Bernaerts, K., Geeraerd, A.H., Van Impe, J.F., Debevere, J., Devlieghere, F., 2006-this issue. Influence of pH, water activity and acetic acid concentration on Listeria monocytogenes at 7 degrees C: data collection for the development of a growth/no growth model. International Journal of Food Microbiology. .]. These data sets consist of growth/no growth data for Listeria monocytogenes as a function of water activity (0.960-0.990), pH (5.0-6.0) and acetic acid percentage (0-0.8% (w/w)), both for a monoculture and a mixed strain culture. Numerous replicates, namely twenty, were performed at closely spaced conditions. In this way detailed information was obtained about the position of the interface and the transition zone between growth and no growth. The main questions investigated were (i) which model type performs best on the monoculture and the mixed strain data, (ii) are there differences between the growth/no growth interfaces of monocultures and mixed strain cultures, (iii) which parameter estimation approach works best for the type II models, and (iv) how sensitive is the performance of these models to the values of their nonlinear-appearing parameters. The results showed that both type I and II models performed well on the monoculture data with respect to goodness-of-fit and predictive power. The type I models were, however, more sensitive to anomalous data points. The situation was different for the mixed strain culture. In that case, the type II models could not describe the curvature in the growth/no growth interface which was reversed to the typical curvatures found for monocultures. This unusual curvature may originate from the fact that (i) an interface of a mixed strain culture can result from the superposition of the interfaces of the individual strains, or that (ii) only a narrow range of the growth/no growth interface was studied (the local trend can be different from the trend over a wider range). It was also observed that the best type II models were obtained with the flexible nonlinear logistic regression, although reasonably good models were obtained with the less flexible linear logistic regression with the nonlinear-appearing parameters fixed at experimentally determined values. Finally, it was found that for some of the nonlinear-appearing parameters, deviations from their experimentally determined values did not influence the model fit. This was probably caused by the fact that only a limited part of the growth/no growth interface was studied.     

The importance of expressing antimicrobial agents on water basis in growth/no growth interface models: a case study for Zygosaccharomyces bailii

In a previous study on Zygosaccharomyces bailii, three growth/no growth models have been developed, predicting growth probability of the yeast at different conditions typical for acidified foods (Dang, T.D.T., Mertens, L., Vermeulen, A., Geeraerd, A.H., Van Impe, J.F., Debevere, J., Devlieghere, F., 2010. Modeling the growth/no growth boundary of Z. bailii in acidic conditions: A contribution to the alternative method to preserve foods without using chemical preservatives. International Journal of Food Microbiology 137, 1-12). In these broth-based models, the variables were pH, water activity and acetic acid, with acetic acid concentration expressed in volume % on the total culture medium (i.e., broth). To continue the previous study, validation experiments were performed for 15 selected combinations of intrinsic factors to assess the performance of the model at 22 °C (60 days) in a real food product (ketchup). Although the majority of experimental results were consistent, some remarkable deviations between prediction and validation were observed, e.g., Z. bailii growth occurred in conditions where almost no growth had been predicted. A thorough investigation revealed that the difference between two ways of expressing acetic acid concentration (i.e., on broth basis and on water basis) is rather significant, particularly for media containing high amounts of dry matter. Consequently, the use of broth-based concentrations in the models was not appropriate. Three models with acetic acid concentration expressed on water basis were established and it was observed that predictions by these models well matched the validation results; therefore a “systematic error” in broth-based models was recognized. In practice, quantities of antimicrobial agents are often calculated based on the water content of food products. Hence, to assure reliable predictions and facilitate the application of models (developed from lab media with high dry matter contents), it is important to express antimicrobial agents' concentrations on a common basis—the water content. Reviews over other published growth/no growth models in literature are carried out and expressions of the stress factors' concentrations (on broth basis) found in these models confirm this finding.     

A quasi-chemical model for the growth and death of microorganisms in foods by non-thermal and high-pressure processing

Predictive microbial models generally rely on the growth of bacteria in laboratory broth to approximate the microbial growth kinetics expected to take place in actual foods under identical environmental conditions. Sigmoidal functions such as the Gompertz or logistics equation accurately model the typical microbial growth curve from the lag to the stationary phase and provide the mathematical basis for estimating parameters such as the maximum growth rate (MGR). Stationary phase data can begin to show a decline and make it difficult to discern which data to include in the analysis of the growth curve, a factor that influences the calculated values of the growth parameters. In contradistinction, the quasi-chemical kinetics model provides additional capabilities in microbial modelling and fits growth-death kinetics (all four phases of the microbial lifecycle continuously) for a general set of microorganisms in a variety of actual food substrates. The quasi-chemical model is differential equations (ODEs) that derives from a hypothetical four-step chemical mechanism involving an antagonistic metabolite (quorum sensing) and successfully fits the kinetics of pathogens (Staphylococcus aureus, Escherichia coli and Listeria monocytogenes) in various foods (bread, turkey meat, ham and cheese) as functions of different hurdles (a_w, pH, temperature and anti-microbial lactate). The calculated value of the MGR depends on whether growth-death data or only growth data are used in the fitting procedure. The quasi-chemical kinetics model is also exploited for use with the novel food processing technology of high-pressure processing. The high-pressure inactivation kinetics of E. coli are explored in a model food system over the pressure (P) range of 207–345 MPa (30,000–50,000 psi) and the temperature (T) range of 30–50 °C. In relatively low combinations of P and T, the inactivation curves are non-linear and exhibit a shoulder prior to a more rapid rate of microbial destruction. In the higher P, T regime, the inactivation plots tend to be linear. In all cases, the quasi-chemical model successfully fit the linear and curvi-linear inactivation plots for E. coli in model food systems. The experimental data and the quasi-chemical mathematical model described herein are candidates for inclusion in ComBase, the developing database that combines data and models from the USDA Pathogen Modeling Program and the UK Food MicroModel.     

Modelling the variability of lag times and the first generation times of single cells of E. coli

A mathematical model combining deterministic and stochastic elements describes the growth and division of single cells. Its deterministic part is based on the model of Baranyi and Roberts [International Journal of Food Microbiology 23 (1994) 277] modelling the gradual adjustment of the cells to a new environment. The stochastic part assumes a random threshold size for the division of a single cell, which accounts for the variability of the individual generation times. Experimental results of the first division times of thousands of single cells using a microscopic flow system could be reproduced with this model, and it has the potential to be used to study the effects of different stress and environmental factors on the distribution of the lag and generation times of individual cells.     

Modelling the variability of lag times and the first generation times of single cells of E. coli

A mathematical model combining deterministic and stochastic elements describes the growth and division of single cells. Its deterministic part is based on the model of Baranyi and Roberts [International Journal of Food Microbiology 23 (1994) 277] modelling the gradual adjustment of the cells to a new environment. The stochastic part assumes a random threshold size for the division of a single cell, which accounts for the variability of the individual generation times. Experimental results of the first division times of thousands of single cells using a microscopic flow system could be reproduced with this model, and it has the potential to be used to study the effects of different stress and environmental factors on the distribution of the lag and generation times of individual cells.     

Model comparison for Escherichia coli growth in pouched food

We recently studied the growth characteristics of Escherichia coli cells in pouched mashed potatoes (Fujikawa et al., J. Food Hyg. Soc. Japan, 47, 95-98 (2006)). Using those experimental data, in the present study, we compared a logistic model newly developed by us with the modified Gompertz and the Baranyi models, which are used as growth models worldwide. Bacterial growth curves at constant temperatures in the range of 12 to 34 degrees C were successfully described with the new logistic model, as well as with the other models. The Baranyi gave the least error in cell number and our model gave the least error in the rate constant and the lag period. For dynamic temperature, our model successfully predicted the bacterial growth, whereas the Baranyi model considerably overestimated it. Also, there was a discrepancy between the growth curves described with the differential equations of the Baranyi model and those obtained with DMfit, a software program for Baranyi model fitting. These results indicate that the new logistic model can be used to predict bacterial growth in pouched food.     

Improvement of new logistic model for bacterial growth

Recently Fujikawa et al. [J. Food Hyg. Soc. Japan, 44, 155-160 (2003)] developed a new logistic model for bacterial growth. In the present study, an adjustment factor in the model was improved. The improved model could successfully describe growth curves of Escherichia coli and Salmonella in liquid media. In particular, the model could describe the linear growth at the early logarithmic phase more accurately than the previous model, being similar in this respect to the Baranyi model. However, the improved model more accurately predicted the rate constant of growth and the duration of the lag time as compared with the Baranyi model. These results showed that the improved model has the potential to successfully predict microbial growth.     

A modified Weibull model for bacterial inactivation

In this paper, a modified Weibull model is proposed to fit microbial survival curves. This model can incorporate shoulder and/or tailing phenomena if they are encountered. We aim to obtain an accurate fit of the “primary” modelling of the bacterial inactivation and to provide a useful and meaningful model for biologists and food industry. A δ parameter close to the classical concept of the D value, established for sterilisation processes, is used in the model. The specific parameterisation of the Weibull model is evaluated for the parameter of interest δ. The goodness-of-fit of the model is compared to the one produced by the model proposed by Geeraerd et al., [Geeraerd, A.H., Herremans, C.H., Van Impe, J.F., 2000. Structural model requirements to describe microbial inactivation during a mild heat treatment. Int. J. Food Microbiol. 59, 185-209.] on experimental data. As our model provides good fits for the different types of survival curves analysed, further research can focus on the development of suitable secondary model types. In this respect, it is interesting to note that the δ parameter is close to the D concept.     

Development of a multi-classification neural network model to determine the microbial growth/no growth interface

Boundary models have been recognized as useful tools to predict the ability of microorganisms to grow at limiting conditions. However, at these conditions, microbial behaviour can vary, being difficult to distinguish between growth or no growth. In this paper, the data from the study of Valero et al. [Valero, A., Pérez-Rodríguez, F., Carrasco, E., Fuentes-Alventosa, J.M., García-Gimeno, R.M., Zurera, G., 2009. Modelling the growth boundaries of Staphylococcus aureus: Effect of temperature, pH and water activity. International Journal of Food Microbiology 133 (1-2), 186-194] belonging to growth/no growth conditions of Staphylococcus aureus against temperature, pH and a_w were divided into three categorical classes: growth (G), growth transition (GT) and no growth (NG). Subsequently, they were modelled by using a Radial Basis Function Neural Network (RBFNN) in order to create a multi-classification model that was able to predict the probability of belonging at one of the three mentioned classes. The model was developed through an over sampling procedure using a memetic algorithm (MA) in order to balance in part the size of the classes and to improve the accuracy of the classifier. The multi-classification model, named Smote Memetic Radial Basis Function (SMRBF) provided a quite good adjustment to data observed, being able to correctly classify the 86.30% of training data and the 82.26% of generalization data for the three observed classes in the best model. Besides, the high number of replicates per condition tested (n = 30) produced a smooth transition between growth and no growth. At the most stringent conditions, the probability of belonging to class GT was higher, thus justifying the inclusion of the class in the new model. The SMRBF model presented in this study can be used to better define microbial growth/no growth interface and the variability associated to these conditions so as to apply this knowledge to a food safety in a decision-making process.     

Modelling the effect of sub(lethal) heat treatment of Bacillus subtilis spores on germination rate and outgrowth to exponentially growing vegetative cells

Spores of Bacillus subtilis were subjected to relatively mild heat treatments in distilled water and properties of these spores were studied. These spores had lost all or part of their dipicolinic acid (DPA) depending on the severity of the heat treatment. Even after relatively mild heat treatments these spore lost already a small but significant amount of DPA. When these spores were inoculated in nutrient medium-tryptone soy broth (TSA)-the non-lethally heated spores started to germinate. Results of classical optical density measurements showed that both phase darkening and subsequent outgrowth could be affected by sub-lethal heat. A study of single cells in TSB showed that lag times originating from exponentially growing cells followed a normal distribution, whereas lag times originating from spores followed a Weibull distribution. Besides classical optical density measurements were made to study the effect of previous heating on the kinetics of the first stages of germination. The germination kinetics could be described by the model as was proposed by Geeraerd et al. [Geeraerd, A.H., Herremans, C.H. and Van Impe, J.F., 2000. Structural model requirements to describe microbial inactivation during a mild heat treatment. International Journal of Food Microbiology 59, 185-209]. Two of the 4 parameters of the sigmoid model of Geeraerd were dependent on heating time and heating temperature, whereas the two other parameters were considered as independent of the heating conditions. Based on these observations, a secondary model could be developed that describes the combined effect of heating temperature and heating time on the kinetics of germination. To have more detailed information of the kinetics of germination samples incubated in TSB were tested at regular time intervals by flow cytometry. To that end the cells were stained with syto 9 to distinguish between the various germination stages. There was a qualitative agreement between the results of flow cytometry and those of optical density measurements, but there was a difference in quantitative terms. The results have shown that germination rate of spores is dependent on previous heating conditions both in the first stage when phase darkening occurs and also during the later stages of outgrowth when the phase dark spore develops to the vegetative cell.     

Development and validation of a mathematical model to describe the growth of Pseudomonas spp. in raw poultry stored under aerobic conditions

Poultry meat spoils quickly unless it is processed, stored, and distributed under refrigerated conditions. Research has shown that the microbial spoilage rate is predominantly controlled by temperature and the spoilage flora of refrigerated, aerobically-stored poultry meat is generally dominated by Pseudomonas spp.

The objective of our study was to develop and validate a mathematical model that predicts the growth of Pseudomonas in raw poultry stored under aerobic conditions over a variety of temperatures.

Thirty-seven Pseudomonas growth rates were extracted from 6 previously published studies. Objectives, methods and data presentation formats varied widely among the studies, but all the studies used either naturally contaminated meat or poultry or Pseudomonas isolated from meat or poultry grown in laboratory media. These extracted growth rates were used to develop a model relating growth rate of Pseudomonas to storage or incubation temperature. A square-root equation [Ratkowsky, D.A., Olley, J., McMeekin, T.A., and Ball, A., 1982. Relationship between temperature and growth rate of bacterial cultures. J. Appl. Bacteriol. 149, 1–5.] was used to model the data. Model predictions were then compared to 20 Pseudomonas and 20 total aerobes growth rate measurements collected in our laboratory. The growth rates were derived from more than 600 bacterial concentration measurements on raw poultry at 10 temperatures ranging from 0 to 25 °C. Visual inspection of the data and the indices of bias and accuracy factors proposed by Baranyi et al. [Baranyi, J., Pin, C., and Ross, T., 1999. Validating and comparing predictive models. Int. J. Food Micro. 48, 159–166.] were used to analyze the performance of the model.

The experimental data for Pseudomonas showed a 4.8% discrepancy with the predictions and a bias of + 3.6%. Percent discrepancies show close agreement between model predictions and observations, and the positive bias factor demonstrates that the proposed model over-predicts growth rate, thus, can be considered fail-safe. Both Pseudomonas spp. as well as total aerobes may be considered good indicators of poultry spoilage.

A properly constructed and validated model for Pseudomonas growth under aerobic conditions can provide a fast and cost-effective alternative to traditional microbiological techniques to estimate the effects of storage temperature on product shelf-life. The model developed here may be used to determine the effect of both initial Pseudomonas concentration and storage temperature on shelf-life of poultry meat under aerobic storage conditions over temperatures from 0 to 25 °C.