Predictive microbiology can provide a means to quickly evaluate the consequence of any changes in formulation or processing. This quantitative method describes the effects of variables, influencing safety, on microbial growth, survival or inactivation. The main factors influencing microbial stability in meat products are temperature, pH and water activity (Buchanan and McDonald). As these factors may vary extensively during food processing, dynamic mathematical models (i.e. involving differential equations) are needed to predict accurately the shelf life of this type of product. Several authors (Zwietering; Van and Baranyi) have developed these dynamic models to describe growth and inactivation of microbial population as a function of time and temperature. The structure of these models imposed the formulation of hypothesis on the behaviour of the microorganism submitted to the temperature change; e.g. no stress situation was induced. Our previous studies have been carried out on the effects of acid, alkaline or osmotic stresses on Listeria monocytogenes growth at 20 or 10 °C (Cheroutre; Cheroutre and Cheroutre). The main results established a complex response of the bacteria and concluded that the dynamic models of temperature could not be applied to the growth under pH or a_w dynamic environment.

Another methodologies were investigated on their usefulness in the field on predictive microbiology, the artificial neural network. An overview of the methodology of artificial neural network modeling can be found in Najjar et al. (1997) and Hajmeer et al. (1997). Geeraerd et al. (1998) described the interacting effects of environmental factors (temperature, pH and % NaCl) on microbial activity by using black box artificial neural networks.

A dynamic model, based on a recurrent neural network, was previously published to describe the growth of L. monocytogenes as a function of fluctuating conditions of pH (acid or alkaline) and concentration of NaCl, at 20 °C (Cheroutre-Vialette and Lebert, 2000b). This article presents a comparison of L. monocytogenes behaviour at 20 °C and lower temperature, 10 °C, in fluctuating conditions of pH and a_w. The dynamic model was improved by taking into account the different growth temperatures.

2. MATERIALS AND METHODS

2.1. Strain and medium

L. monocytogenes 14 (serotype 4b), obtained from an industrial environment, was used throughout the study. All growth experiments were conducted in a tryptic meat broth (TMB) (Fournaud et al., 1973). TMB, regulated at pH 7 and 0% NaCl was called standard medium.

2.2. Experimental procedure

An automated turbidimeter (Bioscreen C, Labsystem, Labsystem France, Les Ulis, France) was used to follow the growth of L. monocytogenes 14 in the micro-titer plates. The working volume in each well of the micro-titer plate was 400 l. Optical density (O.D.) was read at a wavelength of 600 nm. According to the procedure described by Cheroutre-Vialette et al. (1998), for all experiments three conditions were studied: standard, limiting and shock conditions. Under standard and limiting conditions, bacteria were grown in TMB adjusted to the desired a_w and pH values. The growth media were inoculated with a concentration of about 3.10⁷ cfu ml⁻¹, in order to be above threshold of the Bioscreen C. The osmotic variation was achieved by the addition of NaCl (Prolabo, Fontenay Sous Bois, France) according to Chirife and Resnik (1984). Acetic (Carlo Erba, Nanterre, France) acid and NaOH (Prolabo) were added to adjust low and high pH, respectively. The shock condition was defined as follows : the bacteria were grown in standard medium until the beginning of the exponential phase and were then shocked by the abrupt addition of shock solutions. These shock solutions were prepared in order to obtain a final value similar to those indicated for the limiting conditions. For each combination, six growth repetitions were carried out.

2.3. Experimental design

A combination of a factorial design and two central composite design (Fig. 1) were use to assess quantitatively the effects and interactions of NaCl (0–8%) and pH (5.6–9.5) variations on the growth of L. monocytogenes 14 at two temperatures, 10 and 20 °C. For each combination, the shock and limiting conditions were studied. At least, for each temperature, 50 experiments were performed according to 25 growths in shock condition and 25 growths in limiting condition. For each combination of the experimental design, a growth in the standard condition was also performed to verify the homogeneity of the results.

 

 

Fig. 1. Experimental design showing the combination of pH and osmotic variations. Learning base. • Testing base. Validation base.

 

2.4. Data analysis

Averages of the O.D. were calculated for the six repetitions of inoculated media and for the four repetitions of non-inoculated media. The data were then analysed using the procedure described by Bégot et al. (1996). Four quantities were calculated at time t:

1. (O.D._i)_t, the mean of the O.D. of the six repetitions of inoculated media for each combination;

2. (O.D._ni)_t, the mean of the O.D. of the four repetitions of non-inoculated media for each combination;

3. (ΔO.D.)_t=(O.D._i)_t−(O.D._ni)_t;

4. Y_t=log₁₀[(ΔO.D.)_t/(ΔO.D._min)] where ΔO.D._min was the lowest ΔO.D. value above the detection threshold.

As indicated by Cheroutre-Vialette et al. (1998), a modified Gompertz equation (Zwietering et al., 1990) was used to fit the growth curves Y_t=f(t). Growth parameters such as A (logarithmic increase of population), (lag time) and (maximal growth rate) were determined by non-linear regression with STAT-ITCF statistic software (Gouet and Philippeau, Institut technique des céréales et des fourrages, Paris, France). Generation time (GT) was derived from using the relation:

In standard and limiting conditions, the time of inoculation was taken as zero time when considering the growth curve. In shock condition, the time of addition of the shock solution was taken as zero time in the calculation of the growth parameters.

2.5. Recurrent neural network (RNN) model

In the present study, a recurrent multilayer structure which contains one input layer, one hidden layer and one output layer, was used. The architecture of the RNN was previously defined (Cheroutre-Vialette and Lebert, 2000b) and was improved to take into account the temperature in the input layer (Fig. 2):

1. In the input layer, six input parameters: Y_t−Δt, Y_t−2·Δt, Y_t−3·Δt, pH_t−Δt, NaCl_t−Δt (%) and temperature (T_t−Δt) (°C)

2. In the output layer, one output parameter: Y_t which represented the predicted response.

 

 

Fig. 2. Schematic structure of the recurrent neural network.

 

A priori, there are no rules for the choice of the hidden structure. It is determined empirically: the structure that gives the best results is chosen. The optimum neurone number of the hidden layer was iteratively determined by developing several RNNs that vary with the size of the hidden layer (three to nine neurones were tested) and simultaneously observing the change in the mean square of the output error (Fig. 3). This was carried out with the training and testing data. Seven neurones in the hidden layer were determined as the best structure.

 

 

Fig. 3. Effect of the neuron numbers in hidden layer on the error of prediction.

 

The sigmoid function f(x)=1/(1+exp(−x)) was chosen as an activation function for each neurone. The RNN was trained by iteration using a repeated presentation of representative exemplar input/output vector pairs. The weights of the neural connections, initially chosen randomly, are adjusted by a non-linear optimisation technique: the quasi-Newtonian formula of Shanno (1970) in order to minimise a cost function equal to the mean square of the output error. Fig. 1 indicates the repartition of the experiments in the learning, testing and validation bases. The learning base was used to adjust the weights, the testing base to provide over-learning during weight optimisation, and the validation base for validation of results. At least 60% of experiments were included in the learning and testing bases, the last 40% were in the validation base.

The recurrent network software was developed using Matlab software and the Optimisation Toolbox (Mathworks). This software includes the pre-processing of the data, the training of the recurrent network and the visualisation of the results.

3. RESULTS

3.1. Behaviour of L. monocytogenes in dynamic conditions of pH and a_w at 20 and 10 °C

Some differences of L. monocytogenes 14 behaviour were observed between growths carried out in variable environment of pH and a_w (shock condition) and growths carried out in constant environment (limiting condition). The growth parameters, i.e. and GT, calculated with Gompertz equation revealed that the abrupt fluctuations of pH and/or a_w applied during exponential growth of L. monocytogenes (shock condition) did not allow cells to recover growths similar to those obtained in limiting condition, whatever the growth temperature (10 or 20 °C). As indicated by the examples presented in Table 1, the growth continued after the environmental variations with a generation time value different from that observed before the change (standard condition) or that observed when the new environmental conditions were present at the beginning of the culture (limiting condition). These differences were observed whatever the growth temperature and the intensity of simultaneously factors variations, acid-osmotic or alkaline-osmotic, e.g. low variation of the pH and a_w factors (level A or E), higher variation of one of factor (levels B, C or F, G) or high variation of the two factors (level D or G). According to the calculated GT values, a synergic effect between the acid pH or alkaline pH and a_w (% NaCl) was noted, whatever the tested condition. In shock condition, the growth recovery was particularly affected by the large factor variations. Furthermore, this synergic effect was strengthened by the third factor, the temperature, as shown in Table 1.

 

 

Table 1. Generation times, expressed in hours, calculated in limiting and shock conditions for different levels of acid-osmotic or alkaline-osmotic combinations at 10 and 20 °C

In brackets: asymptotic 95% confidence interval.

 

In shock condition, L. monocytogenes 14 responded instantaneously to small changes of pH and a_w. In exchange, large variations induced a lag phase before the growth recovery. The evolution of induced lag times for the different combinations of the experimental design at 20 and 10 °C was represented in Fig. 4a and b, respectively. As shown by this figure, there was a graduation in the bacteria response. The lag phase before the growth recovery was more pronounced especially as the environmental variations were higher. The values calculated at 10 °C were, on average, multiplied by a factor 3, compared to those obtained at 20 °C.

 

 

Fig. 4. Response surface representing the evolution of induced lag times (expressed in hours) of L. monocytogenes 14 in shock conditions for all combinations of the experimental design at 20 °C (a) and 10 °C (b).

 

The present results confirmed our previous studies (Cheroutre and Cheroutre). The main conclusions could be resumed as follows. Several characteristics of L. monocytogenes response in dynamic pH and/or a_w environment, whatever the temperature, were underlined: (i) large fluctuations of pH and/or a_w induced a lag phase, and (ii) growth recovery was different to those observed in previous environment and new environment.

3.2. Simulation of growths by RNN model

The aim of this study was to determine a dynamic model, capable of describing accurately growths in non-variable and variable environmental conditions of pH and a_w according to different growth temperature.

The RNN model simulated with good agreement, compared to experimental data, the growths in limiting conditions (i.e. in constant pH and a_w environment), whatever the combinations (alkaline-osmotic or acid-osmotic) and the temperature (20 or 10 °C) (Fig. 5). Fig. 6 and Fig. 7 reveal that the dynamic model descriptions were satisfactory and illustrated the capability of this model to describe the influence of alkaline-osmotic (Fig. 6) or acid-osmotic (Fig. 7) on the L. monocytogenes behaviour. As indicated on these examples of validation base, the RNN model distinguished the potential impact of shock solutions on the growth recovery according to the culture temperature. Indeed, it was able to reproduce the response of L. monocytogenes according to the intensity of the pH and a_w fluctuations, e.g. the eventual induced lag times and the characteristics of the growth recovery.

 

 

Fig. 5. Comparison between experimental (—) and calculated (---) growth curves in limiting condition of the validation base: pH=6.3, 4% NaCl, at 10 °C (a) and 20 °C (b). Profiles of % NaCl (–––) and pH (–--–--–) are indicated on the graph.

 

Fig. 6. Comparison between experimental (—) and calculated (---) growth curves in shock condition for any alkaline-osmotic combinations of the validation base: at 10 °C: pH=9.1, 1.2% NaCl (a); pH=9.1, 6.8% NaCl (b) and at 20 °C: pH=9.1, 1.2% NaCl (c); pH=9.1, 6.8% NaCl (d). Profiles of % NaCl (–––) and pH (–--–--–) are indicated on the graph.

 

 

Fig. 7. Comparison between experimental (—) and calculated (---) growth curves in shock condition for any acid-osmotic combinations of the validation base: at 10 °C: pH=5.8, 1.2% NaCl (a); pH=5.8, 6.8% NaCl (b) and at 20 °C: pH=5.8, 1.2% NaCl (c); pH=5.8, 6.8% NaCl (d). Profiles of % NaCl (–––) and pH (–--–--–) are indicated on the graph.

 

In conclusion, the modification brought to our previous RNN model (Cheroutre-Vialette and Lebert, 2000b), i.e. the addition of one neuron (representing the temperature value) in the structure of the input layer, was adequate to represent the whole experimental data collected at the different temperatures.

4. DISCUSSION

The possible use of artificial neural network in the field of predictive microbiology has recently inspired several studies (Hajmeer and Geeraerd). The different approaches of these authors concluded that recurrent neural network models were good alternatives for more classical models. The results of this work highlighted the problems associated with the variable conditions and the available models describing the growth of microorganisms in the presence of temperature changes (Zwietering and Van). The structure of these models (based on differential equations) imposed to make the hypothesis that the transposition of results obtained from constant conditions to variable conditions was possible. This hypothesis could not be applied to our experimental data obtained in dynamic conditions of pH and a_w. In this way, the neural network approach allowed to avoid formulating hypothesis on microbial behaviour. The model even revealed a good predictive capacity for the L. monocytogenes behaviour. Indeed, the model developed in this study was assessed with data available in Cheroutre-Vialette and Lebert (2000b), specially with the growths of L. monocytogenes 14 submitted at 20 °C to osmotic shock (NaCl 8%) during approximately 2 h (corresponding to the time of one doubly of population, i.e. one generation time in standard condition) or 8 h (corresponding to four generation times). The adaptation to the shock was different, in the first case, the response was similar to those consequently to abrupt shock, and in the second case, the duration of shock permitted to cells to have behaviour similar to limiting shock. An accurate description of the L. monocytogenes complex response was given by the present RNN model. It is important to underline that the RNN was only trained with data obtained in abrupt shock conditions. This extrapolation demonstrated the high capacity of the artificial neural network for the predictions of growth and representation of microbial behaviour in dynamic environment.

The recurrent neural network will be extended towards another fluctuating variable during time. As can be seen in the present work, the modification of the RNN structure has been minor to take into account an additional variable, the temperature. Although the data used were collected in constant condition of temperature, the developed RNN can take into account fluctuation of this variable.

In future, growths of several microorganisms would be considered. The general network structure could be retained, but parameters, typical for each microorganism and its environment, would be identified and incorporated in the input layer. As indicated by Geeraerd et al. (1998), microorganisms could be differentiated by using their cardinal points, inspired by the work of Rosso et al. (1995).

The facility and capacity of neural network adaptation to new situation give a promising approach in the field of dynamic models. The development of these models will allow the impact of the different steps associated with the production, distribution and retailing of a food to be followed.

REFERENCES

Baranyi et al., 1996. J. Baranyi, A. Jones, C. Walker, A. Kaloti, T.P. Robinson and B.M. Mackey , A combined model for growth and subsequent thermal inactivation of Brochothrix thermosphacta. Appl. Environ. Microbiol. 62 3 (1996), pp. 1029-1035.

Bégot et al., 1996. C. Bégot, I. Desnier, J.D. Daudin, J.C. Labadie and A. Lebert , Recommendations for calculating growth parameters by optical density measurements. J. Microbiol. Methods 25 (1996), pp. 225-232.

Buchanan, 1993. R.L. Buchanan , Predictive food microbiology. Trends Food Sci. Technol. 4 (1993), pp. 6-11.

Cheroutre-Vialette and Lebert, 2000a. M. Cheroutre-Vialette and A. Lebert , Growth of Listeria monocytogenes as a function of dynamic environment at 10 °C and accuracy of growth predictions with available models. Food Microbiol. 17 (2000), pp. 83-92.

Cheroutre-Vialette and Lebert, 2000b. M. Cheroutre-Vialette and A. Lebert , Modelling the growth of Listeria monocytogenes in dynamic conditions. Int. J. Food Microbiol. 42 (2000), pp. 71-77.

Cheroutre-Vialette and Lebert, 2000c. M. Cheroutre-Vialette and A. Lebert , Modelling the growth of Listeria monocytogenes in dynamic condition swith recurrent neural networks. In: J.F.M. Van Impe and K. Bernaerts, Editors, Predictive Modelling in Foods-Conference Proceedings, KUL Leuven/BioTeC, Belgium (2000), pp. 27-30 (ISBN 90-804818-3-1) .

Cheroutre-Vialette et al., 1998. M. Cheroutre-Vialette, I. Lebert, M. Hébraud, J.C. Labadie and A. Lebert , Effects of pH or aw stress on growth of Listeria monocytogenes. Int. J. Food Microbiol. 42 (1998), pp. 71-77.

Chirife and Resnik, 1984. J. Chirife and S.L. Resnik , Unsaturated solutions of sodium chloride as reference sources of water activity at various temperatures. J. Food Sci. 49 (1984), pp. 1486-1488.

Fournaud et al., 1973. J. Fournaud, P. Salé and C. Valin , Conservation de la viande bovine sous emballage plastique, sous vide ou en atmosphère contrôlée. Aspects biochimiques et microbiologiques. In: XIXè Réunion Européennne des Chercheurs en Viande, Paris-1 (1973), pp. 291-313.

Geeraerd et al., 1998. A.H. Geeraerd, C.H. Herremans, C. Cenens and J.F. Van Impe , Application of artificial neural networks as a non-linear modular modeling technique to describe growth in chilled food products. Int. J. Food Microbiol. 44 (1998), pp. 49-68.

Hajmeer et al., 1997. M.N. Hajmeer, I.A. Basheer and Y.M. Najjar , Computational neural networks for predictive microbiology: II. Application to microbial growth. Int. J. Food Microbiol. 34 (1997), pp. 51-66.

McDonald and Sun, 1999. K. McDonald and D.W. Sun , Predictive food microbiology for the meat industry: a review. Int. J. Food Microbiol. 52 (1999), pp. 1-27.

Najjar et al., 1997. Y.M. Najjar, I.A. Basheer and M.N. Hajmeer , Computational neural networks for predictive microbiology: I. Methodology. Int. J. Food Microbiol. 34 (1997), pp. 27-49.

Rosso et al., 1995. L. Rosso, J.R. Lobry, S. Bajard and J.P. Flandrois , Convenient model to describe the combined effects of temperature and pH on microbial growth. Appl. Environ. Microbiol. 61 (1995), pp. 610-616.

Shanno, 1970. D.F. Shanno , Conditioning of Quasi-Newton methods for function minimization. Mat. Comput. 24 (1970), pp. 647-656.

Van Impe et al., 1995. J.F. Van Impe, B.M. Nicolaï, M. Schellekens, T. Martens and J. De Baerdemaeker , Predictive microbiology in a dynamic environment: a system theory approach. Int. J. Food Microbiol. 25 (1995), pp. 227-249.

Zwietering et al., 1990. M.H. Zwietering, I. Jongenburger, F.M. Rombouts and K. Van't Riet , Modeling of bacterial growth curve. Appl. Environ. Microbiol. 56 (1990), pp. 1875-1881.

Zwietering et al., 1994. M.H. Zwietering, J.C. De Wit, H.G.A.M. Cuppers and K. Van't Riet , Modeling of bacterial growth with shifts in temperature. Appl. Environ. Microbiol. 60 (1994), pp. 204-213.

(order Full Text from publisher)