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Modelling the growth of Listeria monocytogenes in dynamic conditions
International Journal of Food Microbiology 55 (2000) 201–207 www.elsevier.nl / locate / ijfoodmicro
Modelling the growth of Listeria monocytogenes in dynamic conditions M. Cheroutre-Vialette, A. Lebert* ` Champanelle, France Station de Recherches sur la Viande, Institut National de la Recherche Agronomique, 63122 Saint-Genes
Abstract A recurrent neural network for the prediction of Listeria monocytogenes growth under pH and a w variable conditions was developed. The use of this model offered the possibility to take into account the consequences of the variations of the factors on L. monocytogenes growth. The effects of solutions, such as NaCl, acetic acid and NaOH, and their interactions on the response of L. monocytogenes cells were studied. Furthermore, the results showed the capacity of the recurrent neural network to predict growths carried out in different experimental conditions without using those used for its elaboration. 2000 Elsevier Science B.V. All rights reserved. Keywords: Listeria monocytogenes; Recurrent neural networks; Dynamic conditions; pH; Water activity
1. Introduction Predictive microbiology combined the knowledge of bacterial growth responses over a range of conditions with the power of mathematical modelling to enable predictions of growth. Mathematical modelling techniques can help to predict how food preservation systems may affect growth kinetics (Whiting and Buchanan, 1994). Most mathematical models developed to simulate the growth of micro-organisms in relation to environmental conditions, were elaborated from data coming from growth carried out in constant conditions of environmental factors, such as a w or pH (Wijtzes et al., 1993; Fernandez et al., 1997). But, food-manufacturing processes can de*Corresponding author. Tel.: 133-4-7362-4179; fax: 133-47362-4610. E-mail address: [email protected] (A. Lebert)
crease the pH of food, produce organic acids, e.g., pickling or fermentation, or reduce water activity, e.g., by addition of an agent such as sodium. These processes are extensively used as mechanisms to prevent microbial growth and to ensure food safety (Presser et al., 1997). Therefore, it is important to understand and to be able to predict the responses of micro-organisms, more particularly pathogenic micro-organisms as Listeria monocytogenes, in the presence of variable environmental factors. In recent years, several investigations which described the growth of micro-organisms in the presence of temperature changes, were carried out (Zwietering et al., 1994; Van Impe et al., 1995). When building these dynamic models, these authors made the hypothesis that the transposition of results obtained from constant conditions to variable conditions was possible. Cheroutre-Vialette et al. (1998) demonstrated the importance of taking into account the variations of
0168-1605 / 00 / $ – see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S0168-1605( 00 )00164-1
202
M. Cheroutre-Vialette, A. Lebert / International Journal of Food Microbiology 55 (2000) 201 – 207
environmental factors, which can occur during a food processing and induce a stress situation for the micro-organisms. The objective of this work was to produce a dynamic model that predicts the growth of L. monocytogenes as a function of fluctuating conditions of acid pH, alkaline pH and concentration of NaCl. To this end, an alternative approach to conventional methods of microbial growth predictions, that is, a recurrent multilayer neural network approach, was used.
2. Material 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 5 7 and a w 5 1 was called standard medium.
2.2. Experimental procedure An automated turbidimeter (Bioscreen C, Labsystem, Labsystem France SA, Les Ulis, France) was used to follow the growth of the strain in the micro-titer plates. The working volume in each well of the micro-titer plate was 400 ml. Optical density (O.D.) was read at a wavelength of 600 nm. According to the procedure expoused 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 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. The
temperature was 208C. For each combination, six growth repetitions were carried out.
2.3. Experimental design The data of L. monocytogenes 14 growths at 208C were taken from an experimental study using a combination of two central composite designs and a factorial design (Fig. 1). The ranges of the different environmental parameters were as follows: NaCl: 0–8%; acid pH: 5.6–7.0 or alkaline pH: 7.0–9.5. Each factor was studied at five levels and for each combination, the shock and limiting conditions were studied. At least 50 experiments were performed according to 25 growths in shock condition and 25 growths in limiting condition.
2.4. Additional experiments Additional experiments were realised and resumed in Table 1. A two-litre fermentor SET2M (Setric Genie Industriel, Inceltech, France) was used. O.D. of the growth was measured with a spectrophotometer (UV-160A, Shimadzu Corporation, Japan) at 600 nm. The protocol was similar to that in Bioscreen C adjusting the different volumes. Growths in shock conditions carried out in the fermentor allowed the study of the osmotic shock effects by continuous addition mode. Seven hundred and fifty milliliters of standard medium were inoculated. At the beginning of exponential phase, 250 ml of osmotic solution
Fig. 1. Experimental design showing the combination of osmotic and pH stresses. m – Learning base; d – testing base; j – validation base.
M. Cheroutre-Vialette, A. Lebert / International Journal of Food Microbiology 55 (2000) 201 – 207
203
Table 1 Additional experiments carried out in Bioscreen C and in fermentor at 208C Addition mode
Time to obtain the addition of 8% NaCl
Bioscreen C
4 steps of 2%
4 h (1 h between steps)
Fermentor
Continuous Continuous
1.8 h 7.7 h
giving a final concentration of 8% NaCl were added using a peristaltic pump. The addition mode of shock solution in Bioscreen C was by steps of 2%.
2.5. 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 ´ Begot et al. (1996). Four quantities were calculated at time t: • (O.D. i ) t , the mean of the O.D. of the 6 repetitions of inoculated media for each combination; • (O.D. ni ) t , the mean of the O.D. of the 4 repetitions of non-inoculated media for each combination; • (DO.D.) t 5 (O.D. i ) t 2 (O.D. ni ) t ; • Yt 5 log 10 [(DO.D.) t /(DO.D. min )] where DO.D. min was the lowest DO.D. value above the detection threshold.
2.6. Recurrent neural network ( RNN) model Neural network (NN) maps inputs to outputs. Supervised neural networks are capable of learning from previous examples through iteration without the requirement of a priori knowledge of the relationships between the process variables. NNs are made of a number of simple, highly connected processing elements (PE) called neurones. The architecture of a NN describes how the NN is constructed from layers of PEs (Hopfield, 1982; Kohonen, 1987). Each PE receives inputs from other PEs or from the outside. The PEs in the input layer only transfer scaled inputs to the appropriate PEs in the hidden layer through
weighted connections. Each PE of the hidden layer and output layer calculates the weighted sum of its inputs and passes the result through a transfer function (Dornier et al., 1995). Most often a nonlinear sigmoid transfer function is employed. The NN is iteratively trained by presenting to it representative exemplar input / output vectors. The weights of the neural connections are adjusted in order to minimise a cost function equal to the mean square of the output error. The weights are usually randomly initialised. It has been shown that one hidden layer of neurones is sufficient to approximate any continuous non-linear function, although more complex networks may be employed in special applications. The distinction between feedforward and recurrent multilayer NNs is the following: for the feedforward multilayer NNs an element of a given layer can only receive information from previous layers; on the contrary, for recurrent multilayer NNs, the values calculated by the NN can be fed back to the NN input layer or any previous layers. The difference in structure induces a difference in training: recurrent multilayer NNs have to be trained on a sequence of predictions, whereas training feedforward multilayer NNs involves only instantaneous predictions. Training a recurrent neural network (RNN) is more timeconsuming but it is able to provide better results than a feedforward NN when simulating the evolution of phenomena with time. RNNs trained to learn dynamic evolutions of a process are more constrained and are forced to find a greater stability as well as a representation of the dynamic links between control and process variables. Therefore, RNNs provide a better prediction confidence than feedforward multilayer NNs that only predict the outputs at a fixed horizon. Furthermore, this technique is more interesting in an advanced control perspective. In the present study, a recurrent multilayer structure which contains one input layer, one hidden layer
204
M. Cheroutre-Vialette, A. Lebert / International Journal of Food Microbiology 55 (2000) 201 – 207
bases, the last 40% were in the validation base. In order to ensure the validity of the study, the growth results carried out in fermentor or in Bioscreen C with various modes of shock exposure were included into the validation base.
3. Results Fig. 2. Schematic structure of the recurrent neural network.
and one output layer, was used. The architecture of the RNN is presented in Fig. 2. It was designed to contain: 1. in the input layer, five input parameters: Yt – Dt , Yt – 2.Dt , Yt – 3.Dt , pH t – Dt and NaCl t – Dt (%) 2. in the output layer, one output parameter: Yt which represented the predicted response. 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 (3 to 10 neurones were tested) and simultaneously observing the change in the mean square of the output error. This was carried out with the training and testing data. Six neurones in the hidden layer was determined as the best structure. The sigmoid function f(x) 5 1 /s1 1 exps 2 xdd 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 overlearning during weights optimisation, and the validation base for validation of results. At least, 60% of experiments were included in the learning and testing
3.1. Growth predictions of the validation base The analysis of the growth predictions in the limiting conditions showed that the RNN represented satisfactorily the experimental data whatever the conditions tested (alkaline–osmotic or acid–osmotic) (results not shown). As shown in Fig. 3A, the RNN was able to predict growth when two parameters vary simultaneously (pH 9.1 and 6.8% NaCl). The different characteristics of the L. monocytogenes response, i.e. induction of a lag time and growth recovery different to those observed in the new environment, were taken into account by the RNN whatever the combination, alkaline–osmotic or acid– osmotic. Furthermore, RNN was able to predict the effect of the type of shocks and their combinations. As indicated in the Fig. 3B, the growth of L. monocytogenes 14 was particularly affected by the combined acid–osmotic shocks (pH 5.6 and 8% NaCl) in exponential phase since no increase of optical density was observed during the experimental period. There was a good agreement between the experimental growth and the prediction.
3.2. Growth predictions of the additional experiments The previous results of the validation base demonstrated the ability of the RNN to predict growths under shock conditions when the pH and a w transitions were carried out abruptly by one step. The objective of additional experiments was to investigate the capacity of the RNN to represent the response of L. monocytogenes cells shocked in exponential phase with 8% NaCl added by repeated steps of 2% NaCl or continuously during a duration of one or four generation times. The effects of adding 8% NaCl in 7.7 h (four generation times) is
M. Cheroutre-Vialette, A. Lebert / International Journal of Food Microbiology 55 (2000) 201 – 207
205
Fig. 3. Comparison between experimental (—) and calculated (? ? ?) growth curves: [A]5Shock pH 9.1 and 6.8% NaCl. [B]5Shock pH 5.8 and 8% NaCl. % NaCl (- - -); pH (– ? –).
shown in Fig. 4A. Fig. 4B shows the growth prediction when NaCl was added by steps of 2%. The extrapolation to new experimental conditions (mode of shock exposure) was made with a good agreement by the RNN. It confirmed that the RNN has the capacity to predict growths carried out in different experimental conditions from those used for its elaboration.
4. Discussion These results obtained at variable conditions showed that neural networks can effectively be used to study the complex effects of fluctuating environmental conditions on micro-organism behaviour. Such dynamic model could follow the microbial impact of different steps associated with production,
206
M. Cheroutre-Vialette, A. Lebert / International Journal of Food Microbiology 55 (2000) 201 – 207
Fig. 4. Comparison between experimental (—) and calculated (? ? ?) growth curves: [A]5Osmotic shock (8% NaCl) applied 7.7 h. [B]5Osmotic shock (8% NaCl) applied by steps of 2%. % NaCl (- - -); pH (– ? –).
distribution and retailing of a food and so could be an important support to HACCP and food safety systems (Buchanan, 1993).
References ´ Begot, C., Desnier, I., Daudin, J.D., Labadie, J.C., Lebert, A., 1996. Recommendations for calculating growth parameters by
optical density measurements. J. Microbiol. Methods 25, 225– 232. Buchanan, R.L., 1993. Predictive food microbiology. Trends Food Sci. Technol. 4, 6–11. ´ Cheroutre-Vialette, M., Lebert, I., Hebraud, M., Labadie, J.C., Lebert, A., 1998. Effects of pH or a w stress on growth of Listeria monocytogenes. Int. J. Food Microbiol. 42, 71–77. Chirife, J., Resnik, S.L., 1984. Unsaturated solutions of sodium chloride as reference sources of water activity at various temperatures. J. Food Sci. 49, 1486–1488. Dornier, M., Decloux, M., Trystram, G., Lebert, A., 1995.
M. Cheroutre-Vialette, A. Lebert / International Journal of Food Microbiology 55 (2000) 201 – 207 Dynamic modeling of crossflow micro filtration using neural networks. J. Membrane Sci. 98, 263–273. Fernandez, P.S., George, S.M., Sills, C.C., Peck, M.W., 1997. Predictive model of the effect of CO 2 , pH, temperature and NaCl on the growth of Listeria monocytogenes. Int. J. Food Microbiol. 37, 37–45. ´ P., Valin, C., 1973. Conservation de la viande Fournaud, J., Sale, ` bovine sous emballage plastique, sous vide ou en atmosphere ˆ ´ Aspects biochimiques et microbiologiques. In: XIXe` controlee. ´ ´ Reunion Europeennne des Chercheurs en Viande, Paris-1, pp. 291–313. Hopfield, J.J., 1982. Neural networks and physical systems with emergent collective computational abilities. Proc. Natl. Acad. Sci. – Biophysics 79, 2554–2558. Kohonen, T., 1987. Self-organization and Associative Memory, 2nd Edition, Springer-Verlag. Presser, K.A., Ratkowsky, D.A., Ross, T., 1997. Modelling the
207
growth rate of Escherichia coli as a function of pH and lactic acid concentration. Appl. Environ. Microbiol. 63, 2355–2360. Shanno, D.F., 1970. Conditioning of quasi-Newton methods for function minimization. Mat. Comput. 24, 647–656. ¨ B.M., Schellekens, M., Martens, T., De Van Impe, J.F., Nicolaı, Baerdemaeker, J., 1995. Predictive microbiology in a dynamic environment: a system theory approach. Int. J. Food Microbiol. 25, 227–249. Whiting, R.C., Buchanan, R.L., 1994. Microbial modelling. Food Technol. 48, 113–120. Wijtzes, T., McClure, P.J., Zwietering, M.H., Roberts, T.A., 1993. Modelling bacterial growth of Listeria monocytogenes as a function of water activity, pH and temperature. Int. J. Food Microbiol. 18, 139–149. Zwietering, M.H., De Wit, J.C., Cuppers, H.G.A.M., Van’t Riet, K., 1994. Modeling of bacterial growth with shifts in temperature. Appl. Environ. Microbiol. 60, 204–213.
Modelling the growth of Listeria monocytogenes in dynamic conditions M. Cheroutre-Vialette, A. Lebert* ` Champanelle, France Station de Recherches sur la Viande, Institut National de la Recherche Agronomique, 63122 Saint-Genes
Abstract A recurrent neural network for the prediction of Listeria monocytogenes growth under pH and a w variable conditions was developed. The use of this model offered the possibility to take into account the consequences of the variations of the factors on L. monocytogenes growth. The effects of solutions, such as NaCl, acetic acid and NaOH, and their interactions on the response of L. monocytogenes cells were studied. Furthermore, the results showed the capacity of the recurrent neural network to predict growths carried out in different experimental conditions without using those used for its elaboration. 2000 Elsevier Science B.V. All rights reserved. Keywords: Listeria monocytogenes; Recurrent neural networks; Dynamic conditions; pH; Water activity
1. Introduction Predictive microbiology combined the knowledge of bacterial growth responses over a range of conditions with the power of mathematical modelling to enable predictions of growth. Mathematical modelling techniques can help to predict how food preservation systems may affect growth kinetics (Whiting and Buchanan, 1994). Most mathematical models developed to simulate the growth of micro-organisms in relation to environmental conditions, were elaborated from data coming from growth carried out in constant conditions of environmental factors, such as a w or pH (Wijtzes et al., 1993; Fernandez et al., 1997). But, food-manufacturing processes can de*Corresponding author. Tel.: 133-4-7362-4179; fax: 133-47362-4610. E-mail address: [email protected] (A. Lebert)
crease the pH of food, produce organic acids, e.g., pickling or fermentation, or reduce water activity, e.g., by addition of an agent such as sodium. These processes are extensively used as mechanisms to prevent microbial growth and to ensure food safety (Presser et al., 1997). Therefore, it is important to understand and to be able to predict the responses of micro-organisms, more particularly pathogenic micro-organisms as Listeria monocytogenes, in the presence of variable environmental factors. In recent years, several investigations which described the growth of micro-organisms in the presence of temperature changes, were carried out (Zwietering et al., 1994; Van Impe et al., 1995). When building these dynamic models, these authors made the hypothesis that the transposition of results obtained from constant conditions to variable conditions was possible. Cheroutre-Vialette et al. (1998) demonstrated the importance of taking into account the variations of
0168-1605 / 00 / $ – see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S0168-1605( 00 )00164-1
202
M. Cheroutre-Vialette, A. Lebert / International Journal of Food Microbiology 55 (2000) 201 – 207
environmental factors, which can occur during a food processing and induce a stress situation for the micro-organisms. The objective of this work was to produce a dynamic model that predicts the growth of L. monocytogenes as a function of fluctuating conditions of acid pH, alkaline pH and concentration of NaCl. To this end, an alternative approach to conventional methods of microbial growth predictions, that is, a recurrent multilayer neural network approach, was used.
2. Material 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 5 7 and a w 5 1 was called standard medium.
2.2. Experimental procedure An automated turbidimeter (Bioscreen C, Labsystem, Labsystem France SA, Les Ulis, France) was used to follow the growth of the strain in the micro-titer plates. The working volume in each well of the micro-titer plate was 400 ml. Optical density (O.D.) was read at a wavelength of 600 nm. According to the procedure expoused 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 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. The
temperature was 208C. For each combination, six growth repetitions were carried out.
2.3. Experimental design The data of L. monocytogenes 14 growths at 208C were taken from an experimental study using a combination of two central composite designs and a factorial design (Fig. 1). The ranges of the different environmental parameters were as follows: NaCl: 0–8%; acid pH: 5.6–7.0 or alkaline pH: 7.0–9.5. Each factor was studied at five levels and for each combination, the shock and limiting conditions were studied. At least 50 experiments were performed according to 25 growths in shock condition and 25 growths in limiting condition.
2.4. Additional experiments Additional experiments were realised and resumed in Table 1. A two-litre fermentor SET2M (Setric Genie Industriel, Inceltech, France) was used. O.D. of the growth was measured with a spectrophotometer (UV-160A, Shimadzu Corporation, Japan) at 600 nm. The protocol was similar to that in Bioscreen C adjusting the different volumes. Growths in shock conditions carried out in the fermentor allowed the study of the osmotic shock effects by continuous addition mode. Seven hundred and fifty milliliters of standard medium were inoculated. At the beginning of exponential phase, 250 ml of osmotic solution
Fig. 1. Experimental design showing the combination of osmotic and pH stresses. m – Learning base; d – testing base; j – validation base.
M. Cheroutre-Vialette, A. Lebert / International Journal of Food Microbiology 55 (2000) 201 – 207
203
Table 1 Additional experiments carried out in Bioscreen C and in fermentor at 208C Addition mode
Time to obtain the addition of 8% NaCl
Bioscreen C
4 steps of 2%
4 h (1 h between steps)
Fermentor
Continuous Continuous
1.8 h 7.7 h
giving a final concentration of 8% NaCl were added using a peristaltic pump. The addition mode of shock solution in Bioscreen C was by steps of 2%.
2.5. 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 ´ Begot et al. (1996). Four quantities were calculated at time t: • (O.D. i ) t , the mean of the O.D. of the 6 repetitions of inoculated media for each combination; • (O.D. ni ) t , the mean of the O.D. of the 4 repetitions of non-inoculated media for each combination; • (DO.D.) t 5 (O.D. i ) t 2 (O.D. ni ) t ; • Yt 5 log 10 [(DO.D.) t /(DO.D. min )] where DO.D. min was the lowest DO.D. value above the detection threshold.
2.6. Recurrent neural network ( RNN) model Neural network (NN) maps inputs to outputs. Supervised neural networks are capable of learning from previous examples through iteration without the requirement of a priori knowledge of the relationships between the process variables. NNs are made of a number of simple, highly connected processing elements (PE) called neurones. The architecture of a NN describes how the NN is constructed from layers of PEs (Hopfield, 1982; Kohonen, 1987). Each PE receives inputs from other PEs or from the outside. The PEs in the input layer only transfer scaled inputs to the appropriate PEs in the hidden layer through
weighted connections. Each PE of the hidden layer and output layer calculates the weighted sum of its inputs and passes the result through a transfer function (Dornier et al., 1995). Most often a nonlinear sigmoid transfer function is employed. The NN is iteratively trained by presenting to it representative exemplar input / output vectors. The weights of the neural connections are adjusted in order to minimise a cost function equal to the mean square of the output error. The weights are usually randomly initialised. It has been shown that one hidden layer of neurones is sufficient to approximate any continuous non-linear function, although more complex networks may be employed in special applications. The distinction between feedforward and recurrent multilayer NNs is the following: for the feedforward multilayer NNs an element of a given layer can only receive information from previous layers; on the contrary, for recurrent multilayer NNs, the values calculated by the NN can be fed back to the NN input layer or any previous layers. The difference in structure induces a difference in training: recurrent multilayer NNs have to be trained on a sequence of predictions, whereas training feedforward multilayer NNs involves only instantaneous predictions. Training a recurrent neural network (RNN) is more timeconsuming but it is able to provide better results than a feedforward NN when simulating the evolution of phenomena with time. RNNs trained to learn dynamic evolutions of a process are more constrained and are forced to find a greater stability as well as a representation of the dynamic links between control and process variables. Therefore, RNNs provide a better prediction confidence than feedforward multilayer NNs that only predict the outputs at a fixed horizon. Furthermore, this technique is more interesting in an advanced control perspective. In the present study, a recurrent multilayer structure which contains one input layer, one hidden layer
204
M. Cheroutre-Vialette, A. Lebert / International Journal of Food Microbiology 55 (2000) 201 – 207
bases, the last 40% were in the validation base. In order to ensure the validity of the study, the growth results carried out in fermentor or in Bioscreen C with various modes of shock exposure were included into the validation base.
3. Results Fig. 2. Schematic structure of the recurrent neural network.
and one output layer, was used. The architecture of the RNN is presented in Fig. 2. It was designed to contain: 1. in the input layer, five input parameters: Yt – Dt , Yt – 2.Dt , Yt – 3.Dt , pH t – Dt and NaCl t – Dt (%) 2. in the output layer, one output parameter: Yt which represented the predicted response. 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 (3 to 10 neurones were tested) and simultaneously observing the change in the mean square of the output error. This was carried out with the training and testing data. Six neurones in the hidden layer was determined as the best structure. The sigmoid function f(x) 5 1 /s1 1 exps 2 xdd 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 overlearning during weights optimisation, and the validation base for validation of results. At least, 60% of experiments were included in the learning and testing
3.1. Growth predictions of the validation base The analysis of the growth predictions in the limiting conditions showed that the RNN represented satisfactorily the experimental data whatever the conditions tested (alkaline–osmotic or acid–osmotic) (results not shown). As shown in Fig. 3A, the RNN was able to predict growth when two parameters vary simultaneously (pH 9.1 and 6.8% NaCl). The different characteristics of the L. monocytogenes response, i.e. induction of a lag time and growth recovery different to those observed in the new environment, were taken into account by the RNN whatever the combination, alkaline–osmotic or acid– osmotic. Furthermore, RNN was able to predict the effect of the type of shocks and their combinations. As indicated in the Fig. 3B, the growth of L. monocytogenes 14 was particularly affected by the combined acid–osmotic shocks (pH 5.6 and 8% NaCl) in exponential phase since no increase of optical density was observed during the experimental period. There was a good agreement between the experimental growth and the prediction.
3.2. Growth predictions of the additional experiments The previous results of the validation base demonstrated the ability of the RNN to predict growths under shock conditions when the pH and a w transitions were carried out abruptly by one step. The objective of additional experiments was to investigate the capacity of the RNN to represent the response of L. monocytogenes cells shocked in exponential phase with 8% NaCl added by repeated steps of 2% NaCl or continuously during a duration of one or four generation times. The effects of adding 8% NaCl in 7.7 h (four generation times) is
M. Cheroutre-Vialette, A. Lebert / International Journal of Food Microbiology 55 (2000) 201 – 207
205
Fig. 3. Comparison between experimental (—) and calculated (? ? ?) growth curves: [A]5Shock pH 9.1 and 6.8% NaCl. [B]5Shock pH 5.8 and 8% NaCl. % NaCl (- - -); pH (– ? –).
shown in Fig. 4A. Fig. 4B shows the growth prediction when NaCl was added by steps of 2%. The extrapolation to new experimental conditions (mode of shock exposure) was made with a good agreement by the RNN. It confirmed that the RNN has the capacity to predict growths carried out in different experimental conditions from those used for its elaboration.
4. Discussion These results obtained at variable conditions showed that neural networks can effectively be used to study the complex effects of fluctuating environmental conditions on micro-organism behaviour. Such dynamic model could follow the microbial impact of different steps associated with production,
206
M. Cheroutre-Vialette, A. Lebert / International Journal of Food Microbiology 55 (2000) 201 – 207
Fig. 4. Comparison between experimental (—) and calculated (? ? ?) growth curves: [A]5Osmotic shock (8% NaCl) applied 7.7 h. [B]5Osmotic shock (8% NaCl) applied by steps of 2%. % NaCl (- - -); pH (– ? –).
distribution and retailing of a food and so could be an important support to HACCP and food safety systems (Buchanan, 1993).
References ´ Begot, C., Desnier, I., Daudin, J.D., Labadie, J.C., Lebert, A., 1996. Recommendations for calculating growth parameters by
optical density measurements. J. Microbiol. Methods 25, 225– 232. Buchanan, R.L., 1993. Predictive food microbiology. Trends Food Sci. Technol. 4, 6–11. ´ Cheroutre-Vialette, M., Lebert, I., Hebraud, M., Labadie, J.C., Lebert, A., 1998. Effects of pH or a w stress on growth of Listeria monocytogenes. Int. J. Food Microbiol. 42, 71–77. Chirife, J., Resnik, S.L., 1984. Unsaturated solutions of sodium chloride as reference sources of water activity at various temperatures. J. Food Sci. 49, 1486–1488. Dornier, M., Decloux, M., Trystram, G., Lebert, A., 1995.
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