Mejlholm, O. and P. Dalgaard (2007b). Modeling and predicting the growth of lactic acid bacteria in lightly preserved seafood and their inhibiting effect on Listeria monocytogenes  J. Food Prot. 70 (11), 2485-2497.

This model includes the effect of seven environmental parameters (temperature, atmosphere (CO₂), water phase salt/water activity, pH, smoke components/phenol, lactate and diactate) on the simultaneous growth of L. monocytogenes and lactic acid bacteria (LAB) in lightly preserved seafood including many ready-to-eat products. Information on the lag time of L. monocytogenes in naturally contaminated lightly preserved seafood is still limited. Therefore, the growth model for L. monocytogenes can be used without lag time (fail safe predictions) or with lag time (more realistic predictions for naturally contaminated products). SSSP uses a relative lag time of 4.5 for L. monocytogenes. This lag time option is not available for LAB because numerous studies have confirmed these bacteria to grow without any lag time in lightly preserved seafood. See the SSSP dialog box and output window below (Fig. 1).

Fig. 1. The graph above shows the predicted growth of L. monocytogenes and LAB for vacuum-packed cold-smoked salmon. Predictions are shown for two products with different smoke intensity (5 or 15 ppm phenol) and without or with added diacetate. As shown SSSP predicts the time needed for the concentrations of L. monocytogenes and LAB to increase 100-fold under the selected product characteristics and storage conditions. The concentrations of L. monocytogenes and LAB shown in the bar at the bottom of the output window was obtained by using the mouse to click on the graph at a specific point in time.

Fig. 2. SSSP can predict growth of L. monocytogenes and LAB for dynamic temperature profiles. Simple temperature profiles can by typed in as 'Series of constant temperatures' whereas actual product temperature profiles most often are entered as 'Temperature profiles from data loggers'.

Primary growth model

The Logistic model with delay and including interaction between Listeria monocytogenes and LAB is shown in Eqn. 1 below. The primary growth model describes how the specific growth rates of L. monocytogenes ([dLm/dt]/Lm_t) and of lactic acid bacteria ([dLAB/dt]/LAB_t) are reduced when the cell concentrations of the two bacteria (Lm_t and LAB_t, cfu g^-1) approaches their maximum values (Lm_max and LAB_maxcfu g^-1). The model is an expansion of the differential form of the simple Logistic model. Eqn. 1 includes the assumption that LAB and L. monocytogenes inhibit each others growth to the same extend that they inhibit their own growth. This has been confirmed for various lightly preserved seafoods (Giménez and Dalgaard, 2004; Mejlholm & Dalgaard, 2007b). To accurately predict growth of L. monocytogenes in lightly preserved seafood such as cold-smoked and marinated (including 'gravad') products it is essential to take into account the inhibiting effect of LAB. As shown in Fig. 1 and Fig. 2 the SSSP software allow these prediction to be carried out conveniently for constant and variable temperature storage conditions.

                    Eqn. 1

Eqn. 1. Primary model for simultaneous growth of Listeria monocytogenes and LAB. t_lag-Lm is the lag time for L. monocytogenes. Other model parameters are described in the text above the equation.

Secondary growth and growth boundary model:

Eqn. 2a and Eqn. 2b  below show the secondary growth models for L. monocytogenes and lactic acid bacteria. These simplified cardinal parameter type models describe how the maximum specific growth rate  (µ_max, h^-1) at a reference temperature of 25°C (µ_max-ref) is reduced when environmental parameters become less favourable for growth. The term for each of the environmental parameters (temperature, water activity (water phase salt), pH, lactic acid, phenol (smoke components), CO₂ (atmosphere) and undissociated diactate) all has a value between 0 and 1. SSSP predicts the growth boundary of L. monocytogenes as the combination of environmental conditions resulting in µ_max = 0 and a specific term (ξ) is included in the cardinal parameter models to take into account the effect of interaction between all the different environmental parameters (Eqn. 2). Like other terms in the secondary model 'ξ' has a value between 0 and 1 (Eqn. 3). With temperature (T), undissociated lactic acid (LAC_U) and undissociated diacetate (DAC_U) as examples, Eqn. 3, 4 and 5 show how the value of the interaction term (ξ) is calculated. This approach to prediction of the growth boundary was first suggested by Yvan Le Marc and colleagues (Le Marc et al. 2002). At DTU Aqua the Le Marc approach to growth boundary modelling has been studied extensively and we find it very valuable (Mejlholm & Dalgaard, 2007a,b; Mejlholm & Dalgaard, 2009).

Listeria monocytogenes secondary model (Eqn. 2a)

Evaluation and validation of the Listeria monocytogenes and lactic acid bacteria models: 

The models included in SSSP for prediction of the simultaneous growth of L. monocytogenes and LAB have been evaluated by comparison of observed and predicted growth in inoculated challenge tests and in naturally contaminated cold-smoked salmon as shown in the Table below. The models performed very well and bias factors for both models were within the range (0.75 < Bias factor < 1.25) suggested for acceptable model validation (Dalgaard, 2002).