Probabilistic modeling of the growth of Listeria monocytogenes: effect of nisin, temperature, and strain in the presence of potassium chloride or potassium sorbate

Figures & data

Table 1. Parameters of the models for temperature (T), nisin, KCl, and strain as the independent variables and relative statistics.

Model	Coefficient	Estimate	SE	P value
SIMPLE MODEL	Constant	1.18	0.46	0.010
	T	0.22	0.019	<0.001
	Nisin	−0.025	0.002	<0.001
	KCl	−0.078	0.099	0.431
	Strain	−1.11	0.19	<0.001
	Goodness-of-fit
	−2lnL	333.970
	HL	16.084 (P = .041)
	Maximum rescaled R^2	0.786
	Percent concordant	87.9%
COMPLEX MODEL	Constant	−5.88	1.50	<0.001
	T	1.34	0.43	0.0017
	Nisin	−0.15	0.04	<0.001
	T × nisin	0.0059	0.001	<0.001
	T × KCl	−0.14	0.045	0.0025
	T × strain	0.22	0.048	<0.001
	T × nisin × strain	−0.005	0.001	<0.001
	Nisin × KCl × strain	0.012	0.004	0.0026
	Goodness-of-fit
	−2lnL	94.047
	HL	0.216 (P = 1.000)
	Maximum rescaled R^2	0.950
	Percent concordant	96.6%

Figure 1. Predicted growth probabilities of Listeria monocytogenes strains with respect to nisin: black lines for ATCC7644, blue lines for 137, and red lines for 120 at different temperatures and at a constant KCl concentration (1.5%). Predictions were plotted by using the parameter values of the complex model [Eq.(2a)] given in Table 1.

Figure 2. Predicted growth probabilities of Listeria monocytogenes strains with respect to temperature: black lines are for ATCC7644, blue lines for 137, and red lines for 120 at different nisin concentrations and at a constant KCl concentration (1.5%). Predictions were plotted by using the parameter values of the complex model [Eq.(2a)] given in Table 1.

Figure 3. Predicted growth probabilities of Listeria monocytogenes strains with respect to temperature: black lines are for ATCC7644, blue lines for 137, and red lines for 120 at different nisin concentrations and at a constant sorbate concentration (0.125%). Predictions were plotted by using the parameter values of the complex model [Eq.(2b)] given in Table 2.

Figure 4. Predicted growth probabilities of Listeria monocytogenes strains with respect to temperature: black lines are for ATCC7644, blue lines for 137, and red lines for 120 at different nisin concentrations and at a constant sorbate concentration (0.125%). Predictions were plotted by using the parameter values of the complex model [Eq.(2b)] given in Table 2.

Table 2. Parameters of the models for temperature (T), nisin, sorbate, and strain as the independent variables and relative statistics.

Model	Coefficient	Estimate	SE	P value
SIMPLE MODEL	Constant	−0.047	0.508	0.926
	T	0.17	0.021	<0.001
	Nisin	−0.056	0.005	<0.001
	Sorbate	−0.033	0.031	0.298
	Strain	1.46	0.254	<0.001
	Goodness-of-fit
	−2lnL	224.897
	HL	9.148 (P = .330)
	Maximum rescaled R^2	0.868
	Percent concordant	92.1%
COMPLEX MODEL	T	0.204	0.026	<0.001
	Nisin	−0.064	0.007	<0.001
	Strain	1.55	0.23	<0.001
	Sorbate × strain	−0.069	0.027	0.0103
	Nisin × sorbate × strain	0.0011	0.00029	<0.001
	T × nisin × sorbate × strain	−0.00003	0.00001	0.0015
	Goodness-of-fit
	−2lnL	213.896
	HL	12.097 (P = .147)
	Maximum rescaled R^2	0.876
	Percent concordant	92.6%

Data availability statement

Data will be made available on request.