Analysis of a molecular predictive mode for the growth of Staphylococcus aureus in pork

Figures & data

Table 1. Mathematical growth models used to predict growth of S. aureus.

Model	Equation^b	Parameter^c
Modified Gompertz^a	Y = Y0 + (Ymax – Y0) × exp {–exp [–μ (t – M)]}	λ =M – ; k =
Logistic^a	Y = Y0 +	λ = M – ; k =
Richards^a	Y =	―

^aAs derived by Zwietering et al. (1990).

^bY: the natural logarithm of bacteria count at any given time, ln cfu/mL; Y_max and Y₀ are the maximum and initial values of Y; m: the relative growth rate growth rate at time = M, which is the inflection point of the curve. l: lag phase; K: specific growth rate; a, b: model coefficients.

Figure 1. Growth curves of S. aureus on pork. a: Growth curves of S. aureus on pork at constant temperature (20°C) obtained using a conventional microbiological method and real-time PCR; b: Growth curves of S. aureus on pork at constant temperature (25°C) obtained using a conventional microbiological method and real-time PCR; c: Growth curves of S. aureus on pork at constant temperature (30°C) obtained using a conventional microbiological method and real-time PCR. The empty red circles represent the mean values of quintuplicate trials of raw data points using a conventional microbiological method; the solid red circles represent the mean values of quintuplicate trials of raw data points using real-time PCR. The red lines represent the modified Gompertz model; the black lines represent the Logistic model; the blue lines represent the Richards model.

Table 2. The growth parameters of S. aureus on pork calculated from modified Gompertz equation, modified Logistic equation, and Richards equation using a conventional microbiological method and real-time PCR.

		Specific growth rate GR/Log cfu·(mL·h)^–1			Lag phase LT/h			The largest concentration of bacteriaMPD/Log cfu·mL^–1
Assay	Temperature°C	Gompertz	Logistic	Richards	Gompertz	Logistic	Richards	Gompertz	Logistic	Richards
Conventional microbiological method^a	7	0.057	0.063	0.044	31.176	26.097	31.571	6.918	6.589	6.636
	10	0.065	0.099	0.076	22.350	19.425	25.504	6.682	6.328	6.405
	15	0.193	0.195	0.153	10.465	9.974	10.027	6.497	6.449	6.445
	20	0.278	0.266	0.342	4.657	3.600	4.640	6.678	6.607	6.635
	25	0.757	0.654	0.381	2.263	2.246	3.656	6.505	6.418	6.374
	30	0.951	0.805	0.826	1.163	0.991	1.01	6.494	6.450	6.475
Real-time PCR^b	7	0.041	0.047	0.053	28.914	24.161	33.187	6.261	6.199	6.192
	10	0.068	0.072	0.094	19.072	17.701	24.086	6.365	6.238	6.605
	15	0.134	0.119	0.136	9.016	8.458	10.029	6.840	6.456	6.436
	20	0.242	0.243	0.281	3.395	3.495	4.074	6.126	6.081	6.233
	25	0.526	0.462	0.451	2.059	2.076	3.212	6.404	6.322	6.359
	30	0.799	0.808	0.940	1.207	0.998	0.993	6.098	6.038	6.082

^aThe original data of these parameters were obtained by conventional microbiological method.

^bThe original data of these parameters were obtained by means of appropriate real-time PCR method.

Table 3. The secondary models (specific growth rate and lag phase) of S. aureus on pork at constant temperature (7 ~ 30°) obtained using real-time PCR and conventional microbiological method.

	Specific growth rate			Lag phase
Assay	GR/Log cfu·(mL·h)^−1			LT/h
Conventional microbiological method^a	Gompertz	Logistic	Richards	Gompertz	Logistic	Richards
	μmax^1/2= 0.0366 ×(T – 2.6169)	μmax^1/2= 0.0353 ×(T – 1.0099)	μmax^1/2= 0.0364 ×(T – 1.8184)	1/lag^1/2= 0.0179 ×(T + 3.2517)	1/lag^1/2= 0.0183 ×(T + 4.1863)	1/lag^1/2= 0.0158 ×(T + 5.4781)
Real-time PCR^b	μmax^1/2= 0.0330 ×(T – 2.1359)	μmax^1/2= 0.0392 ×(T – 2.9533)	μmax^1/2= 0.0391 ×(T – 2.4411)	1/lag^1/2= 0.0196 ×(T + 3.4649)	1/lag^1/2= 0.0196 ×(T + 3.9581)	1/lag^1/2= 0.0175 ×(T + 3.5709)

^aThe original data of these parameters were obtained by conventional microbiological method.

^bThe original data of these parameters were obtained by means of appropriate real-time PCR method.

Figure 2. Lag time of S. aureus in pork at constant temperature (7 ~ 30°C) obtained using a conventional microbiological method and real-time PCR. The solid red triangles represent the mean values of quintuplicate trials of raw data points using a conventional microbiological method; the solid red squares represent the mean values of quintuplicate trials of raw data points using real-time PCR. The red lines represent the modified Gompertz model; the black lines represent the Logistic model; the blue lines represent the Richards model.

Figure 3. Specific growth rate of S. aureus in pork at constant temperature (7 ~ 30°C) obtained using a conventional microbiological method and real-time PCR. The solid red triangles represent the mean values of quintuplicate trials of raw data points using a conventional microbiological method; the solid red squares represent the mean values of quintuplicate trials of raw data points using real-time PCR. The red lines represent the modified Gompertz model; the black lines represent the Logistic model; the blue lines represent the Richards model.

Table 4. Fitting evaluation of growth models (modified Gompertz, Logistic equation, and Richards model) by real-time PCR and conventional microbiological method.

		Conventional microbiological method^a			Real-time PCR^b
Temperature °C	Parameters	Gompertz	Logistic	Richards	Gompertz	Logistic	Richards
7	R^2	0.9887	0.9777	0.9609	0.9987	0.9967	0.9871
	MSE	0.1384	0.0849	0.1440	0.0298	0.0129	0.1148
	Bf	0.9199	0.9339	1.0919	0.9528	0.9678	1.1015
	Af	1.0871	1.0708	1.0927	1.0495	1.0333	1.0823
10	R^2	0.9911	0.9820	0.9739	0.9736	0.9745	0.9816
	MSE	0.2152	0.0075	0.0728	0.2130	0.0664	0.2779
	Bf	0.8313	0.9972	1.0432	0.8464	1.0086	1.0485
	Af	1.2348	1.0027	1.0215	1.1814	1.0080	1.0198
15	R^2	0.9848	0.9864	0.9712	0.9994	0.9977	0.9912
	MSE	0.0134	0.0078	0.1267	0.0051	0.0055	0.1883
	Bf	1.0004	1.0058	1.0299	0.9926	0.9705	0.9934
	Af	1.0103	1.0050	1.0342	1.0074	1.0304	1.0066
20	R^2	0.9959	0.9930	0.9826	0.9788	0.9664	0.9690
	MSE	0.0043	0.0090	0.2439	0.0138	0.0729	0.1504
	Bf	1.0020	1.0038	0.9820	0.9645	0.9017	1.0419
	Af	1.0309	1.0030	1.0252	1.0368	1.1089	1.0023
25	R^2	0.9935	0.9965	0.9877	0.9956	0.9919	0.9831
	MSE	0.0050	0.0064	0.0972	0.0045	0.0165	0.0662
	Bf	1.0019	0.9842	1.1189	1.0045	0.9532	1.0582
	Af	1.0022	1.0161	1.0865	1.0040	1.0490	1.0231
30	R^2	0.9904	0.9854	0.9733	0.9955	0.9903	0.9902
	MSE	0.0050	0.0305	0.1663	0.0207	0.0458	0.2799
	Bf	0.9968	0.9676	1.0791	0.9532	0.9248	1.0915
	Af	1.0032	1.0334	1.0546	1.0490	1.0813	1.0628

^aThe original data of these parameters were obtained by conventional microbiological method. ^bThe original data of these parameters were obtained by means of appropriate real-time PCR method. R² represent correlation coefficients; B_f represent bias factors; A_f represent accuracy factors; MSE represents the mean square error.