Comparative analyses on medium optimization using one-factor-at-a-time, response surface methodology, and artificial neural network for lysine–methionine biosynthesis by Pediococcus pentosaceus RF-1

Figures & data

Table 1. Parameters and variables used in OFAT approach.

Parameter	Variables and concentrations (g/L)
Molasses	1, 3,5,10, and 12 g/L
Nitrogen source	Yeast extract, peptone, palm kernel cake, and fish meal
Fish meal	1, 3, 5, 10, 15, and 20 g/L
Glutamic acid	0.1, 0.3, 0.5, 1.0, and 5.0 g/L
Initial pH	pH 5, 6, 7, and 8

Table 2. Values of central composite design (CCD) variables.

			Values of CCD variables
	Variables	Unit	−α	−1	0	+1	+α
A	Molasses	g/L	1.25	3	6.5	10	11.75
B	Fish meal	g/L	0	3	9	15	18
C	Glutamic acid	g/L	0.13	0.3	0.65	1	1.17
D	Initial pH		4.25	5	6.5	8	8.75

Table 3. CCD design matrix for RSM and ANN studies in the cultivation of P. pentosaceus RF-1.

		(A)	(B)	(C)	(D)
Std	Run	Molasses (g/L)	Fish meal (g/L)	Glutamic acid (g/L)	Initial pH	Lysine (g/L)	Methionine (g/L)
1	6	3	3	0.3	5	4.7	1.75
2	4	10	3	0.3	5	6.96	3.02
3	16	3	15	0.3	5	4.58	1.77
4	3	10	15	0.3	5	8.36	3.26
5	15	3	3	1	5	4.47	2.03
6	25	10	3	1	5	8.57	3.19
7	7	3	15	1	5	4.28	2.09
8	13	10	15	1	5	12.23	3.98
9	14	3	3	0.3	8	4.87	1.99
10	10	10	3	0.3	8	10.57	3.22
11	5	3	15	0.3	8	7.05	2.49
12	29	10	15	0.3	8	8.76	3.59
13	18	3	3	1	8	3.28	1.5
14	23	10	3	1	8	9.36	3.24
15	2	3	15	1	8	3.59	2.08
16	21	10	15	1	8	14.13	4.96
17	20	1.25	9	0.65	6.5	4.18	1.66
18	27	11.75	9	0.65	6.5	9	3.62
19	11	6.5	0	0.65	6.5	9.33	3.65
20	28	6.5	18	0.65	6.5	10.33	3.7
21	1	6.5	9	0.13	6.5	9.29	3.02
22	26	6.5	9	1.17	6.5	10.19	3.36
23	8	6.5	9	0.65	4.25	8.65	3.1
24	24	6.5	9	0.65	8.75	9.52	2.95
25	30	6.5	9	0.65	6.5	10.4	3.62
26	22	6.5	9	0.65	6.5	10.17	2.97
27	19	6.5	9	0.65	6.5	10.21	3.19
28	9	6.5	9	0.65	6.5	9.19	2.68
29	17	6.5	9	0.65	6.5	8.91	3.04
30	12	6.5	9	0.65	6.5	8.46	2.92

Figure 1. Optimization by OFAT on P. pentosaceus RF-1 responses to produce lysine and methionine. (A) Effect of molasses (♦) 1 g/L, (■) 3 g/L, (▴) 5 g/L, (○) 10 g/L, (◊) 12 g/L; (B) effect of nitrogen sources (♦) yeast extract, (□) peptone (▴) PKC (■) fish meal; (C) effect of fish meal (♦) 1 g/L, (■) 3 g/L, (▴) 5 g/L, (∆) 10 g/L, (□) 15 g/L, (•) 20 g/L; (D) effect of glutamic acid (♦) 0.1 g/L, (■) 0.3 g/L, (▴) 0. 5 g/L, (•) 1 g/L, (○) 5 g/L; (E) effect of initial medium pH (♦) pH 5, (■) pH 6, (▴) pH 7, (○) pH 8.

Table 4. Regression model from ANOVA on lysine–methionine biosynthesis.

Source	Sum of square	DF	Mean squares	F-value	Prob > F
Lysine
Model	195.36	14	13.96	9.82	<0.0001	Significant
A	118.8	1	118.8	83.56	<0.0001
B	6.68	1	6.68	4.7	0.0467
C	1.43	1	1.43	1	0.3322
D	3.75	1	3.75	2.64	0.1253
A2	29.04	1	29.04	20.42	0.0004
B2	0.28	1	0.28	0.2	0.6621
C2	0.44	1	0.44	0.31	0.5844
D2	2.72	1	2.72	1.91	0.1871
AB	2.13	1	2.13	1.5	0.2397
AC	14.48	1	14.48	10.18	0.0061
AD	2.21	1	2.21	1.55	0.2321
BC	2.98	1	2.98	2.09	0.1686
BD	0.031	1	0.031	0.022	0.8853
CD	2.13	1	2.13	1.5	0.2397
Residual	21.33	15	1.42
Lack of Fit	18.06	10	1.81	2.76	0.1369	Not significant
Pure Error	3.27	5	0.65
Cor Total	216.71	29
R^2 = 0.9016
Methionine
A	12.02	1	12.02	103.4	<0.0001	Significant
B	0.93	1	0.93	7.98	0.0128
C	0.3	1	0.3	2.6	0.1276
D	0.15	1	0.15	1.29	0.2735
A2	1.08	1	1.08	9.33	0.008
B2	0.26	1	0.26	2.21	0.1577
C2	0.047	1	0.047	0.4	0.5343
D2	0.22	1	0.22	1.85	0.1934
AB	0.24	1	0.24	2.06	0.1713
AC	0.42	1	0.42	3.58	0.078
AD	0.081	1	0.081	0.7	0.4164
BC	0.26	1	0.26	2.19	0.1593
BD	0.27	1	0.27	2.28	0.1518
CD	0.063	1	0.063	0.54	0.4748
Residual	1.74	15	0.12
Lack of fit	1.24	10	0.12	1.24	0.4297	Not significant
Pure error	0.5	5	0.1
Cor total	18.16	29
R^2 = 0.9039

Table 5. Observed, predicted, and absolute deviation of lysine–methionine biosynthesis by ANN.

Std	Observed lysine	Predicted lysine (ANN)	Absolute deviation	Observed methionine	Predicted methionine (ANN)	Absolute deviation
1	4.710	5.210	0.518	1.750	2.035	0.285
2	6.960	6.791	0.165	3.020	3.232	0.212
3	4.581	4.583	0.002	1.770	1.782	0.012
4	8.361	8.202	0.156	3.260	3.290	0.030
5	4.472	4.351	0.113	2.030	1.896	0.133
6	3.573	3.641	0.077	3.190	3.134	0.056
7	4.281	4.345	0.066	2.091	2.131	0.041
8	12.230	11.86	0.368	3.980	4.115	0.135
9	4.870	5.03	0.159	1.993	2.052	0.061
10	10.572	10.73	0.161	3.222	3.419	0.199
11	7.054	6.89	0.152	2.490	2.443	0.047
12	8.763	9.20	0.440	3.590	3.507	0.083
13	3.281	3.25	0.022	1.501	1.623	0.123
14	9.361	9.16	0.191	3.240	3.316	0.075
15	3.592	3.67	0.088	2.080	2.038	0.042
16	14.130	12.41	1.719	4.960	4.171	0.789
17	4.180	6.57	2.391	1.660	2.031	0.371
18	9.001	9.15	0.159	3.620	3.359	0.261
19	9.330	9.52	0.193	3.646	3.205	0.441
20	10.330	10.42	0.089	3.701	3.653	0.0473
21	9.290	9.21	0.084	3.020	3.005	0.015
22	10.191	10.56	0.371	3.361	3.259	0.101
23	8.651	8.99	0.342	3.192	3.001	0.189
24	9.522	8.873	0.647	2.952	2.951	0.002
25	10.410	9.338	1.062	3.619	3.064	0.555
26	10.170	9.338	0.832	2.974	3.064	0.094
27	10.210	9.338	0.872	3.192	3.064	0.126
28	9.191	9.338	0.148	2.682	3.064	0.384
29	8.911	9.338	0.428	3.041	3.064	0.024
30	8.460	9.338	0.878	2.923	3.064	0.144

Table 6. The effect of different normal feed-forward network architectures on the model residual error in the prediction of lysine–methionine biosynthesis by P. pentosaceus RF-1.

Set	Network model	Responses	Learning algorithm	Transfer function hidden	Transfer function output	Training set RMSE	Training set R	Training set DC	Test set RMSE	Test set R	Test set DC
1	4-5-2	Lysine	IBP	Sig	Lin	0.36	0.98	0.98	1.83	0.98	0.85
		Methionine				0.18	0.97	0.94	0.61	0.99	0.85
2	4-5-2	Lysine	IBP	Tanh	Lin	0.37	0.99	0.98	1.91	0.98	0.84
		Methionine				0.15	0.98	0.96	0.65	0.98	0.83
3	4-8-2	Lysine	BBP	Tanh	Lin	0.25	0.99	0.99	1.80	0.99	0.86
		Methionine				0.10	0.99	0.98	0.89	0.84	0.69

Figure 2. Finalized topology of neural network architecture (4-5-2) trained by incremental back propagation (IBP) for the estimation of lysine–methionine biosynthesis.

Figure 3. The level of importance of effective medium constituents on lysine–methionine biosynthesis.

Figure 4. 3D response surface plot for lysine biosynthesis with the interaction between (a) molasses with fish meal, (b) initial pH with molasses, (c) glutamic acid with molasses, and (d) glutamic acid with fish meal as modelled by ANN.

Figure 5. 3D response surface plot for methionine biosynthesis with the interaction between (a) molasses with fish meal, (b) initial pH with molasses, (c) glutamic acid with molasses, and (d) glutamic acid with fish meal as modelled by ANN.

Table 7. Validation results of medium formulation and medium pH as suggested by ANN and RSM model with comparison to OFAT.

Factors	One-factor-at-a-time	ANN	RSM
Molasses (g/L)	5	10.02	9.86
Fish meal (g/L)	5	18	10.06
Glutamic acid (g/L)	0.3	1.17	0.91
Initial pH	7	4.26	5.3
Actual lysine (g/L)	8.052 ± 0.043	16.52 ± 0.18	15.77 ± 0.10
Predicted lysine (g/L)	–	14.45	14.25
Actual methionine (g/L)	2.24 ± 0.118	4.53 ± 0.03	4.21 ± 0.08
Predicted methionine (g/L)	–	4.34	4.28

Figure 6. Comparison on (A) cell density, (B) substrate consumption, (C) lysine, and (D) methionine biosynthesis by P. pentosaceus RF-1 using ANN, RSM, and OFAT in shake-flask experiment: (■) ANN, (□) RSM, (•) OFAT.