Response surface methodology (RSM) identifies the lowest amount of chicken plasma protein (CPP) in surimi-based products with optimum protein solubility, cohesiveness, and whiteness

Figures & data

Table 1. The coded and uncoded values used in optimisation of surimi production.

		Factor level
Independent variable	Code	-α	−1	0	1	+α
Percentage of chicken plasma protein (CPP)	X1	0.5	1.0	1.5	2.0	2.5
Percentage of sorbitol	X2	2	3	4	5	6

Table 2. Factors and comparison between experiment and predicted responses.

	Independent variables		Response variables
			Y1, (mg/ml)		Y2		Y3
Run	X1 (%)	X2 (%)	Experimental	Predicted	Experimental	Predicted	Experimental	Predicted
1	1.00	3.00	32.72 ± 1.03	32.99	0.618 ± 0.02	0.616	75.64 ± 0.01	75.51
2	2.00	3.00	52.19 ± 0.01	49.30	0.697 ± 0.14	0.694	69.32 ± 0.01	69.24
3	1.00	5.00	41.81 ± 0.01	43.82	0.624 ± 0.01	0.624	72.60 ± 0.01	72.62
4	2.00	5.00	29.49 ± 0.01	28.34	0.562 ± 0.01	0.563	71.40 ± 0.01	71.47
5	0.80	4.00	45.08 ± 0.59	43.29	0.632 ± 0.02	0.633	73.87 ± 0.01	73.93
6	2.21	4.00	41.21 ± 1.33	43.88	0.644 ± 0.01	0.645	68.69 ± 0.01	68.69
7	1.50	2.59	35.55 ± 1.53	37.22	0.650 ± 0.03	0.653	73.20 ± 0.01	73.34
8	1.50	5.41	30.84 ± 0.01	30.05	0.568 ± 0.04	0.566	72.96 ± 1.08	72.88
9	1.50	4.00	34.24 ± 0.01	33.96	0.570 ± 0.09	0.572	72.86 ± 0.01	73.21
10	1.50	4.00	31.51 ± 0.29	33.96	0.574 ± 0.06	0.572	73.14 ± 1.73	73.21
11	1.50	4.00	32.92 ± 0.01	33.96	0.594 ± 0.02	0.572	73.46 ± 1.12	73.21
12	1.50	4.00	35.95 ± 0.07	33.96	0.560 ± 0.01	0.572	73.17 ± 1.14	73.21
13	1.50	4.00	35.19 ± 0.01	33.96	0.564 ± 0.01	0.572	73.43 ± 0.58	73.21

where Y₁, protein solubility, Y₂, cohesiveness, and Y₃, whiteness, and X₁, percentage of CPP, and X₂, percentage of sorbitol.

Table 3. Analysis of variance (ANOVA) for the fitted quadratic polynomial model for the response variable.

Source	Degree of freedom	Adjusted sum of square	Adjusted mean square	F-value	P-value	Status
Protein solubility (R^2 = 92.13; Adjusted R^2 = 86.51%)
Regression	5	469.878	93.976	16.39	.001	Significant
Linear	2	51.715	25.858	4.51	.055	Not significant
X1	1	0.352	0.352	0.06	.812	Not significant
X2	1	51.364	51.364	8.96	.020	Significant
Square (quadratic)	2	165.512	82.756	14.43	.003	Significant
X1* X1	1	161.089	161.089	28.09	.001	Significant
X2* X2	1	0.185	0.185	0.03	.863	Not significant
Interaction	1	252.651	252.651	44.05	.000	Significant
X1* X2	1	252.651	252.651	44.05	.000	Significant
Residual Error	7	40.147	5.735
Lack-of-Fit	3	27.511	9.170	2.90	.165	Not significant
Pure Error	4	12.635	3.159
Total	12	510.025
Cohesiveness (R^2 = 96.77; Adjusted R^2 = 94.46)
Regression	5	0.021716	0.004343	41.95	.000	Significant
Linear	2	0.007685	0.003843	37.12	.000	Significant
X1	1	0.000141	0.000141	1.36	.282	Not significant
X2	1	0.007544	0.007544	72.87	.000	Significant
Square (quadratic)	2	0.009103	0.004551	43.96	.000	Significant
X1* X1	1	0.007656	0.007656	73.95	.000	Significant
X2* X2	1	0.002413	0.002413	23.31	.002	Significant
Interaction	1	0.004928	0.004928	47.60	.000	Significant
X1* X2	1	0.004928	0.004928	47.60	.000	Significant
Residual Error	7	0.000725	0.000104
Lack-of-Fit	3	0.000026	0.000009	0.05	.984	Not significant
Pure Error	4	0.000699	0.000175
Total	12	0.022441
Whiteness (R^2 = 99.27; Adjusted R^2 = 98.74)
Regression	5	40.6430	8.1286	189.70	.000	Significant
Linear	2	27.7601	13.8801	323.93	.000	Significant
X1	1	27.5491	27.5491	642.93	.000	Significant
X2	1	0.2111	0.2111	4.93	.062	Not significant
Square (quadratic)	2	6.3292	3.1646	73.85	.000	Significant
X1* X1	1	6.2915	6.2915	146.83	.000	Significant
X2* X2	1	0.0181	0.0181	0.42	.537	Not significant
Interaction	1	6.5536	6.5536	152.95	.000	Significant
X1* X2	1	6.5536	6.5536	152.95	.000	Significant
Residual Error	7	0.2999	0.0428
Lack-of-Fit	3	0.0601	0.0200	0.33	.803	Not significant
Pure Error	4	0.2399	0.0600
Total	12	40.9429

Figure 1. Contour plot and surface plot for the effect of percentage of CPP and percentage of sorbitol on the concentration of protein solubility of surimi.

Figure 2. Contour plot and surface plot for the effect of percentage of CPP and percentage of sorbitol on the cohesiveness of surimi.

Figure 3. Contour plot and surface plot for the effect of percentage of CPP and percentage of sorbitol on the whiteness of surimi.

Table 4. Comparison values of target and predicted responses for different optimum conditions and experiment feasibilities.

					Optimum condition		Predicted response, Y
Goal		Lower	Target	Upper	X1	X2	FITS 1	FITS 2	FITS 3	F/NF
Target	Protein Solubility	29.49	52.18	52.19	0.7929	4.6750	49.09	0.6541	75.58	F
	FITS 1	28.34	49.29	49.30
	Cohesiveness	0.560	0.696	0.697
	FITS 2	0.563	0.693	0.694
	Whiteness	68.69	75.63	75.64
	FITS 3	68.68	75.50	75.51
Maximum	Protein Solubility	29.49	52.19	52.19	0.7929	5.0428	52.19	0.6728	71.82	NF
	FITS 1	28.34	49.30	49.30
	Cohesiveness	0.560	0.697	0.697
	FITS 2	0.563	0.694	0.694
	Whiteness	68.69	75.64	75.64
	FITS 3	68.68	75.51	75.51
Minimum	Protein Solubility	29.49	29.49	52.19	2.2071	5.1857	27.32	0.5756	70.57	NF
	FITS 1	28.34	28.34	49.30
	Cohesiveness	0.560	0.560	0.697
	FITS 2	0.563	0.563	0.694
	Whiteness	68.69	68.69	75.64
	FITS 3	68.68	68.68	75.51

Where X₁ = percentage of CPP (%), X₂ = percentage of sorbitol (%), FITS = predicted response, F = feasible, NF = not feasible.

Table 5. The difference values of experimental and predicted values of response variables under the optimal conditions.

Responses	Experimental value	Predicted value	p-value
Protein solubility (mg/ml)	46.56 ± 1.081a	49.09a	.63
Cohesiveness	.651 ± 0.045a	0.654a	.96
Whiteness	75.55 ± 0.397a	75.58a	.88

Values with same superscripts within row are not significantly different (p > .05).