Optimization of composite cryoprotectant for freeze-drying Bifidobacterium bifidum BB01 by response surface methodology

Figures & data

Table 1. The factor levels coding table of P–B design.

Factors	X1	X3	X4	X6	X7	X8	X10	X11
Variables	Xylo-oligosaccharides	Inulin	Stachyose	Glycine	Arginine	Sodium bicarbonate	Ascorbic acid	Skim milk
	(%)	(%)	(%)	(%)	(%)	(%)	(%)	(%)
1	7	13	11	5.5	4.5	0.8	2.3	25
−1	0	0	0	0	0	0	0	15

Table 2. The factors level coding table of central composite design.

Factors	A: xylo-oligosaccharides (%)	B: arginine (%)	C: skim milk (%)
−1.682	5.318	4.1636	23.318
−1	6	4.3	24
0	7	4.5	25
1	8	4.7	26
1.682	8.682	4.8364	26.682

Table 3. The experimental design and results of Plackett–Burman.

Run	X1	X2	X3	X4	X5	X6	X7	X8	X9	X10	X11	Y1(%)
1	1	−1	1	−1	−1	−1	1	1	1	−1	1	90.59
2	1	1	−1	1	−1	−1	−1	1	1	1	−1	86.50
3	−1	1	1	−1	1	−1	−1	−1	1	1	1	85.28
4	1	−1	1	−1	−1	1	−1	−1	−1	1	1	87.32
5	1	1	−1	1	1	−1	1	−1	−1	−1	1	89.57
6	1	1	1	1	1	1	−1	1	−1	−1	−1	85.07
7	−1	1	1	−1	−1	1	1	−1	1	−1	−1	76.28
8	−1	−1	1	1	1	−1	1	1	−1	1	−1	69.33
9	−1	−1	−1	1	1	1	−1	1	1	−1	1	93.05
10	1	−1	−1	−1	1	1	1	−1	1	1	−1	84.05
11	−1	1	−1	−1	−1	1	1	1	−1	1	1	72.09
12	−1	−1	−1	−1	−1	−1	−1	−1	−1	−1	−1	73.42

X1, X3, X4, X6, X7, X8, X10, X11, respectively represent xylo-oligosaccharides, inulin, stachyose, glycine, arginine, sodium bicarbonate, ascorbic acid and skim milk, while X2, X5, and X9 are three virtual terms to estimate the error.

Figure 1. The effect of factors to survival rate of BB01 (Y₁).

Figure 2. The 95% confidence interval of variable factors for the survival rate of BB01 (Y₁).

Table 4. Design and results of the path of steepest ascent experiment.

Step	X1: xylo-oligosaccharides (%)	X7: arginine (%)	X11: skim milk (%)	Y1 (%)	Y2 (10^11cfu/g)
1	5	5	23	74.80 ± 0.48	2.24
2	7	4.5	25	82.00 ± 0.52	2.45
3	9	4	27	75.12 ± 0.39	2.07
4	11	3.5	29	80.05 ± 0.26	2.19
5	13	3	31	81.53 ± 0.35	2.10

Mean values (n = 3) ± standard error are shown.

Table 5. Design and results of the path of steepest ascent experiment.

Run	X1	X2	X3	Y1 (%)			Y2 (10^11 cfu/g)
				Actual value	Predicted value	Residual	Actual value	Predicted value	Residual
1	−1	−1	−1	59.04	54.119	4.921	1.45	1.457	−0.007
2	−1	−1	1	63.65	59.536	4.114	1.66	1.586	0.074
3	−1	1	−1	73.40	70.119	3.281	1.83	1.891	−0.061
4	−1	1	1	69.15	68.137	1.013	1.62	1.736	−0.116
5	1	−1	−1	63.03	58.403	4.627	1.47	1.365	0.105
6	1	−1	1	65.78	63.421	2.359	1.56	1.509	0.051
7	1	1	−1	61.70	60.174	1.526	1.44	1.524	−0.084
8	1	1	1	58.51	57.792	0.718	1.38	1.384	−0.004
9	−1.68179	0	0	57.55	62.756	−5.206	1.93	1.869	0.061
10	1.68179	0	0	54.89	57.66	−2.770	1.45	1.496	−0.046
11	0	−1.68179	0	44.15	50.957	−6.807	1.07	1.208	−0.138
12	0	1.68179	0	58.51	59.679	−1.169	1.62	1.468	0.152
13	0	0	−1.68179	66.31	72.127	−5.817	1.87	1.847	0.023
14	0	0	1.68179	72.52	74.679	−2.159	1.83	1.838	−0.008
15	0	0	0	91.83	87.927	3.903	2.52	2.684	−0.164
16	0	0	0	87.91	87.927	−0.017	2.64	2.684	−0.044
17	0	0	0	85.83	87.927	−2.097	2.63	2.684	−0.054
18	0	0	0	86.76	87.927	−1.167	2.78	2.684	0.096
19	0	0	0	87.03	87.927	−0.897	2.84	2.684	0.156
20	0	0	0	89.57	87.927	1.643	2.69	2.684	0.006
21	0	0	0	88.25	87.927	0.323	2.77	2.684	0.086
22	0	0	0	90.08	87.927	2.153	2.64	2.684	−0.044
23	0	0	0	89.04	87.927	1.113	2.76	2.684	0.076

X₁, X₂, and X₃ represent xylo-oligosaccharides, arginine and skim milk.

Table 6. ANOVA of the response variables for the hydroxyl free radical scavenging rate (Y1) and the DPPH radical scavenging rate (Y2).

Source	Y1				Y2
	DF	MS	F	Pr > F	MS	F	Pr > F
Model	9	486.9200	27.1940	0.0001***	0.8215	62.4856	0.0001***
X1	1	31.3560	1.7512	0.2085	0.1686	12.8210	0.0034**
X2	1	91.8160	5.1279	0.0413*	0.0815	6.1988	0.0271*
X3	1	7.8651	0.4393	0.5191	0.0001	0.0077	0.9313
X1X2	1	101.2500	5.6546	0.0334*	0.0378	2.8760	0.1137
X1X3	1	0.0800	0.0045	0.9477	0.0001	0.0086	0.9277
X2X3	1	27.3800	1.5292	0.2381	0.0406	3.0890	0.1023
X1^2	1	1568.7000	87.6120	0.0001***	2.0416	155.2868	0.0001***
X2^2	1	2162.1000	120.7500	0.0001***	3.6675	278.9501	0.0001***
X3^2	1	441.4600	24.6550	0.0003***	1.4481	110.1420	0.0001***
Linear	3	43.6790	2.4394	0.1109	0.0834	6.3425	0.0070**
Quadratic	3	1374.2000	76.7470	0.0001***	2.3550	179.1231	0.0001***
Interaction	3	42.9020	2.3961	0.1152	0.0262	1.9912	0.1651
Residual	13	17.9050			0.0131
Lack of fit	5	12.0490	2.6265	0.1082	0.0184	1.8616	0.2071
Pure error	8	3.4682			0.2900
Cor Total	22

***p < .001, extremely significant; **p < .01, very significant; *p < .05.

Figure 3. The trends of Y₁ (survival rate of BB01) with factors.

Figure 4. Contour plots and response surface of xylo-oligosaccharides (X1) and arginine (X2) for the survival rate of BB01 (Y1).

Figure 5. Contour plots and response surface of xylo-oligosaccharides (X1) and skim milk (X3) for the survival rate of BB01 (Y1).

Figure 6. Contour plots and response surface of arginine (X2) and skim milk (X3) for the survival rate of BB01 (Y1).

Figure 7. The trends of Y₂ (viable counts) with factors.

Figure 8. Contour plots and response surface of xylo-oligosaccharides (X1) and arginine (X2) for the viable counts of per unit freeze-dried powder of BB01 (Y2).

Figure 9. Contour plots and Response surface of xylo-oligosaccharides (X1) and skim milk (X3) for the viable counts of per unit freeze-dried powder of BB01 (Y2).

Figure 10. Contour plots and Response surface of arginine (X2) and skim milk (X3) for the viable counts of per unit freeze-dried powder of BB01 (Y2).