Table 1: Plackett-Burman Design (PBD) for screening of medium components
Run No
|
Na2HPO4 (g/L)
|
KH2PO4 (g/L)
|
NaCl (g/L)
|
L-asparagine (g/L)
|
MgSO4 (g/L)
|
Glucose (g/L)
|
CaCl2 (g/L)
|
Activity (U/mL)
|
Predicted Activity (U/ml)
|
1
|
3
|
5
|
30
|
2
|
1
|
0.5
|
0.05
|
4.985
|
4.711
|
2
|
8
|
5
|
10
|
8
|
1
|
0.5
|
0.25
|
10.654
|
10.446
|
3
|
8
|
1
|
30
|
8
|
0.1
|
4
|
0.05
|
8.727
|
8.861
|
4
|
8
|
5
|
30
|
2
|
1
|
4
|
0.05
|
4.505
|
4.773
|
5
|
5.5
|
3
|
20
|
5
|
0.55
|
2.25
|
0.15
|
7.026
|
7.02
|
6
|
3
|
1
|
10
|
2
|
0.1
|
0.5
|
0.05
|
4.204
|
4.181
|
7
|
3
|
1
|
30
|
8
|
1
|
0.5
|
0.25
|
8.952
|
8.563
|
8
|
3
|
5
|
10
|
2
|
0.1
|
4
|
0.25
|
4.001
|
4.428
|
9
|
3
|
5
|
30
|
8
|
0.1
|
4
|
0.25
|
9.484
|
9.046
|
10
|
8
|
1
|
30
|
2
|
0.1
|
0.5
|
0.25
|
3.622
|
3.293
|
11
|
8
|
5
|
10
|
8
|
0.1
|
0.5
|
0.05
|
9.484
|
9.683
|
12
|
3
|
1
|
10
|
8
|
1
|
4
|
0.05
|
10.841
|
10.513
|
13
|
8
|
1
|
10
|
2
|
1
|
4
|
0.25
|
5.1
|
5.006
|
Table 2: Experimental matrix for central composite design (CCD) using RSM and ANN for cultural parameters with actual and predicted L-asparaginase activity (U/ml)
Run No L-asparagine MgSO4 NaCl pH Temperature Activity
|
Coded
|
Uncoded
|
Coded
|
Uncoded
|
Coded
|
Uncoded
|
Coded
|
Non-coded
|
Coded
|
Non-coded
|
Experimental
|
RSM Predicted
|
ANN Predicted
|
1
|
1
|
2
|
-1
|
0.125
|
1
|
2
|
1
|
7.5
|
-1
|
30
|
12.929
|
13.604
|
13.017
|
2
|
-1
|
1
|
1
|
0.2
|
1
|
2
|
1
|
7.5
|
-1
|
30
|
11.235
|
11.852
|
11.323
|
3
|
0
|
1.5
|
0
|
0.162
|
0
|
1.4
|
0
|
7
|
-2.378
|
25.175
|
9.652
|
9.984
|
10.228
|
4
|
0
|
1.5
|
-2.378
|
0.073
|
0
|
1.4
|
0
|
7
|
0
|
33.5
|
16.473
|
15.975
|
16.419
|
5
|
0
|
1.5
|
0
|
0.162
|
0
|
1.4
|
0
|
7
|
0
|
33.5
|
15.787
|
15.662
|
15.714
|
6
|
1
|
2
|
-1
|
0.125
|
-1
|
0.8
|
1
|
7.5
|
-1
|
30
|
15.422
|
14.679
|
15.57
|
7
|
1
|
2
|
1
|
0.2
|
1
|
2
|
-1
|
6.5
|
1
|
37
|
15.31
|
15.027
|
15.463
|
8
|
1
|
2
|
-1
|
0.125
|
1
|
2
|
1
|
7.5
|
1
|
37
|
14.862
|
14.764
|
14.626
|
9
|
-1
|
1
|
1
|
0.2
|
-1
|
0.8
|
1
|
7.5
|
-1
|
30
|
12.131
|
11.737
|
12.317
|
10
|
0
|
1.5
|
0
|
0.162
|
0
|
1.4
|
0
|
7
|
0
|
33.5
|
15.759
|
15.662
|
15.714
|
11
|
-1
|
1
|
1
|
0.2
|
-1
|
0.8
|
-1
|
6.5
|
1
|
37
|
13.644
|
13.171
|
13.336
|
12
|
0
|
1.5
|
0
|
0.162
|
0
|
1.4
|
0
|
7
|
0
|
33.5
|
15.857
|
15.662
|
15.714
|
13
|
1
|
2
|
1
|
0.2
|
1
|
2
|
1
|
7.5
|
1
|
37
|
15.338
|
15.072
|
15.135
|
14
|
-1
|
1
|
-1
|
0.125
|
-1
|
0.8
|
-1
|
6.5
|
-1
|
30
|
11.025
|
11.836
|
11.037
|
15
|
1
|
2
|
-1
|
0.125
|
-1
|
0.8
|
1
|
7.5
|
1
|
37
|
15.24
|
15.961
|
15.564
|
16
|
1
|
2
|
1
|
0.2
|
-1
|
0.8
|
1
|
7.5
|
1
|
37
|
17.089
|
16.875
|
16.946
|
17
|
-1
|
1
|
1
|
0.2
|
1
|
2
|
-1
|
6.5
|
1
|
37
|
12.383
|
13.024
|
12.36
|
18
|
0
|
1.5
|
0
|
0.162
|
0
|
1.4
|
0
|
7
|
0
|
33.5
|
15.717
|
15.662
|
15.714
|
19
|
2.378
|
2.689
|
0
|
0.162
|
0
|
1.4
|
0
|
7
|
0
|
33.5
|
17.073
|
17.115
|
17.096
|
20
|
0
|
1.5
|
0
|
0.162
|
0
|
1.4
|
0
|
7
|
0
|
33.5
|
15.016
|
15.662
|
15.714
|
21
|
-2.378
|
0.310
|
0
|
0.162
|
0
|
1.4
|
0
|
7
|
0
|
33.5
|
10.717
|
10.788
|
10.6
|
22
|
-1
|
1
|
-1
|
0.125
|
1
|
2
|
-1
|
6.5
|
1
|
37
|
13.266
|
13.897
|
13.236
|
23
|
-1
|
1
|
1
|
0.2
|
1
|
2
|
-1
|
6.5
|
-1
|
30
|
12.929
|
11.766
|
12.922
|
24
|
-1
|
1
|
-1
|
0.125
|
1
|
2
|
1
|
7.5
|
1
|
37
|
14.344
|
13.717
|
14.918
|
25
|
0
|
1.5
|
0
|
0.162
|
0
|
1.4
|
-2.4
|
5.8
|
0
|
33.5
|
13.308
|
13.058
|
13.475
|
26
|
0
|
1.5
|
0
|
0.162
|
2.378
|
2.827
|
0
|
7
|
0
|
33.5
|
13.014
|
13.409
|
13.032
|
27
|
-1
|
1
|
-1
|
0.125
|
1
|
2
|
1
|
7.5
|
-1
|
30
|
12.495
|
12.084
|
12.41
|
28
|
0
|
1.5
|
2.378
|
0.251
|
0
|
1.4
|
0
|
7
|
0
|
33.5
|
15.675
|
16.286
|
15.912
|
29
|
0
|
1.5
|
0
|
0.162
|
0
|
1.4
|
0
|
7
|
2.378
|
41.824
|
13.224
|
13.005
|
13.256
|
30
|
1
|
2
|
1
|
0.2
|
-1
|
0.8
|
1
|
7.5
|
-1
|
30
|
15.619
|
15.813
|
16.216
|
31
|
1
|
2
|
-1
|
0.125
|
-1
|
0.8
|
-1
|
6.5
|
1
|
37
|
16.403
|
16.478
|
16.425
|
32
|
1
|
2
|
1
|
0.2
|
1
|
2
|
-1
|
6.5
|
-1
|
30
|
14.19
|
14.242
|
14.276
|
33
|
-1
|
1
|
1
|
0.2
|
-1
|
0.8
|
-1
|
6.5
|
-1
|
30
|
11.515
|
11.79
|
11.482
|
34
|
0
|
1.5
|
0
|
0.162
|
0
|
1.4
|
0
|
7
|
0
|
33.5
|
15.703
|
15.662
|
15.714
|
35
|
-1
|
1
|
-1
|
0.125
|
1
|
2
|
-1
|
6.5
|
-1
|
30
|
12.649
|
12.417
|
12.764
|
36
|
1
|
2
|
1
|
0.2
|
-1
|
0.8
|
-1
|
6.5
|
-1
|
30
|
16.011
|
16.063
|
15.944
|
37
|
1
|
2
|
-1
|
0.125
|
-1
|
0.8
|
-1
|
6.5
|
-1
|
30
|
15.577
|
15.349
|
16.371
|
38
|
-1
|
1
|
-1
|
0.125
|
-1
|
0.8
|
-1
|
6.5
|
1
|
37
|
13.742
|
13.438
|
14.009
|
39
|
0
|
1.5
|
0
|
0.162
|
0
|
1.4
|
0
|
7
|
0
|
33.5
|
15.352
|
15.662
|
15.714
|
40
|
0
|
1.5
|
0
|
0.162
|
-2.378
|
0.270
|
0
|
7
|
0
|
33.5
|
15.731
|
15.281
|
14.5
|
41
|
1
|
2
|
-1
|
0.125
|
1
|
2
|
-1
|
6.5
|
1
|
37
|
15.338
|
15.14
|
15.229
|
42
|
-1
|
1
|
-1
|
0.125
|
-1
|
0.8
|
1
|
7.5
|
-1
|
30
|
11.375
|
11.362
|
11.524
|
43
|
0
|
1.5
|
0
|
0.162
|
0
|
1.4
|
0
|
7
|
0
|
33.5
|
15.969
|
15.662
|
15.714
|
44
|
-1
|
1
|
-1
|
0.125
|
-1
|
0.8
|
1
|
7.5
|
1
|
37
|
12.495
|
13.118
|
12.598
|
45
|
0
|
1.5
|
0
|
0.162
|
0
|
1.4
|
0
|
7
|
0
|
33.5
|
16.067
|
15.662
|
15.714
|
46
|
1
|
2
|
1
|
0.2
|
-1
|
0.8
|
-1
|
6.5
|
1
|
37
|
16.529
|
16.971
|
16.978
|
47
|
-1
|
1
|
1
|
0.2
|
1
|
2
|
1
|
7.5
|
1
|
37
|
13.35
|
13.265
|
13.373
|
48
|
0
|
1.5
|
0
|
0.162
|
0
|
1.4
|
0
|
7
|
0
|
33.5
|
15.156
|
15.662
|
15.714
|
49
|
1
|
2
|
-1
|
0.125
|
1
|
2
|
-1
|
6.5
|
-1
|
30
|
13.826
|
14.134
|
14.151
|
50
|
1
|
2
|
1
|
0.2
|
1
|
2
|
1
|
7.5
|
-1
|
30
|
14.918
|
14.133
|
14.824
|
51
|
-1
|
1
|
1
|
0.2
|
-1
|
0.8
|
1
|
7.5
|
1
|
37
|
13.532
|
13.272
|
13.787
|
52
|
0
|
1.5
|
0
|
0.162
|
0
|
1.4
|
2.378
|
8.189
|
0
|
33.5
|
12.229
|
12.596
|
12.461
|
Table 3: Analysis of Variance (ANOVA) for Plackett-Burman Design for screening of medium components
Source
|
DF
|
Adj SS
|
Adj MS
|
F-Value
|
p-Value
|
Model
|
8
|
176.182
|
22.023
|
51.74
|
0
|
Linear
|
7
|
176.181
|
25.169
|
59.13
|
0
|
Na2HPO4
|
1
|
0.024
|
0.024
|
0.06
|
0.815
|
KH2PO4
|
1
|
0.465
|
0.465
|
1.09
|
0.311
|
NaCl
|
1
|
2.68
|
2.68
|
6.3
|
0.023
|
L-asparagine
|
1
|
167.693
|
167.693
|
393.98
|
0
|
MgSO4
|
1
|
5.078
|
5.078
|
11.93
|
0.003
|
Glucose
|
1
|
0.094
|
0.094
|
0.22
|
0.645
|
CaCl2
|
1
|
0.147
|
0.147
|
0.35
|
0.564
|
Curvature
|
1
|
0.001
|
0.001
|
0
|
0.963
|
Error
|
17
|
7.236
|
0.426
|
|
|
Lack-of-Fit
|
4
|
2.463
|
0.616
|
1.68
|
0.215
|
Pure Error
|
13
|
4.773
|
0.367
|
|
|
Total
|
25
|
183.418
|
|
|
|
|
|
|
|
|
|
S
|
|
R-sq
|
R-sq(adj)
|
R-sq(pred)
|
|
0.65241
|
|
96.05%
|
94.20%
|
91.09%
|
|
Table 4 Analysis of Variance (ANOVA) of RSM-CCD for L-Asparaginase production
Source
|
DF
|
Adj SS
|
Adj MS
|
F-Value
|
P-Value
|
Model
|
20
|
158.443
|
7.9222
|
24.44
|
0.000
|
Linear
|
5
|
98.542
|
19.7084
|
60.81
|
0.000
|
Square
|
5
|
49.694
|
9.9388
|
30.67
|
0.000
|
2-Way Interaction
|
10
|
9.436
|
0.9436
|
2.91
|
0.011
|
Error
|
31
|
10.047
|
0.3241
|
|
|
Lack-of-Fit
|
22
|
8.957
|
0.4071
|
3.36
|
0.032
|
Pure Error
|
9
|
1.090
|
0.1211
|
|
|
Total
|
51
|
168.490
|
|
|
|
S
|
R-sq
|
R-sq(adj)
|
R-sq(pred)
|
0.569291
|
94.04%
|
90.19%
|
80.01%
|
Table 5: Estimated regression coefficient of L-asparaginase activity by RSM-CCD
Term
|
Coef
|
SE Coef
|
T-Value
|
p-Value
|
Constant
|
15.662
|
0.179
|
87.61
|
0
|
L-Asparagine - A
|
1.33
|
0.0865
|
15.38
|
0
|
MgSO4 - B
|
0.0655
|
0.0865
|
0.76
|
0.455
|
NaCl – C
|
-0.3055
|
0.0897
|
-3.4
|
0.002
|
pH – D
|
-0.1074
|
0.0864
|
-1.24
|
0.223
|
Temperature - E
|
0.6352
|
0.0865
|
7.34
|
0
|
A2
|
-0.3023
|
0.0743
|
-4.07
|
0
|
B2
|
0.0829
|
0.0743
|
1.12
|
0.273
|
C2
|
-0.2697
|
0.0873
|
-3.09
|
0.004
|
D2
|
-0.4967
|
0.0737
|
-6.74
|
0
|
E2
|
-0.7367
|
0.0743
|
-9.92
|
0
|
AB
|
0.19
|
0.101
|
1.89
|
0.068
|
AC
|
-0.449
|
0.101
|
-4.46
|
0
|
AD
|
-0.049
|
0.101
|
-0.49
|
0.629
|
AE
|
-0.118
|
0.101
|
-1.18
|
0.249
|
BC
|
-0.151
|
0.101
|
-1.51
|
0.142
|
BD
|
0.105
|
0.101
|
1.04
|
0.304
|
BE
|
-0.055
|
0.101
|
-0.55
|
0.588
|
CD
|
0.035
|
0.101
|
0.35
|
0.73
|
CE
|
-0.031
|
0.101
|
-0.3
|
0.763
|
DE
|
0.039
|
0.101
|
0.38
|
0.704
|
Table 6: Comparison of predictive capability between RSM and ANN
Predictive Ability Measurement
|
RSM
|
ANN
|
R2 Value
|
0.9404
|
0.9846
|
Mean Absolute Percentage Error (MAPE)
|
2.632
|
1.519
|
Root Mean Square Error (RMSE)
|
0.439
|
0.322
|
Mean Absolute Deviation (MAD)
|
1.568
|
1.558
|