Chitinase Expressed as an Inducible Trait in Pseudomonas aeruginosa Schröter P-15 75
were calculated for determination of variable sig-
nificance. Experimental error was estimated by
calculating the variance among the dummy vari-
ables as follows:
Veff (= ∑ Ed)^2 /n, where Veff is the variance of
the concentration effect, Ed is the concentration
effect of dummy variable, and n is the number of
dummy variables.
The standard error (S.E.) of the concentra-
tion effect was the square root of the variance of
an effect and the significance level ( P-value) of
each concentration effect was determined using
student’s test:
t( (^) xi) = E( (^) Xi)/S.E, where E( (^) Xi) is the effect of
variable Xi.
Response Surface Methodology (RSM) To
describe the nature of response surface in the
experimental region and to elucidate the optimal
concentrations of the most significant indepen-
dent variables, a central composite design (CCD;
Box and Behnken 1960 ) was applied, which is
an RSM. Factors of highest confidence levels,
namely, crude glycerol (A), peptone (B), and
colloidal chitin (C) were tested at five levels
(− α, + α, 0, + 1, and − 1). According to the design,
20 treatments trial combinations were executed
(Table 4 ). For predicting the optimal point, the
following second-order polynomial model was
fitted to correlate relationship between indepen-
dent variables and three responses:
where Y is the predicted response, β 0 is a con-
stant, βi is the linear coefficient, βii is the squared
coefficient, βij is the cross product coefficient,
and xi is the dimensionless coded value of ( Xi).
The above equation was solved by using the soft-
ware design expert (Version 7.0.2, State ease inc.,
USA). A 2^5 factorial design with five replicates at
the center point with a total number of 20 trials
were employed (Table 3 ).
Y=+Σ+Σ+Σββββo ixi ijxixj iixi^2
Table 4 Central composite design (CCD) matrix of independent variables and the corresponding experimental and
predicted values
Run No. Factors Response
A: crude glycerol
(ml/l)
B: colloidal chitin
(g/l)
C: peptone
(g/l)
Chitinase activity (Uml−1)
Coded
value
Actual
value
Coded
value
Actual
value
Coded
value
Actual
value
Observed
value
Predicted
value
1 0.00 55.00 0.00 27.50 0.00 28.75 2.18 2.29
2 − 1.00 32.50 1.00 38.75 1.00 39.38 2.42 2.47
3 0.00 55.00 0.00 27.50 0.00 28.75 2.29 2.29
4 − 1.00 32.50 1.00 38.75 − 1.00 18.13 2.69 2.72
5 1.00 77.50 − 1.00 16.25 − 1.00 18.13 2.31 2.25
6 0.00 55.00 − 1.68 8.58 0.00 28.75 2.30 2.39
7 1.00 77.50 1.00 38.75 1.00 39.38 2.20 2.23
8 − 1.68 17.16 0.00 27.50 0.00 28.75 1.55 1.53
9 0.00 55.00 0.00 27.50 0.00 28.75 2.29 2.29
10 0.00 55.00 0.00 27.50 0.00 28.75 2.50 2.29
11 0.00 55.00 0.00 27.50 0.00 28.75 2.32 2.29
12 1.00 77.50 − 1.00 16.25 1.00 39.38 2.06 2.02
13 0.00 55.00 1.68 46.42 0.00 28.75 3.55 3.47
14 0.00 55.00 0.00 27.50 0.00 28.75 2.18 2.29
15 0.00 55.00 0.00 27.50 − 1.68 10.88 2.00 2.03
16 − 1.00 32.50 − 1.00 16.25 − 1.00 18.13 1.68 1.64
17 1.00 77.50 1.00 38.75 − 1.00 18.13 2.40 2.41
18 − 1.00 32.50 − 1.00 16.25 1.00 39.38 1.37 1.35
19 1.68 92.84 0.00 27.50 0.00 28.75 1.80 1.83
20 0.00 55.00 0.00 27.50 1.68 46.62 1.63 1.62