 Introduction
Most of the lipase producers are extracellular in nature and are created through solidstate fermentation and submerged fermentation methods (1). The fungal, mycelial, and yeast lipases are produced using various solid substrates through the solidstate fermentation method (2). This method is costeffective and widely used in industries to produce lipase using fungi. However, lipases from bacteria are produced using submerged fermentation (3). The optimization of media is the main requirement for increasing the quantitative yield by the overproduction of enzymes. Different parameters, such as pH, temperature, agitation speed, inoculum size, incubation time, carbon, and nitrogen sources, have been of great importance for researchers in designing economical media (4). The optimization by one factor at a time (OFAT) is a conventional method that involves changing a single independent factor at a time and keeping other factors constant. The OFAT is a onedimensional approach that is laborious and timeconsuming and does not consider interactions between the factors. The limitations of the OFAT method can be reduced by employing other techniques, such as PlackettBurman design (PBD) and response surface methodology (RSM). The PBD is a method to screen variables that influence the production and removal of the nonsignificant factors to attain a smaller and manageable set of factors (5). Subsequently, the chosen significant factors are optimized by RSM, which assists in studying the interactions between different factors. The RSM comprises a central composite design (CCD) to fit a secondorder polynomial equation (6). Generally, the type of oil used as a carbon source can influence the production of lipase in the submerged technique (7). Usually, vegetable oil, coconut oil, and almond oil increase the yield of lipase. Moreover, lipases produced by submerged fermentation can easily recover and purify the yield (2, 8). Previously, the optimization of Bacillus substilis KUBT4 media was carried out using OFAT method. The present study aimed to optimise the media using RSM and PBD as they allow for the simultaneous optimization of multiple factors.
 Materials and Methods
2.1. PlackettBurman design
To investigate the variables that considerably affect the production of lipase, a screening by PBD was performed using the Minitab statistical software (Release 17, PA, USA). Four independent variables were calculated across a range from a level low (2) to a high level (+2). The factors and levels are presented in table 1. The firstorder polynomial model is the basis of PBD.
where Y represents the response (lipase activity), β_{0} represents the model intercepts, βi represents the linear coefficient, and X_{i} represents the level of the independent variable. The four factors selected included temperature, tryptone, inoculum size, and incubation time. As per the design, a set of thirtyone runs was performed. In all experiments, the remaining factors were kept constant. Lipase assay was performed in triplicates, and the mean of the enzyme activity was considered the response. The factors in the response surface regression analysis with a significance level of ≥ 95% (P=0.05) were considered to have a bigger influence on lipase activity and were further improved using CCD.
2.2. Central composite design
To study the variables that significantly affected the production of lipase, variables were screened by CCD using the Minitab statistical software (Release 17, PA, USA). The CCD was applied to fit a secondorder model that needed only a minimum number of experiments for modeling. Four independent variables, namely temperature (A), tryptone (B), inoculum size (C), and incubation time (D), were used in the experimental design, as listed in table 2. The variables were evaluated across a range from low (2) to high (+2), with six replicates at the central points being utilized in the study. In the present study, thirtyone experiments were conducted in 250 mL conical flasks consisting of 100 mL production media prepared as per the CCD of the four factors at five levels (2,1, 0,+1,+2) and the remaining parameters were constant. The results were used to fit the secondorder polynomial model as expressed by the following equation:
where Y stands for the predicted response (lipase activity), A, B, C, and D for independent variables, as presented in table 2, β_{0 }represents model constant, and β_{1}, β_{2}, β_{3}, and β_{4} represent linear coefficients, β_{11}, β_{22}, β_{33}, and β_{44} represent the quadratic coefficients, and β_{12}, β_{13}, β_{14}, β_{23}, β_{24}, and β_{34} represent crossproduct coefficients.
2.3. Verification experiment
The measured lipase activity values for each variable in the experimental design were inserted for statistical and numerical analysis of the model using Minitab software (Release 17, PA, USA). Analysis of variance (ANOVA) was performed to analyze the variables and responses. Fisher’s Fvalue was calculated using the same software. The polynomial model was expressed by the correlation coefficient (R^{2}) associated with probability (P). The experiment was validated by comparing the actual values obtained from the fermentation process performed using predicted media components to the predicted results by the design. Quadratic models for each graph were plotted as contour plots and surface plots that signified the validity of the mode.
 Results
3.1. Screening of the most significant medium components by PBD
The PBD analysis of four factors showed a significant variation in lipase activity from 6.08 U/ml to 50.12 U/ml in thirtyone experimental runs (Table 3). This variation indicated the influence of the factors on the activity of lipase. The analysis of regression coefficients, tvalue, and Pvalue of four factors are provided in table 4. A larger tvalue is associated with a lower Pvalue indicating higher significance of the model. The results from table 4 and the pareto chart (Figure 1) depict that the factors temperature and incubation time exhibited significant effects on the production of lipase (P=0.005 and P=0.000, respectively). In contrast, tryptone and inoculum size had a positive nonsignificant effect (P=0.363 and P=0.728, respectively). Hence, temperature, tryptone, inoculum size, and incubation time were selected in PBD screening.
3.2. Central composite design
PBD screening experiments depicted that the four factors played a significant role in lipase production. The influence of the interaction of the four factors on lipase production was determined by CCD of RSM using Design Expert software. The factors selected by the PBD were studied at five different levels (2, 1, 0, +1, +2), and thirtyone experiments set with varying factor combinations were performed. Response surface regression analysis using ANOVA was conducted to analyze the significance of model coefficients, and the Pvalues showed the significance of each coefficient and the strength of interaction among each independent variable. The yield observed and predicted by the model equation are shown in table 5, and the analysis of the optimization study by ANOVA is shown in table 6. The contour plots (Figures 27) and surface plots (Figures 813) for lipase production showed the interactive effects among the selected factors, respectively. The model Fvalue of 6.06 from the ANOVA analysis suggested that the model was significant since values of “Prob>F” less than 0.05 designated that model terms were significant. In this case, A, D, AA, BB, CC, DD, and AD were significant model terms. The data was fitted to a secondorder polynomial equation after the coefficients of the regression equation were computed. Hence, the lipase activity (i.e., response [Y]) is expressed in the following equation,
Lipase activity (U/ml) = 31.45  4.37 A + 1.25 B + 0.47 C  8.77 D  3.44 AA  3.14 BB  3.43 CC  1.93 DD + 0.41 AB  0.44 AC + 5.48 AD + 0.29 BC  0.11 BD 0.39 CD
where A represents temperature (°C), B represents tryptone (%), C represents inoculum size (%), and D represents incubation time (hours). The fvalue of lack of fit was 302.46, suggesting that the lack of fit was significant compared to the pure error. The pvalue of lack of fit for the model was 0.000 (<0.05), implying that the model was suitable. The R^{2} value predicted by the model was 0.8414, which is reasonably similar to the adjacent R^{2} value of 0.7027. The Rsquared value must be in a range of 0 to 1.0, and the data of the present study indicated that the model was good. The interaction effects and optimal levels of the factors were determined by plotting the response surface curves.
3.3. Validation of the model
Validation of the experimental model was verified by performing the experiments under optimized conditions of 1% sucrose, 1.5% tryptone, 1.5% olive oil, 0.2% CaCl_{2}.2H_{2}O, 0.1% MgSO_{4}.7H_{2}O, 0.4% of 1% stock solution of FeCl_{3}, and pH 7.5 incubated at 34℃ for 48 h with an agitation speed of 150 rpm. The experiments were carried out in triplicates, and the results were compared. The observed lipase activity (57.85 U/ml) from experiments closely matched the predicted response (58.53 U/ml) from the regression model, confirming the validity of the model.
 Discussion
Sucrose and tryptone are good sources for maximum enzyme production. They showed optimal activity at pH 7.5 and 36ºC. An increase in lipase production was achieved by using 10% inoculum size, incubating for 48 h with agitation at 150 rpm. The most important stages in a biological process are modeling and optimization to improve a system and increase the efficiency of the process without increasing the cost. The classical optimization method (single variable optimization) is not only timeconsuming and tedious but also fails to depict the complete effects of the parameters in the process. Additionally, this method ignores the combined interactions between physicochemical parameters, leading to misinterpretation of results (9). However, this technique will help reduce the number of parameters to be analyzed in further optimization processes, such as PBD and RSM (10). Following the fitting of the data to various models (e.g., linear, two factorials, quadratic, and cubic), an ANOVA revealed that a quadratic polynomial model best captured the reactions of PKO and l(+)lysine.










































Figure 1. Pareto chart showing the effect of four factors on lipase activity.





Table 5. CCD matrix of four variables (in coded and actual units) with observed and predicted response values.





Temperature (°C) (A)

Tryptone (%) (B)

Inoculum size (%) (C)

Incubation time (hrs) (D)

Lipase activity (U/ml)

Observed value

Predicted value

1

1

1

1

10.0

9.6479

0

0

0

0

31.31

31.45143

1

1

1

1

8.98

13.35375

0

0

0

0

31.78

31.45143

1

1

1

1

6.08

11.17958

1

1

1

1

15.0

16.51792

1

1

1

1

15.56

19.47875

1

1

1

1

8.98

8.679583

0

0

0

2

50.12

41.26667

0

0

0

2

10.0

6.203333

2

0

0

0

33.01

26.42333

0

0

2

0

26.12

18.68167

1

1

1

1

9.88

10.94875

0

2

0

0

35.32

21.40333

1

1

1

1

6.09

9.560417

1

1

1

1

8.71

13.47958

0

2

0

0

15.12

16.38667

0

0

0

0

32.01

31.45143

1

1

1

1

7.01

9.12375

1

1

1

1

35.71

40.67375

1

1

1

1

34.51

36.16875

0

0

0

0

30.9

31.45143

2

0

0

0

15.01

8.946667

1

1

1

1

36.34

38.18792

1

1

1

1

30.51

37.47958

1

1

1

1

14.01

20.92792

1

1

1

1

14.23

16.79208

0

0

2

0

22.0

16.78833

0

0

0

0

31.29

31.45143

0

0

0

0

31.98

31.45143

0

0

0

0

30.89

31.45143





































Figure 9. Surface plots for pectinase activity showing the interactive effects of Inoculum size (%) v/s Temperature (℃).





The model was inferred to be significant by the model’s Fvalues of 3.69 and Prob > F values of 0.050. The model was found to be suitable for accurately capturing the genuine relationship between the elements, as indicated by the coefficient of determination (R^{2}=0.775) (11). The R^{2} value obtained from Bidin et al.’s model was higher than the values reported by Kiran et al. (12) for the lipasecatalyzed synthesis of stearoyl (R^{2}=0.565) and palmitoyl (R^{2}=0.720) lactic acid ester, which ranged from 0.565 to 0.720 (13). The results of a study by Osorio et al. (14) demonstrated that the R^{2} value of 0.566 was produced by the novozymecatalyzed transesterification of palm oil stearin with soybean oil. The model was appropriate to reflect the experimental data based on the insignificant lackoffit test results (Fvalue=4.29). Generally, increasing the reaction temperature made the substrates more soluble by removing mass transfer constraints and increasing the enzyme’s accessibility to the substrates (15). However, the high polarity of the solvent used in this reaction (tertbutyl alcohol) greatly enhances the solubility of both substrates by increasing their interaction, which had a direct impact on the reaction and the enzyme. Therefore, even though low temperature was utilized, it
was still possible to achieve large yields thanks to the support of raised impeller speed, high molar ratios, and enzyme employment. Similar profiles for the lipozymecatalyzed synthesis of amino acid esters and isoamyl isobutyrate were described by Soo et al., respectively (16). The authors hypothesized that the operational stability of the enzyme had decreased due to high temperatures. Additionally, applying low temperatures offers advantages, such as reducing power costs and maintaining enzyme stability over prolonged periods of use. However, raising the impeller speed from 175.00 to 325.00 rpm with a constant fixed enzyme amount of 5.75 g resulted in a yield difference of 18.60%. In contrast, keeping a fixed impeller speed of 175.00 rpm led to a yield difference of only 5.20%. This is because the reaction yield will drop when the impeller speed exceeds the ideal level, probably owing to the shearing effect on the molecules of the enzyme (17). The quadratic polynomial model was extremely significant and sufficient to describe the actual link between the response (% yield) and the significant factors, with a very modest Pvalue (0.0001) from the analysis of ANOVA and an acceptable coefficient of determination (R^{2}=0.995). Incorporating caproic acid into rapeseed oil and quantification of diincorporated structured triacyl glycerol as a function of factors were both successfully predicted using quadratic response models. The optimization of lipasecatalyzed synthesis for biodiesel (soybean oil methyl ester) and kojic acid monolaurate was determined by Shieh et al. (18), using a similar model. The researcher also checked the lipase activity of S. hasta, which did not show a significant activity (19). Additional steps involving the isolation of bacteria and purification of lipase can be taken to synthesize nanoparticles, following the procedures outlined by Ali et al. and Peidaei et al. (20, 21). Comparison of predicted and experimental values revealed good correspondence between them, implying that empirical models derived from RSM can be used to adequately describe the relationship between the factors and responses in media to produce lipase from Bacillus substilis KUBT4. These models can then be used to predict lipase yield under any given conditions within the experimental range. We have demonstrated that the optimum synthesis of lipases can be successfully predicted by RSM.