Comparison of estimation capabilities of response surface methodology (RSM) with artificial neural network (ANN) in lipase-catalyzed synthesis of palm-based wax ester

Background Wax esters are important ingredients in cosmetics, pharmaceuticals, lubricants and other chemical industries due to their excellent wetting property. Since the naturally occurring wax esters are expensive and scarce, these esters can be produced by enzymatic alcoholysis of vegetable oils. In an enzymatic reaction, study on modeling and optimization of the reaction system to increase the efficiency of the process is very important. The classical method of optimization involves varying one parameter at a time that ignores the combined interactions between physicochemical parameters. RSM is one of the most popular techniques used for optimization of chemical and biochemical processes and ANNs are powerful and flexible tools that are well suited to modeling biochemical processes. Results The coefficient of determination (R2) and absolute average deviation (AAD) values between the actual and estimated responses were determined as 1 and 0.002844 for ANN training set, 0.994122 and 1.289405 for ANN test set, and 0.999619 and 0.0256 for RSM training set respectively. The predicted optimum condition was: reaction time 7.38 h, temperature 53.9°C, amount of enzyme 0.149 g, and substrate molar ratio 1:3.41. The actual experimental percentage yield was 84.6% at optimum condition, which compared well to the maximum predicted value by ANN (83.9%) and RSM (85.4%). The order of effective parameters on wax ester percentage yield were; respectively, time with 33.69%, temperature with 30.68%, amount of enzyme with 18.78% and substrate molar ratio with 16.85%, whereas R2 and AAD were determined as 0.99998696 and 1.377 for ANN, and 0.99991515 and 3.131 for RSM respectively. Conclusion Though both models provided good quality predictions in this study, yet the ANN showed a clear superiority over RSM for both data fitting and estimation capabilities.


Background
Wax esters are long chain esters that are derived from fatty acids and alcohols with chain lengths of 12 carbons or more. The compounds have many potential applications due to their excellent wetting behavior at interfaces [1] and a non-greasy feeling when applied on skin surfaces. Wax esters are important ingredients in cosmetic formulations (cleansers, conditioners and moisturizers), pharmaceuticals (as an anti foaming agent in the production of penicillin), lubricants, plasticizers and polishes and other chemical industries [2]. Natural waxes originate from animals, vegetables and minerals. Many of the important commercial waxes contain rather high percentages of saturated wax esters, such as beeswax. Other raw materials for saturated and unsaturated wax esters are sperm whale and jojoba oil [2]. Since the naturally occurring wax esters are expensive and limited in access, the need to synthesize the compound has grown. Wax esters have been synthesized via chemical [3] and enzymatic reactions [4]. Enzymatic synthesis uses lower temperatures than chemical synthesis [2].
Wax esters can be produced by alcoholysis of vegetable oils such as palm oil. Palm oil consists of triacylglycerides, which are a combination of glycerol and different fatty acids. Enzymatic synthesis of wax esters from rapeseed fatty acid methyl ester [2] and lipase-catalyzed alcoholysis of crambe and camelina oil [5] have been reported.
One of the most important stages in a biological process is modeling and optimization to increase the efficiency of the process [ [6,7] and [8]]. The classical method of optimization involves varying one parameter at a time and keeping the other constant. This technique is not only time-consuming but also does not depict the complete effects of the parameters in the process and ignores the combined interactions between the physicochemical parameters. In contrast, response surface methodology (RSM) is an effective statistical technique for developing, improving, and optimizing of complex process [ [6] and [9]]. RSM is a collection of statistical and mathematical techniques that can be used to define the relationships between the response and the independent variables [10]. RSM defines the effect of the independent variables, alone or in combination, in the processes. In addition to analyzing the effects of the independent variables, this experimental methodology also generates mathematical model.
Although RSM has so many advantages, and has successfully been applied to study and optimize the enzyme synthesis of flavor ester [ [7] and [11]] and biodiesel (fatty acid alkyl ester) [12] and also optimizing enzyme production from microorganisms [ [13][14][15] and [16]], it is hard to say that it is applicable to all optimization and modeling studies. Baş and Boyacı [6] reported that the second-order polynomial equation was not suitable in explaining the effects of pH and substrate concentration on the initial reaction rate of the enzymatic reaction. Similar observations were made on the data of some RSM articles [[17,18] and [19]].
The past decade has seen a host of data analysis tools based on biological phenomena developed into wellestablished modeling techniques, such as artificial intelligence and evolutionary computing. Artificial neural networks (ANNs) are now the most popular artificial learning tool in biotechnology, with applications ranging from pattern recognition in chromatographic spectra and expression profiles, to functional analyses of genomic and proteomic sequences [20]. An artificial neural network is an information processing paradigm that is inspired by the way biological nervous systems, such as the brain, process information. Indeed an artificial neural network is a massively interconnected network structure consisting of many simple processing elements capable of performing parallel computation for data processing. The fundamental processing element of artificial neural networks (the artificial neuron, unit or nodes) simulates the basic functions of biological neurons [ [6] and [21]].
In the present investigation, RSM and ANN analysis of enzymatic synthesis of wax esters from palm oil and oleyl alcohol was carried out using a commercial immobilized lipase.

Results and discussion
Experimental design along with the observed responses is shown in Table 1.
The computed model F-value of 232 was higher than tabular value of F 0.01(14,15) = 3.56, implying the model are significant at 1% confidence level. The model also showed statistically insignificant lack of fit, as was evident from the lower computed F value (3.95) than the tabular F 0.01 (10,5) value (10.1) at 1% level. On the other hand, the pure error was very low, indicating good reproducibility of the data obtained. With very small P-value (0.0001) from the analysis of ANOVA and a suitable coefficient of determination (R 2 = 0.995), the quadratic polynomial model was highly significant and sufficient to represent the actual relationship between the response (percentage yield) and the significant variables (Table 2). Zhou et al.
reported that satisfactory quadratic response models were obtained for the incorporation of caproic acid into rapeseed oil [22]. Similar model was shown by Shieh et al. [9] and Chen et al.
[23] who determined the optimization of lipase-catalyzed synthesis for biodiesel (soybean oil methyl ester) and kojic acid mono laurate, respectively.

Artificial neural network
Effect of architecture and topology on neural network performance The selection of an optimal neural-network architecture and topology is of critical importance for a successful application. Several neural-network architecture and topologies (the number of hidden neurons, connection types, learning algorithms and transfer functions of input and hidden layers) were tested for the estimation and prediction of lipase-catalyzed synthesis of palm-based wax ester. Table 3 summarizes the top five ANN models.

The effect of learning algorithm and transfer function
Training a neural network model essentially means selecting one model from the set of allowed models that minimizes the cost criterion. We have tested different learning algorithms for training neural network models. All accepted models (RMSE < 0.01, R = 1 and DC = 1) have shown that incremental back propagation (IBP) was the most suitable learning algorithm for prediction of lipasecatalyzed synthesis of palm-based wax ester (Table 3).
According to IBP learning algorithm, in training, a set of inputs is presented to a network of randomly preassigned weights. Each neuron in the hidden and output layers first calculates the weighted sum of its inputs and passes the The type of transfer function employed affects the neural network's learning rate and is instrumental in its performance. In the present work, among all employed transfer functions for hidden and output layers, accepted models (RMSE < 0.01, R = 1 and DC = 1) were produced by linear function for output layer and hyperbolic tangent (Tanh) or Gaussian function for hidden layer that between them, the best models have been obtained by hyperbolic tangent (Tanh) function.

Optimal number of hidden neurons
Although it is important to select the optimal number of hidden neurons carefully, depending on the type and complexity of the task, this usually has to be done by trial and error. An increase in the number of hidden neurons up to a point usually results in a better learning performance. Too few hidden neurons limit the ability of the neural network to model the process, and too many may allow too much freedom for the weights to adjust and, thus, to result in learning the noise present in the database used in training [24]. We tested the effect of number of hidden neurons on the goodness of fit. The results of test-  ing with the two sample experiments, evaluated statistically on the basis of the coefficient of determination (R 2 ), are shown in Figure 1. In all examined cases, the optimum number of hidden neurons was 15, with an obvious increase in the calculation time and overfitting when too many hidden neurons were used. Then the 4-15-1 topology was chosen as the best topology for estimation of wax ester percentage yield.

Artificial neural network analysis of synthesis of palm-based wax ester
The best ANN chosen in the present work was a multilayer full feedforward incremental back propagation network with Tanh transfer function ( Table 3, C11) that consisted of a 4-15-1 topology ( Figure 2). The optimized values of network for learning rate and momentum were 0.15 and 0.8, respectively. The learning was completed in RMSE = 0.00998, R = 1 and DC = 1. In the case of training data set, the coefficient of determination (R 2 ) and absolute average deviation (AAD) were 1 and 0.002844, respectively, whereas for the testing data set, R 2 was 0.994122 and AAD was 1.289405 (Table 4) and for validating data sets R 2 and AAD were, 0.99998696 and 1.377, respectively ( Table 5).
Comparison of predicted and experimental values in training, testing and validating data sets, not only revealed capability of ANN in prediction of known data responses (the data that have been used for training) but also showed the ability of generalization for unknown data (the data that have not been used for training) and implying that empirical models derived from ANN can be used to adequately describe the relationship between the input factors and output in Lipozyme-catalyzed synthesis of wax ester from palm oil and oleyl alcohol.

Comparison of RSM and ANN predicted values
The predicted output values of RSM and ANN are shown in Table 4. Though both the models based on RSM and ANN preformed well and offered stable responses in predicting the combined interactions of the independent variables with respect to the response, yet the ANN based approach was better in fitting to the measured response in comparison to the RSM model. Figure 3 shows the three dimensional plots as function of time, temperature and interaction on wax ester synthesis at substrate molar ratio 1:3 and amount of enzyme of 1.50%. The percentage yield increased with an increase in incubation time. Reaction with temperature 50°C and time 7.5 h, led to the maximum percentage yield (over 80%). The percentage yield was increased from 40 to 50°C and decreased thereafter up to 60°C. The increase in percentage yield is an indication of the conformational change indicating greater unfolding of the enzyme at 50°C than at 30 and 60°C [25]. The effect of varying substrate molar ratio and reaction temperature on alcoholysis at constant reaction time (5 h), and amount of enzyme at 1.50% is as shown in Figure 4. only up to an extent, which decreases thereafter. This indicates that a critical temperature is involved up to which alcoholysis is favored and it is not so after that critical temperature. However percentage yield was lower at 55°C. Meanwhile, the low percentage yield at high substrate molar ratios (Figure 4)      Finally, Figure 9 shows the importance of percentage of effective parameters on the percentage yield. Time with 33.69% is the most important factor on the percentage yield, temperature with 30.68%, amount of enzyme with 18.78% and substrate molar ratio with 16.85% are subsequent degrees of importance.

Optimization of reaction
The optimal conditions for the Lipozyme-catalyzed synthesis of wax esters were predicted as presented in Table 5 along with their predicted and actual values. Among the various optimum conditions, the highest percentage yield (85.2%) was from experiment 3. However, a reaction con-dition of 53.9°C, 7.38 h, substrate molar ratio 1:3.41 and 1.15% amount of enzyme (experiment 1) was chosen as the optimum condition, because experiment 3 used more enzymes to achieve highest percentage yield. Although experiment 1 used more substrates than experiment 3, enzyme is more expensive than substrate. If it was necessary to complete the synthesis within 7 h without the concern for cost, the time factor should be considered first, and then the other factors could be maximized. All the optimum conditions could be used to produce high percentage yield of wax esters. Attention to R 2 and AAD values between actual and estimated responses demonstrated a higher prediction accuracy of ANN compared to RSM.
The quantitative analysis of the products using GC showed that the alcoholysis of palm oil with oleyl alcohol produced esters with different chain length fatty acids. The composition of synthesized esters at optimum condition is presented in Table 6.

Conclusion
This study compared the performance of the RSM and ANN in the estimation of Lipozyme-catalyzed synthesis of wax ester from palm oil and oleyl alcohol. Though both models provided good quality predictions for the four independent variables (reaction time, temperature, amount of enzyme and substrate molar ratio) in terms of the percentage yield of wax esters, yet the ANN methodology showed a clear superiority over RSM as a modeling technique for data sets showing nonlinear relationships. As a modeling technique, artificial neural network was better than RSM for both data fitting and estimation capabilities. Regression-based response surface models require the order of the model to be stated (i.e., second, third or On the other hand, neural networks also have the disadvantage of requiring large amounts of training data in comparison with RSM that offers a large amount of information from a small number of experiments. This advantage of RSM is because of its experimental design [10]. To overcome this ANN problem, in present study we used the RSM idea, and then a statistical experimental design, CCRD, was employed to reduce the number of experiments. Thus, ANN could be a very powerful and flexible tool for modeling the optimization process.

Synthesis and analysis
Different molar ratios of palm oil and oleyl alcohol were added to 10 ml n-hexane, followed by different amounts of enzyme. The mixture of palm oil, oleyl alcohol and Lipozyme IM were incubated in a horizontal water bath shaker (150 rpm) at different reaction temperatures and reaction times. The reactions were analyzed by a gas chromatograph (Hitachi model G-3000, Tokyo, Japan), using an Rtx-65TG capillary column (30 m × 0.25 mm). Helium was used as the carrier gas at a flow rate 30 ml min-1. The temperature was programmed at 2 min at 150°C, 20°C min-1 to 300°C and 10 min at 300°C. The product composition was quantitated by an internal standard method with methyl linoleate as the internal standard. The concentrations of esters were calculated by equation 2: where C is the amount of component x or internal standard, A is area for component x or internal standard and D Rf is detector response factor for component x or internal standard (D Rfx = A x /C x and D Rf IS = A IS /C IS ).
The percentage yield of produced ester was calculated by equation 3:

Response surface methodology analysis
The CCRD design experimental data was used for model fitting in RSM to find the best polynomial equation. This data was analyzed using design expert version 6.06 and then interpreted. Three main analytical steps: analysis of variance (ANOVA), a regression analysis and the plotting of response surface were performed to establish an optimum condition for the alcoholysis. Then, the predicted values obtained from RSM model, were compared with actual values for testing the model. Finally the experimental values of predicted optimal conditions (Table 5) were used as validating set and were compared with predicted values.

Artificial neural network analysis
A commercial ANN software, NeuralPower version 2.5 (CPC-X Software) was used throughout the study. Multilayer normal feedforward and multilayer full feedforward neural networks were used to predict the percentage yields of palm-based wax ester that were trained by different learning algorithms (incremental back propagation, IBP; batch back propagation, BBP; quickprob, QP; genetic algorithm, GA; and Levenberg-Marquardt algorithm, LM). The network architecture consisted of an input layer with four neurons, an output layer with one neuron, and a hidden layer. Molar ratio of palm oil and oleyl alcohol, amount of enzyme, reaction temperature and reaction time were used as networks inputs and the percentage yield of palm-based wax ester, as target output. To determine the optimal network topology, only one hidden layer was used and the number of neurons in this layer and the transfer functions of hidden and output layers (sigmoid, hyperbolic tangent function, Gaussian, linear, threshold linear and bipolar linear) were iteratively determined by developing several networks. Each network was trained until the network root of mean square error (RMSE), average correlation coefficient (R) and average determination coefficient (DC) were lower than 0.01, Three dimensional plot showing the effect of amount of enzyme, substrate molar ratio and their mutual effect on the synthesis of wax esters The CCRD design experimental data was divided into training and testing sets. For training, 26 points were used (Tables 1 and 4). One strategy for finding the best model is to summarize the data, it is well established [32] that in ANN modeling, the replicates at center point do not improve the prediction capability of the network because of the similar inputs. That is why we improved our model by using mean of center points instead of 6 center points (Tables 1 and 4, italic numbers). For testing the network, 4 remaining points were used (Tables 1 and 4, bold numbers). On the other hand, experimental values of predicted optimal conditions (Table 5) were used as validating set.

Verification of estimated data
The estimation capabilities of the techniques, RSM and ANNs were tested. For this purpose, the estimated responses obtained from RSM and ANNs were compared with the observed responses. The coefficient of determination (R 2 ) and absolute average deviation (AAD) were determined and these values were used together to compare ANNs to each other for finding the best ANN model, and the best ANN model with RSM. The AAD and R 2 are calculated by equations 4 and 5, respectively.
where y i,exp and y i,cal are the experimental and calculated responses, respectively, and p is the number of the experimental run.
where n is the number of experimental data. R 2 is a measure of the amount of the reduction in the variability of response obtained by using the repressor variables in the model. Because R 2 alone is not a measure of the model's accuracy, it is necessary to use absolute average deviation (AAD) analysis, which is a direct method for describing the deviations. Evaluation of R 2 and AAD values together would be better to check the accuracy of the model. R 2 must be close to 1.0 and the AAD between the predicted and observed data must be as small as possible.
The acceptable values of R 2 and AAD values mean that the model equation defines the true behavior of the system and it can be used for interpolation in the experimental domain [32].

Optimization of reaction
The predicted optimal conditions could be easily calculated using model equation. The stationary point (minimum or maximum point) of a second order equation is the point where the first derivative of the function equals to zero: The stationary point is found by computing ∂y/∂x 1 and ∂y/ ∂x 2 and setting zero: The system of equations is solved to find the values of x 1 and x 2 . To determine whether the stationary phase is minimum or maximum, the second derivative of the equation  Importance of effective parameters on percentage yield of wax ester Figure 9 Importance of effective parameters on percentage yield of wax ester.