Comparison of estimation capabilities of response surface methodology (RSM) with artificial neural network (ANN) in lipase-catalyzed synthesis of palm-based wax ester
- Mahiran Basri^{1}Email author,
- Raja Noor Zaliha Raja Abd Rahman^{2},
- Afshin Ebrahimpour^{2},
- Abu Bakar Salleh^{2},
- Erin Ryantin Gunawan^{1} and
- Mohd Basyaruddin Abd Rahman^{1}
DOI: 10.1186/1472-6750-7-53
© Basri et al; licensee BioMed Central Ltd. 2007
Received: 24 April 2007
Accepted: 30 August 2007
Published: 30 August 2007
Abstract
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 (R^{2}) 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 R^{2} 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 [[13–15] 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 well-established 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 used in RSM and ANN studies by using four independent variables showing observed values of percentage yield of wax esters synthesis
Temperature (°C) | Time (h) | Molar ratio (mmol) | Amount of enzyme (g) | Actual yield (%) mean ± SD |
---|---|---|---|---|
40 | 2.5 | 2 | 0.1 | 30.2 ± 0.17 |
60 | 2.5 | 2 | 0.1 | 32.9 ± 0.52 |
60 | 7.5 | 2 | 0.1 | 75.5 ± 0.82 |
40 | 2.5 | 4 | 0.1 | 41.8 ± 0.46 |
40 | 7.5 | 4 | 0.1 | 75.2 ± 1.12 |
60 | 7.5 | 4 | 0.1 | 72.9 ± 0.57 |
60 | 2.5 | 2 | 0.2 | 55.6 ± 0.23 |
40 | 7.5 | 2 | 0.2 | 80.8 ± 0.37 |
60 | 7.5 | 2 | 0.2 | 78.7 ± 0.19 |
60 | 2.5 | 4 | 0.2 | 60.6 ± 0.41 |
40 | 7.5 | 4 | 0.2 | 72.4 ± 0.6 |
60 | 7.5 | 4 | 0.2 | 68.6 ± 0.36 |
30 | 5 | 3 | 0.15 | 48.5 ± 0.18 |
70 | 5 | 3 | 0.15 | 48 ± 0.3 |
50 | 0 | 3 | 0.15 | 20 ± 0.15 |
50 | 10 | 3 | 0.15 | 80 ± 0.77 |
50 | 5 | 1 | 0.15 | 70.2 ± 0.66 |
50 | 5 | 5 | 0.15 | 72.5 ± 0.85 |
50 | 5 | 3 | 0.05 | 70.1 ± 1.21 |
50 | 5 | 3 | 0.25 | 82 ± 0.49 |
50 | 5 | 3 | 0.15 | 81.6 ± 0.28 |
50 | 5 | 3 | 0.15 | 82.0 ± 0.51 |
50 | 5 | 3 | 0.15 | 82.4 ± 0.43 |
50 | 5 | 3 | 0.15 | 80.0 ± 0.45 |
50 | 5 | 3 | 0.15 | 82.5 ± 0.78 |
50 | 5 | 3 | 0.15 | 82.7 ± 0.39 |
40 | 7.5 | 2 | 0.1 | 75.2 ± 1.11 |
60 | 2.5 | 4 | 0.1 | 45.5 ± 0.3 |
40 | 2.5 | 2 | 0.2 | 46.2 ± 0.26 |
40 | 2.5 | 4 | 0.2 | 55.4 ± 1.44 |
Response surface methodology
Fitting the data to various models (linear, two factorial, quadratic and cubic) and their subsequent ANOVA showed that reactions of palm oil and oleyl alcohol were most suitably described with quadratic polynomial model (equation 1):
Yield (%) = -334 + 9.05A + 31.8B + 32.4C + 508D - 0.0858A^{ 2 }- 1.29B^{ 2 } - 2.80C^{ 2 } - 655D^{ 2 } - 0.0725AB - 0.0471AC + 0.545AD - 1.49BC - 32.9BD - 32.4CD (1)
where A is the temperature; B the time; C the molar ratio; and D the amount of enzyme.
ANOVA for joint test
Source | Sum of squares | Degree of freedom | Mean square | F-value | Prob > F |
---|---|---|---|---|---|
Model | 9506 | 14 | 679 | 232 | < 0.0001^{a} |
Temperature (A) | 5.86 | 1 | 5.86 | 2 | 0.177^{b} |
Time (B) | 5180 | 1 | 5180 | 1770 | < 0.0001^{a} |
Molar ratio (C) | 19.6 | 1 | 19.6 | 6.7 | 0.0206^{a} |
Amount of enzyme (D) | 359 | 1 | 359 | 123 | < 0.0001^{a} |
A ^{2} | 2020 | 1 | 2020 | 690 | < 0.0001^{a} |
B ^{2} | 1790 | 1 | 1790 | 611 | < 0.0001^{a} |
C ^{2} | 216 | 1 | 216 | 73.7 | < 0.0001^{a} |
D ^{2} | 73.5 | 1 | 73.5 | 25.2 | 0.000154^{a} |
AB | 52.6 | 1 | 52.6 | 18 | 0.000712^{a} |
AC | 3.55 | 1 | 3.55 | 1.22 | 0.288^{b} |
AD | 1.19 | 1 | 1.19 | 0.406 | 0.533^{b} |
BC | 221 | 1 | 221 | 75.6 | < 0.0001^{a} |
BD | 270 | 1 | 270 | 92.5 | < 0.0001^{a} |
CD | 42.1 | 1 | 42.1 | 14.4 | 0.0017^{a} |
Residual | 43.8 | 15 | 2.92 | ||
Lack of fit | 38.9 | 10 | 3.89 | 3.95 | 0.0714^{b} |
Pure error | 4.93 | 5 | 0.985 | ||
Cor total | 9550 | 29 |
Artificial neural network
Effect of architecture and topology on neural network performance
The effect of different neural network architecture and topologies on R^{2} and AAD in the estimation of lipase-catalyzed synthesis of palm-based wax ester obtained in the training and testing of neural networks
Name | Model | Learning Algorithm | Connection Type | Transfer Function Output | Transfer Function Hidden | Training Set R^{2} | Training Set AAD (%) | Testing Set R^{2} | Testing Set AAD (%) |
---|---|---|---|---|---|---|---|---|---|
C11 | 4-15-1 | IBP^{a} | MFFF^{b} | Linear | Tanh^{d} | 1 | 0.002844 | 0.994122 | 1.289405 |
C15 | 4-15-1 | IBP | MNFF^{c} | Linear | Tanh | 1 | 0.014932 | 0.979308 | 3.157524 |
C9 | 4-12-1 | IBP | MNFF | Linear | Tanh | 1 | 0.000794 | 0.934519 | 4.538254 |
C16 | 4-10-1 | IBP | MNFF | Linear | Tanh | 1 | 0.014686 | 0.937174 | 5.3352 |
C10 | 4-10-1 | IBP | MFFF | Linear | Tanh | 1 | 0.002646 | 0.904918 | 6.323364 |
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 lipase-catalyzed 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 result through a transfer function to produce an estimate as output that corresponds to the input data set. The result is compared to the corresponding desired values and the error is back-propagated through the network to adjust the connection weights according to the learning rule. This procedure is repeated iteratively, until the predetermined target RMSE is reached [24].
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
Artificial neural network analysis of synthesis of palm-based wax ester
Predicted percentage yields by ANN and RSM models along with absolute deviation, R^{2}and AAD
ANN Predicted yield (%) | ANN Absolute deviation | RSM Predicted yield (%) | RSM Absolute deviation |
---|---|---|---|
30.19981 | 6.36E-06 | 29.4 | 0.027211 |
32.89836 | 4.98E-05 | 34.4 | 0.043605 |
75.49839 | 2.13E-05 | 75.8 | 0.003958 |
41.79979 | 5.05E-06 | 42.8 | 0.023364 |
75.19847 | 2.04E-05 | 78 | 0.035897 |
72.89809 | 2.62E-05 | 72.5 | 0.005517 |
55.59765 | 4.22E-05 | 54.1 | 0.027726 |
80.79801 | 2.47E-05 | 80.3 | 0.006227 |
78.69785 | 2.74E-05 | 79.1 | 0.005057 |
60.59789 | 3.48E-05 | 59.2 | 0.023649 |
72.39832 | 2.33E-05 | 72.3 | 0.001383 |
68.59837 | 2.38E-05 | 69.3 | 0.010101 |
48.49916 | 1.73E-05 | 46.6 | 0.040773 |
47.99756 | 5.09E-05 | 48.6 | 0.012346 |
19.99912 | 4.42E-05 | 20.2 | 0.009901 |
79.99778 | 2.77E-05 | 81.9 | 0.023199 |
70.19804 | 2.79E-05 | 68.9 | 0.018868 |
72.49749 | 3.46E-05 | 72.5 | 0 |
70.09794 | 2.94E-05 | 67.6 | 0.036982 |
81.99761 | 2.92E-05 | 83.1 | 0.013237 |
81.86748 | 3.08E-05 | 81.9 | 0.000366 |
74.07436 | 0.014969 | 78.0 | 0.037234 |
45.0392 | 0.010128 | 45.9 | 0.00879 |
46.27601 | 0.00165 | 48.0 | 0.038961 |
56.77555 | 0.02483 | 55.0 | 0.00722 |
Solution of optimum condition
Expriment | Temperature (° and C) | Time (h) | Molar ratio (mmol) | Amount of enzyme (g) | ANN Predicted yield (%) | Actual yield (%) | RSM Predicted yield (%) |
---|---|---|---|---|---|---|---|
1 | 53.9 | 7.38 | 3.41 | 0.149 | 83.9 | 84.6 | 85.4 |
2 | 54.6 | 7.33 | 2.07 | 0.123 | 83.3 | 81.9 | 85 |
3 | 55.6 | 6.69 | 3.09 | 0.181 | 84.5 | 85.2 | 84.9 |
4 | 46.8 | 5.72 | 3.57 | 0.195 | 81.1 | 80 | 83.9 |
5 | 50.2 | 5.31 | 2.66 | 0.155 | 80.7 | 79 | 83.5 |
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.
Effect of parameters
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 condition 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.
Composition of ester produced from palm oil alcoholysis at optimum condition
Esters | Percentage (%) |
---|---|
Oleyl laurate | 0.8 ± 0.13 |
Oleyl myristate | 3.8 ± 0.60 |
Oleyl palmitate | 35.5 ± 4.05 |
Oleyl stearate | 4.5 ± 0.25 |
Oleyl oleate | 33.3 ± 1.92 |
Oleyl linoleate | 6.8 ± 0.39 |
Total | 84.6 ± 1.4 |
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 fourth order) [31], but unfortunately most of the packed program produced for the application of RSM use second order model equation and then the major drawback of RSM is to fit the data to a second order polynomial, while ANN tends to implicitly match the input vectors to the output vector [[31] and [32]]. Indeed ANN is a superior and more accurate modeling technique when compared to the RSM as it represents the nonlinearities in much better way [31].
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.
Methods
Materials
Immobilized lipase from Mucor miehei (Lipozyme IM) was produced by Novo Nordisk (Denmark). Palm oil (MW = 3 × average of saponification equivalent of palm oil) was obtained from Southern Edible Oil Sdn. Bhd. (Malaysia). Fatty acid compositions of Malaysian palm oil are 0.1 – 0.3% of lauric acid, 0.9 – 1.5% of myristic acid, 39.2 – 45.2% of palmitic acid, 3.7 – 5.1% of stearic acid, 37.5 – 44.1% of oleic acid and 8.7 – 12.5% of linoleic acid [33]. Oleyl alcohol was obtained from Fluka Chemika (Switzerland). Ester standards, oleyl laurate, oleyl myristate, oleyl palmitate, oleyl stearate, oleyl oleate, oleyl linoleate and methyl linoleate were obtained from Sigma Aldrich (USA). Hexane was obtained from J.T. Baker (USA). All other chemicals were of analytical grade.
Experimental design
A five-level-four-factor central composite rotary design (CCRD) was employed in this study, requiring 30 experiments [34]. The fractional factorial design consisted of 16 factorial points, 8 axial points and 6 center points. The variable and their levels selected for the wax esters synthesis were: time (2.5 – 10 h); temperature (30 – 70°C); amount of enzyme (0.1 – 0.2 g) and substrate molar ratio (1 mmol palm oil to 1 – 5 mmol oleyl alcohol, 1:1 – 1:5). All experiments were carried out at the water activity equal to one.
The experimental data [35 points include CCRD design (Table 1) and optimization data (Table 5)] was divided into three sets: training set, testing set and validating set.
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:
C_{ x }= ( A_{ x }/ A_{ IS })( C_{ IS }D_{ Rf IS }/ D_{ Rf x }) (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:
Percentage yield (%) = [ester produced (mmol)/palm oil used (mmol)] × 100
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, equal to 1 and 1, respectively. Other parameters for network were chosen as the default values of the used software. At the start of the training, weights were initialized with random values and adjusted through a training process in order to minimize network error.
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
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 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 is used. If it is a negative value, the optimum point is a maximum but if it is a positive value, the optimum point is a minimum [32].
Declarations
Acknowledgements
This project was financed by a grant from IRPA Project, No. 09-02-04-0306-EA001, Malaysia.
Authors’ Affiliations
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