# Statistical Design of Experimental and Bootstrap Neural Network Modelling Approach for Thermoseparating Aqueous Two-Phase Extraction of Polyhydroxyalkanoates

^{1}

^{2}

^{3}

^{4}

^{5}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Materials

#### 2.2. Production of PHAs

_{2}HPO

_{4}-7H

_{2}O, 6.7 g/L; KH

_{2}PO

_{4}, 1.5 g/L; (NH

_{4})

_{2}SO

_{4}, 2.5 g/L; MgSO

_{4}-7H

_{2}O, 0.2 g/L; and CaCl

_{2}, 10 mg/L) and 0.5% v/v of trace mineral solution (Na

_{2}EDTA, 6.0 g/L; FeCl

_{3}-6H

_{2}O, 0.29 g/L; H

_{3}BO

_{3}, 6.84 g/L; MnCl

_{2}-4H

_{2}O, 0.86 g/L; ZnCl

_{2}, 0.06 g/L; CoCl

_{2}-6H

_{2}O, 0.026 g/L; and CuSO

_{4}-5H

_{2}O, 0.002 g/L).

#### 2.3. Experimental Design and Statistical Analysis

^{4}) was carried out to investigate the effects and interactions of important parameters in the thermoseparating-based ATPE of PHAs. Four independent parameters, including potassium phosphate concentration (X

_{1}), EOPO concentration (X

_{2}), pH (X

_{3}), and sodium chloride (X

_{4}) were taken into account and studied at two widely spaced levels. The low (−) and high (+) levels of the factors were 8 and 15 wt % for potassium phosphate concentration, 10 and 18 wt % for EOPO concentration, 8 and 10 for system pH, and 0 and 100 mM for sodium chloride addition. The reason behind the choice of the levels of EOPO concentration and phosphate concentration is to ensure the formation of a two-phase with a high enough volume ratio so that the “volume-exclusion” effect does not occur. Volume-exclusion occurs when the free space available for target products in the polymer-rich top phase is reduced, causing partitioning to the bottom phase [22]. System pH levels were chosen based on a literature review of PHAs partitioning [23]. Levels of sodium chloride addition were selected following the results of the previous study where 10 mM of salt addition gave recovery yield as high as 90.9%, while 100 mM of salt addition gave recovery yield as low as 53.5% [24]. These four parameters were chosen due to their potential influence and contribution to the partitioning of PHAs by thermoseparating polymer-based ATPE based on a thorough literature review and previous experimental study [24]. The experiments were conducted in a completely random manner to fulfill the requirement of each run being independent of the influence of an unknown effect. Three replicates of the full factorial design experiments were conducted.

#### 2.4. Partitioning of PHAs in Thermoseparating ATPE

#### 2.5. Quantification of PHAs by Gas Chromatography (GC) Analysis

#### 2.6. Partitioning Behaviors of PHAs

_{T}/Conc

_{B}

_{T}and Conc

_{B}are PHAs concentration of top phase and bottom phase respectively.

_{PHAs}/M

_{Sample}) × 100%

_{PHA}is the mass of PHAs (g) and M

_{Sample}is the total mass of dried sample used (g).

_{r}was defined as the ratio between top phase volume and bottom phase volume:

_{r}= V

_{T}/V

_{B}

_{T}and V

_{B}are top and bottom phase volume respectively.

_{T}× V

_{T})/(Conc

_{E}× V

_{E})

_{T}and Conc

_{E}are the PHAs concentration of top phase and extract, respectively and V

_{E}is the extracted volume.

#### 2.7. Neural Network Methodology

^{2}). In this work, the FFNN was trained using the Levenberg-Marquardt backpropagation technique. This technique is well known to produce FFNN with good generalization and fast convergence. The FFNN is trained iteratively using different numbers of hidden neurons in order to acquire the best model with the lowest MSE and RMSE value with R

^{2}near to one [30]. All of the simulation work regarding neural network modeling and analysis was performed using Matlab software.

## 3. Results and Discussion

#### 3.1. Statistical Experimental Result

^{4}) was conducted to investigate the influence and interaction of four variables, which were potassium phosphate concentration (X

_{1}), EOPO concentration (X

_{2}), pH (X

_{3}), and NaCl addition (X

_{4}) in PHAs partition by thermoseparating-based ATPE. Full factorial designs and the responses are presented in Table 1. It can be seen that there is a wide variation of Kpa (0.402–16.547) and recovery yield (16.8%–93.9%) which is due to the intended variation in the factor combinations and this revealed the significance of optimization in achieving better recovery and purity. From the results in Table 1, it can be seen that run 6 has the highest Kpa (16.5) and yield (93.9%), while run 10 has the highest PF with the value of 1.54. Utilizing Design Expert software, the analysis of variance (ANOVA) was performed to verify the validity of the models, evaluate the statistical significance of all factors, and determine the influence of these factors on the response variables. These models consisted of four main effects, six two-parameter interactions, and four three-parameter interactions, while the last which is one four-parameter interaction was given the assumption of being negligible due to hierarchical reasons [29].

#### 3.1.1. Effect on the “Yield”

^{2}, can be utilized to assess the ratio of total variation ascribed to each fit. With a value always between 0 and 1, R

^{2}larger than 0.75 shows a good fit of the model to the response variable [31], while a value larger than 0.9 is very satisfying in the DOE for the bioprocess [22]. For recovery yield, the high value of R

^{2}, which is 0.9999 demonstrates a good response between the model and the experimental results. This also indicates that the interrelationship between the independent variable can be satisfactorily represented by the model with only less than 0.01% of total variations not able to be explained by the model. The adjusted coefficient of determination, R

^{2}

_{adj}can be used to measure the accuracy of a model for the response variable [6]. The R

^{2}

_{adj}of 0.999 was in a good agreement with the predicted R

^{2}, R

^{2}

_{pred}of 0.982, which shows that the predicted values are compatible with the experimental results.

_{1}and X

_{2}) and interactive model term (X

_{1}X

_{2}) were the significant model terms. By discarding and pooling all statistically insignificant model terms (Prob>F more than 0.05) into the error term and using only significant model terms, the new reduced model was obtained for response variable “Yield”. Using ANOVA, the statistical analysis demonstrated that the reduced model was significant at a confidence level of 95% with the p-value much lower than 0.05 (Prob>F less than 0.0001). By taking into account the significant linear model terms and interactions, the regression analysis of Yield data provided the following first-order model:

_{1}+ 12.52 X

_{2}+ 10.56 X

_{1}X

_{2}

_{1}) had the strongest positive effect on recovery yield. As shown in the experimental design results, the recovery yield is generally higher at high (+) level of X

_{1}where the yield achieves as high as 93.9% for run 6. In the system of higher phosphate concentrations, the strengthened “salting-out” effect reduces the solubility of PHA in the salt-rich bottom phase, by promoting aggregation and hydrophobic interaction. This, in turn, directs PHA partition to the polymer-rich top phase which has lower salt concentration, facilitating the extraction of PHAs to the EOPO-rich phase [33]. This is in accordance with other works in the partitioning of others biomolecules by ATPE, such as collagenase from Penicillium aurantiogriseum [29] and other bioproducts as well. More importantly, it is worth mentioning that the highest yield obtained in the current study is significantly higher than that of the literature which utilized the PEG/phosphate system (40% to 50%) [3].

_{1}, the regression equation also suggested that EOPO concentration (X

_{2}) is a significant positive parameter for recovery yield as well. There are two main forces dominating in the polymer-rich phase, which are the “volume-exclusion” effect and the hydrophobic interaction. As the “volume-exclusion” effect no longer in the picture as mentioned above, the increasingly stronger hydrophobic interaction between polymer-rich phase and PHAs molecules due to increasing concentration of thermoseparating polymers causes PHAs partition preferably to the top phase [32]. Several studies on ATPE also showed similar results, such as for lysozyme [16] and other bioproducts. Another essential point is that the recovery yield was also positively affected by the synergistic positive interaction between phosphate and EOPO concentration (X

_{1}X

_{2}). The simultaneous rise in the level of both parameters had a stronger impact on the increment of recovery yield than the expected add up of those of the individual parameters. The combined effect can be observed in run 6, 7, 10, and 11 where the yield can achieve a high value of at least 85% when both phosphate and EOPO concentration are at high (+) levels.

#### 3.1.2. Effect on the “Partition Coefficient”

_{1}, X

_{3,}and X

_{4}were statistically significant with 95% of confidence and had a significant influence on Kpa. For this response variable, EOPO concentration only gives a slight but positive effect on the intended selection of X

_{2}levels to prevent the “volume-exclusion” effect. Not only that, some of the interactive model terms (X

_{1}X

_{2}, X

_{2}X

_{3}and X

_{2}X

_{3}X

_{4}) were significant at 95% of confidence level as well. The reduced model can be described by the following regression equation:

^{0.5}= 0.95 − 0.43 X

_{1}− 0.057 X

_{3}+ 0.046 X

_{4}− 0.18 X

_{1}X

_{2}+ 0.054 X

_{2}X

_{3}+ 0.033 X

_{2}X

_{3}X

_{4}

^{2}(0.997), it shows that the real relationship between the response variable and independent parameters is adequately represented by the model. This indicates that 99.7% of the variability in response could be explained by the model. The close values of R

^{2}

_{adj}and R

^{2}

_{pred}which are 0.992 and 0.979 respectively demonstrate a good degree of correlation between the theoretical values predicted by the reduced model equation and experimental responses.

_{1}). As shown in Table 1, only Kpa for a high level (i.e., 15 wt %) of X

_{1}gives a value larger than 1 (ranging from the lowest of 1.3 to the highest of 16.5). The same result was also reported in the works of partitioning of collagenase [29] and lysozyme [16]. Also, a positive interaction effect between X

_{1}and X

_{2}was observed, revealing a synergism between the two variables. Therefore, higher Kpa will be achieved with a high level of both potassium phosphate and EOPO concentration, which can be seen especially in run 6 and 10 (with Kpa higher than 12).

_{1}as in run 6.

#### 3.1.3. Effect on the “Purification Factor”

^{2}, this indicated that 96.6% of the experimental data was compatible with the predicted data from the model. The value of R

^{2}

_{adj}was calculated to be 0.943, close to that R

^{2}

_{pred}(0.893), which demonstrates a high degree of correlation between the predicted and observed values. The model can be adequately utilized to predict the data within the range of variables studied. The reduced model can be described by the following first-order model:

_{1}+ 0.11 X

_{2}− 0.067 X

_{1}X

_{2}− 0.062 X

_{2}X

_{3}− 0.077 X

_{1}X

_{3}X

_{4}

_{1}and X

_{2}were significant with 95% of confidence among the investigated independent parameters as shown in the equation. Other than that, the interactions between independent parameters such as X

_{1}X

_{2}, X

_{2}X

_{3,}and X

_{1}X

_{3}X

_{4}also play significant roles in the purification of PHAs by thermoseparating ATPE. As expected of the positive main effect of phosphate concentration, a dramatic increase of PF values can be observed at the elevated levels of this parameter, especially shown in run 10 and 11 with PF greater than 1.5. This was also demonstrated in the partition of collagenase from Penicillium aurantiogriseum by Lima and his colleagues with improving purification when utilizing higher phosphate concentration [29]. Similarly, PF was found to be positively correlated with the EOPO concentration (X

_{2}) as well. This trend is congruent with the purification of other bioproducts utilizing ATPE as reported in the literature. For example, the purification factor of α-amylase from Aspergillus oryzae was increased by threefold at the highest level of PEG concentration (20 wt %) [31]. Study on isolation of lysozyme from crude hen egg white has reported a high PF value was achieved at high polymer concentration as well [32]. Despite that, the simultaneous increase of X

_{1}and X

_{2}, as well as X

_{2}and X

_{3}, has a negative impact on PF. To summarize, PF is the most complicated response variable to be optimized due to the complicated positive contributions from the linear model terms combined with the negative contributions from the interactions between them.

#### 3.2. Feed Forward Neural Network (FFNN) Model Results

^{−17}, RMSE = 3.22 × 10

^{−9}and R

^{2}= 1. The excellent results are assumed due to the application of the resampling method. By providing the FFNN model with a larger set of data, the network was able to generalize properly. However, due to the lack of foreign or unseen data, the possible effect of network overfitting could not be tested.

## 4. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**Figure 3.**Analogy of bootstrap resampling technique: (

**a**) Data distribution in original dataset; (

**b**) data distribution in new datasets after resampling [29].

**Figure 5.**Validation results for Output 1 Partition Coefficients (Kpa) (

**a**); Output 2 Recovery Yield (%) (

**b**); and Output 3 Purification Factor (PF) (

**c**).

Run | X_{1} (wt %) | X_{2} (wt %) | X_{3} | X_{4} (mM) | Kpa | Yield (%) | PF (fold) |
---|---|---|---|---|---|---|---|

1 | 8 | 10 | 10 | 0 | 0.814 | 24.6 | 0.93 |

2 | 8 | 10 | 8 | 0 | 0.646 | 21.4 | 0.93 |

3 | 15 | 10 | 10 | 0 | 3.371 | 57.4 | 1.35 |

4 | 8 | 18 | 8 | 0 | 0.431 | 25.5 | 1.07 |

5 | 8 | 18 | 8 | 100 | 0.402 | 24.8 | 1.04 |

6 | 15 | 18 | 10 | 0 | 16.547 | 93.9 | 1.46 |

7 | 15 | 18 | 10 | 100 | 5.585 | 85.5 | 1.48 |

8 | 15 | 10 | 8 | 0 | 1.554 | 38.3 | 0.95 |

9 | 8 | 10 | 8 | 100 | 0.525 | 16.8 | 0.67 |

10 | 15 | 18 | 8 | 100 | 12.291 | 92.5 | 1.54 |

11 | 15 | 18 | 8 | 0 | 8.047 | 86.8 | 1.52 |

12 | 15 | 10 | 8 | 100 | 1.314 | 32.9 | 1.22 |

13 | 8 | 18 | 10 | 0 | 0.512 | 30.1 | 0.96 |

14 | 15 | 10 | 10 | 100 | 2.322 | 45.5 | 1.04 |

15 | 8 | 18 | 10 | 100 | 0.369 | 22.7 | 1.04 |

16 | 8 | 10 | 10 | 100 | 0.817 | 24.6 | 1.21 |

_{1}, EOPO concentration is X

_{2}, pH is X

_{3}and NaCl addition is X

_{4}and PF is purification factor.

Source | Sum of squares | Degree of freedom | Mean square | F value | Prob>F |
---|---|---|---|---|---|

Model | 12070.8 | 14 | 862.2 | 1007.687 | 0.0247 |

X_{1} | 7323.1 | 1 | 7323.1 | 8558.750 | 0.0069 |

X_{2} | 2507.5 | 1 | 2507.5 | 2930.613 | 0.0118 |

X_{3} | 128.3 | 1 | 128.3 | 149.897 | 0.0519 |

X_{4} | 66.8 | 1 | 66.8 | 78.107 | 0.0717 |

X_{1}X_{2} | 1783.0 | 1 | 1783.0 | 2083.799 | 0.0139 |

X_{1}X_{3} | 20.9 | 1 | 20.9 | 24.462 | 0.1270 |

X_{1}X_{4} | 3.3 | 1 | 3.3 | 3.893 | 0.2986 |

X_{2}X_{3} | 100.5 | 1 | 100.5 | 117.459 | 0.0586 |

X_{2}X_{4} | 7.7 | 1 | 7.7 | 9.000 | 0.2048 |

X_{3}X_{4} | 32.2 | 1 | 32.2 | 37.640 | 0.1029 |

X_{1}X_{2}X_{3} | 33.4 | 1 | 33.4 | 38.978 | 0.1011 |

X_{1}X_{2}X_{4} | 20.5 | 1 | 20.5 | 23.931 | 0.1284 |

X_{1}X_{3}X_{4} | 21.4 | 1 | 21.4 | 25.000 | 0.1257 |

X_{2}X_{3}X_{4} | 22.3 | 1 | 22.3 | 26.093 | 0.1231 |

Residual | 0.9 | 1 | 0.9 | ||

Cor Total | 12071.7 | 15 | |||

R^{2} | 0.9999 | ||||

R^{2}_{adj} | 0.999 | ||||

R^{2}_{pred} | 0.982 |

Source | Sum of squares | Degree of freedom | Mean square | F value | Prob>F |
---|---|---|---|---|---|

Model | 3.568 | 9 | 0.396 | 221.5 | <0.0001 |

X_{1} | 2.891 | 1 | 2.891 | 1615.4 | <0.0001 |

X_{3} | 0.052 | 1 | 0.0516 | 28.8 | 0.0015 |

X_{4} | 0.033 | 1 | 0.0332 | 18.5 | 0.0057 |

X_{1}X_{2} | 0.516 | 1 | 0.516 | 288.5 | <0.0001 |

X_{2}X_{3} | 0.046 | 1 | 0.0460 | 25.7 | 0.0022 |

X_{2}X_{3}X_{4} | 0.018 | 1 | 0.0179 | 10.0 | 0.0265 |

Residual | 0.011 | 6 | 0.0018 | ||

Cor Total | 3.579 | 15 | |||

R^{2} | 0.997 | ||||

R^{2}_{adj} | 0.992 | ||||

R^{2}_{pred} | 0.979 |

**Table 4.**Statistical result of ANOVA for reduced model of the response variable “purification factor (PF)”.

Source | Sum of squares | Degree of freedom | Mean square | F value | Prob>F |
---|---|---|---|---|---|

Model | 0.955 | 6 | 0.159 | 42.6 | <0.0001 |

X_{1} | 0.459 | 1 | 0.459 | 122.9 | <0.0001 |

X_{2} | 0.205 | 1 | 0.205 | 54.8 | <0.0001 |

X_{1}X_{2} | 0.072 | 1 | 0.071556 | 19.2 | 0.0018 |

X_{2}X_{3} | 0.061 | 1 | 0.061256 | 16.4 | 0.0029 |

X_{1}X_{3}X_{4} | 0.095 | 1 | 0.094556 | 25.3 | 0.0007 |

X_{1}X_{2}X_{3}X_{4} | 0.064 | 1 | 0.063756 | 17.1 | 0.0026 |

Residual | 0.034 | 9 | 0.003734 | ||

Cor Total | 0.988 | 15 | |||

R^{2} | 0.966 | ||||

R^{2}_{adj} | 0.943 | ||||

R^{2}_{pred} | 0.893 |

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**MDPI and ACS Style**

Leong, Y.K.; Chang, C.-K.; Arumugasamy, S.K.; Lan, J.C.-W.; Loh, H.-S.; Muhammad, D.; Show, P.L.
Statistical Design of Experimental and Bootstrap Neural Network Modelling Approach for Thermoseparating Aqueous Two-Phase Extraction of Polyhydroxyalkanoates. *Polymers* **2018**, *10*, 132.
https://doi.org/10.3390/polym10020132

**AMA Style**

Leong YK, Chang C-K, Arumugasamy SK, Lan JC-W, Loh H-S, Muhammad D, Show PL.
Statistical Design of Experimental and Bootstrap Neural Network Modelling Approach for Thermoseparating Aqueous Two-Phase Extraction of Polyhydroxyalkanoates. *Polymers*. 2018; 10(2):132.
https://doi.org/10.3390/polym10020132

**Chicago/Turabian Style**

Leong, Yoong Kit, Chih-Kai Chang, Senthil Kumar Arumugasamy, John Chi-Wei Lan, Hwei-San Loh, Dinie Muhammad, and Pau Loke Show.
2018. "Statistical Design of Experimental and Bootstrap Neural Network Modelling Approach for Thermoseparating Aqueous Two-Phase Extraction of Polyhydroxyalkanoates" *Polymers* 10, no. 2: 132.
https://doi.org/10.3390/polym10020132