Analysis of experiments (Box Behnken and regression models)
Based on the data obtained in the Box Behnken design (Tables 1 and 2) and through multiple regression analysis, predictive models have been developed for BT, TPC and AC (Table 3). The models obtained for BT, TPC and AC were significant (p < 0.05) (Tables 4 and 5). To evaluate the quality of the models, the coefficient of determination (R2) was used, which indicates the percentage of the variability of the data that the model can explain. A good model is considered strong when the value of R2 exceeds 70% (Gutiérrez-Pulido & de la Vara Salazar, 2012). In this study, it is relevant to highlight that all models achieved an R2 greater than 87%, which indicates a significant capacity to explain the variability of the data.
Table 2
Box-Behnken experimental design for the extraction of TPC and AC.
| Controllable Factors | | Response Variables |
Run | W | X | Y | | TPC (mg of gallic acid EQ per g) | AC (µmol Trolox EQ per g) |
1 | 4 | 20 | 20 | | 1.62 | 17.52 |
2 | 6 | 20 | 20 | | 1.33 | 16.89 |
3 | 4 | 60 | 20 | | 2.81 | 18.98 |
4 | 6 | 60 | 20 | | 1.53 | 16.43 |
5 | 4 | 40 | 10 | | 2.16 | 18.97 |
6 | 6 | 40 | 10 | | 1.57 | 16.94 |
7 | 4 | 40 | 30 | | 1.33 | 19.00 |
8 | 6 | 40 | 30 | | 1.53 | 15.72 |
9 | 5 | 20 | 10 | | 0.84 | 14.28 |
10 | 5 | 60 | 10 | | 1.93 | 18.12 |
11 | 5 | 20 | 30 | | 0.79 | 15.01 |
12 | 5 | 60 | 30 | | 2.10 | 18.85 |
13 | 5 | 40 | 20 | | 1.70 | 12.48 |
14 | 5 | 40 | 20 | | 1.70 | 12.07 |
15 | 5 | 40 | 20 | | 1.70 | 12.31 |
16 | 5 | 40 | 20 | | 1.68 | 12.09 |
17 | 5 | 40 | 20 | | 1.69 | 12.07 |
W = pH, X = Extraction temperature (°C), Y = Extraction time (min). |
Table 3
Regression models for betaxanthin (BX), betacyanins (BC), total betalains (BT), total phenolic compounds (TPC), and antioxidant capacity (AC).
Response Variables | Regression Model |
BX (mg per- g) | BX = 0.0279 + 0.0351W + 0.00032X + 0.00210Y + 0.00418Z − 0.00474W2 − 0.000080X2 − 0.000013Y2 − 0.000046Z2 + 0.000796W*X + 0.000011W*Y − 0.000065W*Z − 0.000073X*Y + 0.000036X*Z + 0.000009Y*Z |
BC (mg per- g) | BC = -0.0826 + 0.0485W + 0.00178X + 0.00368Y + 0.004605Z − 0.00556W2 − 0.000089X2 − 0.000026Y2 − 0.000043Z2 + 0.000855W*X − 0.000048W*Y − 0.000128W*Z − 0.000110X*Y + 0.000025X*Z + 0.000014Y*Z |
BT (mg per- g) | BT = -0.055 + 0.0836W + 0.00210X + 0.00578Y + 0.00879Z -0.01030W2 − 0.000169X2 − 0.000039Y2 -0.000089Z2 + 0.001652W*X − 0.000037W*Y − 0.000193W*Z -0.000183X*Y + 0.000061X*Z + 0.000023Y*Z |
TPC (mg of gallic acid EQ per- g) | TPC = 5.22–1.93W + 0.0913X − 0.0282Y + 0.179W2 − 0.000132X2 − 0.00227Y2 − 0.01246W*X + 0.0198W*Y + 0.000270X*Y |
AC (µmol Trolox EQ per- g) | AC = 104.0–31.16W − 0.241X − 0.754Y + 3.168W2 + 0.00519X2 + 0.02281Y2 − 0.0241W*X − 0.0312W*Y + 0.00001X*Y |
Table 4
Analysis of Variance (ANOVA) and significance of the regression coefficients for betaxanthin (BX), betacyanins (BC) and total betalains (BT).
| | BX | | BC | | BT |
Sources | DF | ASS | F-value | p-value | | ASS | F-value | p-value | | ASS | F-value | p-value |
Model | 14 | 0.038 | 10.3 | *0.0000 | | 0.059 | 20.0 | *0.0000 | 0.188 | 15.0 | *0.0000 |
Linear | 4 | 0.013 | 12.9 | *0.0000 | | 0.029 | 34.6 | *0.0000 | 0.082 | 22.9 | *0.0000 |
W | 1 | 0.005 | 19.1 | *0.0010 | | 0.007 | 35.3 | *0.0000 | | 0.025 | 27.6 | *0.0000 |
X | 1 | 0.004 | 16.3 | *0.0010 | | 0.010 | 46.5 | *0.0000 | | 0.027 | 30.2 | *0.0000 |
Y | 1 | 0.001 | 3.2 | 0.0940 | | 0.004 | 17.1 | *0.0010 | | 0.008 | 8.9 | *0.0100 |
Z | 1 | 0.003 | 12.8 | *0.0030 | | 0.008 | 39.5 | *0.0000 | | 0.022 | 24.9 | *0.0000 |
Square | 4 | 0.014 | 13.8 | *0.0000 | | 0.015 | 17.3 | *0.0000 | | 0.058 | 16.1 | *0.0000 |
W2 | 1 | 0.004 | 14.3 | *0.0020 | | 0.005 | 24.3 | *0.0000 | | 0.018 | 19.7 | *0.0010 |
X2 | 1 | 0.004 | 15.0 | *0.0020 | | 0.005 | 22.7 | *0.0000 | | 0.017 | 19.4 | *0.0010 |
Y2 | 1 | 0.000 | 1.7 | 0.2120 | | 0.002 | 8.1 | *0.0130 | | 0.004 | 4.4 | 0.0560 |
Z2 | 1 | 0.011 | 42.9 | *0.0000 | | 0.010 | 46.0 | *0.0000 | | 0.042 | 46.7 | *0.0000 |
Interaction of 2 factors | 6 | 0.010 | 6.2 | *0.0020 | | 0.015 | 12.1 | *0.0000 | | 0.049 | 9.0 | *0.0000 |
W*X | 1 | 0.004 | 15.0 | *0.0020 | | 0.005 | 21.4 | *0.0000 | | 0.017 | 18.9 | *0.0010 |
W*Y | 1 | 0.000 | 0.0 | 0.9420 | | 0.000 | 0.1 | 0.7170 | | 0.000 | 0.0 | 0.8910 |
W*Z | 1 | 0.000 | 0.3 | 0.5940 | | 0.000 | 1.4 | 0.2560 | | 0.001 | 0.8 | 0.3990 |
X*Y | 1 | 0.004 | 15.6 | *0.0010 | | 0.009 | 43.9 | *0.0000 | | 0.026 | 28.7 | *0.0000 |
X*Z | 1 | 0.001 | 5.4 | *0.0350 | | 0.001 | 3.3 | 0.0900 | | 0.004 | 4.6 | 0.0500 |
Y*Z | 1 | 0.000 | 0.7 | 0.4150 | | 0.000 | 2.1 | 0.1680 | | 0.001 | 1.4 | 0.2650 |
Error | 14 | 0.004 | | | | 0.003 | | | | 0.013 | | |
Lack of fit | 10 | 0.003 | 3.2 | 0.1350 | | 0.003 | 4.5 | 0.0800 | | 0.011 | 3.7 | 0.1090 |
Pure error | 4 | 0.000 | | | | 0.000 | | | | 0.001 | | |
Total | 28 | 0.041 | | | 0.062 | | | 0.201 | | |
W = pH, X = Extraction temperature (°C), Y = Extraction time (min), Z = solvent ratio water: ethanol (%). ASS = Adjusted Sum of Squares. * Significant coefficient p < 0.05. |
Table 5
Analysis of Variance (ANOVA) and significance of the regression coefficients for total phenolic compounds (TPC) and antioxidant capacity (AC).
| | TPC | | AC |
Source | DF | ASS | F-value | p-value | | ASS | F-value | p-value | |
Model | 9 | 3.132 | 5.8 | *0.0150 | | 111.269 | 12.1 | *0.0020 | |
Linear | 3 | 2.367 | 13.1 | *0.0030 | | 18.393 | 6.0 | *0.0240 | |
W | 1 | 0.484 | 8.0 | *0.0250 | | 8.985 | 8.8 | *0.0210 | |
X | 1 | 1.815 | 30.0 | *0.0010 | | 9.398 | 9.2 | *0.0190 | |
Y | 1 | 0.069 | 1.1 | 0.3220 | | 0.010 | 0.0 | 0.9240 | |
Square | 3 | 0.348 | 1.9 | 0.2150 | | 91.560 | 29.9 | *0.0000 | |
W2 | 1 | 0.135 | 2.2 | 0.1790 | | 42.264 | 41.4 | *0.0000 | |
X2 | 1 | 0.012 | 0.2 | 0.6720 | | 18.169 | 17.8 | *0.0040 | |
Y2 | 1 | 0.217 | 3.6 | 0.1000 | | 21.913 | 21.5 | *0.0020 | |
Interaction of 2 factors | 3 | 0.417 | 2.3 | 0.1640 | | 1.317 | 0.4 | 0.7380 | |
W*X | 1 | 0.248 | 4.1 | 0.0820 | | 0.928 | 0.9 | 0.3720 | |
W*Y | 1 | 0.157 | 2.6 | 0.1510 | | 0.389 | 0.4 | 0.5570 | |
X*Y | 1 | 0.012 | 0.2 | 0.6740 | | 0.000 | 0.0 | 0.9960 | |
Error | 7 | 0.423 | | | | 7.146 | | | |
LAck of fit | 3 | 0.423 | 1360.7 | 0.0000 | | 7.010 | 69.0 | 0.0010 | |
Pure error | 4 | 0.000 | | | | 0.136 | | | |
Total | 16 | 3.555 | | | | 118.415 | | | |
W = pH, X = Extraction temperature (°C), Y = Extraction time (min). ASS = Adjusted Sum of Squares. * Significant coefficient p < 0.05. |
Analysis of the effect of factors on betalain extraction
Tables 4 and 5 show the results from the analysis of variance, where it is evident that the factors analyzed (pH, extraction temperature, extraction time, and water: ethanol solvent ratio exert a significant effect on the concentration of BT, TPC, and AC.
Figure 1 shows the behavior of BX and BC in relation to the change in the combinations from factors analyzed (pH, extraction temperature, extraction time, and water: ethanol solvent ratio). All factors were shown to have a significant effect on the concentration of total betalains. The effect of the factors on BC and BX was very similar, which is why both are referred to simply as “betalains” henceforth.
When evaluating the relationship between pH and temperature (Fig. 1a), it was observed that the concentration of betalains remains at a maximum when it moves from a pH of 4.0 to 5.5 and at the same time that the temperature varies from 10 to 45°C. This behavior coincides with what was reported by Havlíková et al., (1983) who studied betalains from the species Beta vulgaris subjected to high temperatures (50–95°C). Although it is reported that temperature can degrade betalains (Herbach et al., 2004; Tsai et al., 2010), a possible explanation for the stability observed in our conditions is that, within the pH range of 3–7, the dehydrogenation of betacyanins is promoted, transforming them into betaxanthins, as reported by Mikolajczyk-Bator and Czapski, (2017). On the other hand, in the interaction’s pH – time (Fig. 1b) and pH – solvent ratio (Fig. 1c), no significant effect was observed (p < 0.05) in the concentration of betalains.
The interaction temperature – time (Fig. 1d) proved to be significant (p < 0.05). It was observed that the concentration of betalains reaches its maximum value at temperature ranges between 10 and 45°C, especially with extraction times greater than 30 min. It is important to highlight that temperature plays an important role in altering the cellular structure, making it more permeable. Because betalains are stored in cellular vacuoles, mainly in the epidermal tissue (Jackman and Smith 1996), their extraction is facilitated by modifying the cellular structure.
Betalains are reported to be sensitive to temperature (Herbach et al., 2004, 2005, 2006, Tsai et al., 2010; Havlíková et al., 1983). However, in this research an increase in its concentration was observed as the temperature increased, which could indicate that, at 45°C and 30 min of exposure, the extraction of these bioactive compounds is favored, without significantly affecting the degradation of these pigments.
When evaluating the relationship temperature – solvent ratio (Fig. 1e), no significant effect was observed. This behavior is similar to what was previously reported by Sanchez-Gonzalez et al., (2013) in their study of optimization of betalain extraction from the species Opuntia joconostle (the prickly pear known as “xoconostle” in Mexico). Until now, the information available on how different solvents can affect the extraction and stability of betalains is limited. However, in the work of García-Barrera et al. (1998), when investigating betalains from garambullo (Myrtillocactus geometrizans), a better extraction with ethanol compared to water as extraction solvents was reported. This is due to the dehydrating effect of ethanol, which will improve the extraction. It is important to mention that ethanol affects the color of the betalain solution, due to its high electron density and greater nucleophilic character compared to water. During the nucleophilic attack, a very unstable intermediate compound is formed that breaks the system of conjugated double bonds and, as a result, the release of the proton that causes the hydrolysis of betalains, affecting their color properties (García-Barrera et al., 1998).
In relation to time – solvent ratio (Fig. 1f), since no interaction effect was found, it is assumed that no relationship affects the concentration of betalains, at least not at the levels evaluated. The region of maximum concentration is in water: ethanol solvent between 40% and 60%, regardless of the extraction time. It is important to note that, although this interaction was not statistically significant (p < 0.05) in betalain concentration, its individual effect if it had a significant.
Optimization of betalain extraction conditions
The optimal conditions for the extraction of betalains were established at a pH of 4.2, water: ethanol solvent ratio of 55%, temperature and extraction time of 10°C and 60 min, respectively (Table 6). According to the model projections, values of 0.28, 0.27, and 0.55 mg per g were expected for BX, BC, and BT, respectively. Experimental values obtained under these conditions were slightly lower, recording 0.26, 0.25, and 0.51 mg per g respectively. This suggests that the model is capable of predicting the experimental values with remarkable precision.
Table 6
Betalain concentration under optimal extraction conditions.
Conditions | W (4.2) | X (10°C) | Y (60 min) | Z (55%) |
| Predicted value | Experimental value |
BX (mg per g) | 0.28 | 0.26 |
BC (mg per g) | 0.27 | 0.25 |
BT (mg per g) | 0.55 | 0.51 |
Some research has focused on optimizing betalain extraction process, analyzing factors such as solvent, mass-solvent ratio, pH, temperature- and extraction time. For example, Sanchez-Gonzalez et al. (2013), in their study on prickly pear (known as xoconostle in Mexico) Opuntia joconostle, reported that the maximum extraction of betacyanins is achieved, using ethanol: water ratio of 20% with a temperature and extraction time of 17.5°C and 25 min, respectively. Besides, Maran and Priya. (2015) reported temperatures and extraction times of 53°C and 35 min for beets (Beta vulgaris). Kushwaha et al. (2018), whose extraction source was also beets, indicated similar conditions of temperatures (50.04°C), extraction times (10 minutes), and pH (2.5).
These studies reveal that extraction conditions vary between different matrices, with extraction temperature being the most significant factor. As observed for the extraction of betalains from beets, higher temperatures are needed compared to cactus fruits.
Analysis of the effect of pH, temperature, and extraction time on TPC and AC
When evaluating the factors of pH, temperature- and extraction time on the TPC concentration, it was found that only pH and temperature exerted a significant effect on the TPCs. Regarding the relationship between temperature and pH (Fig. 2a), it was observed that the highest concentrations of TPC are obtained under conditions of high extraction temperatures (60°C) and pH values close to 4. In addition, it was done it is evident that the concentration of TPC is not conditioned by the specific levels from factors evaluated, since no significant interaction between them was observed. This same behavior was observed for AC, where the maximum values were obtained under the same conditions that maximized TPC concentrations.
Surface plots (Fig. 3a) show that the AC concentration increased as the extraction process was carried out at temperatures close to 60°C and pH of 4. As previously mentioned, temperature plays an important role in diffusion of compounds due to cell rupture. At 60°C, the highest concentration of TPC was observed, suggesting a notable stability of these compounds against heating processes. This finding agrees with what was described in the research of Palma et al. (2001), where the grape pomace was subjected to various extraction temperatures. In this context, it has been shown that TPCs are closely related to AC since, both components reach their maximum value under the same extraction conditions (Cervantes-Arista et al., 2020; Rojas-Ocampo et al., 2021).
The pH is another factor that influences extraction process. In line with this study, Tabart et al. (2007) obtained the highest concentrations of TPC and AC at acidic pH (pH = 3) by optimizing the extraction of TPC from leaves and buds of black currant (Ribes nigrum). Mai et al. (2020) reports a better extraction of flavonoids from Euonymus alatus under acidic conditions (2.5–3.5), observing a decrease in yield when increasing the pH above 3.5. This has been associated with the fact that pH modifies the ionic strength, which affects the solubility of the compounds and their interactions with the sample matrix (Chaves et al., 2020). Furthermore, it could be explained by the fact that in acidic media the separation of phenolic compounds bound to proteins or carbohydrates is favored (İlbay et al., 2014).
Optimization of TPC and AC extraction conditions
It is relevant to highlight the correlation between TPC and AC, since the optimal conditions for both turned out to be the same. A pH of 4, an extraction temperature of 60°C, and a time of 10.6 min maximized both the TPC and AC concentrations. Predicted values for TPC and AC were 2.81 mg of gallic acid equivalents per g and 21.76 µmol Trolox equivalents per g respectively, while the experimental values were 2.34 mg of gallic acid equivalents per g and 18.60 µmol Trollox equivalents per g for TPC and AC, respectively (Table 7). It is important to mention that the experimental values presented slight differences with respect to the predicted values, which could be due to the presence of other factors that were not considered but are important in the extraction process, such as the mass ratio or the solvent ratio (Tabart et al., 2007). Similar conditions were reported by Kushwaha et al. (2018) who identified optimal extraction conditions of 50°C, 10 minutes, and pH of 2.5 to maximize TPC and AC in beets. This suggests that for efficient TPC extraction, high temperatures and short extraction times are required to prevent degradation, as well as a slightly acidic pH.
Table 7
Concentration of phenolic compounds (TPC) and antioxidant capacity (AC) under optimal extraction conditions.
Conditions | W (4) | X(60°C) | Y (10.6 min) |
| Predicted value | Experimental value |
TPC (mg of gallic acid EQ per- g) | 2.8148 | 2.34 |
AC (µmol Trolox EQ per- g) | 21.7624 | 18.60 |