Optimization of a New Antioxidant Formulation Using a Simplex Lattice Mixture Design of Apium graveolens L., Coriandrum sativum L., and Petroselinum crispum M. Grown in Northern Morocco

A statistical Simplex Lattice Mixture design was applied to develop a new formulation based on a combination of three plants grown in northern Morocco: Apium graveolens L., Coriandrum sativum L., and Petroselinum crispum M. We examined the extraction yield, total polyphenol content (TPC), 2′2-diphenyl-l-picrylhydrazyl (DPPH) radical scavenging activity, and total antioxidant capacity (TAC). The results of this screening study showed that C. sativum L. had the highest content of DPPH (53.22%) and TAC (37.46 ± 0.29 mg Eq AA/g DW) compared to the other two plants, while P. crispum M. showed the highest TPC (18.52 ± 0.32 mg Eq GA/g DW). Furthermore, the ANOVA analysis of the mixture design showed that all three responses (DPPH, TAC, and TPC) were statistically significant, with determination coefficients of 97%, 93%, and 91%, respectively, and fit the cubic model. Moreover, the diagnostic plots showed good correlation between the experimental and predicted values. Therefore, the best combination obtained under optimal conditions (P1 = 0.611, P2 = 0.289, P3 = 0.100) was characterized by DPPH, TAC, and TPC of 56.21%, 72.74 mg Eq AA/g DW, and 21.98 mg Eq GA/g DW, respectively. The results of this study reinforce the view of stimulating the effect of plant combinations to achieve better antioxidant activities, thus providing a better formulation using designs of mixtures for the food industry and in cosmetic and pharmaceutical applications. Moreover, our findings support the traditional use of the Apiaceae plant species in managing many disorders cited in the Moroccan pharmacopeia.


Introduction
In recent decades, natural antioxidants have drawn increased interest [1]. Indeed, polyphenols are secondary metabolite compounds of plants and contain many combinations, including flavonoids, phenolic acids, and other compounds [2,3]. Moreover, a number of recent studies have focused on the biological properties of polyphenols and have revealed that these compounds protect human health against many diseases, especially health problems. The therapeutic efficacy of the combination of medicinal species can be increased with multiple compounds [32]. These suppositions can promote synergy or potentiate a therapeutic effect in the human body, aiming to treat a broader set of conditions or symptoms.
In effect, they are essential for developing new drugs, and their study is of paramount importance today [33,34].
The statistical approach of using designs of experiments (DoEs) is a powerful tool in optimizing mixtures when dealing with multiple components [35]. Designing mixtures based on DoE is a multifactorial approach that relies on well-structured logic and provides faster and more reliable results regarding response optimization [36].
To the best of our knowledge, the use of DoE to study the effect of combinations of the three plants investigated herein has not been previously reported. Our work aims to provide a practical way to design and study an efficient, reproducible, and optimal model with the selected properties to predict an ideal combination characterized by its ability to produce extracts with the highest antioxidant activity and the most significant amounts of TPC from the three plants studied.

Screening Study
The primary plant-derived antioxidants are polyphenols, which have greater antioxidant potency than ascorbic acid on a molar basis [37]. Moreover, according to the literature, polyphenols possess many biological activities in vitro [38]. Parsley, coriander, and celery are rich in polyphenols [39]. The results of the total phenolic contents and the antioxidant activity of the three plant extracts are presented in Figure 1. The values of the total phenolic content in different plant extracts harvested in the Sefrou region in northeastern Morocco using ethanol solvents vary from 10.49 ± 0.30 to 18.52 ± 0.32 mg GAE/g DW; parsley showed the highest amount of polyphenols, followed by celery and then coriander. Further work by Derouich et al. corroborating our results reported TPC results for C. sativum L. as 1.372 ± 0.096, for P. crispum M. as 2.163 ± 0.104, and for A. graveolens L. as 1.739 ± 0.089 g GAE/100 g DW [40]. Additionally, Tang et al. reported high amounts of phenolic compounds in parsley (4.231 g GAE 100 g −1 ) and celery (4.640 g GAE 100 g −1 ) [41]. Different polyphenol contents in coriander seeds were measured (1.555 g GAE 100 g −1 ), and the three plants were also screened using two antioxidant methods [42]. As shown in Figure 1, coriander demonstrated the best total antioxidant activity (37.46 mg AscE/g DW), followed by parsley (33.47 ± 0.29 mg AscE/g DW) and celery (30.32 ± 0.34 mg AscE/g DW). Regarding the DPPH free radical scavenging activity (Figure 1), the hydroethanolic extract of coriander (P2) had the highest DPPH value (53.22%), followed by celery with a value equal to 34.96%, and parsley recorded the lowest trapping potential.
For this screen, the tested samples' DPPH and TAC radical scavenging activities increased in the order of coriander > celery > parsley.
The results of the recent investigation indicate that the extraction yield and total polyphenol content range from 11% to 23% and from 5.65 to 21.98 mg GAE/g of dried plant, respectively, and DPPH% and TAC activity range from 13.16% to 56.21% and from 12.25 to 75.82 (mg AscE/g), respectively. This result confirms the influence of mixing plants on all the responses studied. In this study, the Simplex Lattice Mixture scheme was designed to improve the extraction conditions allowing the best recovery of antioxidant compounds, to describe the relationship of the responses of interest (TAC, DPPH, and TPC) as a function of fluctuations in the proportion of the mixture, and to select the optimal ratios of the mixture according to the criteria in Table 1. This approach gathers the maximum information with the fewest analyses. There are significant differences between the mean values (SD, n = 3) that are followed by various letters in the same row (one-way ANOVA; Tukey's test, p < 0.05).
The evaluation of the quality of the models was tested using the analysis of variance (ANOVA) by Fisher's test (F-value), the probability value (p-value), and the significance of the lack of fit in determining whether the model correctly summarizes the results of the DoE. First, however, the predictive quality of the models was checked using the coefficients of the multilinear regression (R 2 ), the predicted coefficient (R 2 predicted ), and the adjusted coefficient (R 2 adjusted ). In addition, the plot of average and expected residuals against typical values was used to assess the distribution and normality of the residuals, while the significance of the model was checked using the F-test. After this step, we found that all responses fit better with the cubic model.

Statistical Modeling of the TPC, DPPH, TAC Model
The analysis of variance (ANOVA) results, including regression model terms, R 2 , F-value, and probability values, are illustrated in Table 2. The coefficient of determination (R 2 ) value was 0.91. The predicted R 2 of 0.79 is in reasonable agreement with the adjusted R 2 of 0.85 for TAC assays, and the R 2 value is equal to 0.93. The predicted R 2 of 0.82 follows the adjusted R 2 of 0.88 for DPPH. In the case of the TPC assay, R 2 , R 2 adjusted , and R 2 Predicted were equal to 0.97, 0.95, and 0.93, respectively, and the difference between R 2 adjusted and R 2 predicted is less than 0.2, which indicates that the model adequately represents the actual relationship between the components. Furthermore, the F-values of 54.21, 14.93, and 20.33 (Table 2) for the three activities in the cubic model (TPC, TAC, and DPPH, respectively) imply that the model is significant. There is only a 0.01% probability that an F-value this large could occur due to noise. This coupled with the presentation of small p-values (p-value < 0.0001) indicates that this model was accurate in predicting the behavior of the mixtures. Level of statistical significance: * Significant, ** not significant; A-P. crispum M.; B-C. sativum L.; C-A. graveolens L.
The performance of the extract effect is correlated to the coefficient sign [43]. Generally, a negative indication of a coefficient in the fitted model indicates the ability of a variable to decrease the response. In contrast, a positive sign for the coefficient in the model suggests the power of the variable to increase the response [44]. The equation models showed that phenol content and antioxidant activities (TAC and DPPH) were positively and linearly influenced by the mixture AB(A-B); in linear tests, the mixture BC(B-C) gave the lowest coefficient, minor amounts of TPC, and the most insufficient antioxidant activity (DPPH).
The p-values and F-values are utilized as evaluation tools, where the smaller the pvalue and the higher the F-value for each significant coefficient of the cubic model (Table 2) In addition, ternary mixtures with a high proportion ratio of a plant (A) positively influenced the extraction of TPC and antioxidant compounds. The equations obtained from the three models, TPC, TAC, and DPPH, in terms of the natural components, are shown in Table 3. These results indicate that the coefficients determined in the interaction between the three plant extracts revealed the highest synergistic impact. Table 3. The equation of the three models TPC, TAC, and DPPH in terms of the real components.

Response
The Plant phenolic compounds include phenolics acids, flavonoids, and tannins, which are the most important for dietary applications and the most widely studied [45] due to their ability to eliminate the deleterious effects of oxidation in several ways, including preventing ROS buildup, chelating metal ions [46], inhibiting lipid peroxidation, and enhancing antioxidant enzymes [47]. However, the recovery of phenols is a tedious task [15] which depends on many factors, essentially the nature of the plant [48] and the polarity of the solvent used [26].
Currently, no universal extraction procedure is suitable for extracting all plant phenolic compounds [28]. Thus, it is necessary to establish an optimized process for recovering phenolic compounds from formulations using a combination of three plants.
Regarding the validity and accuracy of the model, both plots can confirm the fit of the model, including the standard probability plot (Figure 2a The interpretation of the contour lines in Figure 2c,d demonstrates that the extraction of total polyphenols using the herbal mixture with the ratio of 56.67% P1, 33.33% P2, and 10% P3 gave the highest antioxidant activities, which can confirm a synergistic effect between these three herbs, in which the interaction between them demonstrates a better result than their isolated actions. Moreover, the optimum plant mixture given by the desirability analysis (Table 4) was a ternary mixture that consisted of 61.1% P1, 28.9% P2, and 10% P3.

TAC Model
Total antioxidant activity (TAC) represents the ability of a compound to inhibit the oxidative degradation of lipids [49]. Lipid peroxidation involves the oxidative deterioration of lipids with unsaturation used to measure the peroxide level during the initial stage of lipid oxidation. Peroxides are formed during linoleic acid oxidation, which react with Fe 2+ to form Fe 3+ . These ions form a complex with thiocyanate [50]. The response of the surface plots of the TAC antioxidant assay is shown in Figure 3a,b, illustrating the impact of combining and mixing the three plants. It is seen in Figure 3c,d that when the ratio of plant A (parsley) increased in the mixtures of the three plants, the TAC values increased significantly. On the contrary, when the plant C (celery) ratio increased in the mix, the values of the total antioxidant activity decreased significantly. The simultaneous optimization of the ternary mixture of the three plants led to the optimal formulation based on the functions of desirability, which has the ratios of 0.611, 0.289, and 0.100 (Table 4) for parsley, coriander, and celery, respectively. The current findings suggest that the formulations have different effects on different antioxidant assays.

DPPH Model
The DPPH assay is used to test the ability of compounds to act as radical scavengers and is frequently used to assess the antioxidant capacity of foods [42,51]. A previous study by Ranneh et al. showed that the herbal mixture significantly affected DPPH scavenging capacity synergistically [52].
The current findings suggest that the formulations have different effects on different antioxidant assays.
The effect of the herbal mixture on the antioxidant activities is illustrated in the threedimensional (3D) surface plot generated from the models (Figure 4). Each point on the graph represents different proportions of components in the mixture. Three components, P. crispum M., C. sativum L., and A. graveolens L., are included in the 3D surface plots; experimental data for the DPPH test, shown in  The lowest DPPH (13.65%) was obtained in test 6 under conditions of 56.67% P1, 10% P2, and 33.33% P3. Moreover, the optimal mixture of solvents given by the desirability analysis (Table 4) confirms the same ternary mixture, which consists of 61.1% P1, 28.9% P2, and 10% P3.
The simultaneous optimization of the ternary mixture of the three plants led to the optimal formulation based on the functions of desirability, which has the ratios of 0.611, 0.289, and 0.100 (Table 4) for P1, P2, and P3, respectively.

Numerical Optimization Using Desirability Function
This study aimed to develop a mixture of three plants (parsley, coriander, and celery) according to the criteria described in the material and methods section. Of the two solutions calculated by the software, the value of the function with the highest D was chosen as the optimal solution, which corresponds to the proportions given in Table 1.
The desirability function was optimized to maximize the mixtures' total phenolics and antioxidant capacity (DPPH and TAC). The results are presented in Table 4. The simultaneous optimization, including all responses, suggested that the ternary mixture, which consists of 61.1% P1, 28.9% P2, and 10% P3, was the most appropriate to obtain the best combination of variables.

Samples
The three plants chosen for this study belong to the Apiaceae family:

Extraction Procedure
The aerial part of the three plants was used in this study. After drying under shade, plants were powdered and mixed in different proportions. The mixture was then extracted according to the following procedure: a ratio of 1:10 was used to prepare a mixture of the three plants in different proportions. To prepare these mixtures, we added 10 mL of 70% hydroethanolic solution (V/V) to 1 g of each mixture of three plants, and with mechanical agitation, they were macerated for one week in the dark at room temperature. The final extracts obtained were filtered (Whatman, No. 1, Merck KGaA, Darmstadt, Allemagne), and the obtained solutions were concentrated using a rotary evaporator. The extracts were stored at 4 • C until use for the in vitro tests.

Total Phenolic Content (TPC)
A modification of the Folin-Ciocalteu method [31] determined the total phenolic content as follows: 50 µL extract was mixed with 450 µL Folin-Ciocalteu reagent (0.2 N) for 5 min, and then 450 µL sodium carbonate (Na 2 CO 3 ) solution (75 g L −1 ) was added. This mixture was incubated at room temperature in dark conditions for 2 h, and the absorbance was read at 760 nm by a UV/visible Jenway 6505 scanning spectrophotometer. The gallic acid solutions underwent the same procedure and were used to plot a calibration curve (standard curve equation, y = 1.0778x + 0.1057, R 2 = 0.9994) of absorbance against log concentration (mg/mL). The results were calculated as gallic acid equivalent (GAE) per mg of extract. Tests were carried out in triplicate.

DPPH Free Radical Scavenging Test
The optimized extracts were tested for the scavenging effect on DPPH (2,2-diphenyl1picrylhydrazyl) radicals according to the method described by Menezes et al. [53]. A total of 50 µL of the ethanolic extract of the plant mixture was added to 825 µL of ethanolic solution of DPPH (60 µM). After 60 min of incubation, the absorbance was measured at 517 nm using a spectrophotometer. Tests were carried out in triplicate, and the results are given as mean ± SD.
The percentage of inhibition was calculated using the following equation: where A 0 is the absorbance of the control (without sample). A 1 is the absorbance in the presence of the sample.

Total Antioxidant Capacity (TAC) Test
The total antioxidant capacity assay was performed according to El Ghouizi et al. [54] using 1 mL of reagent solution containing 0.6 M of sulfuric acid, 28 mM sodium phosphate, and 4 mM ammonium molybdate with 100 µL of each extract. The solution was then incubated in a water bath at 95 • C for 90 min. The absorbance was then registered at 695 nm against the blank with ethanol in a spectrophotometer (Jasco V-530). TAC determination was carried out in triplicate, and a standard curve (y = 4.2744x + 0.065, R 2 = 0.9996) of ascorbic acid (Acs. E g −1 dry weight) was established.

Experimental Methodology (Mixture Design of Experiment)
The design of the experiment's approach is a robust tool to understand and optimize the components of a mixture, with a considerable decrease in the number of experiments and a better understanding of the mechanism of the process studied [55]. Herein, the effect of the interaction of P. crispum M. (P1), C. sativum L. (P2), and A. graveolens L. (P3) was studied on three responses: (i) DPPH free radical scavenging activity, (ii) the total antioxidant capacity (TAC), and (iii) the total phenolic content (TPC) was described by the second-order Scheffé model (Equation (2)) [56], so that the predictions of the mixture of plants could be made empirically for each answer and the sum of the proportions of the plants is equal to 1 (Equation (3)), taking into consideration that there is no secondary constraint on the proportion of the components [57].
In addition, 23 formulations were suggested and conducted in random order using Design-Expert software to account for any randomized hidden effects (Table 5). Table 5 shows the boundaries of the mixture components, and the geometric location of the experimental plan points is illustrated in Figure 5. Once the modeling is complete, the last stage of the study is optimization, which consists of finding the optimal proportions of each plant according to the established constraints. In this study, the numerical optimization method was applied using the desirability function (D) [58], because it allows us to modify the weight and importance of both the components of the mixture and the responses. The limits and constraints selected for optimization using the D function are given in Table 5.

Statistical Analysis
Graph Pad Prism 8.0 was used for the statistical analysis, and comparisons between different samples were performed by ANOVA followed by Tukey's test.

Conclusions
The response surface methodology was successfully utilized to optimize the extraction of phenolic antioxidants from three plants of the Apiaceae family. Coriander had the highest phenolic content and thus showed strong antioxidant activities, followed by celery and parsley. The current work is the first report regarding the optimization of phenolic antioxidants in the Apiaceae family and showed that the ternary combination of the three plants was effective, and the best combination was fixed according to the analysis of the software. Our findings enhance the idea of the stimulating effect of the plant towards better antioxidant activities. Our results also prove the possible beneficial use of the optimized formula in the food and pharmaceutical industries. Future study is needed to identify the phytochemical composition to further understand the effects of these extracts.