Combination of Chemically-Characterized Essential Oils from Eucalyptus polybractea, Ormenis mixta, and Lavandula burnatii: Optimization of a New Complete Antibacterial Formulation Using Simplex-Centroid Mixture Design

This study aims to identify the volatile profile of three essential oils obtained from Eucalyptus polybractea cryptonifera (EPEO), Ormenis mixta (OMEO), and Lavandula burnatii briquet (LBEO) and to examine their combined antibacterial activity that affords the optimal inhibitory ability against S. aureus and E. coli using simplex-centroid mixture design and checkerboard assay. Essential oils (EOs) were isolated by hydrodistillation and characterized using gas chromatography-mass spectrometry (GC-MS) and gas chromatography coupled with flame-ionization detector (GC-FID). The antibacterial activity was performed using disc diffusion and microdilution assays. The chemical analysis revealed that 1,8-cineole (23.75%), p-cymene (22.47%), and α-pinene (11.20%) and p-menthane-1,8-diol (18.19%), α-pinene (10.81%), and D-germacrene (9.17%) were the main components detected in E. polybractea and O. mixta EOs, respectively. However, L. burnatii EO was mainly represented by linalool (24.40%) and linalyl acetate (18.68%). The EPEO, LBEO, and OMEO had a strong antibacterial effect on S. aureus with minimal inhibitory concentrations (MICs) values ranging from 0.25 to 0.5% (v/v). Furthermore, the combination of 1/2048 MICEPEO + 1/4 MICLBEO showed a synergistic antibacterial effect on S. aureus with a FIC index of 0.25, while the formulation of 1/4 MICEPEO + 1/4 MICOMEO demonstrated an antibacterial synergistic activity on E. coli with a FIC index of 0.5. Moreover, the simplex-centroid mixture design reported that the most effective combinations on E. coli and S. aureus correspond to 32%/28%/40% and 35%/30%/35% of E. polybractea, O. mixta, and L. burnatii, respectively. Presented information highlights the action of antibacterial formulations of these EOs and suggests their potential applications as alternatives to commercialized drugs to contract the development of bacteria causing serious infections and food deterioration.


Introduction
Infectious diseases triggered by antimicrobial resistance (AMR) are among the key issues impacting morbidity and fatality in patients sufering from such problems.Te AMR has become a main public health concern that threatens the efective treatment of a broad range of infections caused by bacteria, fungi, viruses, and parasites no longer vulnerable to the common antibiotics used to prevent them.For multiple decades, bacteria causing common or severe infections have developed resistance to each novel antibiotic coming to market.Te impact of antimicrobial resistance concerning the public health charge is quite difcult to predict.Te Center for Disease Control and Prevention (CDC) estimated that more than two million people per year are afected with antibiotic-resistant infections, with at least 23,000 deaths as a consequence of infectious diseases.In light of this fact, it is crucial to take action to prevent a developing healthcare crisis [1].In fact, natural products represent a source of safe and efective agents which can be used as alternative to antimicrobial medications since their continuous use can increase the resistance of microorganisms, thus decreasing the efciency of these drugs [2].Essential oils (EOs) have been broadly employed for treating various ailments due to their famous antimicrobial activities [3].Nowadays, EOs have been suggested and proved as antimicrobial products in complementary medicine.Tese properties are associated with the complex bioactive compounds of EOs, especially terpenes, aldehydes, phenylpropanoids, alcohols, esters, and ketones, which possess varied antimicrobial actions [4].Tese bioactive molecules may act through diferent modes of action to apply their antimicrobial efect.Generally, EOs can induce membrane disruption and metabolic damages leading to cell death [5].Te application of EOs has been restricted due to their efects on sensory characteristics, specifcally at elevated doses.Terefore, it is imperative to detect minimum inhibitory concentration for EOs and to evolve EO formulations in order to obtain synergistic efects, thus diminishing the amounts of EOs impacting the organoleptic properties without altering their antimicrobial efects [6].Numerous works have established synergism between EOs using the checkerboard method without highlighting optimal EO formulations.However, only a few studies have recently used mixture design [7][8][9][10].Te mixture design approach can diminish the number of tests and predicted results can be modeled graphically and statistically aiming to minimize the total error.Trough this approach, the accurate amounts of diferent EOs can be optimally associated to attain better mixtures [7].In this context, we selected three medicinal plants to test the single and combined antibacterial efect of their EOs on pathogenic strains.Tese plants were chosen based on our previous ethnobotanical surveys which have demonstrated their therapeutic and culinary virtues [11][12][13][14].In addition, some in vitro studies have revealed their signifcant antimicrobial abilities [8,15,16].
Eucalyptus polybractea, also named blue-leaved or blue mallee, is a multistemmed mallee eucalypt.Tis species belongs to the Myrtaceae family [17].Eucalyptus has been used in traditional medicine to heal a variety of disorders including fu, fever, colds, sores, muscular pains, internal aches, and infammation [18].Tis plant oil is chiefy characterized by 1,8-cineole.Te volatile oils derived from this genus are widely applied for pharmaceuticals, cosmetics, and food crops.Indeed, Eucalyptus oils have been reported to exhibit signifcant antibacterial, antifungal, antiinfammatory, and antioxidant properties [15,19].
Ormenis mixta, known as wild chamomile, is an endemic species of western and central Morocco.Tis plant belongs to the Asteraceae family and is usually used as general tonic, neurotonic, and aphrodisiac.It is endowed with antiinfectious, parasiticidal, antimutagenic, anticholesterol, and wound-healing properties [12].It was previously reported that the plant oil is mainly characterized by Dgermacrene and 1,8-cineole and possess promising antioxidant, anti-infammatory, antidiabetic, and antimicrobial properties [20].
Lavandula burnatii, commonly known as Burnat's lavender, is a perennial herb native to the Mediterranean region and attributed to the Lamiaceae family.It has slender, graygreen leaves and bluish-purple fowers [21].Previous phytochemical investigations showed that lavender essential oils are rich in linalool, linalyl acetate, and camphor.Prior research indicated that the antimicrobial efects of lavender oils are mainly related to their bioactive compounds [16,22].
Previous investigations have reported the antibacterial efects of the three studied EOs.Indeed, it has been reported that the OMEO and its major constituents, such as p-menthane, germacrene D, and α-pinene, exhibit powerful antibacterial properties against various strains, especially Escherichia coli and Staphylococcus aureus [20,[23][24][25].Numerous studies reported the antimicrobial properties of the species belonging to the genus Lavandula and Eucalyptus, mainly Lavandula stoechas, Lavandula intermedia, and Eucalyptus globulus against a plethora of microbial strains [26][27][28].
Te present investigation aims to analyze the phytochemistry of the EOs extracted from Eucalyptus polybractea cryptonifera (EPEO), Ormenis mixta (OMEO), and Lavandula burnatii briquette (LBEO) and evaluate their single antimicrobial activity as well as to determine the combination that afords the optimal inhibitory ability against the tested bacterial strains.Consequently, the simplex-centroid mixture design was employed to create polynomial models elucidating the relationship between the antibacterial efect and the amount of each volatile oil.Eucalyptus polybractea cryptonifera, Ormenis mixta, and Lavandula burnatii briquette were selected based on their medicinal applications.To the best of our knowledge, the essential oils derived from these plants have not been the subject of previous investigations.Hence, this is the frst research aiming to combine these plants' essential oils and elucidate their antimicrobial and phytochemical characteristics.
Te following points represent the hypothesis of this study: (i) Te phytochemical analysis of the studied EOs will reveal the presence of diverse chemical compounds that could be responsible for the antimicrobial properties of these EOs (ii) Every single EO will exhibit important antimicrobial activity against the tested bacterial strains, demonstrating their potential as natural antibacterial agents 2 Advances in Pharmacological and Pharmaceutical Sciences (iii) Te optimal mixtures of EPEO, OMEO, and LBEO resulting from the simplex-centroid mixture design will exhibit enhanced antibacterial efects compared to the single EOs (iv) Te polynomial models will elucidate the quantitative relationship between the amount of each oil in the mixture and its corresponding antibacterial efect, providing valuable insights into the synergistic interactions of the studied EOs Te samples were dried to a constant weight for 10 days at 25 °C in a dark place, crushed employing an electric blender, and sieved to attain a fne powder.Extraction of EOs from the plant aerial parts was executed by the hydrodistillation technique using Clevenger-type device.Tis technique features a recycling system and operates at atmospheric pressure.Te system enables the preservation of mass plant/water proportion at its initial level.Trough each extraction, 500 g of the dried aerial part of each plant was placed in a 1 L fask, and then 800 ml of distilled water was added.Te solution was heated to boiling temperature (100 °C) during 3 h; the released steams traversed the column and passed out of the condenser in a liquid form (extraction was performed in three separate replicates (n � 3)).At the end of the distillation process, two phases were noticed, an organic phase (EOs) and an aqueous phase (aromatic water).Te attained oils were desiccated by anhydrous sodium sulfate and kept at 4 °C pending upcoming tests.

GC-FID Analysis.
Analytical GC was performed using a Hewlett-Packard (HP/Agilent 6890) device equipped with a FID apparatus.Te separation was accomplished using an HP-5 MS no-polar capillary column (length 30 m, diameter 0.25 mm, flm thickness 0.25 μm).
Te column temperature was set from 50 °C to 200 °C at 4 °C/min.Te chromatography carrier gas (nitrogen) was fxed to 1.4 ml/min, and split injection mode was used with a 1/50 split ratio; the temperature of injector and detectors (FID) was set at 250 °C.Te volume of oils (diluted 1/20 v/v in methanol) injected was approximately 1 μl.Te device was controlled by an "HP Chem station" computer system, which managed its operation and allowed the monitoring of chromatographic analyses.

GC-MS Analysis.
Te GC-MS analysis was executed with a Hewlett-Packard gas chromatography (HP6890) equipped with a mass spectrometry system (HP 5973).Chromatographic separations were carried out using an HP-5 MS capillary column (30 m × 0.25 mm i.d., 0.25 μm flm thickness).Te carrier gas was helium whose fow rate was fxed at 1.4 ml/min.Te volatile compounds were identifed based on their retention indices (RIs) and MS, which were compared with those obtained in the literature [30,31].Moreover, the mass spectra (MS) of various compounds were verifed using standardized data from chemical libraries, including the NIST 2022 and the Wiley 275.Finally, commercialized standards (terpenes with purities ranged between 80 and 98%) were also used for external standardization.

Antibacterial Assays.
Prior to formulation, the antibacterial activities of E. polybractea, O. mixta, and L. burnatii EOs were investigated separately.In order to assess the EOs antibacterial activity, the frst step was the use of the disc difusion method which allowed identifying the concentration giving a response classifed as sensitive.Second, the minimum inhibitory concentration (MIC) and minimum bactericidal concentration (MBC) were determined for each EO.

Microorganisms.
Te EOs were examined against two reference bacterial strains: Escherichia coli ATCC 25922 and Staphylococcus aureus ATCC 29213.Both strains were obtained from the laboratory of Microbial Biotechnology and Bioactive Molecules, Science, and Technology Faculty, Fez.Before being used, the strains were reactivated by subculturing in Luria-Bertani (LB) plates at 37 °C for 18-24 h.

Disc Difusion Method.
Te antimicrobial activity of the studied EOs was determined using the agar disc difusion method with minor reforms [32].Tis method has been used as a frst step to assess the inhibition diameters generated by the EOs around the disk.
A fresh culture suspension was prepared in sterile saline solution and adjusted to 0.5 McFarland (10 8 CFU/mL), then inoculated into Mueller Hinton Agar (MHA) plates and incubated briefy for 20 min, and the culture's excess was eliminated.Te sterile paper discs (6 mm diameter) were soaked with 5 μl of pure EO from each plant before being put Advances in Pharmacological and Pharmaceutical Sciences on an inoculated agar plate.In addition, gentamicin (50 μg/ disc) and kanamycin (50 μg/disc) were employed as standards to identify the sensitivity of the tested strains, while DMSO (5 μL; 5%) was used as growth control.Tese plates were maintained at 4 °C for 3 h and then incubated at 37 °C for 24 h.After incubation, the inhibition zone diameters were measured in millimeters using a digital Vernier caliper (Mitutoyo).Te results were represented as the mean-± standard deviation for three separate tests (n = 3).

Determination of MIC and MBC.
MICs of EPEO, OMEO, and LBEO were assessed using the broth microdilution assay in 96-well microplates as previously explained [32,33] with minor adjustments.Bacteriological agar was employed as an emulsifer of EOs in a culture medium at 0.15% (v/v), and p-iodo-nitrotetrazolium chloride (INT) 95% (Sigma-Aldrich) was used as a bacterial growth indicator.First, a microtiter plate was flled from the second to the twelfth well, with 50 μl of Mueller-Hinton broth (MHB) supplemented with agar (0.15%).Ten, 100 μL of EOs dilution prepared in MHB with agar (0.15%) was added to the frst test well of each microtiter row.Next, 50 μl of scalar dilution was moved from the second to the eleventh.Te 12 th well was considered as growth control.Ten, 50 μL of the bacterial suspension prepared and adjusted to 0.5 McFarland (10 8 CFU/mL) was deposited in each well.
Te plates were incubated at 37 °C for one day (24 h).Ten, 5 μl of INT was added to each well.After 2 hours of incubation, the MIC was defned as the maximum EOs dilution where the white-to-red color shift was unnoticeable.Tests were conducted in triplicate (n � 3).MBC was evaluated by subculturing 15 μL from each negative well on LB agar plates and incubating for 18-22 h at 37 °C.MBC was the lowest concentration at which no growth was detected.Moreover, the MBC/MIC ratios were also determined to identify the possible mechanism of the studied EOs [34].

Synergism Testing.
Te checkerboard technique was performed to verify synergistic interactions between the tested EOs against bacterial strains [35].
Te tested sample concentrations were prepared in MHB containing 0.15% bacteriological agar.On the microplate xaxis, 25 μL of the weakest active EO concentration, which corresponds to the highest MIC value of EO (determined by microdilution assay) was added to the well from the 1 th to the 11 th one.Regarding the y-axis, 25 μL of each higher active EO concentration, which consists of the lowest MIC value of EO (determined by microdilution assay) was added to each well.Te 12 th well served as a negative control.Ten, 50 μL of the bacterial suspensions, at a concentration of 2 × 10 6 UFC/mL, was added to each well.
Tereafter, the microplate was incubated at 37 °C for 18 to 20 h.After that, 10 μL of resazurin was added to each well as a bacterial growth indicator.After incubation at 37 °C for 90 min, bacterial growth was detected by reduction of blue dye (resazurin) to pink (resorufn).Experiments were perfomed in triplicate (n � 3).
Te synergy was evaluated based on the instructions described by the American Society for Microbiology [36].

Experimental Design
2.5.1.Mixture Design.Te optimization and evaluation of antibacterial activity were generated using an augmented simplex-centroid design for three compounds [37].For this, ten trials were conducted, using three pure EOs at the triangle's vertices (E 1 − E 2 − E 3 ), binary mixtures at the three triangle's sides (E 4 − E 5 − E 6 ), equiproportional mixture of the EOs at the triangle's centroids (central point) (E 7 ), and control points (E 8 − E 9 − E 10 ).
Te experiment of the equal proportionate mixtures has been tripled to determine the lack of the model ft.Ultimately, 12 th experiments were used in the current exploratory design (Figure 1).
Factors (E 1 , E 2 , and E 3 ) are used to explain response variation in a mixture, and they represent a portion of each experimental component in the mixture, which has a value range between 0 and 1 without constraints [38], with E 1 : the proportion of EOEO E 2 : the proportion of OMEO E 3 : the proportion of LBEO Te responses assessed in this investigation were the antibacterial action against two bacteria, including S. aureus and E. coli.Next, the data were ftted to a special cubic model employing least-squares regression to reveal the unidentifed coefcients in the following equation [39]: where Y is the MIC response in % (v/v).δ 1 , δ 2 , and δ 3 are the coefcients of linear terms.δ 12 , δ 23 , and δ 23 are the coefcients of binary terms.δ 123 is the coefcient of ternary term.ε is the error term.

Statistical Analysis.
Te F LOF/PE ratio between the mean square lack of ft (MS LOF ) and the mean square pure error (MS PE ) was used to ensure the accuracy of the model 4 Advances in Pharmacological and Pharmaceutical Sciences with observations.High F LOF/PE values signify a mismatch to the model [40,41].Moreover, the validation of the ftted models was verifed using the ANOVA F-test.To determine the statistical signifcance of the model, we used the ratio between the mean square regression (MS R ) and the mean square residual (MS r ) [42].Ten, the quality of the assumed model was further assessed using the coefcient of determination R 2 .In fact, it is frequently presented as a percentage (%) and used to assess the correlation among observed and expected responses [43], whereas Student's t-test was employed to determine the importance of the model's coefcients [44].Tis analysis was executed applying JMP software version 14 and Design Expert version 12.

Optimization Tools.
Te contour plot and 3D surface, based on iso-response curves, were employed to identify the ideal EOs formulation, resulting in the required responses.Tese curves were used to look for the factors modifcation intervals to get the desired response [43,45].Besides, the desirability test was applied to identify the desired response values based on the optimal conditions.Tanks to this tool, we can provide the precise optimum setting with a percentage between 0 and 1.A value of 1 is given when factors result in the maximum desired response, whereas a value of 0 signifes an inadmissible response [46].
EOs generally include compounds derived from two major groups: monoterpenes and sesquiterpenes (hydrocarbons and their derivatives) [47].Monoterpenes are a chemical family of terpenes that possess two isoprene units per component with a structural formula of C 10 H 16 (monoterpenes hydrocarbons).Monoterpenes may be linear (acyclic) or comprise a single (monocyclic) or double rings (bicyclic) [48].Modifed terpenes, such as oxygen-containing components are known as oxygenated monoterpenes.Furthermore, sesquiterpenes are secondary metabolites consisting of 15-carbon components containing three isoprenoid units and representing a multifaceted and heterogeneous subclass of bioactive molecules [47,49].
Te chemical analyses of EPEO, OMEO, and LBEO, including the percentage of each constituent, elution order, molecular formula, and retention index, are summarized in Table 1.A total of 70 volatile components have been detected in the three studied EOs.Indeed, twenty-fve, twenty-nine, and thirty-three components were identifed in EPEO, OMEO, and LBEO, representing 98%, 94.82%, and 97.47% of these oils, respectively.
Tis diference may be ascribed to several factors, including environmental conditions (soil type, precipitation, and climate), plant origin, harvesting time, extraction and processing methods, and phenological stage of plant concerned, and it could be genetically determined [41,55,56].

Single Antibacterial Activity.
Results of the antibacterial activity of EPEO, OMEO, and LBEO examined by disc difusion method against two bacterial strains are summarized in Figure 2. Te inhibition zone diameter values are depending on the tested EOs' nature and the tested species' susceptibility.LBEO, EPEO, and OMEO showed an important antibacterial efect against S. aureus with respective inhibition zone diameters of 24.66 ± 1.45, 18.4 ± 0.655, and 14.9 ± 0.75 mm.Moreover, this noticeable antibacterial efect has been also revealed against E. coli with 17.13 ± 2.85 mm, 11.03 ± 1.05 mm, and 8.52 ± 0.82 mm for EPEO, LBEO, and OMEO, respectively.Tese efects are less efective compared with the standard antibiotics (gentamicin and kanamycin), which may be explained by the fact that antibiotics are particular antimicrobial drugs with specifc site of action on bacteria from the one hand [66].On the other hand, EOs consist of a large number of bioactive compounds, which may lead to antagonistic interactions, thus limiting the antimicrobial activities of EOs.
Te quantitative antibacterial values (MIC and MBC) of the three tested EOs against S. aureus and E. coli are presented in Table 2.
All studied EOs have presented signifcant antibacterial activity.In fact, S. aureus appears to be the most sensitive strain to the three EPEO, LBEO, and OMEO, with MIC values ranging from 0.25 to 0.5% (v/v).Indeed, LBEO and EPEO have the strongest antibacterial activity with MIC values of 0.25% (v/v).Moreover, noticeable antibacterial efect has also been revealed for OMEO with MIC equal to 0.5% (v/v).
However, a lower antibacterial efect has been shown against E. coli with MIC values ranging from 1 to 6% (v/v).In fact, LBEO exhibited the highest antibacterial activity (1% v/v) followed by EPEO (2% v/v), while OMEO showed the weakest antibacterial efect (6% v/v).Tis is to note that the standard antibiotics gentamicin and kanamycin have shown MIC values ranging from 8 to 32% (v/v) against both strains.Te MBC values of the three tested EOs are quite similar to the MIC values obtained against E. coli and S. aureus.However, for EPEO, the MBC value was twice as high as the MIC.Concerning this bactericidal efect, it has been found that the Grampositive (Gram+) bacterial strain is more sensitive to EPEO, LBEO, and OMEO than the Gram-negative (Gram−) bacteria.
Te antibacterial activity of EOs could be elucidated by the molecular interaction of the functional groups of their components with the bacterial cell wall, causing wholecell lysis.In order of elution on HP-5MS, b components identifed by RI and MS.c Retention index determined from alkanes series (C9-C31).d Retention index from data libraries (NIST) [30,31].Bold values represent the proportions of the major components for each oil.
Advances in Pharmacological and Pharmaceutical Sciences Liberation of internal components from the cell is a good indicator of membrane integrity, with small ions such as phosphate and potassium that have a tendency to difuse before large molecules such as RNA and DNA and other substances [28,67].Moreover, the resistance of Gramnegative (Gram − ) bacteria is strongly linked to the composition of their cell wall which limits the difusion of hydrophobic components such as EOs and their bioactive components through the lipopolysaccharide (LPS) layer [68,69].However, LPS are absent in Gram-positive bacteria, which possess a cell wall mainly constituted by a peptidoglycan layer facilitating the difusion of EOs through cell membrane and thereby distributing cell permeability and binding with vital macromolecules, such as proteins, DNA, and RNA and thus causing cell death [66].
Previous investigations have reported the antibacterial efects of the three studied EOs.Our fndings are consistent with those reported by Ouedrhiri et al. [20] who showed that OMEO causes a signifcant inhibition on Gram + bacteria (S. aureus and B. subtilis), while a weak antibacterial efect was determined against Gram − bacteria, including Pseudomonas aeruginosa and E. coli [8,20].
As it can be observed, the Gram − strains are more resilient than the Gram + ones.Indeed, the Gram − have an envelope that consists of three layers.Te frst layer is the outer membrane, a protective and a unique feature that distinguishes Gram − from Gram + bacteria [3].Te outer membrane of Gram − strains is the principal reason for resistance to a broad variety of antimicrobial agents including essential oils due to their hydrophobic characteristics [10].Besides, the Gram − strains can change their hydrophobic properties via mutations, creating resistance to EOs, while the Gram + ones do not have this strong layer, which makes Gram − bacteria more resistant than Gram + ones [70].
Nevertheless, it has been previously shown that the major constituents of OMEO (p-menthane, germacrene D, and α-pinene) exhibit antibacterial efect against E. coli and S. aureus [20,[23][24][25].Terefore, the lower antibacterial action found against Gram − bacteria might account for an antagonistic interaction among its volatile compounds.Indeed, numerous researches have shown that the antibacterial efect of EOs is controlled by the intricate interplay between their minor and major constituents.In some cases, these components are active against bacterial cells when evaluated separately [20,71].
To the best of our knowledge, there is no literature data demonstrating the antibacterial activity of LBEO.However, numerous studies reported the antibacterial activity of the genus Lavandula.Indeed, Bouyahya et al. [72] showed that Lavandula stoechas exhibits antibacterial activity with some variability depending on the tested bacteria, experimental methods used, and/or chemical composition of the EOs.In addition, similar fndings have been reported by Dadaliogÿlu and Evrendilek and Cherrat et al. [73,74].
Furthermore, Garzoli et al. [62] showed that lavandin (Lavandula intermedia) EO exhibits bactericidal activity against a wide range of pathogenic bacteria.Tis efect can  Te research suggests that the antimicrobial activity of the LBEO could be associated with its high content of oxygenated monoterpenes which are highly effective against microbial cells [77].
In addition, EPEO has not gained much attention regarding its antibacterial properties.In this context, we have investigated this study to report the antibacterial activity of this plant.Djenane et al. and Oyedeji et al. [78,79] obtained similar results with some variability against a panel of bacteria.Our EO exhibited signifcant bacteriostatic and bactericidal efects against E. coli and S. aureus compared to the results obtained by Fahad et al. [50], while these fndings are corroborated with those reported by Assaggaf et al. [80], which indicated a strong antibacterial efect at low MIC and MBC values.Tese diferences may be attributable to the variations in the EOs' chemical composition and variations in the experimental conditions as well as to bacterial strains tested.
Te mechanism of EPEO, LBEO, and OMEO remains unresolved.Nevertheless, it has been found that other EOs have many antibacterial mechanisms [68,81,82].Indeed, the mechanisms of action include the capacity to cross the cell membrane, the disturbance in the electron respiratory chain, and the leakage of electrolytes [81].Other mechanisms have shown that EO components inhibit the quorum sensing signaling pathways, thus decreasing the bacterial resistance [83][84][85].
Besides, the antimicrobial properties of EOs can be attributed to the composition, functional groups of the bioactive compounds, and their synergistic interactions.Generally, terpenes and terpenoids are the main groups of EOs.Tey are characterized by a small molecular weight.Te terpenoids group can be partitioned into alcohols, ketones, esters, phenols, aldehydes, epoxides, and ethers [81].Many terpenoid compounds have demonstrated signifcant antimicrobial efects against various Gram + and Gram − strains, especially thymol, geraniol, carvacrol, linalyl acetate, menthol, piperitone, and linalool which are the major compounds of terpenoids.Tese compounds are able to interact with membrane proteins and disrupt the outer and inner membrane of bacteria, resulting in bacterial death [70,80].3 displays the mixtures design, which comprises diferent mixtures of OMEO, LBEO, and EPEO, along with the observed responses for each experiment on S. aureus and E. coli.Te experiments were conducted randomly and each response is the mean of three repetitions.Te results demonstrated that the equiproportional mixture of three EOs and the ternary mixture (0.167: OPEO/0.167:OMEO/0.667:LBEO) were the most performant formulations, presenting the highest antibacterial activity against the two studied strains.

Statistical Validation of the Postulated Model.
Te experimental response data were statistically analyzed to confrm the chosen model for each bacterial strain, which represents the relationship between responses and factors.
Te variance analysis reveals that the regression main impact is statistically signifcant for the two examined responses since their risk signifcance (p value) is less than 0.05 (0.0001 * and 0.001 * for E. coli and S. aureus, respectively).In addition, the F ratio(R/r) calculated for both studied responses are higher than the theoretical value at the 95% confdence level.As shown in Table 4, the F ratio(R/r) for E. coli (117.694) and S. aureus (29.41) exceeded the tabular value of F at a 95% confdence level.Besides, the ANOVA F-test indicated that the both postulated models had no lack of adjustment, because their p values were higher than 0.05 (0.07 and 0.051).Te computed F Ratio(LOF/PE) of the investigated responses was also observed to be lower than the theoretical value F (0.05;3.2) � 19.16 at the 95% confdence level.
Te coefcients of determination R 2 for S. aureus and E. coli are 97% and 99%, respectively.Tese values indicate a sufcient agreement between the experimental values and those predicted by the ftted model.Tese fndings were supported by the graph in Figure 3, which shows that the curves of observed values as a function of predicted values look exactly like a straight line.

Factors Efects and the Fitted Model of Both Responses.
Te impact of all investigated factors, their corresponding tstudent statistical values, and the p values, are summarized in Table 5. Te mathematical model coefcients were statistically signifcant when their p values were lower than 0.05, while those with a p value higher than 0.05 were excluded from the presumed model.
Te statistically signifcant coefcients for the MIC response of E. coli are linear terms (δ 1 , δ 2 , and δ 3 ), binary interaction terms between EPEO and OMEO (δ 12 ) as well as OMEO and LBEO (α 23 ) and fnally ternary term (δ 123 ).Tese outcomes showed that the antibacterial action on E. coli is dependent on all terms in the modulated mathematical model, except for the coefcient associated with the binary term (α 13 ) between EPEO and LBEO.
Te mathematical model was estimated according to the following formula: Regarding the response MIC S.aureus , all the terms in the adapted mathematical model (δ 1 , δ 2 , δ 3 , δ 12 , δ 13 , and δ 123 ) are statistically signifcant, except for the coefcient representing the binary mixture of EPEO and LBEO (α 13 ).Tese fndings refect that the antibacterial efect against this bacterial strain depends on all interactions except those obtained by EPEO * LBEO.Advances in Pharmacological and Pharmaceutical Sciences Te predictive mathematical mode was determined as follows:

Advances in Pharmacological and Pharmaceutical Sciences
(5)

Formulation Optimization and Desirability Study.
Te optimization process adopting the mixture design approach enables us to determine the optimal formulation of the three EOs demonstrating the best MIC value, that is to say, the smallest concentration which exhibits the highest sensitivity.Te smallest MIC values noticed during the experiments were 0.5% and 0.125% for E. coli and S. aureus, respectively.Consequently, a formulation of the three EOs allowing to obtain responses smaller than or equal to these values will be elucidated.
In the present research, it is important to emphasize that the ternary mixture indicates stronger antibacterial activity against both bacteria than single oils and binary mixtures.Tis positive combination is depicted in Figure 4, where the optimum mixture zone is situated in the center of the triangle.Te contour plot and 3D surface (Figure 4) demonstrate the interaction among each component of the mixtures.Tis graph illustrates changes in response, with the dark blue zone representing weak MIC values and greater bacterial potential.However, the green to orange hue indicates elevated MIC values.Hence, the mixture design approach optimized the amounts of individual active constituents to generate an optimal formulation established by its potent antibacterial activity.

(i) Efect of the EOs formulation against E. coli
Te MIC E. coli response achieved in the various tests ranged from 0.5 to 6% (Table 3).Figure 4(a) indicates the contour and surface plots of the MIC E. coli response found with diverse mixtures of the EPEO, OMEO, and LBEO.A MIC value equal to 0.40% was determined as a compromise against E. coli.From the 2D and 3D mixing graph, we can conclude that a mixture of EPEO, OMEO, and LBEO, is necessary to achieve this MIC value.In addition, the desirability function (Figure 5(a)) exhibited the precise amounts of EPEO, OMEO, and LBEO leading to the desired MIC value of 0.37%.Tus, the desirability test revealed that there is a 99.9% chance of reaching this value using the following mixture: 32%, 28%, and 40% of EPEO, OMEO, and LBEO, respectively.(ii) Efect of the EOs formulation against S. aureus Te results of the microdilution assay indicated that the MIC S.aureus response varied between 0.125 and 0.5% (Table 3).Moreover, 2D and 3D mixture plots (Figure 4(b)) illustrated the optimal compromise zone, revealing that the mixture comprising EPEO, OMEO, and LBEO is required to attain the desired MIC of about 0.12%.In fact, the desirability function (Figure 5(b)) confrms this fnding, indicating that the ternary mixture with the following proportion (35 : 30 : 35 v/v/v) EPEO, OMEO, and LBEO leads to the best achievable MIC value (0.11%), with a compromise percentage of 99.9%.Tese outcomes demonstrate the synergistic interaction between these components.
Numerous investigators are currently using a mixture design methodology to assess the potential interactions between various mixture constituents in order to estimate the optimal formulation [38,43,86,87].
Zieniuk and Be ˛tkowska [86] employed the mixture design approach to evaluate and optimize the synergistic antibacterial efect among tea tree, rosewood, and lavender EOs against E. coli, Listeria monocytogenes, and Rhodotorula mucilaginosa.Within this line, the synergistic efects of Eucalyptus camaldulensis, Mentha pulegium, and Rosmarinus ofcinalis EOs against bacteria responsible for nosocomial infections were also investigated using a simplexcentroid design [38].In addition, Fadil et al. [43] optimized the proportions of Tymus.vulgaris L., R. ofcinalis L., and Myrtus communis EOs by applying a centroid mixture design.Te optimal formulation corresponded to 45% of myrtle and 55% of thyme EOs, which showed synergistic activity against Salmonella typhimurium strain.

Interaction between EOs.
Te mixture contour plot of E. coli and S. aureus responses, generated by the three EOs, EPEO, OMEO, and LBEO, elucidates the impact of the simultaneous optimization.Te optimal compromise area for the two strains indicated that the desired MIC requires a ternary mixture of the abovementioned EOs (Figure 6).
Te mixture of these components allowed particularly oxygenated monoterpenes (1,8-cineole, p-menthane, and  linalool) and monoterpene hydrocarbons (p-cymene and α-pinene) to assemble.Each volatile compound has diferent sites within the bacterial cell where it can act [88].Te oxygenated terpenoids, including 1,8-cineole, p-menthane, and linalool, are the major antibacterial constituents as compared with the terpene hydrocarbons, which lack hydroxyl groups (-OH) [39,89].In addition, the combination of minor and/or major constituents may be responsible for the synergistic efect on bacteria [90].p-Cymene and α-pinene are not efective antibacterials when acting alone, but their combination with oxygenated terpenoids such as linalool and/or 1,8-cineole has shown promising antibacterial activities.Terefore, p-cymene can swell bacterial cell membranes, facilitating the difusion of linalool and 1,8cineole into the cell membrane, leading to bacterial death.
In this respect, to our knowledge, the current study reports for the frst time the synergistic activity of 1,8cineole, p-Menthane-1,8-diol, and linalool.In addition, this combination could increase the levels of components with antimicrobial properties, such as D-limonene, c-cadinene, and α-pinene [97,98].
Taken together, these fndings provide scientifc evidence for potential applications of studied oils in combination to 14 Advances in Pharmacological and Pharmaceutical Sciences develop novel and efective antimicrobial agents, which may be useful in food packaging, food preservation, and elaboration of biopharmaceuticals.However, further investigations on the antibacterial action of these oils alone and/or in mixture are strongly required to clearly describe in detail how they could interact with each type of bacteria.Furthermore, in the literature, the results showed that the three EOs have efectively inhibited the growth of foodborne pathogens in vitro, whereas their action in food system model (in vivo) has not been reported.Indeed, more studies are needed in this subject to validate the possible applications of the three studied oils as natural additive in foods to persevere their microbiological security.Concerning the efect of the tested EOs combination treatment against E. coli, it has been found that the combinations of 1/4 MIC EPEO + 1/4 MIC OMEO had an antibacterial synergistic activity with a FIC index of 0.5, whereas the combination 1/2 MIC EPEO + 1/8 MIC OMEO exhibited partial synergy with a FIC index of 0.625.Te combinations of EPEO/LBEO and LBEO/OMEO demonstrated a synergistic and partial synergistic efect against E. coli.
In contrast, four combinations showed partial synergy with a FIC index ranging from 0.50024 to 0.625.Each checkerboard assay produces diverse combinations.However, the FIC values of the most efcient combination are employed to assess the FIC index [71].
Taken together, the binary combinations between the three tested EOs had a greater antibacterial efect (synergistic) than the application of EOs alone, when tested against E. coli and S. aureus.It has been demonstrated that the minor compounds are involved in antibacterial efect and may exhibit synergistic interactions with other constituents [68].Te synergistic efect observed in this research between the studied EOs could be explained by the molecular interaction of the functional groups (monoterpene hydrocarbons, oxygenated monoterpenes, and sesquiterpene hydrocarbons).Tey integrate and disrupt the cell membrane and thereby facilitate the uptake of the active compounds, leading to cell lysis [99].
Other investigations also reported a synergic efect among O. mixta, Eucalyptus, and Lavandula EOs with other EOs [8,20,70,100,101].In fact, Ouedrhiri et al. [20] highlighted the efect of the combination of O. Mixta and Pelargonium asperum EOs.Te results showed that O. mixta MIC decreased from 2 to 0.007813% (v/v) against S. aureus after combination with Pelargonium asperum EOs.On the other hand, a synergistic activity was attained between Eucalyptus and Dracocephalum EOs against S. aureus and E. coli [70].
Furthermore, Moussii et al. [101] showed that the combination of lavender, wormwood, and rosemary EOs display a synergistic efect against Gram + and Gram − bacteria.A number of reports have proposed certain specifc mode of action of antibacterial interaction that produce synergism outcomes, including modulating certain common biochemical pathways, inhibiting the protective enzymes, and using the active agents on the cell wall to increase the absorption of other antimicrobials [102].In addition, volatile compounds derived from various medicinal plants possess hydroxyl functions (-OH) in their structure, which potentiate the antibacterial properties of terpenes [103].
Furthermore, the presence and position of functional groups in EO compounds may efectively modulate its antibacterial efect [66,104].In fact, in Gram − bacteria, the presence of phenolic groups in carvacrol and thymol have been shown to interact with the outer membrane constituents, causing its breakdown and thereby leading to the liberation of LPS and increasing the membrane permeability with signifcant loss of ATP [105].Moreover, some components such as carvone, which have a hydroxyl group (in position 3), appear to be responsible for its interaction with the bacterial wall, causing signifcant injury, especially in Gram+ bacteria [106].Furthermore, it has been demonstrated that the antibacterial activity of terpene aldehydes is related to the electronegative characteristics of aldehyde group [107].In fact, aldehydes can act on bacterial cell wall, restricting its biological functionality, especially electron transfer.

Conclusion
In this exploratory investigation, we reported the antibacterial formulation of three EOs derived from Eucalyptus polybractea cryptonifera, Ormenis mixta, and Lavandula burnatii briquet using checkerboard and mixture design approaches.Te antibacterial action of these EOs depends on the proportion of each constituent and the target bacteria.As a result, it has been shown that the MIC values were considerably reduced using the combination of E. polybractea, O. mixta, and L. burnatii.Tese efects are mainly ascribed to the synergistic action of the major and/or minor molecules identifed in the combined EOs.Te most efective combinations on E. coli and S. aureus correspond to 32%, 28%, and 40% and 35%, 30%, and 35% of E. polybractea, O. mixta, and L. briquet, respectively.Tese antibacterial formulations may be suitable as alternative to commercialized antibacterial and preservative agents, which are increasingly becoming nonactive against a panel of bacterial strains causing serious infections and undesirable deteriorations of some food-based products.

Figure 1 :
Figure 1: An overview of the simplex-centroid design for threecompound mixtures.

Figure 2 :
Figure 2: Screening of antibacterial action by disc difusion method of EPEO, LBEO, and OMEO and standard antibiotics (gentamicin and kanamycin) against S. aureus and E. coli.

Figure 3 :
Figure 3: Curves of the observed values according to the predicted values for the two studied responses (a) E. coli and (b) S. aureus.Te red lines show the curve of actual values of MIC as a function of those predicted for both tested strains.Te blue horizontal lines indicate the mean of the observed values.

Figure 5 :
Figure 5: Desirability plot revealing the precise proportions of LBEO, OMEO, and EPEO leading to the best antibacterial action against E. coli (a) and S. aureus (b).

Furthermore, 1 /
2048 MIC EPEO + 1/4 MIC LBEO showed a synergistic antibacterial activity on S. aureus with a FIC index of 0.25, while the combination of 1/4096 MIC EPEO + 1/ 2 MIC LBEO has shown a partial synergistic efect with a FIC index of 0.5002.Moreover, the combination of 1/4 MIC L- BEO /1/2 OMEO also presented a partial synergistic activity, with a FIC index value of 0.75.

Figure 6 :
Figure 6: Mixture plot showing the optimal combination zone among O. mixta, E. polybractea, and Lavandula briquit against bacterial strain.
[29]Plant Material and EOs Extraction.Te aerial parts (stems, leaves, and fowers) of Eucalyptus polybractea cryptonifera, Ormenis mixta, and Lavandula burnatii briquet were harvested during the period between March and April at the fowering stage, since this is the best time to use plant essences more efectively[29].Te three plants were collected in the region of Taounate, Morocco (34 °32′ 09″ N, 4 °38′ 24″ W).Plant authenticity was carried out by the botanists of the Sidi Mohamed Ben Abdellah University, Fez, Morocco, and deposited under voucher codes of BLMUP 386-388.

Table 2 :
[76]IC and MBC values of EPEO, LBEO, and OMEO against bacteria strains using microdilution assay.Advances in Pharmacological and Pharmaceutical Sciences be attributed mainly to the dominant presence of linalool (41.60%) in this oil.Indeed, Silva et al.[75]also attributed Ocimum basilicum EO activity to linalool.Furthermore, Hussain et al.[76]have demonstrated that Ocimum basilicum EO and linalool compound display antibacterial and antifungal actions against E. coli, S. aureus, B. subtilis, and Aspergillus niger.
a Final bacterial concentration was 10 6 CFU/mL.bGentamicin and kanamycin were used as references.8

Table 3 :
Various combinations generated by the chosen mixture design and response data for each trial.Experiments were carried out after randomization.b Each response is the average of three replicates. a

Table 4 :
Variance analysis for the three ftted models.

Table 5 :
Estimated regression coefcients for the uncompleted cube regression model.

Table 6 :
FIC indices of the combined antibacterials against the tested bacterial strains.