Optimization of Synthesis of Silver Nanoparticles Conjugated with Lepechinia meyenii (Salvia) Using Plackett-Burman Design and Response Surface Methodology—Preliminary Antibacterial Activity

Abstract

In the present investigation, an ethanolic fraction (EF) of Lepechinia meyenii (salvia) was prepared and fractionated by gradient column chromatography, and the main secondary metabolites present in the EF were identified by HPLC-MS. Silver nanoparticles (AgNPs) were synthesized and conjugated with the EF of Lepechinia meyenii (salvia). The AgNPs synthesis was optimized using Plackett-Burman design and response surface methodology (RSM), considering the following independent variables: stirring speed, synthesis pH, synthesis time, synthesis temperature and EF volume. The AgNPs synthesized under the optimized conditions were characterized by UV visible spectroscopy (UV-VIS), Fourier Transform Infrared Spectroscopy (FT-IR), Dynamic Light Scattering (DLS) and Scanning Transmission Electron Microscopy (STEM). The antibacterial activity of the AgNPs against Staphylococcus aureus (ATCC^® 25923) was evaluated. The following flavonoids were identified: rosmarinic acid, diosmin and hesperetin-7-O-rutinoside. The optimized conditions for the synthesis of nanoparticles were pH 9.45, temperature 49.8 °C, volume of ethanolic fraction 152.6 µL and a reaction time of 213.2 min. The obtained AgNPs exhibited an average size of 43.71 nm and a resonance plasmon of 410–420 nm. Using FT-IR spectroscopy, the disappearance of the peaks between 626.50 and 1379.54 cm⁻¹ was evident with the AgNPs, which would indicate the participation of these functional groups in the synthesis and protection of the nanoparticles. A hydrodynamic size of 47.6 nm was obtained by DLS, while a size of 40–60 nm was determined by STEM. The synthesized AgNPs conjugated with the EF showed a higher antibacterial activity than the EF alone. These results demonstrate that the AgNPs synthesized under optimized conditions conjugated with the EF of the Lepechinia meyenii (salvia) presented an increased antibacterial activity.

1. Introduction

Because plant extracts contain phytochemicals such as terpenoids, flavonoids, tannins, phenol derivatives, plant enzymes, proteins and reducing sugars [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18], they can act in the reduction of metal ions coming from precursor salts [6,19,20,21,22,23,24,25,26,27]. Therefore, they can act as protective agents required for the synthesis and stabilization of nanoparticles (NPs) [19,28]. The utilization of plants not only influences the morphology and stability of nanoparticles but also enhances their biological properties [21,29]. The green synthesis of nanoparticles using plant extracts has gained considerable attention for biomedical applications [19,30]. The potential use of plant-based nanoparticles for cancer treatment has been reviewed [31], and the application of silver and gold nanoparticles is an active area of research [31,32,33,34,35]. There is an increased interest in the use nanoparticles to improve chemotherapeutic limitations such as undesirable side effects [7,36,37,38], multidrug resistance [39,40], cytotoxicity [37,41,42,43,44], and pharmacokinetic and pharmacodynamic challenges such as low oral bioavailability [42,45,46].

Plants can be an inexpensive and non-toxic source for the biosynthesis of AgNPs and have the potential for scale-up in the production of nanoparticles with different morphological and size characteristics. Therefore, methods have been developed by green chemistry for the biosynthesis of AgNPs, using the aqueous extract of various plant species [47]. For instance, silver nanoparticles synthesized with biological reducing agents have been achieved, with an average size of 19.65 ± 13.49 (nm) and with defined spherical shapes [47]. Our research group previously synthesized silver nanoparticles and carboxymethyl chitosan (AgNPs-CMC), which were characterized in functionalized cotton fabric [20,48]. Furthermore, we also synthesized silver nanoparticles that were reduced and stabilized with an aqueous extract of Thelypteris glandulosolanosa (Raqui-raqui), forming silver nanoparticles (AgNPs-RR) [19]. A hydrodynamic size of 39.16 nm was reported, and an average diameter of 31.45 nm was characterized with STEM [19]. Furthermore, their anti-cancer activity against various cancer cell lines has been investigated as a potential strategy for breast and lung cancer treatment [19]. Further progress has been made in bionic metalized nanocoatings with bactericidal and antiviral activities, which facilitate specific cytotoxicity and improve the stabilization of nanoparticles [49].

Optimization is one of the essential steps in the development of a synthesis protocol, and the evaluation of the interaction of reaction parameters influencing the biosynthesis of AgNPs and their optimization is necessary for the efficient reduction of metal ion as silver (Ag⁺) to silver nanoparticles (Ag⁰) using different bioreducers [50]. There is little information in the literature regarding process optimization by green synthesis methods for AgNPs using active principles or plant secondary metabolites. The combined effects of all the factors influencing a process can be explained with the response surface methodology (RSM), which can predict the optimal levels of each parameter and their corresponding response values to eliminate the limitations of a single-factor optimization process [51]. The Plackett-Burman design provides an effective and rapid way to identify the relevant variables to be used for optimization [52,53]. Furthermore, the RSM uses an experimental design called central composite design (CCD) to obtain a polynomial equation representative of the experimental data and describes the behavior of the parameters by applying an analysis of variance for model adequacy [50]. The use of Plackett-Burman design and RSM has been reported for phenol degradation by Candida tropicalis [52] and Pseudomonas aeruginosa [52,54], production of α-amylase by Aspergillus oryzae [55], and production of citric acid from pineapple waste [56]. Therefore, this study aimed to investigate the synthesis of AgNPs, using the ethanolic fraction (EF) from Lepechinia meyenii (salvia), to evaluate the antibacterial activity of these nanoparticles against Staphylococcus aureus (ATCC^® 25923) and to optimize the AgNPs biosynthesis parameters using Plackett-Burman design and RSM.

2. Materials and Methods

2.1. Reagents and Materials

The following reagents obtained from Sigma-Aldrich (St. Louis, MO, USA) were used: petroleum ether, ethyl acetate, ethanol, silver nitrate, potassium dihydrogen phosphate (pa ≥ 99%), sodium hydroxide (pa ≥ 99%). In addition, Staphylococcus aureus (ATCC 25923) (Merck Millipore, Burlington, MA, USA), Trypticase soy agar (TSA) and Trypticase soy broth (TSB) (Liofilchem, Abruzzi, Italy) were used in the experiment.

2.2. Equipment

The following equipment was used: UHPLC chromatograph (Dionex Ultimate 3000 UHPLC, Thermo Scientific, Waltham, MA, USA), mass spectrometer (Q Exactive Plus, Thermo Scientific), UV-Visible spectrophotometer (Evolution 220, Thermo Scientific), Dynamic Light Scattering (DLS, Zetasizer Nano ZS, Malvern Panalytical, Worcestershire, UK), scanning transmission electron microscope (JEOL 2200FS STEM, with hexapolar corrector CEOS).

2.3. Preparation of Plant Extract of Lepechinia meyenii (Salvia) and Ethanolic Fraction

Green leaves of Lepechinia meyenii were harvested from the district of Pocsi located in the province and department of Arequipa, Peru, located at 3040 m elevation. Leaves were washed three times using distilled water and then further washed with Milli-Q water. All the water was removed, and the leaves were sprayed, dried, pulverized and sieved in 100 mesh. This sample was defatted using petroleum ether. For the preparation of the 80:20 ethanol:water extract, 100 g of the defatted sample was weighed on an analytical balance (Mettler Toledo). Then, 500 mL of 80:20 ethanol/water solution was added, and it was sonicated in the ultrasound bath under the following conditions: 40 °C, 1 h, 40 KHz and low power; then, it was centrifuged at 5000 rpm for 5 min. To obtain the ethanolic fraction (EF), a gradient column chromatography was performed using Silica Gel 60 (0.063–0.200 mm) as stationary phase, and a column head was prepared for the sample, which consisted of 5 g of silica gel embedded with 15 mL of the ethanolic extract. The following solvents were used as mobile phase in order of increasing polarity: petroleum ether, ethyl acetate and ethanol. The obtained fractions were monitored by thin layer chromatography. The corresponding eluates were obtained according to the polarity of the solvents, choosing the ethanolic fraction for the synthesis of nanoparticles and the identification of their secondary metabolites by HPLC-MS.

2.4. Identification of Flavonoids by HPLC-MS

A UHPLC chromatograph was obtained by injecting 3 µL of the ethanolic fraction (EF) using a Luna Omega C18 column (100 Å150 × 2.1 mm, 1.6 µm, Phenomenex, Torrance, CA, USA) with a temperature of 40 °C and flow rate 0.25 mL/min, with eluents A: H₂O 1% HCOOH and B: IN 1% HCOOH. Full mass spectrometry (MS) scan parameters were used in the range of –20 to 1500 m/z, with a resolution of 70 000 microscans, an automatic gain control (AGC target) of 1 × 10⁶ and a maximum IT of 100 ms.

2.5. Silver Nanoparticle (AgNPs) Biosynthesis

Silver nitrate solutions (0.1 M, AgNO₃) were also freshly prepared in Milli-Q water under dark conditions, as previously described [57]. The green synthesis of AgNPs was performed as previously described [19], with some adjustments. For instance, 20 mL of AgNO₃ (1 mM) was used as precursor, to which different volumes of the EF were used for the reduction of Ag into Ag⁰ state by mixing it with a final concentration of 0.5 mM AgNO₃. These mixtures of plant extract and AgNO₃ were temperature-controlled at 50 °C with continuous stirring. The solution was alkalinized by adding drops of 0.1 N NaOH until a basic pH between 9 and 10 was obtained. The reduction of Ag ions in solution was monitored by a visible color change and periodic mixture sampling by measuring in the UV-Visible Evolution 220 (λ 300 to 700 nm). The AgNPs were centrifuged at 12,500 rpm for 15 min, washed three times with Milli-Q water and finally washed with ethanol. The resulting AgNPs were dried at 40 °C for 48 h. The synthesis conditions were developed according to the experimental design matrix proposed by RSM.

2.6. Characterization of Biosynthesized AgNPs

2.6.1. UV-Visible Spectra Analysis

The biosynthesized AgNPs silver nanoparticles were evaluated and monitored by a UV-VIS spectrophotometer. Each assay was defined according to the experimental design employed at each stage of the RSM. The spectral scanning was performed at 350–650 nm for the determination of the peak corresponding to the resonance plasmon of the nanoparticles at 411 nm. Spectrophotometric readings were performed using a quartz cuvette with a step width of 1 cm. The absorbance determination was performed at 411 nm wavelength.

2.6.2. Dynamic Light Scattering (DLS)

The distribution of the size of AgNPs was analyzed by DLS (Zetasizer Nano ZS) as previously described [19]. For the reading, 1.5 mL of sample was added to a polypropylene cuvette, and the following reading parameters were considered: dispersing medium, refractive index (RI) and dynamic viscosity (Cp).

2.6.3. Scanning Transmission Electron Microscopy (STEM)

The STEM sample was prepared by a drop of reaction sample on the copper-coated grid, and excess solution was removed by drying under a mercury lamp for 5 min as previously described [58], with some minor modifications. The sample was dried for 48 h in a chamber with a relative humidity (RH) of 30% and a temperature of 25 °C. To ensure that the nanoparticles were not in a conglomerated or structurally aggregated state at the bond level, a sonication treatment was performed for 30 min.

2.6.4. FT-IR Spectrometry

The amount of silver in the nanoparticles was quantified using Fourier-transform infrared spectroscopy (FTIR) (Nicolet IS50, Thermo Scientific) equipped with the diamond crystal as previously reported [19]. Aliquots of the corresponding samples (EF and AgNPs) were taken and placed in the diamond ATR lens; previously, a spectral background was taken in the 4000 to 400 cm⁻¹ spectrum range in transmittance mode. After the reading for each sample, the ATR accessory was cleaned with Kimtech cloths and isopropyl alcohol to avoid cross-contamination between samples.

2.7. Antibacterial Activity

The antibacterial activity was evaluated by the standard well diffusion method. Inoculations of the bacteria E. coli (ATCC 25922) and S. aureus (ATCC 25923) were prepared at a concentration of 1.02 × 10³ CFU/mL and 1.36 × 10⁴ CFU/mL, respectively, as previously described [21]. Then, 20 μL of the inoculum was measured and plated uniformly on the surface of the Mueller Hinton agar (MH). Then, 3 wells of 7 mm diameter were made, distributed equidistantly in the Petri dish, and 20 μL of the AgNPs or EF was added. The plates were then incubated for 24 h at 37 °C; then, the inhibition zone was measured around the well using a vernier caliper [59].

2.8. Plackett-Burman Design

The screening of process parameters was undertaken using the Plackett-Burman design, which is an effective method used to select significant factors from many variables potentially affecting the process [52]. In this study, an 8-run Placket-Burman design was performed to evaluate seven variables (including two dummy variables), and each variable was examined at two levels: the low level (−1) and high level (+1) as shown in

Table 1. Levels of the variables tested in the Plackett-Burman design for AgNPs biosynthesis.

#	Variables	Symbol	Unit	Experimental Value
				Low (−1)	High (+1)
1	Stirring speed	X1	RPM	300	900
2	Synthesis pH	X2		8	10
3	Synthesis time	X3	min	140	330
4	Synthesis temperature	X4	°C	45	55
5	Ethanolic fraction (EF) volume	X5	µL	50	200
6	Dummy	F1		0	0
7	Dummy	F2		0	0

. The values of the two levels were based on our preliminary results. The effect of the individual variables was calculated using Equation (1).

$$E\left(X_i\right)=2({\displaystyle \sum }{M}_i^{+}-M_i^{-})/N$$

(1)

where $E\left(X_i\right)$ is the effect of the tested variable $\left(X_i\right)$, $M_i^{+}$ and $M_i^{-}$ represent the high and low values, respectively, and $N$ is the total number of trials.

Experimental error was determined by estimating the variance between the two dummy variables using Equation (2).

$$V_{eff}={\displaystyle \sum }{\left(E_d\right)}^2/n$$

(2)

where $V_{eff}$ is the variance of the effect, $E_d$ is the effect for the dummy variable, and $n$ is the number of dummy variables used in the experiment.

The standard error (SE) of the effect was the square root of $V_{eff},$ and the significance (p-value) of the effect of each variable was calculated by Student’s t-test.

2.9. Response Surface Methodology (RSM)

The optimal levels of the significant factors and the variable interactions were analyzed by central composite design (CCD) [52]. In this study, a five-factor, three-level CCD with 32 runs was utilized. The tested variables (stirring speed, synthesis pH, synthesis time, synthesis temperature, and ethanolic fraction volume) were denoted as X₁, X₂, X₃, X₄ and X₅, respectively. Each of the variables was assessed at three different levels, combining factorial points (−1, +1) and the central point (0), as shown in

Table 2. Levels of the variables tested in the central composite design (CCD) for AgNPs biosynthesis.

#	Variables	Symbol	Unit	Coded Level
				−1	0	+1
1	Stirring speed	X1	RPM	400	500	600
2	Synthesis pH	X2		9	9.5	10
3	Synthesis time	X3	min	180	210	240
4	Synthesis temperature	X4	°C	48	49.5	51
5	Ethanolic fraction (EF) volume	X5	µL	120	150	180

.

The second-order model used to fit the response to the independent variable (absorbance at 411 nm) is shown in Equation (3).

$$Y={\beta }_0+{\displaystyle \sum }_{i=1}^k{\beta }_i{X}_i+{\displaystyle \sum }_{i=1}^k{\beta }_{ii}{X}_i^2+{\displaystyle \sum }_{i=1}^k{\beta }_{ij}{X}_i{X}_j$$

(3)

where $Y$ is the predicted response (maximum absorbance at 411 nm); $X_i$ and $X_j$ are the input variables that influence the response $Y$; $k$ is the number of variables; ${\beta }_0$ is the constant term; ${\beta }_i$ is the ith linear coefficient; ${\beta }_{ii}$ is the ith quadratic coefficient; and ${\beta }_{ij}$ is the ijth interaction coefficient.

2.10. Statistical and Data Analysis

The evaluation of the significance for each of the independent variables $X_i$ of the AgNPs biosynthesis process was performed by calculating the degrees of freedom of each variable. Then, the Sum of Squares (SS), the Mean of the Sum of Squares (MSS) and the calculation of the F₀ statistic were developed. Analysis of variance (ANOVA) was performed to determine the significance of model and regression coefficients. The quality of the polynomial equation was examined by the determination coefficient (R²), and the statistical significance by Fischer´s F-test. The response surface and contour plots of the predicted responses of the model were used to assess the interactive relationship between the significant variables. Design-Expert version 8.0 (Stat-Ease Inc., Minneapolis, MN, USA) was used for designing the experiments, regression, and graphical analysis of the data. The statistical analysis was carried out with GraphPad version 6.01 (GraphPad Software, San Diego, CA, USA).

3. Results and Discussion

3.1. Identification of Flavonoids by HPLC-MS

Figure 1a,b show the chromatograms of the ethanolic extract and ethanol fraction (EF), respectively. The chromatogram of the extract showed compounds that included saccharides, organic acids, amino acids, cinnamic and caffeic acid derivatives, lignans, flavonoids, triterpenes and fatty acids. In the retention time zone between 0 and 15 min, the most intense signal corresponds to rosmarinic acid (12.66 min), while in the zone between 15 and 30 min, the most intense signals were not conclusively determined; however, it is possible that they correspond to diterpenes derived from carnosic acid [60]. In addition, the following flavonoids were identified with their respective retention times: apigenin 6,8-C-di-glucopyranoside (9.01 min), quercetin rutinoside (10.27 min), quercetin glucuronide (10.32 min), isoquercetrin (10.40 min), kaempferol-7-O-neohesperidoside (11.13 min), hesperetin-7-O-rutinoside (12.26 min) and diosmin (12.36 min). The chromatogram of the ethanolic fraction also shows rosmarinic acid as the most intense signal (12.63 min). In addition, the following flavonoids were identified with their respective retention times: hesperetin-7-O-rutinoside (12.22 min) and diosmin (12.36 min). Similar investigations have reported the presence of rosmarinic acid as the major component in ethanolic or methanolic extracts of Lepechinia meyenii (salvia), with retention times around 12.09 min [61] and 14.5 min [62,63]. Likewise, Zuo et al. [62] reported the presence of hesperidin and diosmetin, from which diosmin is derived.

3.2. UV-Visible Spectra Analysis

Figure 2 shows the UV-visible spectra of the AgNPs showing the absorbance at different time intervals. The formation and optimization of AgNPs was monitored by UV-visible spectroscopy by measuring the absorbance in the scanning range from 350 to 700 nm. An absorption maximum peak was seen between 410 and 420 nm, corresponding to the surface plasmon resonance (SPR). An increase in absorbance with respect to synthesis time was also observed, reaching a maximum at 240 min, with a maximum absorbance of 0.35 absorption units (AU). The presence of these peaks has been previously reported and demonstrates the formation of silver nanoparticles monitored by the bioreduction process of silver ions (Ag⁺) to AgNPs (Ag⁰) by UV-visible spectroscopy [64]. Furthermore, the visible color change and the appearance of the characteristic surface plasmon resonance (SPR) peak between 400 and 500 nm indicates the formation of AgNPs [65].

The reduction of silver ions (Ag⁺) present in the reaction solution was mediated by the reducing effect of the added volume of EF from Lepechinia meyenii (salvia), which was validated by the change of the reaction color to a translucent golden yellow color with the formation of AgNPs. This correlates with a previous study that reported that the UV-visible spectra obtained from the formed AgNPs revealed an absorbance peak maximum of AgNPs between 410 and 420 nm due to the surface plasmon resonance (SPR) effect [66]. Another study reported a gradual increase in color density as an indicator of the increase in the rate of AgNPs formation in the reaction mixture [67]. Furthermore, UV-visible spectroscopy is considered as one of the important procedures to establish the development of metal nanoparticles [68]. The maximum absorbance peak for AgNPs has been reported to range between 400 nm [69,70,71] and 432 nm [67].

3.3. FT-IR Spectrophotometry

FTIR spectroscopy for ethanolic fraction (EF) was carried out to determine the possible bioactive compounds with the ability to reduce Ag⁺ ions and stabilize the formed nanoparticles [72,73]. As observed in Figure 3a, there are some transmission peaks at 3320.30, 2972.57, 2878.84, 1379.54, 1087.90, 1045. 53, 879.98 and 804.00 cm⁻¹. The band in the range of 3000 to 3400 cm⁻¹ is the indicator of stretching of the OH⁻ group within free hydroxyl groups or may be an indicator of OH groups attached to aromatic structures, which confirms the existence of phenolic compounds in the EF [74]. The band between 2972.57 and 2878.84 cm⁻¹ is an indicator of the presence of carboxylic acids [75]. The band at 1379.54 cm⁻¹ would correspond to S=O or the N-O group [76]. The band observed at 1087.90 and 1045.53 cm⁻¹ demonstrates the alcohols used in the C-OH extract and the band between 879.98 and 804 cm⁻¹ demonstrates an out-of-plane stretching in the C=C or an out-of-plane stretching of the C-H in aromatic structures or S-OR bonds within ester compounds [76]. Finally, the band at 629.50 cm⁻¹ corresponds to a bending in the C=C bond or stretching in alkyl halides [76].

Figure 3b shows the spectrum of the synthesized AgNPs conjugated with the ethanolic fraction of Lepechinia meyenii (salvia). Three representative peaks are observed at 3318.90, 1636.48 and 560.80 cm⁻¹, which present some changes in shape and position compared to the peaks observed in the ethanolic extract. The appearance and change of position of the peaks at 3600–3200 cm⁻¹ and 1610–1550 cm⁻¹ indicates the presence of OH groups and carboxylic acids and probably NH amine groups, in the protection agents that act as stabilizers from the Lepechinia meyenii (salvia) ethanolic fraction [76]. It was also observed that the position of the band at 1379.54 cm⁻¹ in the ethanolic fraction was displaced to a lower region at 1636.48 cm⁻¹, indicating the possibility of an asymmetrical stretching of carboxylic (COO⁻) anions and the stretching of amino groups, which are capable of attracting silver ions and providing an electron source for the process of reduction [77,78].

3.4. Dynamic Light Scattering (DLS)

Figure 4 shows the size distribution by DLS of the AgNPs using the ethanolic fraction with the optimized synthesis parameters applying response surface methodology (RSM); an average hydrodynamic diameter of 43.71 ± 17.37 nm was obtained. A previous study that optimized AgNPs synthesis conditions using RSM reported an average hydrodynamic diameter of 37.65 nm [79], which agrees with the obtained results in the current study.

3.5. Scanning Transmission Electron Microscopy (STEM)

STEM provides information on sample size and morphology by providing high resolution images of samples by focusing on the primary electron beam and detecting secondary or backscattered electron signals [80]. Figure 5 shows the morphology and size (below 60 nm) of the synthesized AgNPs conjugated with the ethanolic fraction of Lepechinia meyenii (salvia). These results are in agreement with a previous study that reported the spherical shape and the particle size between 20 and 60 nm for AgNPs [79,81].

3.6. Screening of Important Variables Using Plackett-Burman Design

Table 1 shows the initial levels of the variables tested in the Plackett-Burman design for AgNPs biosynthesis. As shown in

Table 3. Effects of the variables and statistical analysis of the Plackett-Burman design for AgNPs biosynthesis.

	Effect	Coefficient	Standard Error	F-Value	p-Value Prob > F
Intercept		0.3792	0.0076
Stirring speed (X1)	−0.4264	−0.2240	0.0076	6277.4	0.0003 a
Synthesis pH (X2)	0.6013	0.3124	0.0076	12485	0.0002 a
Synthesis time (X3)	−0.0232	−0.0116	0.0076	18.62	0.0927
Synthesis temperature (X4)	0.0746	0.0506	0.0076	192.17	0.0102 a
Ethanolic fraction volume (X5)	0.4689	0.2460	0.0076	7591.8	0.0003 a

Predicted R² = 0.9998; adjusted R² = 0.9995; ^a 5% significance level.

, the analysis of the regression coefficients reported that synthesis pH, synthesis temperature and ethanolic fraction volume had positive effects on the predicted response (maximum absorbance at 411 nm), whereas stirring speed and synthesis time had negative effects. It was determined that these five variables have greater significance in the biosynthesis process of AgNPs. The multiple linear statistical model is represented below, with the values coded by Equation (4).

$$Y=0.3792-0.2240 X_1+0.3124 X_2-0.0116X_3+0.0506 X_4+0.2460 X_5$$

(4)

3.7. Optimization by Response Surface Methodology

3.7.1. RSM Regression Equation and Model Analysis

CCD was used to assess the interaction between the significant factors to optimize the biosynthesis of AgNPs conjugated with the ethanolic fraction of Lepechinia meyenii (salvia). The results obtained from the experimental in-tests were related to the estimated (predicted) and experimental (observed) values. A second-order polynomial mathematical model to calculate the optimal levels in the experimental design was proposed to provide adequate fit between the estimated (predicted) and experimental (observed) values [82]. Therefore, multiple regression analysis was used, and the second-order polynomial equation is shown in Equation (5).

$$\begin{array}{cc}Y=0.7739& +0.0405X_2+0.0534X_3+0.0961X_4+0.0405X_5+0.0488X_2^2\\ & +0.0964X_3^2+0.0440X_4^2+0.05290X_5^2+0.1941X_3^2\hfill \\ & -0.0568X_3{X}_5+0.0604X_4{X}_5\hfill \end{array}$$

(5)

Table 4. ANOVA for response surface quadratic model for AgNPs biosynthesis.

	Mean Square	F-Value	p-Value Prob > F
Model	0.079971	1.78	0.163
Stirring speed (X1)	0.002665	0.06	0.812
Synthesis pH (X2)	0.039277	0.88	0.370
Synthesis time (X3)	0.039423	0.88	0.369
Synthesis temperature (X4)	0.068427	1.53	0.243
Ethanolic fraction volume (X5)	0.221741	4.94	0.048 a
X12	0.018172	0.40	0.538
X22	0.074038	1.65	0.225
X32	0.086656	1.93	0.192
X42	0.280797	6.26	0.029 a
X52	0.060600	1.35	0.270
X1X2	0.032861	0.73	0.410
X1X3	0.027797	0.62	0.448
X1X4	0.005964	0.13	0.722
X1X5	0.023081	0.51	0.488
X2X3	0.000755	0.02	0.899
X2X4	0.603069	13.44	0.004 a
X2X5	0.005216	0.12	0.740
X4X3	0.051540	1.15	0.307
X4X5	0.000459	0.01	0.921
X5X3	0.058407	1.30	0.278
Lack of fit	0.050558	1.33	0.386

Adjusted R² = 0.9723; ^a 5% significance level.

shows the adequacy of the model using ANOVA; the F-value of the model was 1.78, and the linear term ethanolic fraction volume ($X_5$), the quadratic term synthesis temperature* synthesis temperature ($X_4^4$), and the interactive term synthesis pH* synthesis temperature ($X_2{X}_4$) were significant for the predicted response (maximum absorbance at 411 nm). The R² is the coefficient of determination used to measure the goodness of fit of the model [83], and the obtained adjusted R² was 0.9723 between the predicted (estimated) response values and the experimental (observed) response values for maximum absorbance at 411 nm, indicating that the model had a high correlation and a satisfactory response prediction. The adjusted R² can correct the value of R² for the size of the sample and the number of terms in the model [84].

3.7.2. Mutual Interactions between the Significant Factors

The response surface plots and their corresponding contour plots are shown in Figure 6. Each response surface plot represents the effect of two independent variables while the other variables are maintained at zero; the shape of the corresponding contour plot indicates if the interaction between the independent variables is significant [52]. As shown in Figure 6a, each response surface of Y indicates a clear valley, indicating that the optimum apex exhibited a bimodal behavior. The effect of synthesis pH (X₂) and synthesis temperature (X₄) on absorbance while keeping stirring speed (X₁), synthesis time (X₃) and ethanolic fraction volume (X₅) constant are depicted in Figure 6a. An increase in Y could be achieved when the synthesis temperature ranged between +0.2 and +0.6, and the synthesis pH ranged from −0.2 to +0.6, which indicates that Y increases as synthesis pH and synthesis temperature increased towards optical synthesis conditions. The even running distribution of the contour plot suggests that the mutual interaction between the two independent variables (X₂, X₄) was significant.

As shown in Figure 6b, each response surface of Y indicates a clear peak, which reflects the optimum point is inside the design boundary. The effect of synthesis temperature (X₄) and ethanolic fraction volume (X₅) on absorbance while keeping stirring speed (X₁), synthesis pH (X₂) and synthesis time (X₃) constant are depicted in Figure 6b. An increase in Y could be achieved when the synthesis temperature ranged between +0.6 and +1.0, and the ethanolic fraction volume ranged from +0.5 to +1.0, which indicates that Y increases as synthesis temperature and ethanolic fraction volume increased towards optimum conditions. The contour plot showed a clearly elongated running on plot, suggesting that the interaction between synthesis temperature (X₄) and ethanolic fraction volume (X₅) was not significant on Y.

Figure 6c shows that each response surface of Y indicates a clear peak, which suggests that the optimum point is inside the design boundary. The effect of synthesis temperature (X₄) and synthesis time (X₃) on absorbance while keeping stirring speed (X₁), synthesis pH (X₂) and ethanolic fraction volume (X₅) constant are depicted in Figure 6c. An increase in Y could be achieved when the synthesis temperature ranged between +0.8 and +1.0, and the synthesis time ranged from −0.7 to −1.0, which indicates that Y increases as synthesis temperature increased and synthesis time decreased to optimum conditions. The contour plot shows a clearly elongated running on plot, suggesting that the interaction between synthesis temperature (X₄) and synthesis time (X₃) was not significant on Y. The optimized conditions for the synthesis of nanoparticles were pH 9.45, temperature 49.8 °C, volume of ethanolic fraction 152.6 µL and a reaction time of 213.2 min.

3.8. Antibacterial Activity

Figure 7 shows the results of the antimicrobial activity of the biosynthesized AgNPs. The synthesized AgNPs conjugated with the ethanolic fraction showed a higher antibacterial activity against Escherichia coli ATCC 33876 with respect to the ethanolic fraction (EF) alone, with inhibition halos of 5.33 and 3.66 mm, respectively. Similarly, the synthesized AgNPs conjugated with the ethanolic fraction presented a larger inhibition halo (6.33 mm) compared to the EF alone (1 mm) against Staphylococcus aureus ATCC 25923. The antimicrobial effects determined for nanoparticles can be partially explained due to the binding capacity of nanoparticles to the bacterial cell membrane, which may lead to an increase in membrane permeability [76]. It has also been reported that nanoparticles can alter the enzymatic activity of bacteria through interaction with sulfhydryl (SH) groups of bacterial enzymes [76].

4. Conclusions

The ethanolic fraction (EF) of Lepechinia meyenii (salvia) was found to contain rosmarinic acid, diosmin and Hesperetin-7-O-rutinoside. Silver nanoparticles (AgNPs) were synthesized using the ethanolic fraction, which was optimized using Plackett-Burman design and response surface methodology (RSM). The optimized conditions for the synthesis were a synthesis pH of 9.45, synthesis temperature of 49.8 °C, volume of ethanolic fraction volume of 152.6 µL and synthesis time of 213.2 min. The optimized silver nanoparticles presented a surface plasmon resonance (SPR) with an absorption maximum between 410 and 420 nm, presenting an average hydrodynamic size of 43.71 nm by DLS and 40–60 nm by STEM. The silver nanoparticles synthesized with the ethanolic fraction presented an enhanced antibacterial activity against Escherichia coli ATCC 33876 and Staphylococcus aureus ATCC 25923 compared to the ethanolic fraction alone.