The statistic results for both CoMFA and CoMSIA models are shown in Table 1. The internal validation of leave-one-out cross-validated q² and non-cross validated coefficient r² are commonly applied as a criterion of robustness and predictive ability of a QSAR model. The commonly accepted values for a satisfactory QSAR model are q² > 0.5 and r² > 0.8 [12]. A highly predictive CoMFA model with LOO cross-validated q² of 0.638 and correlation values r² of 0.984 were obtained. The steric contribution and electrostatic contribution were 50.5% and 49.5% for the QSAR model. The standard error of estimate and F-test value were 0.236 and 139.126, respectively. The yielded r²_bs value 0.993 for CoMFA (SDbs = 0.007) further supported the statistical validity of the developed models.

The statistical results of the best CoMSIA model are also listed in Table 1. The good cross-validated q² of 0.855 (>0.5) and the non-cross-validated coefficient r² of 0.986 (>0.8) were obtained based on the steric, electrostatic, H-bond donor/acceptor, and hydrophobic fields that explained 5.8, 32.6, 14.0, 30.4 and 17.1% of the variance from the QSAR model, respectively. The non-cross-validated coefficient s and F value are 0.216 and 208.320, respectively. The cross-validation results suggested that CoMSIA model had a better predictive ability than the CoMFA model in this study. The yielded r²_bs value 0.997 for CoMSIA (SDbs = 0.003) further supports the statistical validity of the developed CoMSIA models. The predictive ability of the models was validated with the correlation coefficient r²_pred = 0.971/0.996 (>0.6) for each models, indicating that both CoMFA and CoMSIA models should have high predictive abilities for DPPH• scavenging activity of phenolic acids. The experimental and predicted activities in the training and test sets are shown in Table 2.

Although the internal validation with a high value of LOO cross-validated q² obtained for both CoMFA and CoMSIA models was necessary and important, it was not sufficient for a QSAR model with a high predictive power [13]. Therefore, the predicting activity of an external test set with seven compounds was performed using all the CoMFA and CoMSIA models. The squared correlation coefficient values between the observed and predicted values of the test set compounds with intercept (r²) and without intercept (r₀²) were calculated. The validation criteria proposed by Golbraikh and Tropsha applied to the regression analysis must satisfy the following conditions [12,13]: (1) q² > 0.5; (2) r²_pred > 0.6; (3) [(r²_pred-r₀²)/r²] < 0.1; (4) 0.85 ≤ k ≤ 1.15, where q² is the cross-validated correlation coefficient after the leave-one-out procedure; r²_pred is correlation coefficient for test set predictions; r₀² is the correlation coefficient for the regression through origin for experimental versus predicted activities. k is the slope of regression lines through the origin.The statistical results of the test set are given in Table 1. The values of the cross-validated q² and correlation coefficient r²_pred for test set predictions, [(r²_pred−r₀²)/r²], and k of CoMFA and CoMSIA models satisfy the criteria.

CoMFA and CoMSIA contour maps analyses were performed to visualize the important regions in 3D molecules where the steric, electrostatic, hydrogen-bond donor/acceptor, and hydrophobic fields may affect the DPPH• scavenging activity of the studied compounds. The weight of StDev*Coeff was used to calculate the field energies for all fields in CoMFA and CoMSIA models. The highly active compound 11 was shown as the template ligand for all contour map positions.

The crucial structural components for the free radical scavenging activity concluded from our CoMFA and CoMSIA analyses were validated using phenolic acids from eight previous publications listed in Table 3according to the radical scavenging activity ranked from the highest to the lowest. The structure/activity relationship of phenolic acids from previous publications could be explained by structural criteria obtained from the present study.

The para-OH substituent important for the high free radical scavenging activity of phenolic acids was validated with previous research data (Table 3) [4,10,18]. The electron-donating and/or hydrophobic groups (e.g., OH and OCH₃) in the meta-position-promoted activities of phenolic acids in the publications [4,10,14,19,20,21,22], satisfy the second criterion. For example, Abramovic et al. investigated the DPPH• radical scavenging activity of hydroxycinnamic acids that have in common a para-OH structur, but differ in their meta-substituents (i.e., OH or OCH₃) on the ring [19].

The hydroxyl group has electron-donating and hydrogen-bond donor properties, satisfying the second and third criteria, whereas the OCH₃ group is hydrophobic, satisfying the secondary criterion. Therefore, the radical scavenging activity of phenolic acids was following such an order: caffeic acid (R₃: OH) > sinapic acid (R₃ and R₅: OCH₃) > ferulic acid (R₃: OCH₃) > umbellic acid (R₂: OH) > p-coumaric acid (R₃, R₅, and R₂: H). The presence of an ortho-OH on the ring acted as a hydrogen-bond donor group or electron-donating group enhancing the activities of phenolic acids in the publications [4,10,18,19,21], satisfying the third criterion. For example, umbellic acid (ortho-OH) showed greater activity than p-coumaric acid (ortho-H) [19], or 2,4-dihydroxybenzoic acid (ortho-OH) had a greater activity than p-hydroxybenzoic acid [4].

The DPPH• scavenging activity of phenolic acids in agreement with the steric property at the X-position was validated with previous research data too [18,20]. For example, 3,4-dihydroxy-phenylacetic acid with a bulky side chain (X: CH₂COOH), showed greater activity than protocatechuic acid with a smaller side chain (X: COOH) [18]. Dihydroferulic (X: CH₂CH₂COOH) and ferulic acids (X: CH=CHCOOH) showed greater activities than vanillic acid (X: COOH) [20]. The phenolic acid with CH₂CH₂COOH at X-position had a greater activity than the one with CH=CHCOOH. This may be explained with the high capacity to donate protons for the “side-chain-saturated” phenolic acid [20].

Common food phenolic acids were randomly selected for the study. The 3D-QSAR models were established from the training data set of 17 phenolic acids. The experimental biological activity values were measures of the Trolox equivalent antioxidant capacity (TEAC) for DPPH• scavenging. For QSAR modeling, the DPPH• scavenging activity was converted into logarithmic activities. The techniques used to generate the QSAR models were comparative field analysis (CoMFA, SYBYL-X 1.2) and comparative molecular similarity index analysis (CoMSIA, SYBYL-X 1.2). Another seven phenolic acids were randomly chosen as the testing set to check the predictive powder of QSAR models. The critical structural characteristics of phenolic acids associated with free radical scavenging activities were analyzed. Literature data were also applied to verify the reliability of the structure-activity relationships. All chemicals, including phenolic acid standards, were purchased from Sigma-Aldrich (Shanghai, China).

The determination of DPPH• scavenging activities of the studied compounds were performed according to the previously reported procedure using a Synergy 2 Multi-Mode Microplate Reader (BioTek, Winooski, VT, USA) [23]. Briefly, each reaction mixture contained 100 μL of sample solutions and 100 μL of 0.2 mmol/L DPPH• solution. The TEAC is defined as the concentration of Trolox (6-hydroxy-2,5,7,8-tetramethylchroman-2-carboxylic acid) solution with equivalent antioxidant potential of a 1 mmol/L concentration of the compound. The DPPH• solution was added into each well to initiate the reactions, absorption at 515 nm was determined every minute for 40 min. The blank contained only 200 μL of solvent, and the control consisted of 100 μL of solvent and 100 μL of 0.2 mmol/L DPPH•. Triplicate tests were conducted. The DPPH• scavenging activity was expressed as pTEAC = −logTEAC.

The DPPH• radical scavenging assay was applied for studies of effect of structural properties of phenolic acids on free radical scavenging activity. A total of 17 phenolic acids (training set) were used to establish QSAR modeling (Table 2). Another seven compounds (test set) were applied to validate the final model.

Molecular structure building was accomplished using the molecular modeling program from the SYBYL-X 1.2 software (Tripos, St. Louis MO, USA) on a Windows operation system. The energy minimizations of each structure were conducted with the Powell method using the Tripos force field [24], where a convergence criterion of 0.005 kcal/(mol Ǻ) was used as the termination of the Powell conjugate gradient algorithm and the maximum iterations were set to 1,000 steps. The partial atomic charges were calculated using the Gasteiger-Hückel method. Other parameters were default. Molecular superimposition of phenolic acids in the training set (Table 2) on the template structure was performed by database alignment method in SYBYL. The most active compound 11 was chosen as a template for superimposition and the common structure was the phenol, assuming that its conformation represented the most bioactive conformation of the phenolic acids. The 3D-view of 17 aligned molecules (training set) are shown in Figure 3.

Comparative molecular field analysis (CoMFA) and comparative molecular similarity index analysis (CoMSIA) are the 3D-QSAR methods that use statistical correlation techniques to analyze the quantitative relationship between the biological activity for a set of compounds with a special alignment, and their three-dimensional electronic, steric properties, plus hydrogen bond donor/acceptor and hydrophobic properties specifically for CoMSIA. In this study CoMFA [25] was started with the QSAR option of SYBYL-X 1.2 in the Tripos force field. A 3D cubic lattice with a grid spacing of 2 Å in x, y, and z directions was created to encompass the aligned molecules in order to obtain the CoMFA and CoMSIA descriptor fields. The energies of steric (Lennard-Jones potential) and electronic (Coloumb potential) fields were calculated using a sp³ carbon atom as the steric probe atom and a + 1 charge for the electrostatic probe. The cutoff value for both steric and electrostatic interactions was set at 30.0 kcal/mol. In CoMSIA analysis [26], steric, electrostatic, hydrophobic, hydrogen bond donor and hydrogen bond acceptor properties were evaluated. Gaussian-type distance dependence was used to calculate the similarity indices. The default attenuation factor (α = 0.3) was used. There were no cutoff limits in CoMSIA analysis.

The method of partial least square (PLS) implemented in the QSAR module of SYBYL was used to construct and validate the models. The CoMFA and CoMSIA descriptors were used as independent variables, and the biological activities in pTEAC values were used as dependent variables in PLS regression analysis to derive 3D-QSAR models using the standard implementation in the SYBYL-X 1.2 package [27]. The Leave-One-Out (LOO) was performed to obtain the optimum number of components, which consequently was used to develop the final non-cross-validated model determined by the cross-validation coefficient q², the non-cross-validated coefficient r² and its standard error s and F-test values for the model evaluation. To further assess the robustness and statistical confidence of the derived QSAR models, bootstrap analysis for 10 runs was performed. CoMFA and CoMSIA contour maps that intuitively reflect and analyze the different field effects on the activity [28] were obtained by interpolation of the pair-wise products between the PLS coefficients and the standard deviations of the corresponding CoMFA or CoMSIA descriptor values.