#### 2.1. Construction of QSAR Models

The experimental antioxidant potencies, expressed as IC

_{50} values for the inhibition of LPO measured via the TBARS assay in ovariectomized (OVX) rat brain homogenate against Fe

^{3+}-induced LPO [

25,

37,

38], of the selected compounds (

**1**–

**70**) are given in the Supplementary Information (Table S1, which is a spreadsheet in Microsoft Excel format also displaying the chemical structures). Specifically, IC

_{50} of a compound represents the concentration that inhibits 50% of LPO; thus, a smaller number represents a higher potency in this regard. In comparison with alternative chemometric and cheminformatics tools, the advantage of a descriptor-based approach for the development of predictive QSAR models focusing on LPO inhibitory activity has been shown recently [

39]. Therefore, we applied the latter strategy to pursue our computational study reported here. The negative logarithm of the IC

_{50} value (in molar concentration, M) was chosen as the dependent variable, and various descriptors of the test compounds available through the Project Leader module of the CAChe software were considered as independent variables for the creation of QSAR models:

The best statistical models are shown in

Equations 1–

8. We believe that the somewhat modest correlations were due to the combination of limited structural diversity in the training set and confines of the

in vitro experimental procedure relying on an actual, heterogeneous biological medium [

33] rather than a well-defined chemical model for LPO [

40]. Nevertheless, all of them satisfied the requirement for statistical significance with

p < 0.001 from analysis of variance (ANOVA). The values of phenolic O–H’s bond dissociation enthalpy (BDE, kcal/mol), a shape index (κ-type, first order, SI

_{κ1}), the solvent-accessible surface area (SA, Å

^{2}), lipophilicity (expressed as the logarithm of the

n-octanol/water partition coefficient; logP), and the eigenvalues of a frontier orbital (HOMO, eV) were the descriptors present in the QSAR models obtained, and these descriptors were also included in Table S1.

The first four equations represent models created from the use of only a single molecular descriptor.

Equation 4 provided the largest

F-value (the ratio of the model’s explained variance to its unexplained variance, considering

F of 15 as threshold value for model selection). This indicated that logP (

i.e., a descriptor related to lipophilicity) had the best predictive value among parameters found to give the best one-descriptor

Equations (1–

4; BDE, SI

_{κ1}, SA and logP), confirming thereby the previously established significance of lipophilicity regarding LPO inhibition [

40]. In addition, logP was a steady descriptor included, when equations of acceptable statistical significance were searched using two or more independent variables, while other variables in these QSAR models were either BDE (

Equation 5), HOMO (

Equation 6), SI

_{κ1} (

Equation 7), or BDE and HOMO (

Equation 8), respectively. Altogether, inclusion of descriptors other than logP in

Equations 5–

8 decreased the F-values but, with the exception of including SI

_{κ1} (

Equation 7), improved correlation (

i.e., increased the r value).

The extended spin distribution in the phenoxyl radical (ArO

^{•}) derived from the parent phenolic antioxidant (ArOH; e.g., E2) after it donates its H from the phenolic OH to a free radical to terminate the propagation of a radical reaction has been suggested to be an important contributor for the radical scavenging activity [

41,

42]. A smaller value of this parameter projects a more stable ArO

^{•} and, consequently, better antioxidant potency [

40]. Nevertheless, correlation of BDE with extended spin distribution, as well as with the enthalpy of single-electron transfer and the ionization potential (IP) were also noted [

40]. Therefore, the BDE was considered for the construction of QSAR models in this context. The BDE increases with the increasing electron withdrawal by the substituents surrounding ArOH; in other words, O–H bond is weakened by increasing the electron density and strengthened by decreasing the electron density within the bond [

43]. Accordingly, electron donating group(s) on the A-ring of an estrogen should positively impact the antioxidant potency compared to that of the unsubstituted E2 (

**1**). Concurring,

Equations 1,

5 and

8 correctly predict that the inhibition of LPO decreases with increasing BDE. This tendency is expected, because compounds that can easily donate the hydrogen of the phenolic OH to break the cascade of radical-mediated reactions are those with low BDE. This process is schematically shown in

Figure 2[

44]; where LH represents a lipid molecule, LOO

^{•} is the product of a very fast O

_{2}-addition to the chain initiator [

45] formed by the reaction LH → L

^{•} upon the attack by ROS, and LOOH is lipid hydroperoxide. The chain-breaking reaction ArOH + LOO

^{•} → ArO

^{•} + LOOH prevents LPO cycle propagated by an H-atom exchange reaction (LOO

^{•} + LH → LOOH + L

^{•}) that regenerates the chain initiator. The pathway drawn in red represent the actual chain-breaking H-atom transfer, while the blue portion of

Figure 2 implicates the conversion of the phenoxyl radical (ArO

^{•}) back to the phenolic compound (ArOH) by an endogenous reductant AH such as ascorbate, which is converted to its oxidized form A’ in the process [

44].

The HOMO energy (the energy required to remove an electron from the highest occupied molecular orbital) has also been connected to the ability of a phenolic compound to donate electrons to free radicals. According to Koopman’s theorem and the molecular orbital theory [

40], it determines the IP. Therefore, the involvement of the HOMO energy as descriptor refining two different QSAR models (

Equations 6 and

8, respectively) was not unexpected, although it did not qualify alone to be among the one-parameter equations giving statistically acceptable correlation. Nevertheless, it was noticeable that correlation increased when this descriptor was also used in the two-parameter equations in addition to logP and BDE, respectively. It is noteworthy that the best three-parameter equation also included HOMO (

Equation 8) and, provided a larger r-value than BDE and logP without this descriptor (

Equation 5). The influence of a topological index related to the shape of a molecule was also revealed. The SI

_{κ1} quantifies the number of cycles in the compound [

46,

47].

Equations 2 and

7 predict that a large SI

_{κ1} value improves the antioxidant potency of an E2-related polycyclic phenol. SA also gave a good correlation and had apparent descriptive value considering the TBARS assay as a measure of LPO inhibition by these compounds. These descriptors were calculated at an optimized geometry in water using the conductor-like screening model (COSMO) for solvation [

48].

Equation 3 suggests that a higher antioxidant activity could be obtained with molecules having a higher SA.