The Correlation Between Electronic Structure and Antimalarial Activity of Tetrahydropyridines

In this study, correlations between electronic structure and the antimalarial activities reported for a group of 21 tetrahydropyridines were evaluated by multivariate methods. Simple and multiple linear regressions, principal component analyses, and linear discriminant analyses were employed to evaluate possible correlations between quantum-mechanical descriptors and pharmacological activity. The results obtained provide useful information on the position of active sites of tetrahydropyridines and identify some specific features associated with active derivatives. Based on these findings, simple substitution rules are proposed for designing more efficient tetrahydropyridine derivatives.


Introduction
According to the World Health Organization (WHO), malaria is one of the most deadly diseases caused by parasites.This acute febrile illness is typical of tropical and subtropical regions, and is currently endemic in 99 countries.In 2012 alone, more than 207 million cases of malaria were reported around the world, of which 627,000 culminated in death. 1 Malaria is caused by four different species of protozoan parasites, of which Plasmodium falciparum is the most dangerous, being responsible for the lethal form of the disease.Unfortunately, P. falciparum is also the most resistant specie to currently employed treatments. 2 Malaria thus continues to present a worrying threat.Despite several studies regarding possible vaccine candidates, there are still no licensed vaccines, and continuous preventive treatments are the only way to reduce the frequency of infection. 1,3Furthermore, a gradual increase in resistance of some parasite strains to the currently employed drugs has been observed, which makes the search for new antimalarial compounds all the more relevant.
In this context, tetrahydropyridines (THP) derivatives have shown to be promising compounds.The latter are commonly prepared by highly efficient and economical multicomponent reactions (MCR). 4A wide range of derivatives with varied characteristics can be easily synthesized simply by adjusting the initial substrates.In particular, metal-free compounds can be obtained when organic catalysts are employed, and these are of great interest for medical applications. 4n general, THP-based compounds present several distinct biological properties, such as antiparasitic, antimicrobial, anticancer, antiviral, and so on. 4,5Recent studies performed by Misra et al. have shown that these compounds display promising antimalarial activity. 4In their

Experimental data
In this report, a set of 21 THP derivatives, whose antimalarial activities were reported by Misra et al., 4 was evaluated to investigate possible quantitative structureactivity relationships (QSAR).Figure 1 shows the basic structure common to all the compounds studied here (properly numbered for QSAR studies).The nature of the substituents R 1 , R 2 , and R 3 , as well as the biological activity (percentage of inhibition of Schizonts of P. falciparum, %ISPf; and drug concentration necessary to promote 50% inhibition of Schizonts of P. falciparum, IC 50 ), are outlined in Table 1.For simplicity, the same molecule numbers of the experimental work were adopted.
The first biological descriptor presented in Table 1 is the percentage of inhibition of Schizonts of P. falciparum (%ISPf). 4In the experimental work, this descriptor was evaluated at two stages.Initially, the activities of all the compounds (from 1 to 21) were evaluated at four distinct concentrations: 10, 5, 2.5, and 1.25 µg mL −1 .Subsequently, additional experiments employing reduced concentrations (0.78, 0.39, 0.19, 0.09, and 0.05 µg mL −1 ) were conducted for compounds that had presented 100% efficiency in the first stage (higher concentrations).
In this study, only the %ISPf values evaluated at 1.25 µg mL −1 , %ISPf 1.25 (presented in Table 1), were considered for classificatory analyses (PCA and LDA).This choice was based on the fact that, in addition to characterizing the activity of most of the compounds, the %ISPf values at this concentration better discriminate between active and potentially inactive compounds.For information about %ISPf at distinct concentrations see reference 4.
However, as can be observed in Table 1, the biological index, %ISPf, reported in the experimental work is not an absolute descriptor of the compound's activity.For instance, it is impossible to distinguish the antimalarial potency of the compounds 1, 3, 4, 8, 12, 16, 18, and 20 at 1.25 µg mL −1 , since they all produce 100% inhibition.This finding is evidenced at lower concentrations (0.05 µg mL −1 ), where the dissimilarity of the activity of these compounds is revealed. 4onsequently, preliminary fittings were performed in order to get more appropriate descriptors for predictive studies (SLR and MLR).For this purpose, we consider that the biological activity (%ISPf) dependence with drug concentration (C) may be described by a logistic equation:  , and R 3 are defined in Table 1). 4here p represents the slope of the curve at its midpoint, and IC 50 value is the targeted activity index that represents the drug concentration necessary to promote 50% inhibition of Schizonts of P. falciparum.Since this descriptor is obtained from the drug response at distinct concentrations, it better describes the real activity of the compounds.The IC 50 values derived from the fittings are presented in the last column of Table 1 (for details about the fittings see Supplementary Information).
By analyzing the values of IC 50 , one can see that, although the %ISPf 1.25 indexes are not good quantitative descriptors of the THP's biological activity, they are indeed good indexes for classifying the compounds into active and non-active subsets, justifying their use in the classificatory studies.

Geometry optimization
The geometry optimizations were performed by considering ten distinct initial structures for each molecule.Molecular dynamics (MD) calculations were performed at relatively high temperature with a view to obtaining weakly correlated structures.The MD simulations were performed with the aid of the Gabedit computational package 11 by considering the molecules in contact with a reservoir at 1000 K, during 1 ps (steps with 0.01 ps). 12n order to avoid possible convergence problems, all the resulting structures were subsequently pre-optimized using a PM6 (Parametric Method 6) semi-empirical quantummechanical method in a Restricted Hartree-Fock (RHF) approach. 13These pre-optimizations were performed until relatively low gradients were obtained (0.01), such that the resulting structures were as close as possible to the equilibrium conformation of the compounds.The MOPAC2012 computational package was employed. 14,15fter pre-optimizations, a comparative analysis of the total energy values, E T , (derived from PM6 calculations) associated with each compound's conformer was conducted to identify the most stable structure (E T = E T(min) ) and other structures with sufficiently low E T values (specifically E T < E T(min) + k B T 300 ).All the selected structures were then compared by evaluating the root mean square deviation of atomic positions (RMSD-AP) of each conformer In the present work, RMSD-AP = 2 Å was a cutoff parameter for defining molecular similarity.This criterion is commonly adopted in studies of docking with small ligand molecules, where simulated and experimental conformations are compared. 16In our case, conformers with RMSD-AP < 2 Å were considered as equivalent structures, and the lowest energy conformation alone was evaluated in the next steps.The Qmol computational package was employed in all RMSD-AP analyses, 17 and the positions of heavy atoms only (not hydrogen) were considered.
As the last step of the geometry study, all the (pre-optimized) relevant structures, obtained from RMSD-AP analyses, were fully optimized in a DFT approach.The optimization was performed in vacuo, employing a Becke's LYP (B3LYP) exchange-correlation (XC) functional, 18,19 and 6-31G basis set.All the calculations in this step were carried out with the GAMESS computational package. 20

Single point calculations
Single point (SP) calculations were performed for each of the 21 selected and optimized structures (as well as possible additional low energy conformers), with the aim of extracting electronic information on the compounds.
A collection of 195 indexes, mainly related to the energy, bond orders, electric charge, electric dipole, and frontier molecular orbitals, was obtained and organized in a single data file for subsequent statistical analyses.Table 2 presents a brief description of each electronic index.
For the cases where two or more structures were obtained from the RMSD-AP study, each electronic descriptor, A, was estimated by the expected value, 〈A〉, given by: where n represents the total number of dissimilar structures of a given compound; ΔE T i represents the total energy difference between the i-th structure and the most stable structure (E T = E T(min) ); k B represents the Boltzmann constant; and T is the temperature (considered equal to 300 K).
All the SP calculations were performed through a DFT approach, employing three distinct XC functionals: B3LYP, X3LYP, 21 and PBE0; 22 6-31G(1p,1d) basis set was adopted in all the cases.All these functionals are hybrid ones, with slight differences between them: (i) X3LYP is a B3LYPlike functional, adjusted to better describe unbounded interactions, and (ii) PBE0 presents a distinct XC functional in relation to the B3LYP.The results presented here relate mainly to the DFT/B3LYP/6-31G(1p,1d) approach.X3LYP and PBE0 functionals were considered so as to check the robustness of the B3LYP findings.

Correlation studies
Distinct multivariate methods were employed to evaluate correlations between the electronic structure and the biological activity of the THP derivatives.
Simple and multiple linear regressions were first performed with the aim of obtaining predictive equations capable of estimating the biological activity based on linear combinations of a few electronic descriptors.To avoid overfitting effects, a maximum of three independent variables (electronic descriptors) was employed in MLR analyses. 23In this sense, all the combinations with up to three variables of the whole set of descriptors (195 electronic indexes) were considered.The quality of the regressions were evaluated by analyzing the correlation parameter between the predicted and the experimental values of the dependent variable for each regression.Since %ISPf parameters are not good quantitative descriptors of a compound's activity, IC 50 values were considered as the dependent variable in linear regressions.Subsequently, PCA and LDA were employed for pattern recognition and compound classification, respectively.For this purpose, %ISPf 1.25 indexes were employed to define active and non-active compounds.
In PCA, a new orthogonal coordinate system is generated by linear combinations of the original electronic descriptors (independent variables), which are a convenient means of analyzing similarity between compounds. 24,25The resulting principal axes, called principal components (PCs), are ordered according to the maximum variance of the data set: PC 1 presents more statistical information than PC 2 ; PC 2 presents more statistical information than PC 3 ; and so on.
Finally, in LDA, a discriminant function (DF) is obtained through a linear combination of electronic descriptors. 26DF is constructed in such a way that it is able to promote the highest distinction between active and nonactive subgroups of compounds.By defining a delimiting parameter (the DF cutoff), the molecules can be classified as active or not, according to their DF score.A "stepwise" procedure, based on Mahalanobis distance criterion (validated by F statistic), was adopted so as to minimize the number of descriptors necessary for DF construction. 26,27DA calculations were performed employing the commercial software SPSS. 27SLR, MLR, and PCA studies were performed using our homemade statistical package.

Results and Discussion
In this section, only the results relating to electronic descriptors derived from the DFT/B3LYP/6-31G(1p,1d) approach are presented.The same trends and conclusions were obtained for PBE0 and X3LYP functionals.
Following the similarity criteria outlined for RMSD-AP analysis, only one conformer was obtained for each derivative (for details see Supplementary Information).

Simple and multiple linear regressions
Linear regressions were performed employing all the combinations of up to three independent variables (SLR: 195, MLR 2 : 18,915, and MLR 3 : 1,216,865 combinations).As the dependent variable, we considered distinct functional forms of IC 50 : IC 50 , log(IC 50 ), and (1/IC 50 ).Equation 3 illustrates the more representative regression equation (with correlation parameter of R corr = 0.91) obtained by considering 1/IC 50 as the dependent variable.Figure 2 shows a comparison between experimental data and values predicted by equation 3.
The descriptors involved are the bond order of atoms 28 and 29, and the net charge on atoms 15 and 29 of the basic structure of the THP molecule.A quite similar regression equation was also obtained for the descriptors BO 28-29 , CHAR MP 29 , and CHAR MP 32 ; however, since atoms 15 and 32 are located at equivalent positions of rings B and B', it contains the same physical information as equation 3 (see Supplementary Information for details).
The BO descriptor illustrates the strength of the chemical bond between two atoms.In general, high bond orders indicate an excess of electrons in the region between the atoms, and thus a strong chemical bond; low values of BO indicate a lack of electrons in the bond region, indicating a weak linkage of the two atoms.The CHAR descriptor is defined as the difference between the number of electrons on an isolated atom and the calculated fraction of the molecular electronic population located on it.Negative net charges are associated with an excess of electrons and positive charges with a lack of electrons.
The presence of the descriptors CHAR MP 15 and CHAR MP 32 in the most representative linear equations suggests that rings B and B' can play an important role in the inhibitory mechanism of the drugs.The electronic The Correlation Between Electronic Structure and Antimalarial Activity of Tetrahydropyridines J. Braz.Chem.Soc.260 indexes CHAR MP 29 and BO 28-29 , in turn, are associated with the ring A', which marks another active site of the molecule.
In general, the regression equation obtained indicates that active derivatives must present the following features: (i) Strong chemical bond between atoms 28 and 29 and (ii) Excess of electrons (or low positive charge) on atoms 29 and 15 (or 32).
These trends can be adjusted by choosing appropriate R 1 and R 2 substituents.For instance, an electron donating group attached to position 16 (or 33) of the ring B (or B') could induce a high electronic population at carbon 15 (or 32).On the other hand, the addition of electron withdrawing groups on position 27 of the ring A could promote an excess of negative charge on atom 29.However, the substituent in this case should not be a strong electron withdrawing specie, for fear of weakening the chemical bond between atoms 28 and 29.
Despite the useful information provided by equation 3, it is important to note that 1/IC 50 values do not promote a good dispersion of the experimental data.As can be seen in Figure 2, there is some data agglomeration at low values of 1/IC 50 .This feature, in addition to the absence of significant regressions for IC 50 and log (IC 50 ) functional forms, suggests that classificatory and/or pattern recognition methods could be appropriated.Such analyses are performed in the following sections.

Principal component analysis
PCA studies were performed considering the entire data set (21 cases × 195 descriptors), with a view to better evaluating similarities between the electronic structures of the compounds.Figure 3 shows a plot of the first and second components (PC 1 and PC 2 ) derived from this PCA study (full PCA).
Compounds 15 and 16 present a quite different electronic structure from the others.These compounds are the only ones that present thiophene-2-carboxaldehyde as rings B and B', being very distinct from the other derivatives.Figure 4 shows a plot of the first and second components (PC 1 and PC 2 ) of a full PCA performed after removing compounds 15 and 16 from the data set.
Note that two distinct groups can be observed.However, there appears to be no direct relationship between the observed clusters and the biological activity of the compounds.Indeed, these groups are mainly associated with R 1 substituents.In general, compounds with PC 1 scores lower than −2.5 present R 1 = 4-methoxy, while higher values are observed for the other structures (a same trend was observed even for compounds 15 and 16, see Figure 3).This result suggests that changes in the rings A and A' can induce significant alterations in the electronic structure of the compounds; however, it has no direct influence on their biological activity.Indeed, this information is complementary to MLR results.Despite the presence of BO 28-29 and CHAR MP 29 descriptors in the equation 3, which are indexes relating to ring A', it is necessary the presence of one electronic descriptor associated with ring B (or B') to obtain significant correlations (CHAR MP 15 or CHAR MP 32 ).This result suggests that the rings B and B' play an important role in the antimalarial activity of THPs.

Linear discriminant analysis
LDA was performed with the aim of identifying which electronic descriptors better discriminate between active and non-active compounds.The %ISPf observed at 1.25 µg mL −1 (%ISPf 1. 25 ) was employed to identify    (4)   The descriptors involved are the total energy (E T ) and Löwdin's net charge on atom 17 (CHAR LP 17 ) (similar results were also obtained from considering atoms 15, 32, and 34, which are not shown for simplicity).E T represents the total energy of the compound and can be correlated with the stability of the molecule.The CHAR descriptor has the same definition as presented before.Table 3 summarizes some statistical information about the values obtained for these descriptors for each subset of molecules (active, non active and the whole set).
In general, higher total energy and a more negative charge on site 17 (by Löwdin's partition) are observed in active molecules.Non-active compounds are also observed to present larger dispersion of the descriptors, mainly regarding E T values, which indicates that the non-active subgroup is much more heterogeneous than the active one.
The DF obtained (equation 4) shows a statistical significance higher than 99.84% (Wilk's Lambda = 0.489, χ 2 = 12.867 with 2 degrees of freedom, and p < 0.0016) and correctly classifies 95.2% of the molecules.The same hit percentage was obtained by leave-one-out cross validation (in which each molecule is tested with a model derived from all the other molecules).
Figure 5 shows the DF scores plot.The centroids for active and non-active molecules are respectively 0.927 and −1.019.The obtained cutoff is −0.046, such that: (i) if DF > -0.046, the compound is predicted to be active and (ii) if DF < -0.046 the compound is predicted to be non-active.
Note that just one of the non-active THP derivatives (compound 11) is misclassified by this rule.
According to the trends presented in Table 3, the DF obtained indicates that two essential features must be observed in active compounds: (i) high total energy and (ii) high negative (or low positive) net charge on site 17 (similar results were obtained by considering sites 15, 32, and 34, not shown).
The energy component suggests that active compounds are supposed to be more (thermodynamically) unstable molecules.In our systems such high values of E T can be also related to compounds with a reduced electronic structure, i.e., molecules a lower number of electrons in their structure (see Figure S9 in Supplementary Information).Since the number of electrons are frequently associated with the molecule volume, this result can suggest that derivatives with reduced volume (smaller ligands) tend to present higher antimalarial activity.
Such consideration, indicates the possibility that not just topological, but also lipophilic properties could be associated with THP's activity.As a matter of fact, lipophilic parameters (such as octanol-water partition coefficient, log P) usually provide valuable information about the interaction of the molecules with cell membranes,  being a very important descriptor in QSAR studies. 28Since such parameters often present some dependence with molecular volume of the compounds (in general larger molecules present higher hydrophobicity [29][30][31] ), the presence of E T descriptor in DF equation, can suggest the relevance of hydrophobicity in the biological activity of the compounds.Indeed, in our case it is possible to observe a linear dependence between the hydrophobic parameter, log P, and IC 50 values of THP's (see Figure S10 in Supplementary Information), what reinforces that E T parameter carries more information about molecule size than stability.Nevertheless, since the evaluation of lipophilic/topological parameters is not in the scope of the present work, more profound studies are still necessary in this subject.
Despite of the apparent relevance of the hydrophobicity discussed above, the presence of the descriptor CHAR in equation 4 indicates that electrostatic interactions can play an important role in the compounds' activity, suggesting that site 17 can be linked to inhibitory mechanisms of THP derivatives.In fact, very accurate DFs can be also obtained from considering sites 15, 32, or 34, which represent equivalent positions in relation to site 17 in the THP basic structure.Figure 6 illustrates these molecular sites.It is important to note that sites 15 and 32 were also identified as relevant sites by MLR studies, suggesting that the biological activity of the compounds is mainly associated with R 2 substituents.In particular, all the relevant sites are related to meta positions (in relation to the main structure), and are prone to be tuned by the appropriate choice of R 2 .
As can be seen in Figure 5, only one of the compounds is misclassified by the LDA model.Compound 11 is defined as a non-active derivative in the experimental work, 4 although it is classified as an active molecule by its DF score.The optimized structure of this compound is presented in Figure 7.Note that this derivative has a large group attached to the rings B and B', which is composed of a single bounded ring.At room temperature, these structures can rotate very easily around the bond axis, hindering, for example, the possible coupling of this compound to some biological target.In this sense, although this molecule presents a CHAR LP 17 value typical of an active compound, the steric hindrance disturbs specific couplings that can be relevant to the antimalarial activity of these molecules, turning it into a non-active compound.
In this context, the misclassification of compound 11 reinforces our hypothesis that the rings B and B' have an important role in compound activity, demonstrating that the active sites of THP derivatives can in fact be located on it.It is also consistent with the relevance of hydrophobicity in the activity of the compounds, since the lateral groups of this molecule make it a very hydrophobic molecule.These considerations confirm that the antimalarial properties of the compounds can be truly enhanced by an appropriate choice of R 2 substituents, indicating, however, that large attached groups must be avoided in these rings, as already stated from the evaluation of E T parameter.
In addition to the substitutions proposed in the SLR and MLR section, the presence of halogens, hydroxylated, or alkoxylated groups attached to sites 15, 17, 32, and 34 could also lead to a high negative net charge on these positions.3][34][35] Nevertheless, as observed for compound 11, we need to consider that the presence of such groups on R 2 position could impede the action of the molecule, deactivating it.Thus, we believe that small electron donating groups attached on position 16 (or 33) of the rings B and B' and weak electron withdrawing groups attached on position 27 of the rings A and A' could be an interesting alternative means of obtaining THP derivatives with improved biological activity.
In order to test these hypotheses, additional calculations were performed for new derivatives.Two types of substitutions were tested: (i) R 2 = H and R 1 = NO 2 , F, CF 3 and CH 3 C=O (small electron withdrawing groups) and (ii) R 1 = H and R 2 = NH 2 , F, CH 3 and CCH (small electron donating groups); all the substitutions were performed on para positions.Fluorine were inserted in R 1 and R 2 because this element can promote both the effects: electron withdrawing by induction and electron releasing by resonance. 36The effect of each substitution was evaluated by comparing the changes induced on E T , CHAR LP 17 , BO 28-29 , CHAR MP 15 and CHAR MP 29 descriptors, in relation to those observed in compound 12 (R 1 = R 2 = H).Table 4 presents the percentage change for each index: (+) means an increase in the parameter while (−) represents a reduction of the value.All the substitutions result in lower E T values than those obtained for compound 12, which is an undesired effect for obtaining active derivatives.This result is associated with the increase of the number of electrons in the resulting structures.In particular smaller changes are observed for 1a and 3a.
Substitutions performed at the rings A and A' (type a) promote a desired increase in the electron density on atom 29 (more negative charge), except for 2a; however, undesired small effects are concomitantly induced on CHAR MP 15 , CHAR LP 17 and BO 28-29 descriptors.For substitutions promoted in R 2 , we can observe that 1b, 2b and 3b promote a desired increase in the electron density on atoms 15 and 17 (more negative charges) as expected.However, small undesired changes on BO 28-29 and CHAR MP 29 parameters are also observed for all the cases, including 4a.These results evidence the relevance of substitutions on both the rings, A (A') and B (B').
Balancing both, favorable and unfavorable changes in the parameters presented in Table 4 (accordingly to LDA and MLR results), it is possible to suggest some promising substitutions to achieve active compounds.For instance, R 1 = (NO 2 ) / R 2 = (NH 2 ) (1a-1b) and R 1 = (CH 3 C=O) / R 2 = (NH 2 ) (4a-1b) may be cited as the two most promising compounds in the evaluated set.Individually these groups have shown the desired effect on the rings were they were attached, with small negative interference on others relevant parameters.
Complementary calculations, employing the same optimization and single point methodology described before, indicate that the compounds obtained from 1a-1b and 4a-1b substitutions are indeed active derivatives.DF scores of 1.558 and 1.581 and IC 50 values of 0.052 and 0.078 were respectively obtained for 1a-1b and 4a-1b substitutions, pointing out these compounds as active ones (DF > −0.046), with very low values of IC 50 ; and then good alternatives for further in vitro / in vivo tests.

Conclusions
The correlation between the electronic structure and antimalarial activity of a set of 21 tetrahydropyridines derivatives was evaluated by distinct multivariate methods.
Predictive equations obtained by multiple linear regressions indicate positions 15, 32, and 29 as important sites for drug activity.The results demonstrate that active derivatives must present a strong chemical bond between atoms 28 and 29 and a high net negative charge (or low positive charge) on atoms 29 and 15 (or 32).
PCA results show that much of the electronic structure of THP derivatives is defined by R 1 substituents.However, it was also observed that they are not directly associated with the biological response of the compounds.By LDA, it was possible to define a discrimination function with high statistical significance.The obtained function combines just two electronic indexes and is able to correctly predict around 95% of the compounds, suggesting that active derivatives present high total energy and a high negative (or low positive) net charge on meta positions of rings B and B' (atoms 15, 17, 32. and 34 of the main structure), which is compatible with MLR results.The results also suggest that large substituents must be avoided, since steric interactions could disturb the effective interaction between active sites of the molecules and their biological environment.The relevance of lipophilicity was also observed, but more studies are still necessary on this subject.
Based on these findings, we recommend the addition of small electron donating groups on position 16 (or 33) and electron withdrawing groups on position 27, as alternative means of obtaining THP derivatives with enhanced antimalarial activity.

Figure 1 .
Figure 1.Basic structure of THP derivatives and numeration employed in QSAR studies (R 1 , R 2 , and R 3 are defined in Table1).4

Figure 3 .
Figure 3. PC 1 versus PC 2 from a PCA study involving the whole data set.

1 Figure 4 .
Figure 4. PC 1 versus PC 2 from full PCA performed excluding molecules 15 and 16 from the data set.

Figure 5 .
Figure 5. Discriminant function scores of active and non-active compounds.Dotted line indicates the cutoff value (-0.046).

Figure 6 .
Figure 6.Relevant sites for the discrimination of biological activity in THP derivatives.

Table 1 .
4escription of the THP derivatives and biological activity descriptors: percentage of inhibition of Schizonts of P. falciparum at 1.25 µg mL −1 (%ISPf 1.25 ),4and IC 50 values obtained by logistic fits (see Supplementary Information)

Table 2 .
Electronic descriptors employed in this work i Electric charge associated to the i-th atom of the compound structure (Mulliken partition) two groups of compounds: (i) active compounds with %ISPf 1.25 ≥ 86 and (ii) non-active compounds with %ISPf 1.25 < 86.Equation 4 presents the best DF obtained, which promotes the most significant separation between these two groups.

Table 3 .
Statistical information regarding the relevant descriptors identified by LDA

Table 4 .
Changes induced by substitutions on rings A, A', B and B' in relation to compound 12