QSAR modeling of antiradical and antioxidant activities of flavonoids using electrotopological state...

DOI: 10.2478/s11532-007-0047-3Research article

CEJC 5(4) 2007 1094–1113

QSAR modeling of antiradical and antioxidantactivities of flavonoids using electrotopological state

(E-State) atom parameters

Supratim Ray, Chandana Sengupta and Kunal Roy∗

Drug Theoretics & Cheminformatics Lab,Division of Medicinal & Pharmaceutical Chemistry,

Department of Pharmaceutical Technology,Jadavpur University, Kolkata 700 032, India

Received 10 July 2007; accepted 13 August 2007

Abstract: In the present paper QSAR modeling using electrotopological state atom (E-state)parameters has been attempted to determine the antiradical and the antioxidant activities of flavonoidsin two model systems reported by Burda et al. (2001). The antiradical property of a methanolic solutionof 1, 1-diphenyl-2-picrylhydrazyl (DPPH) and the antioxidant activity of flavonoids in a β-carotene-linoleic acid were the two model systems studied. Different statistical tools used in this communicationare stepwise regression analysis, multiple linear regressions with factor analysis as the preprocessingstep for variable selection (FA-MLR) and partial least squares analysis (PLS). In both the activities thebest equation is obtained from stepwise regression analysis, considering, both equation statistics andpredictive ability (antiradical activity: R2 = 0.927, Q2 = 0.871 and antioxidant activity: R2 = 0.901,Q2 = 0.841).c© Versita Warsaw and Springer-Verlag Berlin Heidelberg. All rights reserved.

Keywords: Flavonoids, antioxidant, QSAR

1 Introduction

Flavonoids are a group of naturally occurring polyphenolic compounds ubiquitously found

in fruits and vegetables [1–3]. Common family members of flavonoids include flavones,

flavonols, flavanones, isoflavones, biflavanones, catechins and anthocyanidins. Flavonoids

are a chemical class of benzo-γ-pyrone derivatives. The structural differences in each

flavonoid family result from the variation in the number and substitution patterns of

∗ E-mail: kunalroy [email protected]

S. Ray et al. / Central European Journal of Chemistry 5(4) 2007 1094–1113 1095

the hydroxyl groups and the extent of glycosylation of these groups [4]. Structural di-

versity of flavonoids allows them to exhibit antineoplastic, antihepatitis, antibacterial,

anti-inflammatory, antimutagenic, antiallergic, antithrombic, antiviral and vasodilatory

activities [5–7]. The potent antioxidant activity of flavonoids, their ability to scavenge hy-

droxyl radicals, superoxide anions and lipid peroxy radicals could be their most important

functions that underlie many of the above processes in the body [8].

Oxidative damage is implicated in many disease conditions as is shown in epidemiolog-

ical, clinical and laboratory research on flavonoids and other antioxidants. Quercetin, one

of the potent antioxidant biflavonoid compounds, has been shown to alleviate oxidative

injury by modulation of gene expression leading to suppression of production of reactive

oxygen and nitrogen species conferring an antiapoptotic activity [9]. It has been reported

recently that fisetin, chrysin, morin, 3-hydroxyflavone have antioxidant and antihemolytic

effects [10]. Galangin, its derivatives viz. quercetin, morin, myricetin, oligomeric proan-

thocyanidins and flavanones have been shown to inhibit the oxidation of lipids hence can

be utilized in prevention and treatment protocols for inflammatory conditions like cancer,

asthma, liver disease, cardiovascular disease and muscular degeneration [11, 12]. Intake

of antioxidant compounds present in food is an important factor in protecting health.

Flavonoids, which occur both in edible plants and in foodstuffs derived from plants as

in fruits, vegetables, red wine and tea, form substantial constituents of the human diet.

Therefore, flavonoids given as additives in foodstuffs have the potential to be applied to

the prevention and treatment of human diseases [13].

Flavonoids and its derivatives account for more than 4000 in number, further, the

antioxidant properties of each are very different. It is a complex task to select the

most effective of antioxidants from this large pool of flavonoids [14]. These character-

istics make flavonoids popular subjects for Quantitative structure-activity relationship

(QSAR) studies. Khlebnikov et al. [15] reported a QSAR model to predict antioxidant

activity of flavonoids in chemical, enzymatic and cellular systems using physicochemical

and structural descriptors. A QSAR study was performed on flavonoids derivatives as

p561ck tyrosinekinase inhibitor using hydration energy and logP as a predictor parame-

ter [16]. Badhan et al. [17] computed in silico modeling of the interaction of flavonoids

with human-p-glycoprotein nucleotide-binding domain. Karawajczyk et al. [18] reported

a QSAR model by neural network modeling to investigate the properties of flavonoids

influencing the binding to bilitransloase. A density functional study of flavonoids com-

pounds with anti-HIV activity was done using the multiple linear regression method [19].

QSAR for flavonoids-mediated inhibition of breast cancer resistance protein was done us-

ing three structural descriptors [20]. A study involving multiple linear regression (MLR)

and partial least squares (PLS) regression applied on flavonoid compounds with anti-HIV

activity have been reported [21]. Structure-radical scavenging activity relationships of

flavonoids were performed using simple indicator variables by MLR method [22]. Farkas

et al. [14] reported quantitative structure-antioxidant activity relationships of flavonoids

using constitutional, topological and connectivity indices by PLS method. In the present

paper, we have modeled the antiradical and antioxidant activities of flavonoids data set

1096 S. Ray et al. / Central European Journal of Chemistry 5(4) 2007 1094–1113

reported by Burda et al. [23] using electrotopological state atom (E-state) parameters by

stepwise regression, factor analysis followed by multiple linear regression (FA-MLR) and

PLS.

2 Computational

2.1 Electrotopological state atom (E-state) index

Structural specificity of a drug molecule is exhibited at an atomic or fragmental level

rather than at the molecular level. In the drug-receptor interaction phenomenon, a por-

tion of the molecule (pharmacophore) may play a more important role than the other

segments. Though basic information for constitution of topological indices are derived

from the atomic level such as the count of atoms, bonds, paths of bonds, etc., most of

the indices are applied to the entire molecule after summation of all components over the

whole molecule. Thus QSAR studies at the atomic or fragmental level are justified in the

present context [24].

The electrotopological state (E-state) atom index developed by Hall and Kier [25] is an

atom level descriptor encoding both the electronic character and topological environment

of each skeletal atom in a molecule. The E-state of a skeletal atom is formulated as an

intrinsic value Ii plus a perturbation term ΔIi, arising from the electronic interaction

within the molecular topological environment of each atom in the molecule.

The intrinsic value has been defined as the ratio of a measure of electronic state (Kier-

Hall valence state electronegativity) to the local connectivity. The number of the most

reactive valence electrons that are involved in chemical reactions and bond formations are

considered in the expression of I to encode the electronic feature. To reflect differences

in electronegativity among the atoms, principal quantum number is employed in the

expression of I. The topological attribute is accounted for by using adjacency count of

atom. The intrinsic value of an atom i is defined as

I = [(2/N)2δv + 1]/δ (1)

In Eq. (1), N stands for principal quantum number, δv and δ indicate the count of va-

lence electrons and sigma electrons, respectively, associated with the atom i in the hydro-

gen suppressed graph. The intrinsic electrotopological state calculated according to Eq.

(1) produces different values for an atom in different degrees of substitution (branching).

The values are also different for different atoms having differences in electronegativity.

The intrinsic values increase with increase in electronegativity or electron-richness and

decrease with increase in branching (substitution).

The perturbation factor for the intrinsic state of atom i is defined as

ΔIi =∑j �=i

Ii − Ij

r2ij

(2)


In Eq. (2) rij stands for the graph separation factor, i.e., count of skeletal atoms in

the shortest path connecting the atoms i and j (including both atoms).

Summation of intrinsic state of an atom and influence of the field is called electro-

topological state of the atom.

Si = Ii +∑j �=i

ΔIij (3)

It is a representation of molecular structure information as it varies with changes in

structural features including branching, cyclicity, homologation, heteroatom variation,

and changes in relative positions of different groups. The electrotopological state consid-

ers both bonded and non-bonded interactions. The bonded component depends simply

on differences in electronegativity among the adjacent atoms. The non-bonded inter-

actions may be through inductive effect across the skeleton and is a function of graph

separation factor and electronegativity differences. Thus, electrotopological state repre-

sents electronic distribution information modified by both local and global topology. The

information encoded in the E-state value for an atom is the electronic accessibility at that

atom.

The E-state index has been projected as a useful tool in the context of QSAR studies

and reported to have the power to identify atoms or fragments in the molecules that are

important for the biological activity [26–28]. We have in our earlier studies, also used

E-state parameters to explore QSAR of ligands acting on pharmacologically relevant

targets of contemporary interest [29–37]. In continuation with these efforts, the present

communication will show the utility of E-state parameters in QSAR studies by exploring

QSAR of antiradical properties of flavonoids as studied in a methanolic solution of 1,

1-diphenyl-2-picrylhydrazyl (DPPH) [38] and antioxidant activity of flavonoids in a β-

carotene-linoleic acid model system [39] as reported by Burda et al. [23].

2.2 Methods

The equations were developed using 1) stepwise regression, 2) factor analysis followed by

multiple linear regression (FA-MLR) and 3) partial least squares analysis.

2.2.1 Stepwise Regression

In stepwise regression [40], a multiple term linear equation was built step-by-step. The

basic procedure involved (1) identifying an initial model, (2) iterative “stepping”, i.e.,

repeatedly altering the model of the previous step by adding or removing a predictor

variable in accordance with the “stepping criteria”, (F = 4 for inclusion; F = 3.9 for

exclusion in our case) and (3) terminating the search when stepping was no longer possible

as per the stepping criteria, or when a specified maximum number of steps was reached.

At each step all variables were reviewed and evaluated to determine which one would

contribute most to the equation. That variable was then included in the model, and the

process started again. A limitation of the stepwise regression search approach is that


it presumes that there is a single “best” subset of X variables and seeks to identify it.

There is often no unique “best” subset, and all possible regression models with a similar

number of X variables as in the stepwise regression solution should be retro-fitted to check

whether some other subsets of X variables might be better.

2.2.2 FA-MLR

In the case of FA-MLR [41, 42], a classical approach to the MLR technique was used as

the final statistical tool for developing classical QSAR relations and FA was used in the

data-preprocessing step to identify the important descriptors contributing to the response

variable and avoid collinearities among them. In a typical FA procedure, the data matrix

is first standardized, and subsequently, the reduced correlation matrix is constructed. An

eigenvalue problem is then solved and the factor pattern can be obtained from the cor-

responding eigenvectors. The principal objectives of FA are to display multidimensional

data in a space of lower dimensionality with minimum loss of information (explaining

>95% of the variance of the data matrix) and to extract the basic features behind the

data with the ultimate goal of interpretation and/or prediction. FA was performed on the

data set(s) containing biological activity and all descriptor variables, which were to be

considered. The factors were extracted by principal component method and then rotated

by VARIMAX rotation (a kind of rotation which is used in principal component analysis

so that the axes are rotated to a position in which the sum of the variances of the loadings

is the maximum possible) to obtain Thurston’s simple structure. The simple structure is

characterized by the property that as many variables as possible fall on the coordinate

axes when presented in common factor space, so that the largest possible number of factor

loadings becomes zero; this is done to obtain numerically comprehensive picture of the

relatedness of the variables. Only variables with non-zero loadings in such factors where

biological activity also has non-zero loading were considered important in explaining the

variance of the activity. Further, variables with non-zero loadings in different factors were

combined in a multivariate equation.

2.2.3 PLS

PLS is a generalization of regression, which can handle data with strongly correlated

and/or noisy or numerous X variables [43, 44]. It gives a reduced solution, which is

statistically more robust than MLR. The linear PLS model finds “new variables” (latent

variables or X scores) which are linear combinations of the original variables. To avoid

overfitting, a strict test for the significance of each consecutive PLS component is nec-

essary and then stopping when the components are nonsignificant. Application of PLS

thus allows the construction of larger QSAR equations while still avoiding overfitting and

eliminating most variables. PLS is normally used in combination with crossvalidation to

obtain the optimum number of components. This ensures that the QSAR equations are

selected based on their ability to predict the data rather than to fit the data. In case of

PLS analysis on the present data set, based on the standardized regression coefficients,

the variables with smaller coefficients were removed from the PLS regression until there


was no further improvement in Q2 value irrespective of the components.

2.3 Data treatment and software

The antiradical activities of flavonoid [23] compounds were converted to logarithmic scale

(pC) (Table 1) and then used for subsequent QSAR analyses as the response variables.

The antioxidant activities of flavonoid [23] compounds (Table 3) were used as % antioxi-

dant activity, AAFL as reported, for subsequent QSAR analyses as the response variable.

For antiradical activity, 29 compounds (set 1) and for antioxidant activity 24 compounds

(set 2) were considered in the present study. All the compounds (sets 1 and 2) contain 17

common atoms (excluding hydrogens). The atoms were numbered keeping serial numbers

of the common atoms same in all the compounds (as shown in Fig. 1). The electrotopo-

logical states of the 17 common atoms for all of the compounds (set 1 and set 2) were

determined using a GW-BASIC program ELECTRO1 developed in our group [45]. The

program uses only the connection table in a specific format along with values for intrin-

sic state of different atoms as input. To the output file obtained, the biological activity

data was introduced to make it ready for subsequent regression analysis. The stepwise

regression and FA and MLR were performed using the statistical software SPSS [46]. PLS

was performed using statistical software MINITAB [47]. The statistical qualities of the

MLR equations [48] were judged by the following parameters: variance (R2a), correlation

coefficient (R), standard error of estimate (s) and variance ratio (F ) at specified degree

of freedom (df). If not stated otherwise, all accepted MLR equations have regression co-

efficients and F ratio significant at 95 and 99% levels, respectively,. The generated QSAR

equations were validated by leave-one-out or LOO method [49, 50] using MINITAB soft-

ware [47] and the calculated parameters are predicted residual sum of squares (PRESS),

standard deviation based on PRESS (SPRESS), standard deviation of error of prediction

(SDEP) [50] and cross validation R2 (Q2). Q2 is calculated according to the following

formula

Q2 = 1 −∑

(Yobs − Ycal)2∑

(Yobs − Y )2(4)

In Eq. (4), Y means average activity value of the entire data set while Yobs and Ycal

represent observed and LOO estimated activity values. Standard deviation of error of

prediction (SDEP) [51] is calculated according to the formula

SDEP =

√PRESS

n(5)

In Eq. (5) PRESS is the predicted residual sum of squares using (leave-one-out)

statistics and n is the number of components.


Fig. 1 General structure of flavonoids: the common atoms have been numbered 1-17.

3 Results and Discussion

3.1 QSAR of antiradical activity of flavonoids

The results obtained from different statistical methods are described below and the in-

terpretations of the equations are also depicted.

3.1.1 Stepwise regression

Using stepping criteria based on F value (F = 4.0 for inclusion; F = 3.9 for exclusion),

different equations were derived after successive addition of E-state parameters.

pC = −0.750(±0.079)S3 + 1.287(±0.073)

n = 29, R2 = 0.770, R2a = 0.762, Q2 = 0.773, R = 0.878

s = 0.329, PRESS = 4.804, F = 90.40, (df1.27), SDEP = 0.407, SPRESS = 0.422

(6)

Using single best parameter (S3), Eq. (6) could explain and predict 76.2% and 73.3%

respectively of the antiradical scavenging potency.

pC = −0.628(±0.086)S3 − 0.732(±0.281)S10 + 1.343(±0.069)

n = 29, R2 = 0.818, R2a = 0.804, Q2 = 0.776, R = 0.904


(7)

On inclusion of S10 along with S3, it is observed that there is significant increase

in the statistical quality of the equation (explained and predicted variance of 80.4% and

76.6% respectively of antiradical scavenging potency). The best trivariate and tetravariate

equations are given below.

pC = −0.895(±0.111)S3 − 0.800(±0.243)S10 + 0.699(±0.219)S2 + 1.428(±0.065)

n = 29, R2 = 0.870, R2a = 0.855, Q2 = 0.805, R = 0.933


(8)


Table

1C

hem

ical

stru

cture

san

dob

serv

edan

dca

lcula

ted

free

radic

alsc

aven

ging

pot

ency

ofth

ese

lect

edflav

onoi

ds.

Com

p.

Com

pound

R1

R2

R3

R4

R5

R6

R7

R8

C2

pC

No.

Nam

e=

C3

Obsa

Calb

A1

Mori

nO

HO

HO

HH

OH

HO

HH

+1.9

84

1.9

15

A2

Taxifolin

OH

OH

OH

HH

OH

OH

H−

1.9

76

1.9

72

A3

Kaem

pfe

rol

OH

OH

OH

HH

HO

HH

+1.9

70

1.9

08

A4

Fust

inO

HH

OH

HH

OH

OH

H−

1.9

63

2.0

60

A5

Gala

ngin

OH

OH

OH

HH

HH

H+

1.9

62

1.8

80

A6

Ruti

nO

-GR

OH

OH

HH

OH

OH

H+

1.9

58

1.8

52

A7

Quer

ceti

nO

HO

HO

HH

HO

HO

HH

+1.9

53

1.9

32

A8

Lute

olin-7

-O-g

luH

OH

O-g

luH

HO

HO

HH

+1.9

42

1.7

33

A9

Quer

ceti

n-3

-O-g

lu-7

-O-r

ha

O-g

luO

HO

-rha

HH

OH

OH

H+

1.9

38

1.8

71

A10

Lari

cytr

inO

HO

HO

HH

HO

HO

HO

CH

3+

1.9

27

1.9

44

A11

Laricy

trin

-3’-O

-glu

OH

OH

OH

HH

O-g

luO

HO

CH

3+

1.9

23

2.0

24

A12

Robin

etin

OH

HO

HH

HO

HO

HO

H+

1.9

15

2.0

50

A13

Fiset

inO

HH

OH

HH

OH

OH

H+

1.8

97

2.0

25

A14

Myrice

tin

OH

OH

OH

HH

OH

OH

OH

+1.8

62

1.9

56

A15

Kaem

pfe

rol

O-r

ha

OH

O-r

ha

HH

HO

HH

+1.8

48

1.8

31

3,7

-di-rh

aA

16

3-h

ydro

xy

OH

HH

HH

HH

H+

1.8

19

1.4

95

flav

one

A17

Apig

enin

-7-O

-glu

HO

HO

-glu

HH

HO

HH

+1.5

41

1.7

09

A18

Hes

per

etin

HO

HO

HH

HO

HO

CH

3H

−1.4

77

0.8

59

A19

Vitex

in3,5

,7,3

’,H

OH

OH

O-g

luH

HO

HH

+1.3

22

1.0

56

A20

4’,5’-hex

am

ethox

yO

CH

3O

CH

3O

CH

3H

HO

CH

3O

CH

3O

CH

3+

1.1

00

1.3

72

flav

one

A21

Nari

ngen

inH

OH

OH

HH

HO

HH

−0.7

99

0.8

68

A22

Nari

ngin

HO

HO

-neo

hes

pH

HH

OH

H−

0.6

72

1.0

16

A23

7-h

ydro

xy

HH

OH

HH

HH

H+

0.4

47

0.3

16

Fla

vone

A24

Fla

vanone

HH

HH

HH

HH

−0.4

14

0.4

71

A25

Fla

vone

HH

HH

HH

HH

+0.1

76

−0.1

51

A26

Chry

sin

HO

HO

HH

HH

HH

+0.0

41

0.2

09

A27

Apig

enin

HO

HO

HH

HH

OH

H+

−0.1

54

0.2

27

A28

8-m

ethox

yH

HH

OC

H3

HH

HH

+−0

.154

0.1

41

flav

one

A29

5-h

ydro

xy

HO

HH

HH

HH

H+

−0.2

21

−0.2

54

flav

one

Glu

=glu

cose

,R

ha

=rh

am

nose

,N

eohes

p=

neo

hes

per

idin

,G

R=

β-D

-Glu

-α-L

-Rha;T

hes

esu

gars

are

connec

ted

via

thei

rglu

cosi

de

OH

gro

up

toth

eflav

onoid

saTaken

from

Ref

.[2

3];

bFro

mE

q.

(10).


pC = −1.393(±0.197)S3 − 2.537(±0.633)S10 + 1.346(±0.294)S2 + 2.009(±0.690)S4

+ 2.725(±0.449)

n = 29, R2 = 0.904, R2a = 0.888, Q2 = 0.837, R = 0.951

s = 0.268, PRESS = 2.932, F = 56.63, (df4.24), SDEP = 0.318, SPRESS = 0.349(9)

From Eqs. (8) and (9) it is observed that successive addition of S2 and S4 increases

the explained variance (85.5% and 88.8% respectively) and predicted variance (80.5%

and 83.7% respectively) of antiradical scavenging potency of flavonoids. The parameter

S2 implies the impact of the phenyl ring at position 2. Presence of electron withdrawing

groups on the phenyl ring increases the value of S2 activity in comparison to a phenyl ring,

which is unsubstituted or substituted with other groups. Again S4 implies the importance

of the keto group at position 4. Van Acker et al. [52] also reported the presence of 4-keto

functionality as a structural requirement for free radical scavenging activity of flavonoids.

The best pentavariate equation is given below.

pC = −1.378(±0.176)S3 − 3.432(±0.656)S10 + 1.359(±0.262)S2

+ 2.231(±0.621)S4 + 0.236(±0.888)S6 + 2.884(±0.405)

n = 29, R2 = 0.927, R2a = 0.911, Q2 = 0.871, R = 0.963


(10)

The standard errors of the respective E-state indices are mentioned within parentheses.

From the above equations (6–10) it was observed that there is significant gradual increase

in the values of R2 (0.770 to 0.927), R2a (0.762 to 0.911) and Q2 (0.733 to 0.871) after

gradual addition of parameters. The final Eq. (10) could explain and predict 91.1%

and 87.1% respectively of the variance of antiradical scavenging potency. The positive

coefficient of S2, S4 and S6 indicate that activity increases with increase in E-state value

of atoms 2, 4 and 6 respectively while the negative coefficient of S3 and S10 indicate that

activity decreases with increase in E-state value of atoms 3 and 10 respectively. The

values of E-state parameters of the compounds present in the final equations and the

intercorrelation among the E-state parameters for antiradical activity data modeling are

shown in Table 1A and 2A respectively in the supplementary materials section. Table 2A

indicates that some of the E-state parameters used in the stepwise regression equations

are highly intercorrelated. However, as the leave-one-out prediction statistics of these

equations are very good (for example Eq.(10), Q2 = 0.871), we have accepted these

equations with a note of the intercorrelation among descriptors.

3.1.2 FA-MLR

From the factor analysis on the data matrix consisting of free radical scavenging potential

data (pC) of flavonoids and E-state indices, it was observed that 7 factors could explain

the data matrix to the extent of 95.8%. The free radical scavenging potency is highly

loaded with factor 3 (loaded in S3, S4) and moderately loaded in factor 2 (loaded in


S14, S16 and S17) and factor 4 (loaded in S2). Based on the results of FA (Table 2), the

following equation with two variables was derived:

pC = 0.635(±0.256)S2 − 1.003(±0.125)S3 + 1.360(±0.073)

n = 29, R2 = 0.814, R2a = 0.800, Q2 = 0.761, R = 0.902


(11)

Table 2 Factor loading of the variables (antiradical inhibition potency (pC) and predictor

variables) after VARIMAX rotation.

F1 F2 F3 F4 F5 F6 F7 Communalities

pC −0.258 −0.354 −0.768 −0.340 −0.019 −0.075 −0.166 0.931S1 0.202 0.256 0.262 0.025 0.879 0.041 0.195 0.988S2 0.234 0.226 0.224 0.889 −0.006 0.014 0.108 0.958S3 0.197 0.373 0.650 0.577 0.056 −0.122 0.163 0.977S4 0.590 0.449 0.574 0.073 0.000 0.141 0.263 0.974S5 0.827 0.298 0.350 0.115 −0.094 0.181 0.198 0.990S6 0.954 0.074 0.053 0.061 −0.126 −0.001 0.076 0.945S7 0.896 0.217 0.171 0.206 0.083 0.220 0.132 0.994S8 0.765 0.311 0.101 0.319 0.090 0.247 0.073 0.868S9 0.337 0.086 0.027 −0.008 −0.019 0.927 0.057 0.985S10 0.773 0.360 0.297 0.150 −0.106 0.326 0.201 0.995S11 −0.344 −0.193 −0.226 −0.023 0.875 −0.069 −0.091 0.987S12 0.426 0.650 0.456 0.153 −0.003 0.139 0.375 0.995S13 0.320 0.359 0.281 0.222 0.137 0.081 0.775 0.985S14 0.175 0.751 0.267 0.401 −0.023 0.036 0.165 0.856S15 0.458 0.638 0.151 0.426 −0.091 0.161 0.263 0.924S16 0.171 0.931 0.146 0.062 0.070 0.025 0.032 0.929S17 0.417 0.718 0.351 0.205 0.065 0.157 0.308 0.978% Variance 0.282 0.216 0.127 0.104 0.090 0.069 0.068 0.958

The standard errors of the respective E-state indices are mentioned within parenthesis.

Eq. (11) could explain and predict 80.0% and 76.1% respectively of the variance in the

antiradical scavenging potency. The negative coefficient of S3 indicates that activity

decreases with an increase in E-state value of atom 3. The parameter S3 indicates the

importance of hydroxyl group at position 3 for antiradical activity. The parameter S2

implies the impact of phenyl group at position 2 and its substituents on the biological

activity. Presence of hydroxyl group on the phenyl ring increases the activity.

3.1.3 PLS

The number of optimum components optimized by crossvalidation was 2 to obtain the

final equation. Based on the standardized regression coefficients, the following variables

were selected for the final equation:

pC = 0.137S6 − 0.328S5 − 0.782S4 − 0.521S3 + 0.845

n = 29, R2 = 0.826, R2a = 0.813, Q2 = 0.783, R = 0.908

PRESS = 3.90, F = 61.81, (df2.26), SDEP = 0.367, SPRESS = 0.387

(12)


Eq. (12) could explain and predict 81.3% and 78.3% respectively of the variance of

the antiradical activity. The positive coefficient of the variable S6 indicates that the anti-

radical activity increases with increase in the E-state value of atom 6 while the negative

coefficients of S5, S4, and S3 indicate that the activity decreases with increase in E-state

values of atoms 5, 4 and 3. However, S4 showed positive coefficients in Eqs. (9) and (10).

The positive coefficients of S4 in eqs. (9) and (10) may be due to its high intercorrelation

with S10 (r = 0.897).

3.2 QSAR of antioxidant activity of flavonoids

The results obtained from different statistical methods are described below and the in-

terpretations of the equations are also depicted.

3.2.1 Stepwise regression

Using stepping criteria based on F value (F = 4.0 for inclusion; F = 3.9 for exclusion),

different equations were derived after successive addition of E-state indices.

AAFL = −104.95(±23.35)S1 + 608, 81(±131.45)

n = 24, R2 = 0.479, R2a = 0.455, Q2 = 0.381, R = 0.692


On using single best parameter (S1), Eq. (13) could explain and predict 45.5% and

38.1% respectively of the antioxidant activity. The parameter S1 implies the importance of

oxygen atom at position 1. The parameter S1 has negative contribution to the antioxidant

activity.

AAFL = −16.59(±5.10)S3 − 85.27(±20.41)S1 + 496.73(±115.05)

n = 24, R2 = 0.653, R2a = 0.620, Q2 = 0.564, R = 0.808


AAFL = −14.71(±4.66)S6 − 24.31(±4.93)S3 − 79.59(±17.19)S1 + 463.21(±96.91)

n = 24, R2 = 0.768, R2a = 0.734, Q2 = 0.691, R = 0.877


From Eqs. 14 and 15 it is observed that inclusion of S6 and S3 along with S1 increase

the explained variance (62.0 and 73.4% respectively) and predicted variance (56.4 and

69.1% respectively) of the antioxidant activity of flavonoids. The parameter S6 implies

the effect of hydroxyl substituent at position 6. Presence of hydroxyl group increases the

activity.


The best tetravariate equation is given below.

AAFL = 16.86(±3.35)S14 + 13.40(±3.14)S6 − 38.95(±4.40)S3

− 61.05(±12.12)S1 + 348.43(±68.99)

n = 24, R2 = 0.901, R2a = 0.888, Q2 = 0.841, R = 0.949


The standard errors of the respective E-state parameters are mentioned within parenthe-

ses. From the above equations (13–16) it was observed that there is significant gradual

increase in the values of R2 (0.479 to 0.901), R2a (0.455 to 0.888) and Q2 (0.381 to 0.841)

after gradual addition of E-state indices. The final Eq. (16) could explain and predict

88.8% and 84.1% respectively of the variance of antioxidant activity. The positive co-

efficient of S14 and S6 indicate that activity increases with increase in E-state values of

atoms 14 and 6 respectively while the negative coefficient of S3 and S1 indicate that ac-

tivity decreases with increase in E-state value of atoms 3 and 1 respectively. The values

of E-state parameters of the compounds present in the final equations and the intercorre-

lation among the E-state parameters for antiradical activity data modeling are shown in

Table 3A and 4A respectively in the supplementary materials section. Table 4A indicates

that some of the E-state parameters used in the stepwise regression equations are highly

intercorrelated. However, as the leave-one-out prediction statistics of these equations are

very good (for example, Eq. (16), Q2 = 0.841), we have accepted these equations with a

note of the intercorrelation among descriptors.

3.2.2 FA-MLR

From the factor analysis on the data matrix consisting of antioxidant activity data (AAFL)

of flavonoids and E-state indices, it was observed that 6 factors could explain the data

matrix to the extent of 96.2%. The antioxidant activity is highly loaded with factor 4

(loaded in S3) and moderately loaded with factor 3 (loaded in S1 and S11). Based on the

results of FA (Table 4), the following equation was derived with three variables:

AAFL = 21.25(±9.08)S9 − 16.546(±4.63)S3 − 86.91(±18.55)S1 + 481.15(±104.68)

n = 24, R2 = 0.728, R2a = 0.687, Q2 = 0.582, R = 0.853


The standard errors of the respective E-state parameters are mentioned within paren-

thesis. Eq. (17) could explain and predict 68.7% and 58.2% respectively of the variance

of the antioxidant activity. The negative coefficient of S3 and S1 indicates that activity

decreases with increase in E-state values of atoms 3 and 1 respectively. The positive

coefficient of S9 indicates that the antioxidant activity increases with increase in E-state

value of atom 9.


Table

3C

hem

ical

stru

cture

san

dob

serv

edan

dca

lcula

ted

antiox

idan

tac

tivity

ofth

ese

lect

edflav

onoi

ds.

Com

p.

Com

pound

R1

R2

R3

R4

R5

R6

R7

R8

AA

FL

No.

Nam

eO

bsa

Calb

B1

Kaem

pfe

rol

OH

OH

OH

HH

HO

HH

65.3

060.5

8B

2G

ala

ngin

OH

OH

OH

HH

HH

H64.9

061.5

6B

3Q

uer

cetin

OH

OH

OH

HH

OH

OH

H63.6

036.7

6B

4R

obin

etin

OH

HO

HH

HO

HO

HO

H61.7

054.7

9B

5Fis

etin

OH

HO

HH

HO

HO

HH

61.6

051.7

3B

6K

aem

pfe

ride

OH

OH

OH

HH

HO

CH

3H

60.0

059.2

2B

73-h

ydro

xy

OH

HH

HH

HH

H59.4

072.0

5flav

one

B8

Lari

cytr

inO

HO

HO

HH

HO

HO

HO

CH

328.5

034.0

0B

9Lari

cytr

in-3

’-O

HO

HO

HH

HO

-glu

OH

OC

H3

26.2

030.5

0O

-glu

B10

Myri

cetin

OH

OH

OH

HH

OH

OH

OH

18.4

039.7

7B

11

3,5

,7,3

’,4’,5’-

OC

H3

OC

H3

OC

H3

HH

OC

H3

OC

H3

OC

H3

2.6

0−1

1.6

9hex

am

ethox

yflav

one

B12

3,5

,7,3

’,4’-

OC

H3

OC

H3

OC

H3

HH

OC

H3

OC

H3

OH

1.1

0−5

.92

pen

tam

ethox

yflav

one

B13

Lari

cytr

in-3

,3’-O

-di-glu

O-g

luO

HO

HH

HO

-glu

OH

OC

H3

1.1

03.1

7B

14

Quer

cetin-3

-O-g

lu-7

-O-r

ha

O-g

luO

HO

-rha

HH

OH

OH

H−6

.20

−2.2

9B

15

Lari

cytr

in-3

,7,3

’-O

-tri

-glu

O-g

luO

HO

-glu

HH

O-g

luO

HO

CH

3−6

.20

−8.4

5B

16

Rutin

O-G

RO

HO

HH

HO

HO

HH

−10.2

6.5

0B

17

Mori

nO

HO

HO

HH

OH

HO

HH

63.5

064.4

4B

18

Fla

vone

HH

HH

HH

HH

−1.5

0−4

.88

B19

5-h

ydro

xy-fl

avone

HO

HH

HH

HH

H−4

.00

−19.7

4B

20

7-h

ydro

xy-fl

avone

HH

OH

HH

HH

H0.0

0−0

.815

B21

Chry

sin

HO

HO

HH

HH

HH

−20.8

−15.9

5B

22

8-m

ethox

y-fl

avone

HH

OC

H3

HH

HH

H−2

9.2

−10.4

8B

23

Vitex

inH

OH

OH

glu

HH

OH

H−2

9.6

−27.8

2B

24

Lute

onin

-7-O

-glu

HO

HO

-glu

HH

OH

OH

H−2

5.3

−22.2

1

Glu

=glu

cose

,R

ha

=rh

am

nose

,G

R=

β-D

-Glu

-α-L

-Rha;th

ese

sugars

are

connec

ted

via

thei

rglu

cosi

de

OH

gro

up

toth

eflav

onoid

s.aTaken

from

Ref

.[2

3];

bFro

mE

q.

(16)


Table 4 Factor loading of the variables (antioxidant activity (AAFL) and predictor vari-

ables) after VARIMAX rotation.

F1 F2 F3 F4 F5 F6 Communalities

AAFL −0.008 −0.070 −0.550 −0.798 0.158 −0.069 0.979S1 0.170 0.024 0.938 0.236 0.028 0.117 0.989S2 0.557 0.664 −0.062 0.391 0.128 0.253 0.974S3 0.414 0.586 0.044 0.645 −0.106 0.173 0.985S4 0.700 0.524 −0.069 0.394 0.126 0.212 0.989S5 0.852 0.387 −0.111 0.181 0.178 0.188 0.938S6 0.944 0.158 −0.112 −0.029 −0.018 0.095 0.991S7 0.903 0.286 0.110 0.088 0.236 0.136 0.843S8 0.764 0.417 0.150 0.070 0.239 0.024 0.987S9 336 0.050 −0.024 −0.125 0.924 0.047 0.994S10 0.787 0.461 −0.120 0.116 0.316 0.186 0.990S11 −0.349 −0.388 0.841 −0.030 −0.044 −0.087 0.995S12 0.492 0.757 −0.099 0.244 0.107 0.314 0.976S13 0.361 0.464 0.136 0.167 0.071 0.760 0.910S14 0.273 0.891 −0.121 0.025 −0.032 0.160 0.935S15 0.419 0.809 −0.047 0.114 0.167 0.248 0.900S16 0.141 0.927 −0.115 0.036 −0.012 −0.069 0.983S17 0.415 0.839 0.016 0.172 0.132 0.245 0.975% Variance 0.315 0.314 0.112 0.090 0.068 0.060 0.962

3.2.3 PLS

The number of optimum components was 4 to obtain the final equation (optimized by

crossvalidation). Based on the standardized regression coefficients, the following variables

were selected for the final equation:

AAFL = 13.93S14 − 11.25S11 + 32.17S10 + 27.55S1

− 21.18S4 − 32.66S3 − 20.36S2 − 46.18S1 + 361.05

n = 24, R2 = 0.898, R2a = 0.876, Q2 = 0.834, R = 0.947

PRESS = 4615.1, F = 41.86, (df4.19), SDEP = 13.86, SPRESS = 15.58

(18)

Eq. (18) could explain and predict 87.6% and 83.4% respectively of the variance of the

antioxidant activity. The positive coefficient of the variable S14, S10 and S7 indicate that

the antioxidant activity increases with increase in the E-state value of atom 14, 10 and

7 respectively while the negative coefficients of S11, S4, S3, S2 and S1 indicate that the

activity decreases with increase in E-state values of atoms 11, 4, 3, 2 and 1 respectively.

The values of E-state parameters of the compounds present in the final equations and the

intercorrelation among the E-state parameters for antiradical activity data modeling are

shown in Table 3A and 4A respectively in the supplementary materials section.


4 Overview

For antiradical activity of flavonoids in set 1, the Q2 value (0.871) is highest in Eq. (10)

(Table 5). Figure 2 also shows that the observed and calculated values according to

Eq. (10) show good linear relation. The equations obtained from all three statistical

techniques, indicate that S3 has negative coefficient for antiradical activity. S3 indicates

the importance of hydroxyl group at position 3 for antiradical activity. In the previous

QSAR report [22] on the same data set the reported R value is 0.938 (n = 29), while in

our best model the R value is 0.963 (n = 29). In case of antioxidant activity of flavonoids

(set 2), the Q2 value (0.841) is highest in Eq. (16) (Table 5). Figure 3 also shows that

the observed and calculated values according to Eq. (16) show good linear relation. The

equations obtained from all three statistical techniques, indicates that S3 and S1 have

negative coefficient for antioxidant activity. S1 implies the effect of oxygen function at

position 1 and S3 indicates the importance of hydroxyl group at position 3 needed for

antioxidant activity. In the previous QSAR report on antiradical activity [14] on the

same data set with n = 24 the squared correlation coefficient (r2) between observed and

calculated values and sum of squared residual between observed and calculated values are

0.285 and 1042.37 respectively, while in our model (Eq. 10) with same data set (n = 24)

the r2 and sum of squared residual values (n = 24) between observed and predicted value

are 0.888 and 128.55 respectively. For both the models (antiradical and antioxidant), the

intercorrelation among the parameters used in equations are shown in Table 2A and 4A,

respectively, in the supplementary materials section and utmost care was exercised to

avoid collinearities among the variables. Flavonoids are polyphenolic compounds classified

as benzo-γ-pyrone derivatives with a basic structure that consists of 15 carbon atoms

arranged in three rings (Fig. 1). There is diversity in the structures among flavonoid

compounds, the structural differences in each flavonoid family result from the variation in

the number/substitution pattern of the hydroxyl groups and the extent of glycosylation of

these groups. These structural variations are responsible for various activities of flavonoid

compounds. On the other hand, E-state indices is a representation of molecular structure

information as it varies with changes in structural features including branching, cyclicity,

homologation, heteroatom variation, and changes in relative positions of different groups.

Thus, electrotopological state represents electronic distribution information modified by

both local and global topology. The information encoded in the E-state value for an atom

is the electronic accessibility at that atom. The E-state index has been projected as a

useful tool in the context of QSAR studies and reported to have power to identify atoms

or fragments in the molecules, which are important for the biological activity.


Table 5 Statistical qualities of the equations in two activity models.

Antiradical activity (pC) Antioxidant activity (AAFL)

Types of Equation R2 Q2 F Types of Equation R2 Q2 Fstatistical statisticalAnalysis Number Analysis NumberStepwise 6 0.770 0.733 90.40 Stepwise 13 0.479 0.381 20.19

7 0.818 0.766 58.24 14 0.653 0.564 19.768 0.870 0.805 55.96 15 0.768 0.691 22.119 0.904 0.837 56.63 16 0.901 0.841 43.0710 0.927 0.871 58.48

FA-MLR 11 0.814 0.761 56.89 FA-MLR 17 0.728 0.582 17.80PLS 12 0.826 0.783 61.81 PLS 18 0.898 0.834 41.89

Fig. 2 Correlation between observed (pC) and calculated antiradical activity values ac-

cording to Eq. (10)

5 Conclusions

For both, antiradical and antioxidant activity models, the final equations (10, 11, 12

and 16, 7, 18) obtained from three techniques are of acceptable statistical quality and

predictive potential considering the leave-one-out prediction statistics. The models also

show the utility of E-state parameters in QSAR study for a better understanding about

the contribution of atoms or fragments in the molecules towards imparting biological

activity.


Fig. 3 Correlation between observed (AAFL) and calculated antioxidant activity values

according to Eq. (16)

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