molecular modeling of pyridine derivatives for cox-2 inhibitors: quantitative structure–activity...

ORIGINAL RESEARCH

Molecular modeling of pyridine derivatives for COX-2 inhibitors:quantitative structure–activity relationship study

Amrita Dwivedi • A. K. Srivastava •

Ajeet Singh

Received: 4 March 2013 / Accepted: 6 August 2013 / Published online: 24 September 2013

� Springer Science+Business Media New York 2013

Abstract Quantitative structure–activity relationship

studies were performed on a set of compounds of pyridine

acyl sulfonamide derivative to understand the structural

features influencing the affinity toward the COX-2 enzyme

inhibition. In the present study, the density functional

theory-based descriptors were calculated at B3LYP/6-

31?G* level in gas phase. However, empirical molecular

descriptors were calculated with the help of different

softwares. Number of physicochemical, topological, and

electronic descriptors were computed, and the calculated

results revealed that the descriptors based on softness (S),

hardness (g), chemical potential (l), and the lowest unoc-

cupied molecular orbital energy seem to be responsible

factor for in vitro inhibition activity of COX-2 enzyme.

The possible descriptors which we have calculated for the

present series of compounds were selected for multiple

linear regression analysis. Various regression models have

been tested and the regression analysis data indicate that

some of the descriptors provide valuable information

toward designing of new COX-2 enzyme inhibitors with

high efficacy. The predictive ability of the models was

cross validated by observation of the low residual activity

values and appreciable cross validated R2 values (R2CV)

obtained by leave one out technique.

Keywords COX inhibition � DFT-QSAR �Regression analysis � Molecular descriptor �Frontier electron density

Introduction

Quantitative structure–activity relationship (QSAR) mod-

els are regression models used in the chemical and bio-

logical sciences and engineering. Like other regression

models, QSAR models relate measurements on a set of

‘‘predictor’’ variables to the behavior of the response var-

iable. QSAR represents an attempt to correlate activities or

properties with structural descriptors of compounds. To

correlate and predict physical, chemical and biological

activity from molecular structure is a very important and an

unsolved problem in theoretical and computational chem-

istry as well (Hu et al., 2003). QSAR analysis has been

widely used to modify lead compounds and to minimize

the toxic effects (Plummer, 1995). It provides better sense

to understand the interaction mechanisms between chemi-

cal compounds and biological targets (Gao and Hansch,

1996; Lien and Gao, 1995; Hansch et al., 1996). The

fundamental hypothesis of QSAR is that biological activity

is a function of molecular structure. Thus, molecules with

similar structures exert similar biological activities, and

changes in structure are thought to modulate biological

activities.

Cyclooxygenase (COX) is one of the key enzymes that

are responsible for the production of proinflammatory

prostaglandins and other isotypes of this compound, which

in turn play a pivotal role in gastrointestinal protection. It is

now established that two distinct isoforms of this enzyme

exist. The first one is the constitutive form (COX-1)

expressed virtually in all tissues, which is involved in the

Electronic supplementary material The online version of thisarticle (doi:10.1007/s00044-013-0691-4) contains supplementarymaterial, which is available to authorized users.

A. Dwivedi � A. K. Srivastava (&) � A. Singh (&)

QSAR Research Laboratory, Department of Chemistry,

University of Allahabad, Allahabad 211002, UP, India

e-mail: [email protected]

A. Singh

e-mail: [email protected]

123

Med Chem Res (2014) 23:1865–1877

DOI 10.1007/s00044-013-0691-4

MEDICINALCHEMISTRYRESEARCH

http://dx.doi.org/10.1007/s00044-013-0691-4

production of prostaglandins, important in gastrointestinal

protection (Vane, 1971; Smith and Willis, 1971). The

second isoform (COX-2) that is largely restricted to the

brain and kidney. During normal physiology COX-2 levels

are undetectable in most tissues. The level of COX-2 is

induced under the conditions of immunological insult (such

as inflammation) (Needleman and Isakson, 1997; Masferrer

et al., 1992). Hence, selective and potent inhibitors of

COX-2 might be anti-inflammatory without the side effects

associated with traditional NSAIDs (Non-Steroidal Anti-

inflammatory Drugs) such as aspirin, which inhibit both

COX-1 and COX-2 in a nonselective manner.

3D structure of COX-1 and COX-2 shows very much

similarities such as each consisting of a long, narrow

hydrophobic channel however, the difference of single

amino acid between two isoform of COX enzyme arises

difficulties for the selectivity of many COX inhibitory

drugs. The most critical structural feature conferring sen-

sitivity to inhibition by COX-2 is exchange of valine in

COX-2 at positions 434 and 523 in place of isoleucine in

COX-1 (Hawkey, 1999). This difference increases the

volume of the COX-2 side pocket, which is thought to be

the binding site of many selective drugs. Another factor

which increases sensitivity of drug toward COX-2 is

exchange of histamine at position 513 in COX-1 in place of

arginine in COX-2. Overall larger size of the central

channel of the COX-2 binding pocket increases selectivity

of drugs toward COX-2 enzyme.

Since a long time, attempts have been made by different

research groups for designing of various COX-2 inhibitors

experimentally; however, the QSAR studies on COX-2

inhibitor is scarce in the literature (Singh and Bhardwaj,

2010; Zarghi et al., 2009, 2010; Garg et al., 2003; Sarkar

and Mostafa, 2009). As part of a continuing effort to

develop COX-2 inhibitor, Zhu et al. (2011) recently

reported the synthesis of various pyridine acyl sulfonamide

derivatives as novel COX-2 inhibitors. Sulfonamide is a

promising skeleton that has shown not only the COX-2-

selective inhibition but also the minimization of the risk

potential of unwanted side effects. The two combined

substructures, pyridine ring and sulfonamide, might exhibit

synergistic effect and inflammatory activities. The objec-

tive of present study is to perform a QSAR study on the

present series to correlate the physicochemical and struc-

tural requirements of these compounds to exhibit optimal

inhibitory potency toward COX-2 enzyme which will in

turn help in the modeling of COX-2 inhibitors.

Theoretical background

In the present study, steric parameters such as molecular

weight (Mw), molecular volume (Mv), molar refractivity

(Mr), parachor (Pc), index of refraction (IOR), surface

tension (st), density (D), molecular connectivity (v);

topological parameters such as Balaban indices (J), Wiener

index (W), mean Wiener index (WA), Balaban centric index

(BAC), information theoretic index (ID); electronic

parameters such as equalized electronegativity (Xeq),

polarizability (Pz); hydrophobic parameter such as parti-

tion coefficient (log P); and other parameters based on

density functional theory (DFT) calculations such as total

energy, dipole moment, highest occupied molecular orbital

energy (HOMO), the lowest unoccupied molecular orbital

energy (LUMO), hardness (g), chemical potential (l),

electrophilicity index (w), and softness (S) have been cal-

culated for all the derivatives of pyridine presented in the

series. Out of above descriptors, Mw, Mv, Mr, Pc, st, D,

IOR, and Pz were calculated by means of ACD Lab Chem.

Sketch version 12.0 Software (2009), whereas v, J, W, WA,

and BAC were evaluated by means of E-Dragon Software

(Tetko et al., 2005). DFT descriptors such as total energy,

dipole moment, HOMO, LUMO, g, l, w. and S were per-

formed with the help of the Turbomole program package

(Turbomole v6.0, 2009) using Becke’s three-parameter

exchange functional with correlation functional (Becke,

1993) of Lee, Yang, and Parr (B3LYP) (Lee et al., 1988;

Puzyn et al., 2008). All the species were fully optimized in

gas phase with 6-31?G* basis set, and harmonic vibra-

tional frequency calculations were used to confirm that the

optimized structures were minima, as characterized by

positive vibrational frequencies (Muller et al., 2001). The

statistical significance of the models was determined by

examining the regression coefficient, the standard devia-

tion, the number of variables, the cross validation leave-

one-out statistics, and the proportion between the cases and

variables in the equation (Coats et al., 1985). We have used

Hansch analysis for developing the models (Hansch and

Leo, 1995). The multiple regression analysis was used to

derive the correlation using SPSS 7.5 version program. The

detailed descriptions of the parameters that are used in the

present study are given in the supporting information.

Results and discussion

QSAR studies were performed on a set of compounds of

pyridine acyl sulfonamide derivative (Zhu et al., 2011).

The biological activity data of these compounds were

correlated with different steric parameters such as st, D, ID,

and molecular connectivity (3v and 5v); topological

parameters such as W, WA, Balaban connectivity distance

index (J); and DFT parameters such as S, g, l, and LUMO,

which have been found to be useful in QSAR-based drug

modeling (Srivastava et al., 2008a, b, c; Agarwal et al.,

2003, 2005, 2006; Khadikar et al., 2002, 2003a, b, 2005a,

1866 Med Chem Res (2014) 23:1865–1877

123

b). Structural details of the compounds with their experi-

mental activity (log IC50) and indicator parameter values

are given in Table 1. Indicator parameters are not QSAR

parameters; however, they will be used as dummy

parameters that indicate the significance of any particular

group or species at a particular substitution site in a given

series of drugs. In this study, we have taken the indicator

parameters as I1, I2, I3, I4, I5, and I6 and corresponding

indicator parameters are given in Scheme 1. In Table 1, the

value of indicator parameter is 1 if that group is present at a

particular position. For example, I4 indicator parameter is

considered as 1 ifN

(pyridine) is present at R2

position (11–14).

Various physicochemical, topological, and 3D parame-

ters which are used for making various significant models

are given in Table 2. Statistically significant models were

obtained when some of the physicochemical and topolog-

ical parameters such as st, D, ID, molecular connectivity

(3v and 5v), W, WA, Balaban connectivity distance index

(J) and DFT parameters such as S, g, l and LUMO are

combined with the indicator parameter.

The first step in obtaining a statistically significant

model is to investigate whether any collinearity exists

between the parameters used. This is achieved by obtaining

correlation matrix; such a matrix obtained in the present

case for the physicochemical, topological, and indicator

parameters along with respective activities is shown in

Table 3, and the one obtained for DFT parameter and

indicator parameter along with activities is shown in

Table 4. In practice, every term in correlation matrix [0.5

can be taken as suspicious because of collinearity.

The stepwise development of model along with changes

in statistical qualities on gradual addition of descriptors

pIC50 ¼ þ1:551 �0:588ð ÞS� 2:862

n ¼ 24; R ¼ 0:760; R2 ¼ 0:577; R2A ¼ 0:588;

SE ¼ 0:218; Fð1�22Þ ¼ 30:004; Q ¼ 3:486:

ð1Þ

Equation 1 explains only 57.7 % variance in the COX-2

inhibitory activity. It shows that descriptor S contributes

positively. Based on variance percentage, it is not a very

good significant equation; addition of indicator parameter

I6 , however, slightly improves the statics of the equation.

pIC50 ¼þ 1:557 �0:482ð ÞS

� 0:308 �0:186ð ÞI6 � 2:828

n ¼ 24; R ¼ 0:854; R2 ¼ 0:729; R2A ¼ 0:704;

SE ¼ 0:178; Fð2�21Þ ¼ 28:294; Q ¼ 4:798:

ð2Þ


inhibitory activity. It shows that indicator parameter I6 has

negative coefficient suggesting that the group presented by

I6 contributes negatively toward the activity of drugs.

Based on variance percentage, it is not a very good

significant equation; addition of another indicator

parameter I4 , however, slightly improves the statics of

the equation.

pIC50 ¼þ 1:488 �0:382ð ÞS

� 0:296 �0:147ð ÞI6

� 0:288 �0:161ð ÞI4 � 2:421

n ¼ 24; R ¼ 0:917; R2 ¼ 0:840; R2A ¼ 0:817;

SE ¼ 0:140; Fð3�20Þ ¼ 35:128; Q ¼ 6:550:

ð3Þ


inhibitory activity. It shows that indicator parameter I4 has

negative coefficient suggesting that the group presented by

I4 contributes negatively toward the activity of drugs.

Based on variance percentage, it is not a very good

significant equation; addition of another indicator

parameter I5 , however, slightly improves the statics of

the equation.

pIC50 ¼þ 1:378 �0:311ð ÞS

� 0:239 �0:122ð ÞI6

� 0:307 �0:129ð ÞI4

þ 0:212 �0:124ð ÞI5 � 1:902

n ¼ 24; R ¼ 0:951; R2 ¼ 0:905; R2A ¼ 0:884;

SE ¼ 0:111; Fð4�19Þ ¼ 45:011; Q ¼ 8:568:

ð4Þ

Equation 4 explains 90.5 % variance in the COX-2

inhibitory activity. It shows that indicator parameter I5

has positive coefficient suggesting that the group presented

by I5 contributes positively toward the activity of drugs.

Introducing g parameter in place of S parameter also gives

significant model. Based on variance percentage, it is a

good significant equation and model.

pIC50 ¼� 76:188 �17:23ð Þg

þ 0:228 �0:124ð ÞI5

� 0:240 �0:122ð ÞI6

� 0:301 �0:129ð ÞI4 þ 12:590

n ¼ 24; R ¼ 0:951; R2 ¼ 0:904; R2A ¼ 0:884;

SE ¼ 0:111; Fð4�19Þ ¼ 44:946; Q ¼ 8:568:

ð5Þ

Equation 5 explains 90.4 % variance in the COX-2 inhib-

itory activity. It shows that descriptor g contributes nega-

tively. Thus, Eqs. 4 and 5 represent best model among all

the obtained models.

Med Chem Res (2014) 23:1865–1877 1867

123

Table 1 Biological activity and indicator parameter of pyridine acyl sulfonamide derivatives

S

NH O

OO

R1

R2

Compound no. R2 R1 I1 I2 I3 I4 I5 I6 pIC50

1

N

H 0 0 1 0 0 0 4.801

2

N

F 0 0 0 0 0 0 4.932

3

N

Cl 0 0 0 0 0 0 5.180

4

N

Br 0 0 0 0 1 0 5.310

5

N

CH3 0 0 0 0 0 1 4.740

6 S

N

NHO

O O

H

H 1 0 1 0 0 0 5.102

7 S

N

NHO

O O

F

F 0 0 0 0 0 0 5.252

8 S

N

NHO

O O

Cl

Cl 0 0 0 0 0 0 5.468

1868 Med Chem Res (2014) 23:1865–1877

123

Table 1 continued


9

S

N

NHO

O O

Br

Br 0 0 0 0 1 0 5.553

10 S

N

NHO

O O

Br

CH3 0 0 0 0 0 1 5.070

11

N

F 0 0 0 1 0 0 4.917

12

N

Cl 0 0 0 1 0 0 4.900

13

N

Br 0 0 0 1 1 0 5.108

14

N

CH3 0 0 0 1 0 1 4.712

15

N

H 0 0 1 0 0 0 5.056

16

N

F 0 0 0 0 0 0 5.201

17

N

Cl 0 0 0 0 0 0 5.222

18

N

Br 0 0 0 0 1 0 5.443

19

N

CH3 0 0 0 0 0 1 5.097

Med Chem Res (2014) 23:1865–1877 1869

123

Table 1 continued


20

S N

NHO

O O

H

H 0 0 1 0 0 0 5.432

21 S N

NHO

O O

F

F 0 0 0 0 0 0 5.585

22 S N

NHO

O O

Cl

Cl 0 0 0 0 0 0 5.721

23 S N

NHO

O O

Br

Br 0 1 0 0 1 0 6.097

24 S N

NHO

O O

H3C

CH3 0 0 0 0 0 1 5.252

I1 = 1 if R2 is

S

N

NHO

O O

H

I2 = 1 if R2 isS N

NHO

O O

Br

I3 = 1 if R1 is H

I4 = 1 if R2 is

N

I5 = 1 if R1 is Br

I6 = 1 if R1 is CH3

1870 Med Chem Res (2014) 23:1865–1877

123

The models which are less significant compared with 4

and 5

pIC50 ¼0:056 �0:02ð Þst

þ 0:503 �0:4ð ÞI2 þ 1:933

n ¼ 24; R ¼ 0:861; R2 ¼ 0:741; R2A ¼ 0:717;

SE ¼ 0:174; Fð2�21Þ ¼ 30:095; Q ¼ 4:949:

ð6Þ


inhibitory activity. It shows that descriptor st and indicator

parameter I2 contribute positively toward the activity of

drugs. Based on variance percentage, it is not a very good

significant equation; therefore new model is required for

good explained variance.

pIC50 ¼þ 0:337 �0:188ð ÞI5

� 0:051 �0:199ð ÞI6

� 0:355 �0:198ð ÞI4

� 29:753 �12:528ð Þl� 0:259

n ¼ 24; R ¼ 0:878; R2 ¼ 0:771; R2A ¼ 0:723;

SE ¼ 0:172; Fð4�19Þ ¼ 16:003; Q ¼ 5:105:

ð7Þ


inhibitory activity. Based on variance percentage, it is not a

very good significant equation; therefore, new model is

required for good explained variance.

pIC50 ¼0:358 �0:407ð ÞI2

� 0:172 �0:364ð ÞI1

þ 1:241 �0:669ð ÞD

þ 0:00009 �0:00009ð ÞW þ 3:185

n ¼ 24; R ¼ 0:887; R2 ¼ 0:787; R2A ¼ 0:742;

SE ¼ 0:166; Fð4�19Þ ¼ 17:524; Q ¼ 5:343:

ð8Þ


inhibitory activity. It shows that descriptor D and

W contribute positively, and indicator parameter I1

contributes negatively toward the activity of drugs. In

this model, descriptor D and W show slight correlation

(Table 3) and it is not a very good significant equation,

therefore new model required for good explained variance.

pIC50 ¼þ 0:360 �0:406ð ÞI2

� 0:185 �0:364ð ÞI1

þ 1:234 �0:668ð ÞD

þ 0:108 �0:075ð ÞWA þ 2:802

n ¼ 24; R ¼ 0:888; R2 ¼ 0:788; R2A ¼ 0:744;

SE ¼ 0:166; Fð4�19Þ ¼ 17:693; Q ¼ 5:349:

ð9Þ


inhibitory activity. It shows that descriptor WA contributes

positively. In this model, descriptor D and WA show slight

correlation (Table 3)and it isnot averygoodsignificantequation,

therefore new model required for good explained variance.

pIC50 ¼þ 0:360 �0:405ð ÞI2

� 0:187 �0:364ð ÞI1

þ 1:235 �0:667ð ÞD

þ 0:051 �0:034ð Þ3vþ 2:941

n ¼ 24; R ¼ 0:888; R2 ¼ 0:789; R2A ¼ 0:744;

SE ¼ 0:166; Fð4�19Þ ¼ 17:718; Q ¼ 5:349:

ð10Þ


inhibitory activity. It shows that descriptor molecular

connectivity (3v) contributes positively. In this model,

descriptor D and 3v show slight correlation (Table 3) and it

is not a very good significant equation, therefore new

model required for good explained variance.

pIC50 ¼þ 0:359 �0:404ð ÞI2

� 0:201 �0:365ð ÞI1

þ 1:239 �0:663ð ÞD

þ 0:084 �0:056ð Þ5vþ 2:959

n ¼ 24; R ¼ 0:889; R2 ¼ 0:790; R2A ¼ 0:746;

SE ¼ 0:165; Fð4�19Þ ¼ 17:890; Q ¼ 5:388:

ð11Þ

For I1:

S

N

NHO

O O

H group at R2 position For I4: N group at R2 position

For I2:

S N

NHO

O O

Br group at R2 position For I5: -Br group at R1 position

For I3: H at R1 position For I6: -CH3 group at R1 position

Scheme 1 Different indicator

(I) parameters

Med Chem Res (2014) 23:1865–1877 1871

123


inhibitory activity. It shows that descriptor molecular

connectivity (5v) contributes positively. In this model,

descriptor D and 5v show slight correlation (Table 3) and It

is not a very good significant equation.

pIC50 ¼þ 0:359 �0:401ð ÞI2 � 0:220 �0:366ð ÞI1

þ 1:247 �0:657ð ÞD� 0:740 �0:494ð ÞJ þ 0:461

n ¼ 24; R ¼ 0:890; R2 ¼ 0:792; R2A ¼ 0:748;

SE ¼ 0:164; Fð4�19Þ ¼ 18:100; Q ¼ 5:427: ð12Þ

Table 2 Values of the calculated empirical and DFT-based parameters for 1–24

Compound no. st D W WA3v 5v J LUMO g S l ID

1 55.6 1.361 626 4.092 6.013 3.419 1.848 -0.07651 0.100 4.996 -0.177 4.146

2 53.9 1.423 736 4.304 6.424 3.581 1.845 -0.07936 0.100 5.005 -0.179 4.207

3 57.4 1.450 736 4.304 6.424 3.581 1.845 -0.08015 0.100 5.013 -0.180 4.207

4 58.3 1.633 736 4.304 6.424 3.581 1.845 -0.08024 0.100 5.025 -0.180 4.207

5 53.2 1.322 736 4.304 6.424 3.581 1.845 -0.07468 0.098 5.092 -0.175 4.207

6 62.6 1.471 2689 6.182 10.482 6.225 1.517 -0.09193 0.096 5.210 -0.188 4.881

7 60.0 1.547 3265 6.583 11.303 6.549 1.509 -0.09657 0.096 5.224 -0.193 4.759

8 64.5 1.575 3265 6.583 11.303 6.549 1.509 -0.09681 0.096 5.224 -0.193 4.759

9 65.6 1.800 3265 6.583 11.303 6.549 1.509 -0.09662 0.094 5.296 -0.191 4.759

10 58.7 1.412 3265 6.583 11.303 6.549 1.509 -0.28083 0.096 5.220 -0.185 4.759

11 53.9 1.423 736 4.304 6.424 3.581 1.845 -0.08925 0.096 5.220 -0.185 4.207

12 57.4 1.450 736 4.304 6.424 3.581 1.845 -0.08729 0.097 5.167 -0.184 4.207

13 58.3 1.633 736 4.304 6.424 3.581 1.845 -0.08757 0.097 5.167 -0.184 4.207

14 53.2 1.322 736 4.304 6.424 3.581 1.845 -0.08214 0.097 5.130 -0.180 4.207

15 55.6 1.361 626 4.092 6.013 3.419 1.845 -0.07885 0.098 5.125 -0.176 4.146

16 53.9 1.423 736 4.304 6.424 3.581 1.848 -0.08189 0.097 5.131 -0.180 4.207

17 57.4 1.450 736 4.304 6.424 3.581 1.845 -0.08231 0.097 5.138 -0.180 4.207

18 58.3 1.633 736 4.304 6.424 3.581 1.845 -0.08215 0.097 5.170 -0.179 4.207

19 53.2 1.322 736 4.304 6.424 3.581 1.845 -0.07730 0.097 5.154 -0.174 4.207

20 62.6 1.471 2689 6.182 10.482 6.225 1.517 -0.09651 0.095 5.285 -0.191 4.881

21 60.0 1.547 3265 6.583 11.303 6.549 1.509 -0.10113 0.094 5.341 -0.195 4.759

22 64.5 1.575 3265 6.583 11.303 6.549 1.509 -0.10136 0.091 5.508 -0.192 4.759

23 65.6 1.800 3265 6.583 11.303 6.549 1.509 -0.10190 0.088 5.665 -0.190 4.759

24 58.7 1.412 3265 6.583 11.303 6.549 1.509 -0.09447 0.092 5.447 -0.186 4.759

Table 3 Correlation matrix between empirical parameters and indicator parameter

pIC50 st D I1 I2 I3 W WA3v 5v J ID

pIC50 1.000

st 0.798 1.000

D 0.798 0.773 1.000

I1 -0.073 0.219 -0.033 1.000

I2 0.574 0.376 0.483 0.043 1.000

I3 -0.163 0.075 -0.257 0.466 -0.093 1.000

W 0.650 0.808 0.465 0.165 0.265 -0.028 1.000

WA 0.649 0.811 0.465 0.185 0.260 -0.027 0.999 1.0003v 0.648 0.812 0.463 0.188 0.260 -0.020 0.999 1.000 1.0005v 0.642 0.815 0.454 0.209 0.256 0.014 0.998 0.999 0.999 1.000

J -0.632 -0.817 -0.441 -0.239 -0.249 -0.063 -0.994 -0.996 -0.996 -0.999 1.000

ID 0.611 0.815 0.421 0.315 0.227 0.110 0.973 0.980 0.980 0.986 0.991 1.000

1872 Med Chem Res (2014) 23:1865–1877

123


inhibitory activity. It shows that descriptor Balaban

connectivity distance index (J) contributes negatively. It

is not a very good significant equation.

pIC50 ¼þ 0:365 �0:398ð ÞI2

� 0:274 �0:374ð ÞI1

þ 1:244 �0:649ð ÞD

þ 0:436 �0:283ð ÞIDþ 1:418

n ¼ 24; R ¼ 0:892; R2 ¼ 0:796; R2A ¼ 0:753;

SE ¼ 0:163; Fð4�19Þ ¼ 18:533; Q ¼ 5:472:

ð13Þ


inhibitory activity. It shows that descriptor ID contributes

positively. However, variance is low so that this model is

not a very significant equation.

pIC50 ¼ 0:061 �0:019ð Þst

þ 0:437 �0:377ð ÞI2

� 0:278 �0:4ð ÞI1

� 0:098 �0:21ð ÞI3 þ 1:671

n ¼ 24; R ¼ 0:894; R2 ¼ 0:799; R2A ¼ 0:757;

SE ¼ 0:161; Fð4�19Þ ¼ 18:883; Q ¼ 5:553:

ð14Þ


inhibitory activity. It is not a very good significant

equation.

pIC50 ¼þ 0:297 �0:151ð ÞI5

� 0:084 �0:155ð ÞI6

� 0:343 �0:159ð ÞI4

� 24:002 �7:173ð ÞLUMOþ 3:121

n ¼ 24; R ¼ 0:924; R2 ¼ 0:853; R2A ¼ 0:822;

SE ¼ 0:138; Fð4�19Þ ¼ 27:559; Q ¼ 6:696:

ð15Þ


inhibitory activity. This model equation shows that the

LUMO descriptors contribute negatively toward activity. It

is not a very good significant equation. Where n is the

number of compounds in the dataset, R is the correlation

coefficient, R2 is the coefficient of determination, R2A is the

adjusted coefficient of determination, SE is the standard

error of estimate, F is the variance ratio (Bikash et al.,

2003; Diudea, 2001), and Q is the quality of fit (Pogliani,

1994, 1996).

The above equations show that the coefficients of st, W,

WA, ID, D and molecular connectivity of third and fifth

order are positive this indicate that more bulkier, denser

group having more branching is favorable for the activity.

The negative coefficient of J in the above model is probably

due to its high collinearity with other parameters. The

negative sign of coefficients of indicator I1 and I3 is showing

that the group presented by I1 and I3 at R2 and R1 positions

(see footnote of Table 1), respectively, has a negative

influence on activity and should not be used for the future

drug modeling at R2 and R1 positions, respectively. The

positive sign of coefficients of indicator parameter I2 is

showing that the group presented by I2 at R2 group (see

footnote of Table 1) has a positive influence on activity and

should be used at R2 position for future drug modeling.

DFT-based calculated models reveal that the parameters

g, l, LUMO have negative coefficient, while one of them is

positive (S). Indicator parameter (I4, I6) have negative

coefficient, while I5 have positive. Thus, the decrease in

values of these parameters g, l, and LUMO and the

absence of the group indicated by I4, and I6 at R2 and R1

positions, respectively (see footnote of Table 1), are

favorable for the inhibitory activity. Similarly, the increase

in the value of S parameter and the presence of group

indicated by I5 at R1 position (see footnote of Table 1) are

favorable for the inhibitory activity. In all the above

equations, R, R2, and R2A are substantially high and SE is

fairly low, indicating that these models are statistically

significant in all the statistical terms.

Out of several QSAR models, models (4) and (5) show

best results. In order to confirm that the model with

excellent statistics has excellent predictive power too, we

Table 4 Correlation matrix between DFT-based parameters and indicator parameter

pIC50 l g el S I4 I5 I6

pIC50 1.000

l -0.647 1.000

g -0.752 0.695 1.000

el -0.734 0.969 0.846 1.000

S 0.760 -0.687 -0.998 -0.841 1.000

I4 -0.426 0.051 0.112 0.063 -0.101 1.000

I5 0.460 -0.062 -0.159 -0.117 0.190 0.046 1.000

I6 -0.385 0.327 -0.018 0.252 0.007 0.046 -0.263 1.000

Med Chem Res (2014) 23:1865–1877 1873

123

have evaluated quality factor Q. The predictive power as

determined by the Pogliani Q parameter for the model

expressed by Eqs. 4 and 5 (Q = 8.568) confirms that this

model has excellent statistics as well as excellent predictive

power.

According to Eqs. 4 and 5, the compounds having the

highest value of softness parameter, the lowest value of

hardness parameter, and the presence of bromine (–Br) at

R1 position show the highest inhibitory effect toward COX-

2 enzyme. Focusing on Tables 1 and 2, we find that 23 has

the maximum value of softness parameter, minimum value

of hardness parameter, and besides, Br is also present at R1

position, which all indicate that 23 inhibits COX-2 enzyme

more potentially, which is in good agreement with exper-

imental finding and SAR studies (Zhu et al., 2011).

Predicted and residual activity values for models (4) and

(5) are given in Table 5. Predicted values are the calculated

activities obtained from models (4) and (5), and the

residual values are the differences between the observed

biological activities and calculated activities The plot of

observed pIC50 verses predicted pIC50 for Eqs. 4 and 5 is

shown in graphical format (Figs. 1, 2), and the predicted R2

values were found to be fairly larger.

Further, we have calculated the molecular electrostatic

potential (MESP) and frontier orbitals for quantitative ana-

lysis of the activity of the present series using DFT methods by

employing 6-31?G* basis set in gas phase. The calculated

MESP at iso-value of 0.06 revealed that 22 and 23 have quite

less negative potential on sulfonamides group than that of the

rest of the compounds (Supporting information Fig. S1), and

also the frontier orbitals (HOMO and LUMO) of 22 and 23

were away from sulfonamides group and mostly concentrated

on benzene ring. However, in rest of the compounds, the

frontier orbitals are dispersed (Supporting information Fig.

S2). The calculated results of MESP and frontier orbitals

suggest that the activity of compound depends upon the less

negative potential on sulfonamide group and that the frontier

orbitals lie on one side of the compounds. The predicted

results also support the experimental observation.

Cross validation

The cross validation analysis was performed using leave-

one-out method (Cramer et al., 1988), in which oneTable 5 Comparison between observed and predicted activities and

their residual values

Observed

activity

Equation 4 Equation 5

Predicted

activity

Residual Predicted

activity

Residual

1 4.801 4.982 -0.181 4.971 -0.170

2 4.932 4.994 -0.062 4.979 -0.047

3 5.180 5.005 0.175 4.994 0.186

4 5.310 5.233 0.077 5.238 0.072

5 4.740 4.875 -0.135 4.868 -0.128

6 5.102 5.276 -0.174 5.284 -0.182

7 5.252 5.296 -0.044 5.299 -0.047

8 5.468 5.296 0.172 5.299 0.169

9 5.553 5.607 -0.054 5.626 -0.073

10 5.070 5.051 0.019 5.051 0.019

11 4.917 4.983 -0.066 4.990 -0.073

12 4.900 4.911 -0.011 4.922 -0.022

13 5.108 5.123 -0.015 5.097 0.011

14 4.712 4.621 0.091 4.628 0.084

15 5.056 5.159 -0.103 5.162 -0.106

16 5.201 5.168 0.033 5.170 0.031

17 5.222 5.177 0.045 5.177 0.045

18 5.443 5.433 0.010 5.451 -0.008

19 5.097 4.960 0.137 4.960 0.137

20 5.432 5.380 0.052 5.383 0.049

21 5.585 5.457 0.128 5.459 0.126

22 5.721 5.687 0.034 5.680 0.041

23 6.097 6.115 -0.018 6.099 -0.002

24 5.252 5.364 -0.112 5.364 -0.112

Fig. 1 A plot showing comparison between observed activity and

predicted activity based on model no. 4

Fig. 2 A plot showing comparison between observed activity and

predicted activity based on model no. 5

1874 Med Chem Res (2014) 23:1865–1877

123

compound is removed from the dataset and the activity is

correlated using the rest of the dataset. The cross validated

R2 in each case was found to be very close to the value of

R2 for the entire dataset, and hence, these models can be

termed as statistically significant. Cross validation provides

the values of PRESS, SSY, predictive square error (PSE),

R2CV and R2

A from which we can test the predictive power of

the proposed model. These statistical parameters can be

calculated from following equations:

PRESS ¼X

Xobs � Xcalð Þ2 ðiÞ

SSY ¼X

Xobs � Xmeanð Þ2 ðiiÞ

PSE ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPRESSp

=n ðiiiÞ

R2CV ¼ 1� PRESS

SSYðivÞ

R2A ¼ 1� r2

� � n� 1

n� p� 1

� �: ðvÞ

It is argued that PRESS is a good estimate of the real

predictive error of the model, and if it is smaller than SSY,

then the model predicts better than chance and can be

considered as statistically significant. Furthermore, the

ratio of PRESS/SSY can be used to calculate the approx-

imate confidence intervals of prediction of a new com-

pound. To be a reasonably perfect QSAR model, PRESS/

SSY should preferably be smaller than 0.4. Also, if PRESS

value is transformed in a dimensionless term by relating it

to the initial sum of squares, we obtain R2CV i.e., the

complement to the traces on of unexplained variance over

the total variance. The PRESS and R2CV have good prop-

erties. However, for practical purposes of the end users, the

use of square root of PRESS/n, which is called PSE, is

more directly related to the uncertainty of the predictions.

The PSE values also support our results. The calculated

cross validated parameters confirm the validity of the

models. All the requirements for an ideal model have been

fulfilled by model nos. 4 and 5; that is why, we have

considered these two models as the best models. R2A takes

into account the adjustment of R2. R2A is a measure of the

percentage of explained variation in the dependent vari-

able, which takes into account the relationship between the

number of cases and the number of independent variables

in the regression model, whereas R2 will always increase

when an independent variable is added. R2A will decrease if

the added variable does not reduce the unexplained vari-

able enough to offset the loss of decrease of freedom.

Predictive error of coefficient of correlation (PE)

The PE (Chaterjee et al., 2000) is yet another parameter

used to decide the predictive power of the proposed mod-

els. We have calculated PE values of all the proposed

models, and they are reported in Table 6. It is argued that if

the values of R \ PE, then such correlation is not signifi-

cant; however, if values of R [ PE by several folds (at least

three times), then the values are correlated. However, if

values of R [ 6PE, then mathematically the correlation is

unquestionably good. For all the models developed, the

condition R [ 6PE is satisfied, and hence, they can be said

to have a good predictive power.

Conclusions

The current study was performed to examine the applica-

bility of the empirical and DFT-based descriptors in QSAR

analysis for studying the biological activities of a series of

pyridine acyl sulfonamide derivatives which are known as

potent nonsteroidal anti-inflammatory and analgesic

agents. The obtained QSAR results based on empirical

parameters and DFT-based descriptors demonstrate that the

Table 6 Cross validated parameters and PE for the proposed models

Model no. n Parameter used PRESS SSY PRESS/SSY R2CV PSE R 1 - R2 PE 6PE

4 24 S ? I4 ? I5 ? I6 0.235 2.229 0.105 0.895 0.099 0.951 0.095 0.013 0.078

5 24 g ? I4 ? I5 ? I6 0.236 2.228 0.106 0.894 0.099 0.951 0.096 0.013 0.078

6 24 st ? I2 0.637 1.827 0.349 0.651 0.169 0.861 0.259 0.035 0.210

7 24 l ? I4 ? I5 ? I6 0.564 1.900 0.297 0.703 0.153 0.878 0.229 0.031 0.186

8 24 D ? I1 ? I2 ? W 0.525 1.939 0.271 0.729 0.147 0.887 0.213 0.028 0.168

9 24 D ? I1 ? I2 ? WA 0.521 1.943 0.268 0.732 0.147 0.888 0.212 0.029 0.174

10 24 D ? I1 ? I2 ? 3v 0.521 1.943 0.268 0.732 0.147 0.888 0.211 0.029 0.174

11 24 D ? I1 ? I2 ? 5v 0.517 1.947 0.266 0.734 0.146 0.889 0.210 0.028 0.168

12 24 D ? I1 ? I2 ? J 0.512 1.952 0.262 0.738 0.146 0.890 0.208 0.028 0.168

13 24 D ? I1 ? I2 ? ID 0.502 1.962 0.256 0.744 0.145 0.892 0.204 0.028 0.1.67

14 24 st ? I1 ? I2 ? I3 0.495 1.969 0.251 0.749 0.143 0.894 0.201 0.027 0.162

15 24 LUMO ? I4 ? I5 ? I6 0.362 2.102 0.172 0.828 0.123 0.924 0.147 0.020 0.120

Med Chem Res (2014) 23:1865–1877 1875

123

DFT-based descriptors are in very good agreement with

experimental findings. However, the calculated empirical

parameters also shed light on factors which influence the

activity. Among the DFT-based parameters, such as S, g, l,

and LUMO, the descriptors S and g were found to be the

most prominent to affect the activity.

Further, the calculated QSAR model, MESP, and fron-

tier orbital results revealed that the electron-donating group

at R1 position will activate the ring (e.g., –CH3), and it will

reduce the activity; however, the deactivating nature at R1

position with electron-donating group (e.g., –Br) will

enhance the activity of the present series of drug. Fur-

thermore, our calculated results also demonstrate that the

group of pyridine derivatives (11–14) at R2 position will

reduce the activity.

Acknowledgments The author A. K. Srivastava gratefully

acknowledges the grant under the Grant No. 40-70/2011 (SR) from

the University Grants Commission (UGC), New Delhi, India. Author

A. Singh wishes to acknowledge the award of Dr. D. S. Kothari’s

postdoctoral fellowship by the UGC, New Delhi, India.

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