**TWO DIMENSIONAL- QUANTITATIVE STRUCTURE ACTIVITY **
**RELATIONSHIPS -2, 3 DIARYLTHIOPHENES AS SELECTIVE **

**COX-1/-2 INHIBITORS **

MUKESH C. SHARMA^{*}, D. V. KOHLI, SMITA . SHARMA^{a},
S. C. CHATURVEDI^{b }

*Department of Pharmaceutical Sciences Dr.H.S.Gour.University Sagar (M.P) *
*470003 India*

*a**Department of Chemistry Yadhunath Mahavidyalya Bhind (M.P) 477001 India *

*b **School of Pharmacy D.A.V.V.University Indore (M.P) 452 001 India *

A Quantitative Structure Activity Relationship Study on a series of substituted 2, 3 DIARYLTHIOPHENES AS SELECTIVE COX-2 AND COX-1 INHIBITORS was made using combination of various thermodynamic electronic and spatial descriptors. Several statistical expressions were developed using stepwise multiple liner regression analysis.

The best quantitative structure activity relationship models were further validated by
leave-one-out method of cross-validation. The best quantitative structure activity
relationship COX-1 model was selected having a correlation coefficient (r) of 0.8672 and
cross-validated correlation coefficient (Q^{2}) of 0.76 and COX-2 model was selected having
a correlation coefficient (r) of. 0.9070 and cross-validated correlation coefficient (Q^{2}) of
0.85. The study indicates that thermodynamic descriptors (torsion energy, LogP, HF,
Ovality, molar refractivity and Vander Waals energy) and electronic descriptor (HOMO,
lowest unoccupied molecular orbital) play an important role for the non-steroidal anti-
inflammatory drugs. The quantitative structure activity relationship study provides
important structural insights in designing of COX -1/-2 Inhibitors.

(Received June 5, 2009; accepted July 15, 2009)

*Keywords: QSAR, 2, 3 Diarylthiophenes As Selective Inhibitors, COX-1/-2 *

**1. Introduction **

Inhibition of prostaglandin production with non-steroidal anti-inflammatory drugs (NSAIDs) has been widely used for the treatment of both acute and chronic inflammatory diseases. [1] These compounds have had significant side effects which potentially limit their use in a large proportion of the potential patient population. [2] Arachidonic acid is converted to prostaglandins by at least two isoforms of the enzyme cyclooxygenase. [3, 4].The constitutive form of this enzyme (COX-l) is responsible for the normal production of prostaglandins. An inducible form of cyclooxygenase (COX-2) is primarily responsible for the production of prostaglandins at sites of inflammation. Non-steroidal anti-inflammatory agents (NSAID) are widely used in the treatment and management of pain and inflammation. These compounds inhibit the enzyme cyclooxygenase (COX) and thus prevent the formation of prostaglandins at elevated levels causing inflammation [5]. It has been reported that selective inhibition of second isoform of the enzyme, cyclooxygenase-2 (COX-2) (induced during inflammation) may provide the therapeutic benefit without causing gastric ulceration associated with the classical agents [6]. The improved safety profile of COX-2 inhibitors may allow the use of these new agents for long-term prophylactic use in certain chronic diseases [7]. This has led intense efforts in search for potent and selective COX-2 inhibitors, as the next generation of anti-inflammatory agents.Thus our main

*Corresponding author: [email protected]

objective is to design specific inhibitors of COX-2 in the hope that these molecules may be further explored as powerful non-ulcerogenic anti-inflammatory agents.2, 3-diarylthiophenes In addition nowhere quantitative structure activity analysis has been reported for2, 3-diarylthiophenes. Thus such studies may help for the design and synthesis of better selective COX-2 inhibitors. The major objective of this study is to explore the physicochemical properties which are helpful in the designing of selective COX-1/ COX-2 inhibitors with better efficacy and reduced toxicity. The objective can be fulfilled by structural requirement which is explored through QSAR study and then exploited to optimize activity of compounds of selected series.

**2. Materials and methods **

A part of our efforts to create QSAR models shows substantial predictive promise for the designing of new compounds with enhanced biological activity. In the present work, we correlated 2,3 DIARYLTHIOPHENES AS SELECTIVE COX-2 AND COX-1 INHIBITORS Yves Leblanc.et.al [8] (Table- 1).All computational work was performed on Pentium IV Dual Core Work station-using software In QSAR study, the logarithmic form of depending data set was considered which is having less skewness as compared to the non-logarithmic one. The inhibitory concentration (IC50 in µM) of COX-2, COX-1 was converted into pIC50 (negative logarithm of IC50 in mole) used as a dependent variable. The series was divided into a training set of 18 compounds including S-1 to S-18 (Table 1), and a test set of 7 compounds including T-1 to T-7 (Table 1), The molecular modelling study was performed using CS ChemOffice 6.1 [9], while the regression analysis was carried out on VALSTAT [10]. Structures of all compounds were sketched using builder module of the program. The sketched structures were subjected to energy minimization via steepest descent method using force field until the RMS gradient value become smaller than 0.001 kcal/molA° . The energy minimized molecules have been subjected to re- optimization via Austin model (AM1) [11] method until the RMS gradient attained a value lesser than 0.0001 kcal/molA° using MOPAC [12]. The geometry optimization of the lowest energy structure was carried out using EF routine. Calculated thermodynamic descriptors included critical temperature (T), ideal gas thermal capacity (C),Critical pressure (Pc), boiling point (BP), Henry’s law constant (H), bend energy (Eb), heat of formation (Hf), total energy (TE), and partition coefficient (PC). Steric descriptors derived were Connolly accessible area (CAA), Connolly molecular area (CMA), Connolly solvent excluded volume (CSEV), exact mass (EM), molecular weight (MW), principal moment of inertia-X component (PMI-X), principal moment of inertia-Y component (PMIY), principal moment of inertia-Z component (PMI-Z), molar refractivity (MR), and Ovality (OVAL). Electronic descriptors such as dipole (DPL), electronic energy (ElcE), highest occupied molecular orbital energy (HOMO), lowest unoccupied molecular orbital energy (LUMO), repulsion energy (NRE),VDW-1,4-energy (E14), Non-1, 4-VDW energy (E), and total energy (E) were calculated. Multiple linear regression (MLR) analysis was used to investigate the correlation between biological activity and physicochemical properties. The MLR was performed by using the VALSTAT [11] by the stepwise method. The highest correlation of independent variables with dependent variable was chosen for deriving the QSAR model. The statistical values, multiple correlation coefficient (r), standard errors (s), cross validation r2 (q2) and standard error of prediction (SPRESS) were used to evaluate the obtained QSAR models.

**Multiple linear regression analysis **

The stepwise multiple regression analyses were carried out using the statistical software openstat2, version 6.5.1, designed and standardized by Bill Miller and Stat Val. Correlation matrix was obtained to justify the use of more than one variable in the study. The variables used were with maximum correlation to activity and minimum inter-correlation with each other. From the statistical viewpoint, the ratio of the number of samples (N) to the number of variables used (M) should not be very low; usually it is recommended that N/M≥5.

The QSAR equations were constructed for efficacy data of both species of malarial
parasite with the physcio-chemical descriptors and indicator variables. The statistical quality of the
equations[13] was judged by the parameters like correlation coefficient (r), explained variance (r^{2}),

standard error of estimate(s) and the variance ratio or overall significance value (F).The accepted
equations are validated for stability and predictive ability using “leave –one-out” and cross
validation technique. The statistical parameters used to access the quality of the models are the
predictive sum of squares (PRESS) of validation. Finally, the standard cross-validation correlation
coefficient r^{2 }and q^{2} are also calculated.

PRESS = Σ (Ypred - Y obs)^{2}
S_{press} =√ PRESS/ (n-k-1)
n= no. of compounds used for cross-validation

y_{i}= experimental value of the physic-chemical property for the ith sample
y= value predicted by the model built without the sample i

*Table-1: Physicochemical Parameters and Inhibitory Activity of 2, 3 diarylthiophenes as selective cox-1/-2 *
*inhibitors *

S

R_{2}
R_{3}

R_{1}

**S.N**
**o **

**R1 R2 R3 IC_50 **

**COX-**
**2 **

**IC_50 **
**COX-1 **

**PIC_50 **
**COX-1 **

**PIC_50 **
**COX-2 **

1 SO_{2}Me F Br 0.005 0.60 5.78 3.70

2 F SO_{2}Me Br 0.02 1.1 6.04 4.31

3 SO2Me F H 0.25 100 8 5.41

4 F SO_{2}Me H 4.3 50 7.69 6.64

5 SO_{2}Et F H 30 50 7.69 7.47

6 SO2NH2 F H 0.03 1.3 6.12 4.48

7 F SO2NH2 H 0.67 2.7 6.43 5.84

8 SO_{2}NH_{2} C(Me)_{2}OH H 30 50 7.67 7.47

9 SO_{2}NH_{2} F CH(Me)_{2} 0.01 0.23 5.37 4

10 SO2NH2 F CO2Me 0.07 1.0 6 4.85

11 SO_{2}NH_{2} F C(Me)_{2}OH 0.41 5.4 6.73 5.62

12 F SO_{2}NH_{2} C(Me)_{2}OH 1.6 50 7.69 6.21

13 F SO_{2}NH_{2} CO_{2}Me 30 50 7.69 7.47

14 SO2NHMe F H 7.2 50 7.69 6.87

15 SO_{2}NHAc F H 5.4 50 7.69 5.75

16 SeO_{2}Me F H 0.55 32 7.51 3.69

17 CONH2 F H 30 3.2 6.51 7.47

18 COMe F H 30 0.75 8.75 7.47

19 CO_{2}H F H 30 50 7.69 7.47

20 CO_{2}Me F H 30 17 5.88 7.47

21 CHO F H 30 0.98 5.99 7.47

22 CN F H 30 0.21 5.32 7.47

23 CH_{2}OH F H 30 0.35 5.54 7.47

24 SMe F H 30 0.34 5.53 7.47

25 SOMe F H 30 15 7.17 7.47

**Statistical Parameters[14] **

The prime purpose of developing QSAR models is usually prediction of the activity. It is often assumed that provided the correlation is a “good” one (as indicated typically by a high correlation coefficient), then the QSAR can be used to give reliable predictions of bioactivity.

QSAR analysis is based on regression analysis. Regression analysis correlates independent X variables (e.g., physiochemical parameters, indicator variables) and dependent Y variable (e.g., biological data). The equations obtained by regression analysis are analyzed by following parameters:

**Correlation coefficient (r): It is the relative measure of quality of fit of the model **
because its value depends on the overall variance of the dependent variable. It ranges from 0 to 1.

A value of 1 means there is perfect correlation between the biological data and the explanatory variables. A correlation coefficient of 0 means there is no correlation at all. A QSAR equation can be accepted if the ‘r’ is greater than 0.8 for in vivo biological data’s and greater than 0.9 for in vitro biological data’s and if standard deviation is not much larger than standard deviation of biological data.

*Table 1. Comparisons of Observed and Leave One Out Predicted PIC50 Value of Compounds Used *
*Equations … *

Sr.no. Obs.act (-PIC) COX1

Obs.act (-PIC)COX2

Pred. act Model-1

COX2

Pred. act Model-1

COX1

1 5.78 3.70 4.79051 5.82754

2 6.04 4.31 4.80594 6.11089

3 8 5.41 5.78665 8.13969

4 7.69 6.64 7.15339 7.71

5 7.69 7.47 7.8123 7.77821

6 6.12 4.48 7.8123 6.26312

7 6.43 5.84 5.64039 6.47855

8 7.67 7.47 7.8123 5.11085

9 5.37 4 4.73663 5.07918

10 6 4.85 4.945 6.14753

11 6.73 5.62 5.75145 6.8058

12 7.69 6.21 6.98459 7.71465

13 7.69 7.47 7.93371 7.71465

14 7.69 6.87 6.91945 7.71465

15 7.69 5.75 5.94775 7.71465

16 7.51 3.69 4.88451 7.53443

17 6.51 7.47 7.8123 6.58826

18 8.75 7.47 7.8123 5.92344

19 7.69 7.47 7.8123 7.16311

20 5.88 7.47 7.8123 7.21303

21 5.99 7.47 7.8123 5.87367

22 5.32 7.47 7.8123 5.18619

23 5.54 7.47 7.8123 5.6489

24 5.53 7.47 7.8123 5.6121

25 7.17 7.47 7.8123 7.213

Obs = observed activity, Pred= Predicted activity

**Square of correlation coefficient (r**^{2}**): It is a measure of the explained variance, most **
often presented as a percentage value.

r2= 1-ΣΔ2/Sy
S_{yy} = overall total variance
S_{yy} = Σ (y_{obs}-y_{mean})^{2} = [Σ y2 – (Σy)2]/n

Σ Δ2 = SSQ = sum of squared error

Standard Error of Estimate (SEE): It is an absolute measure of the quality of fit. Its value considers the number of objects n and the number of variables k. Therefore, S depends not only on the quality of fit but also on the number of degree of freedom DF= n-k-1.

S2 = Σ Δ2 / n-k-1 = (1-r2) Syy / n-k-1 Where, n-k-1 = Degrees of Freedom

*Table 5. Cox-1 Cross Validation Parameters For Significant Equations. *

**a****bsr**^{2}^{b}**Q**^{2}^{c}**S****PRESS** **d**

**SDEP **

**Model-1 ** 0.4612 0.2138 0.4276 0.1175

**Model-2 ** 0.6249 0.4397 0.3287 0.0267

**Model-3 ** 0.7791 0.4619 0.2718 0.3371

**Model-4 ** 0.6121 0.2710 0.1281 0.2318

**Fischer’s Value (F-value): It indicates F-ratio between the variance of calculated and **
observed activity. It is the measure of the level of statistical significance of the regression model.

The number of variable being included to derive the model has stronger influence than in the case of the standard deviation so only F values being larger than the 95% significance limits are acceptable. The use of the model containing the larger number of variable is justified if the resulting partial F value indicates 95% significance for the new introduction of the new variable. If the calculated F-value is greater than the tabulated value then the equation is said to be significant at particular level of confidence.

F= r2(n-k-1) / k (1-r2)

*Table-6 COX-2 cross validation parameters for significant equations. *

**a****bsr**^{2}^{b}**Q**^{2}^{c}**S****PRESS**

**d****SDEP **

**Model-1 ** 0.1461 0.1287 0.3182 0.5430

**Model-2 ** 0.2143 0.5512 0.3901 0.2145

**Model-3 ** 0.3206 0.6712 0.5721 0.3612

**T-test: This is a method for determining the significance level of the regression coefficient **
particular parameter in a model. When the sample size and population standard deviation is
unknown, t-value is calculated and the number obtained is compared to a table containing the
Student’s t-distribution at different confidence levels and degree of freedom. If the computed value
is larger than the tabulated number then the coefficient can be considered as significant.

Validation of the models is crucial in order to assure their predictive potential. The predictive ability of a model (Internal validation) can be indicated by cross validation of the model generated by regression.

*Table 7. Correlation matrix of model-cox-1 *

**Parameters HF VDWE MR **

**HF ** 1.0000

**VDWE ** 0.22164 1.0000

**MR ** 0.651751 0.729153 1.0000

** Cross Validation: The most common form of cross-validation is ‘leave one out’ or Jack-**
knife method, in which each data value is left out in turn and a model is derived using the
remainder of the data. A value can than be predicted for every data point in the set and compared
with the true observed value. This is repeated for every data point in the set and permitted the
calculation of a “cross-validated r2” also written as q2. Cross validation r2 values are typically
lower than the normal but are considered more indicative of the predictive ability of the equation.

Indeed q^{2} can be negative values (unlike r^{2}). Thus, whereas r2 value is a measure of quality of fit,
q2 is a measure of quality of prediction. A value greater than 0.6 is considered to be useful.

q2 = 1-PRESS / Σ(y_{obs}- y_{mean})^{2}

A more robust alterative to leave one out method is to divide the data set in to two or more
groups while one as training set and another as test set. The model generated by the training set is
used to calculate the activities of compounds of test set and compared with their biological
activity. This is done for every data in test set and ‘r^{2}pred’ is calculated.

pred_ r^{2} = SD – PRESS/ SD

Where, SD is the sum of squared deviation between the biological activities of the test set and the mean activity of the training set molecules and PRESS is the sum of squared deviation between predicted and actual activity values from every molecule in the test set.

*Table 8. Correlation Matrix Of Model-Cox-2 *

**Parameters MR Ovality HOMO **

**MR ** 1.0000

**Ovality ** 0.395950 1.0000

**HOMO ** 0.323234 0.446623 1.0000

**PRESS: It is the predictive residual sum of squares or the predicted extra sum of squares. **

It is the sum of overall compounds of the squared difference between the actual and predicted values for the independent variables. Smaller the value of PRESS statistics indicates better prediction. If it is appreciably larger than the error sum of square of model, it is likely that there are outliers in data.

PRESS = Σ (Ypred - Y obs)2

**SPRESS: It is the standard deviation of prediction derived from the PRESS. It is the sum of **
squared error of prediction, divided by the number of degree of freedom. It is taken as the criterion
for the optimum number of components in various techniques like PLS.

**SDEP: It is the standard deviation of the error of predictions. It corresponds to SPRESS but the **
only difference being that the number of degree of freedom is not considered in the calculation of
this value SDEP = PRESS/ n

**Bootstrapped r**** ^{2}**: r

^{2}bs is correlation coefficient obtained when regression is done using repeated data from the data set used to build the equation. During bootstrapping one data from the data set can be selected as many times while other can be left .Bootstrap r

^{2}should be near to the normal r

^{2}. The three criteria r, s and f value refer to the fit of the data i.e., the predictive ability inside the model and others like PRESS, SPRESS etc., check the predictive ability outside the model.

**3. Results and discussion **

The 25 compounds belonging to diaryl furanones category (Table.1) were divided into two
sets, 18 compounds were taken in the training set and 7 compounds were taken in the test set
(Table 1). The biological activities data for diaryl furanone derivatives were taken from literature
[8]. The IC_{50} values for both COX-1 and COX-2 were transformed into –log [PIC50*10-^{6}] i.e.

pIC50. Stepwise regression analysis was performed by taking pIC50 as dependent variable and descriptors calculated from chemoffice 6.1 as independent variables.

**COX-1 **

BA= [4.04601(± 0.859089)] +HF [-0.0323814(± 0.0185784)] +logP [0.0203999(±

0.0223441)] +Ovality [0.0100504(± 0.00661578)] +TE [-0.0093099(± 0.0251623)]

n=18, r=0.8867, r^2=0.79357, q2 = 0.71,variance=0.115275, std=0.339522,F=31.7973
The tetravariant model No. 1 explained 88.6% of the variance in activity. The standard
error of estimate of the derived coefficients is less in making a higher t value, hence rendering the
terms statistically significant. The observed t values of the descriptors HC, logP, Ovality and DE
are greater than the tabulated t value at 95% confidence interval. The data showed an overall
internal statistical significance level better than 99.9%. The dependency among the
physicochemical parameters was checked by observing an inter correlation amongst the
parameters (i.e., ICAP).The tetravariant model No. 1 was also found to be statistically significant
with a comparatively lesser r^{2} value. The model was found to have a fairly good predictive ability,
as reflected by the cross-validation data. Internal consistency of the models was tested by
exploiting leave-one-out and bootstrapping methods of cross-validation. The models were found to
be robust having a fairly good predictive ability, as evident from the higher q2 (0.71), and low
SPRESS and SDEP values. The model was tested further for outliers by utilizing the Z score
values and no compound was found to be an outlier, which suggested that the model is able to
explain the structurally diverse analogues. The r^{2 }bs is at par with the conventional squared
correlation coefficient (r2). Randomization test data (Chance < 0.001) revealed that the results
were not based on chance correlation.

BA= [3.74773(± 0.755394)] +LogP [-0.0287275(± 0.0160425)] +Ovality [0.0208738(±

0.0191271)] +BE [0.0125142(± 0.00584014)]

n=18, r=0.83696,r^2=0.7704, q2 = 0.80,variance=0.0842067,std=0.290184,F=26.542

**COX-2 Graph of Observed Vs calculated biological activity**

0 1 2 3 4 5 6 7 8 9

0 1 2 3 4 5 6 7 8

**Calculated Predicited Biological Activity**

** O****b****ser****ved**** B****io****lo****g****ical**** A****ct****ivi****ty**

Series1 Linear (Series1)

*Fig. A plot between observed activity and predicted activity for COX-2 *

The trivariant model No.2 explained 77.04% of the variance in activity. The standard
error of estimate of the derived coefficients is less in making a higher t value, hence rendering the
terms statistically significant. The observed t values of the descriptors logP, Ovality and BE are
greater than the tabulated t value at 95% confidence interval. The data showed an overall internal
statistical significance level better than 99.9%. The trivariant model No. 2 was also found to be
statistically significant with a comparatively lesser r^{2} value. The model was found to have a fairly
good predictive ability. Internal consistency of the models was tested by exploiting leave-
one-out and bootstrapping methods of cross-validation. The models were found to be robust
having a fairly good predictive ability, as evident from the higher q2 (0.80), and low S_{PRESS} and
SDEP values. The model was tested further for outliers by utilizing the Z score values and no
compound was found to be an outlier, which suggested that the model is able to explain the
structurally diverse analogues. The r^{2 }bs is at par with the conventional squared correlation
coefficient (r2). Randomization test data (Chance < 0.001) revealed that the results were not based
on chance correlation.

**COX-1 Graph of Observed Vs Calculated Predicted **
**activity**

0 2 4 6 8 10

0 5 10

**Calculated Predicted biological **
**activity**

**O****b****ser****ved**** b****io****lo****g****ical** **act****ivi****ty** Series1

Linear (Series1)

*Fig. A plot between observed activity and predicted activity for COX-1 *

BA= [3.89782(± 0.674334)] +HF [-0.0295238(± 0.0154761)] + VDWE [0.0130842(±

0.0178486)] +MR [0.0116066(± 0.00508151)].3n=18,r=0.86728,r^2=0.8217, q2 = 0.76,variance=0.081009,std=0.284621,F=30.5305

The model No. 3 obtained for COX-1 inhibition is found to explain 82.1% of the variance
in activity. It is statistically significant with an F value exceeding 99.9% confidence level. The
model is having good predictive ability, which is evident from the obtained q2 and r^{2}bs values.

The low values of SPRESS, SDEP, and Sbs also reflect the statistical significance of the model.

**Descriptors calculated for the Equations **

S. No. Descriptor Type

1 Heat of Formation (HF) Thermodynamic

2 Boiling Point (BP) Thermodynamic

3 Critical Pressure (CP) Thermodynamic

Critical Temperature (CT) Thermodynamic

5 Critical Volume (CV) Thermodynamic

7 Henry's Law Constant (HLC) Thermodynamic

8 Ideal Gas Thermal Capacity (IGTC) Thermodynamic

9 LogP Thermodynamic

10 Melting Point (MP) Thermodynamic

11 Molar Refractivity (MR) Thermodynamic

12 Standard Gibbs Free Energy (SGFE) Thermodynamic

13 Connolly Accessible Area (CAA) Steric

14 Connolly Molecular Area (CMA) Steric

15 Connolly Solvent-Excluded Volume (CSEV) Steric

16 Ovality (OVA) Steric

17 Principal Moment of Inertia - X (PMI-X) Steric 18 Principal Moment of Inertia - Y (PMI-Y) Steric 19 Principal Moment of Inertia - Z (PMI-Z) Steric

20 Dipole Moment (D) Electronic

21 Dipole Moment -X Axis (DX) Electronic

22 Dipole Moment -Y Axis (DY) Electronic

23 Dipole Moment -Y Axis (DZ) Electronic

24 Electronic Energy (EE) Electronic

25 HOMO Energy (HOMO) Electronic

26 LUMO Energy (LUMO) Electronic

27 Repulsion Energy (RE) Electronic

28 Bend Energy (Eb) Thermodynamic

29 Charge-Charge Energy (CCE) Thermodynamic

30 Charge-Dipole Energy (CDE) Thermodynamic

31 Dipole— Dipole Energy (DDE) Thermodynamic

32 Non-1, 4 VDW Energy (Ev) Thermodynamic

33 Stretch Energy (SE) Thermodynamic

34 Stretch-Bend Energy (SEE) Thermodynamic

35 Torsion Energy (E_{t}) Thermodynamic

36 Total Energy (E) Thermodynamic

37 Van der Waals e 1,4 Energy (VDWE) Thermodynamic

38 VDW 1,4 Energy (VDWE) Thermodynamic

**COX-2 **

BA= [4.67922(± 0.636593)] +LogP [-0.0331651(± 0.0201496)] +MR [0.00850745(±

0.00745097)] +BE [0.0988542(± 0.195762)]

n=18, r=0.84047, r^2=0.75605, , q2 = 0.69,variance=0.191668, std=0.4378, F=23.2285 Model 4 has good correlation between biological activity and parameters as r = 0.84 and explains 75% variance in COX-2 activity. Low standard deviation of the model demonstrates accuracy of the model. The model showed overall significance level better than 99%, with the F = 23.2285 .Value of chance is less than 0.01, which shows there is significant relationship between LogP, MR (Molar- Refractivity), BE (Bend Energy) and biological activity.

BA= [4.12797(± 0.386667)] +MR [-0.0259112(± 0.0115931)] +OVALITY [0.0131825(±

0.00439019)] + HOMO [0.166785(± 0.112537)]

n=18,r=0.907058,r^2=0.802754,q2=0.85,variance=0.0618087,std=0.248614,F=47.96

Equation explains 80.2% of the variance in activity with low standard error of estimation.

The model showed overall significance level better than 99%, with the F = 47.96 .Value of chance is less than 0.01, which shows there is significant relationship between MR (Molar- Refractivity), BE (Bend Energy) VDWE, and biological activity.

*Table. Descriptors Used Qsar Equations *
S.

N

HOMO ^{b}Ovality ^{c}logp ^{d}BE ^{e}TE LUMO HF MR

1 -9.03911 1.66721 5.5932 19.6669 -3.6144 -0.937434 26.5457 14.9055 2 -9.05988 1.69255 4.4175 21.4386 2.19236 -0.677617 29.1047 13.6483 3 -9.22597 1.77186 6.2837 18.5811 -3.69162 -0.906798 29.342 15.3969 4 -9.07392 1.7535 6.3977 18.0953 -2.51626 -0.895331 29.5672 15.8331 5 -9.10245 1.70207 5.222 21.7702 3.24286 -0.68178 29.1408 14.5759 6 -9.15363 1.73609 4.8395 12.8389 -10.7322 -0.885528 21.0903 14.1973 7 -9.1028 1.59765 3.6638 15.4426 4.04463 -8.26792 23.8189 12.9401 8 -9.60331 1.74131 5.53 13.5939 -9.79753 -9.34106 20.4546 14.6887 9 -8.69329 1.63072 5.7954 17.428 -6.16985 -0.4886 29.611 14.6167 10 -8.00458 1.59323 4.051 15.6408 5.51998 -0.29779 22.6602 13.4039 11 -8.1345 1.62998 5.985 13.2643 -2.88737 -1.50493 24.769 14.4636 12 -8.88987 1.64804 3.7857 14.4966 4.66737 -0.674764 15.9496 13.2508 13 -9.23619 1.58615 4.8012 15.2438 22.7475 -1.00958 31.8985 14.9854 14 -8.90007 1.70839 3.942 21.4703 -0.8644 -1.21176 42.9158 13.9726 15 -9.3558 1.8442 5.6439 13.2496 -1.55999 -1.01765 34.8464 15.7208 16 -9.24992 1.73621 4.5381 12.5012 1.22963 -0.947252 31.9908 14.5216 17 -7.50826 1.71617 3.3624 428.494 0.796735 -2.34849 25.64356 13.2644 18 -9.32468 1.81316 5.3808 12.9805 -5.02994 -0.986669 33.3215 15.257 19 -9.06656 1.63896 3.2351 12.8511 26.4875 -0.325483 39.5644 12.1006 20 -9.06818 1.6282 5.3491 11.8906 28.3449 -0.943651 44.3221 12.1636 21 -9.23272 1.58815 4.1852 10.5134 24.2551 -1.0876 42.6045 11.2084 22 -8.77935 1.60122 4.9546 11.2551 23.1178 -0.873245 38.2313 11.6641 23 -9.27997 1.61001 5.086 11.2891 22.4226 -0.856412 41.6869 11.6998 24 -9.05705 1.58346 4.9583 11.371 23.521 -1.04938 42.4844 11.6722 25 -8.97787 1.6421 5.1483 10.6832 20.5362 -1.12411 40.8298 11.5191

BA= [3.95633(± 0.439126)] +BE [-0.0229962(± 0.0113975)] +LUMO [0.0111466(±

0.0100943)] +Part.coeff. [0.0131032( ± 0.00359353)]

n=18, r=0.812038, r^2=0.759406, *q2=0.63 variance=0.0753585, std=0.274515, *
F=38.7209

Model shows good correlation coefficient (r=0.812 between descriptors such as BE, MR,
Partt.coff). Squared correlation coefficient (r^{2}) of 0.7594, which explains 63.4% variance in
biological activity. Model also indicates statistical significance >99.9% with F-values F= 38.72
Cross-validated Square correlation coefficient of the model was 0.6026, which shows good
internal predictivity of the model.

**4. Conclusions **

The descriptor HOMO, LUMO, MR, Ovality, VDEW, LogP, TE in the models represents the sum of electrostatic, Thermodynamics, terms resulting from the interaction of three dipoles.

The descriptor bears a positive coefficient, which suggests significance of dipole–dipole interactions for the COX-1, COX-2 activity. The Van der Waals energy is a thermodynamic parameter which can be defined as the sum of pair wise Vander Waals interaction energy terms for atoms separated by exactly four chemical bonds, related to the structure of the molecule itself. The coefficient of the descriptor VDWE bears a positive sign in the COX-1 model 1 which indicates that increase in the HF,LogP,TE between atoms separated by 3 chemical bonds is conducive to the activity, which in the present case is applicable to the substituents in the Sulphur atoms COX-1, COX-2 moiety. The descriptor bears negative coefficient in the model, suggesting increase in the bulkiness of the substituents and molecular solvent accessible surface area is not conducive to the activity. Predicted activity data of model-1, COX-1 and Model 3 COX-2 were shown in (Table-3) and results of the leave-one-out cross validation for model-1, 2, 3 and 4 are shown in Table-5 and 6.It is evident from the QSAR studies that in COX-1 model-3, thermodynamic descriptors (HF, VDWE, MR). Negative contribution of Heat Formation (attractive forces between active substituents and enzyme-binding sites) and positive contribution VDEW, MR in biological activity indicates that minimizing parameters with suitable substituents enhances the activity. COX-2 Molar Refractivity Negative contribution of total energy (electron density in the enzyme cavity) to the biological activity indicates that minimizing the total energy of the molecule decreases the activity, HOMO positive biological activity indicates that minimizing parameters with suitable substituents enhances the activity. Based on the QSAR model obtained from series, for the design of the new molecules.

**Acknowledgements **

The authors are thankful Prof.E.V.Subrmanym N.G.S.M Pharmaceutical Sciences Derlakatte Mangalore (Karnataka) India for given valuable suggestions.

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