## Mukesh Chandra Sharma et al /Int.J. PharmTech Res.2010,2(2)

1378

F value, the more stringent was the significance level: F test ‘‘in’’ as 4 and F test ‘‘out’’ as 3.99. The variance cutoff was set at 0, and scaling was auto scaling in which the number of random iterations was set at 100.The following statistical parameters were considered for comparison of the generated QSAR models: correlation coefficient (r), squared correlation coefficient (r2), predictive r2 for external test set (pred r2) for external validation, and Fischer’s (F).The predicted r2 (pred_r2) value was calculated using Eq. 1, where yi and yˆi are the actual and predicted activities of the i^{th }molecule in the test set, respectively, and ymean is the average activity of all molecules in the training set. Both summations are over all molecules in the test set. The pred_r^{2 }value indicates the predictive power of the current model for

was 0.9581 and coefficient value were found to be

cross (Q^{2})

# F

test

validated squared

was

0.9262.

# The

correlation other data

=160.2108,

pred_r^{2 }

=

0.3840,

pred_r^{2}se

= 0.6413.

For model

coefficient

(R^{2}) was

0.9440, cross

2 the correlation validated squared

correlation coefficient values were found to 0.7064, pred_r^{2}se =

value (Q^{2}) 0.8987, and the other be F test = 118.1064, pred_r^{2 }= 0.6559. The equations were

generated help of equations

for assuming the biological activity with the physicochemical descriptor values. The showed the correlation between biological

activity

and

physicochemical

descriptor

values.

Model 2 L o g 1 0 ( I C _ 5 0 ) = - 0 . 0 9 8 8 T _ T _ C _ 7 + 0 . 3 8 3 6 T _ 2 _ + 0.2205 T_C_O_2 + 5.2935 S _ 3

the external test set as follows ∑ (y_{i}-yˆ_{i}) pred_r^{2 }= 1 - ∑ (y_{i}-y_{mean }2

)^{2 }

(1)

Optimum Components = 4, Degrees of Freedom = 16, n = 16, r^{2}= 0.8361, q2= 0.6416, F test = 54.374 r2 se = 0.361, q2 se = 0.6864, pred_r^{2 }= 0.7361, SEE = 0.041,

Internal validation was carried out using leave-one-out (q2, LOO) method. For calculating q2, each molecule in the training set was eliminated once and the activity of the eliminated molecule was predicted by using the model developed by the remaining molecules. The q2 was calculated using the equation which describes the internal stability of a model:

q^{2 }=1 -

∑ (y_{i}-yˆ_{i}) ----------------------- (2) ∑ (y_{i}-y_{mean}) 2 2

Where y_{i}, and yˆ_{i }are the actual and predicted activity of the _{i}th molecule in the training set, respectively, and y_{mean }is the average activity of all molecules in the training set.

RESULT AND DISCUSSION Biological activity data and various physico-chemical parameters were taken as dependent and independent variables and correlations were established using PLS method. When the compounds were subjected to under

goes PLS using step

method to developed QSAR models by wise forward-backward variable selection

# SECV=

0.630,

# SEP=0.170,

best ran r^{2}=0.265,

b e s t _ r a n _ q 0.236 2 = Zscore_ran_q2= _ran_q^{2 }= <0.001

_ Zscore ra n r2

0.216,

_ α_ran_r^{2 }_

=

_

= 0.383,

<0.0001^{, }

α

To improve the external predictivity of the model, PLS analysis with the same data set was performed, which resulted in a coefficient of correlation of 0.5428 and an internal predictive power of 42%, with the good external predictivity of 58%. T_T_C_7 contributes in the same manner as above. T_C_O_2 de ines the total number of carbons connected with four single bonds and makes a negative contribution to activity.

Model 3 Log10 (IC_50) = -1.5099 kappa3 + 0.5766 SdssCE- index + 15.4845 Optimum Components = 4, Degrees of Freedom = 16, n = 16, r^{2}= 0.6951, q2= 0.531, F test = 42.431, r2 se = 0.3725, q2 se = 0.546, pred_r^{2 }= 0.6541, SEE = 0.175,

# SECV= 0.218 SEP=0.390, best ran r^{2 }=

0.425

__ Zscore ran r2 b e s t _ r a n _ 0.316^{, }=0.431, = q 2 Zscore_ran_q2= 0.032, α_ran_r^{2 = }<0.001 __ <0.0001^{, }α _ran_q^{2 }=

Model-I

and

Model-II,

for both

the

methods

mode, four QSAR models, Model-III were developed

respectively

as

shown

below

and

other

good

model

predicted activity shown abstract. descriptors like Polarizability AHC,

Various 2D Polarizability

AHP, chi1, 1-pathcount, chi3cluster, kappa3, Hydrogen count, SaaCH count, SdssC count that are responsible for PPAR γ/δ agonistic activity were calculated. The different statistical models were developed using Partial Least Square (PLS) method. The models showed the better correlation between biological activity and physicochemical descriptor values. For model 1 the correlation coefficient (R^{2})

Model –2 shows good squared correlation coefficient (r^{2}) of 0. 6951, explains 69.51% variance in biological activity. This model also indicates statistical significance >99.9% with F values F = 42.431. Cross validated squared correlation coefficient of this model was 0.8039, which shows the good internal prediction power of this model. The graph of observed vs. predicted biological activities for the training and the test molecules is shown in Figure.