Medicinal Chemistry Research

, Volume 21, Issue 10, pp 3087–3103

Quantitative structure–activity relationship and design of polysubstituted quinoline derivatives as inhibitors of phosphodiesterase 4

Authors

    • School of Pharmaceutical SciencesShobhit University
  • Vertika Gautam
    • School of Pharmaceutical SciencesShobhit University
  • Ranjit Singh
    • School of Pharmaceutical SciencesShobhit University
Original Research

DOI: 10.1007/s00044-011-9831-x

Cite this article as:
Gaurav, A., Gautam, V. & Singh, R. Med Chem Res (2012) 21: 3087. doi:10.1007/s00044-011-9831-x

Abstract

2D quantitative structure–activity relationships (2D QSAR) and hologram quantitative structure–activity relationship (HQSAR) studies were performed on a series of polysubstituted quinoline derivatives as inhibitors of phosphodiesterase 4 (PDE4). The dataset was divided into training set and test set by K-means clustering. 2D QSAR study was carried out using stepwise linear regression analysis, replacement method and enhanced replacement method. Statistically significant equations with high correlation coefficient (R2 = 0.817) and low standard deviation (SD = 0.272) were obtained. The robustness of the models was confirmed with the help of leave one out cross validation (Rcv2 = 0.740), Y scrambling (R2 = 0.374), and by predicting the activities of test molecules (Rpred2 = 0.627). A good correlation of topology, steric and polar features of polysubstituted quinoline derivatives with the PDE4 inhibitory activity was achieved. HQSAR calculations were carried out using various combinations of fragment size, hologram length and fragment type. The best HQSAR model was obtained with an R2 value of 0.952 and \( R_{\text{cv}}^{2} \) value of 0.783. The test-set of molecules was predicted by the HQSAR model. The results of 2D QSAR and HQSAR studies were used to design new molecules and to predict their activity using the developed models.

Keywords

PhosphodiesteraseHQSARQSARK-means clusteringEnhanced replacement methodReplacement method

Introduction

Phosphodiesterases (PDEs), a super family of 11 isozymes, are responsible for the hydrolysis of cyclic nucleotides (cAMP and cGMP) (Francis et al., 2000). Cyclic nucleotides are important intracellular secondary messengers in cell function, relaying the signals from hormones at specific cell-surface receptors (Robinson et al., 1968). An increase of cAMP due to the stimulation of adenylyl cyclase or the inhibition of PDEs affects the activity of immune system and inflammatory cells (Giembycz and Dent, 1992; Kammer, 1988; Nicholson et al., 1991; Torphy and Undem, 1991). Thus, PDE4, a cAMP-specific PDE, received much attention as a target for the treatment of the diseases like asthma and Chronic Obstructive Pulmonary Disease (COPD) (Christensen and Torphy, 1994). Since the discovery of rolipram as a selective inhibitor of PDE4, a number of molecules have been designed to enhance the activity and to reduce the side effects such as nausea, vomiting, psychotropic activity, and increased gastric secretion (Horowski and Sastre-y-Herandez, 1985; Zeller et al., 1984; Puurunen et al., 1978). PDE4 inhibitors based on benzofuran, indazole, pyrazolo[3,4-c]pyridine and pyrazolo[4, 3-c]quinoline-3-one nucleus have been the subject of study in recent past (Duplantier et al., 1998). Research efforts have also been directed toward optimization of PDE4 inhibition activity of polysubstitued quinolines (Woodrow et al., 2009; Lunniss et al., 2009). However, the task still remains largely unaccomplished. Thus, a need for developing new, selective, and potent inhibitors of PDE4 is always there.

A successful QSAR model not only helps in better understanding of the structure–activity relationship of a class of molecules, but gives an in-depth analysis about the lead molecules to be used in the further studies (Gupta et al., 2003). Hence, we initiated 2D QSAR and HQSAR (Tripos, Inc., St. Louis, MO) studies as validated tools for QSAR analysis of polysubstitued quinolines as PDE4 inhibitors. A 2D QSAR technique is of particular interest since it eliminates the need for determining 3D structure, putative binding conformation, and molecular alignment (Gupta et al., 2003). A great number of structural molecular descriptors were explored using the stepwise multiple linear regression analysis, replacement method and recently proposed enhanced replacement method to select the best subset of variables for 2D QSAR study. HQSAR model generates a molecular fingerprint of the 2D structure of the molecule and cuts it into fragments to determine its contribution toward biological activity of the molecule (Tripos, Inc., St. Louis, MO). HQSAR can suggest intuitionist guidelines for structural modification during the design of novel molecules. HQSAR calculations were carried out by using various combinations of distinct parameters which include fragment size, hologram length and fragment type. The resulting QSAR equations and 2D fingerprint property contributions can be useful for the future development of PDE4 inhibitors with improved target site affinity.

Experimental

Data series

A series of polysubstitued quinoline derivatives, with reported activities, was used for this study (Woodrow et al., 2009; Lunniss et al., 2009). The experimental PDE4 inhibitory activity of the data set was measured on isolated guinea pig ventricular PDE4. The molecular structures, experimental IC50 and −log IC50 (pIC50) of the above series are depicted in Table 1. IC50 is defined as the micro molar concentration of PDE4 inhibitor necessary to reduce PDE4 activity by 50% relative to a reaction mixture containing PDE4 without any inhibitor (Woodrow et al., 2009; Lunniss et al., 2009).
Table 1

Structure and experimental pIC50 values for the dataset

https://static-content.springer.com/image/art%3A10.1007%2Fs00044-011-9831-x/MediaObjects/44_2011_9831_Tab1a_HTML.gif
https://static-content.springer.com/image/art%3A10.1007%2Fs00044-011-9831-x/MediaObjects/44_2011_9831_Tab1b_HTML.gif
https://static-content.springer.com/image/art%3A10.1007%2Fs00044-011-9831-x/MediaObjects/44_2011_9831_Tab1c_HTML.gif

Molecular descriptors

Molecular modeling and calculation of various parameters required for QSAR model development was performed using VLife MDS (VLife Technologies, Pune, MS). Structures of the molecules were drawn using the 2D builder module of VLife MDS. Biologically active conformations were identified by subjecting the structures to conformational analysis followed by energy minimization to a RMS gradient of 0.001. Molecular descriptors were computed using the QSARPro module of VLife MDS. Parameters such as topological indices, structural keys, E-state indices, physical properties, topological polar surface area (TPSA), VSA descriptors, BCUT descriptors, aromaticity indices, randic indices, etc., were calculated (Table 2). Some more descriptors were added to the descriptor-pool using the program Bioclipse (Ola et al.,2007; Ola et al.,2009).
Table 2

Descriptors involved in the developed models

Cpd

SKMostHydrophilic

SsNH2count

PolarSurfaceAreaExcludingPandS

SsClE-index

SsCH3count

Mol.Wt.

DipoleMoment

chi4pathCluster

SulfursCount

SdsCHE-index

10a

0.222

1.000

97.550

0.000

3.000

364.404

3.310

4.801

0.000

0.000

10

0.356

1.000

90.120

0.778

1.000

392.887

4.914

3.664

2.000

0.000

11a

0.199

1.000

106.780

0.000

1.000

406.441

3.917

4.661

1.000

0.000

12a

0.370

1.000

94.310

0.000

1.000

419.504

2.277

3.820

1.000

0.000

14a

0.549

0.000

105.590

0.000

1.000

434.472

2.555

4.275

1.000

0.000

14b

0.200

1.000

147.080

0.000

1.000

442.496

3.933

4.275

1.000

0.000

14c

0.192

1.000

114.620

0.000

3.000

400.458

2.894

4.443

1.000

0.000

15a

0.379

1.000

102.150

0.000

1.000

431.515

5.141

4.275

1.000

0.000

15b

0.346

1.000

125.940

0.000

0.000

428.471

4.424

4.275

1.000

0.000

15c

0.357

1.000

102.150

0.000

0.000

403.461

5.329

3.835

1.000

0.000

15d

0.328

1.000

102.150

0.000

0.000

409.509

4.926

3.835

1.000

0.000

15e

0.255

1.000

115.040

0.000

0.000

404.449

6.294

3.835

1.000

0.000

15f

0.331

1.000

127.070

0.000

0.000

462.553

2.235

4.730

2.000

6.301

15g

0.276

1.000

123.410

0.000

1.000

461.541

3.341

5.335

1.000

8.094

15

0.323

0.000

97.390

0.000

3.000

385.444

3.260

3.830

1.000

0.000

16c

0.314

1.000

120.610

0.000

2.000

463.514

3.555

4.768

1.000

0.000

16d

0.397

1.000

111.380

0.000

4.000

489.595

2.747

4.912

1.000

0.000

16

0.567

0.000

81.430

0.000

3.000

408.478

3.452

4.051

1.000

0.000

17a

0.316

1.000

157.710

0.000

3.000

504.567

6.547

5.916

1.000

0.000

17

0.476

0.000

107.210

0.000

3.000

410.453

3.702

4.051

1.000

0.000

18

0.400

1.000

150.540

0.000

1.000

499.547

0.982

5.218

1.000

0.000

19a

0.402

1.000

123.410

0.000

2.000

447.515

6.356

4.731

1.000

0.000

19

0.148

1.000

111.380

0.000

2.000

371.417

2.462

3.760

1.000

0.000

20

0.350

1.000

132.640

0.000

3.000

477.541

2.231

5.224

1.000

0.000

2

0.169

1.000

142.610

0.000

1.000

357.390

4.099

3.664

1.000

0.000

34

0.344

1.000

142.920

0.404

1.000

375.835

6.646

3.664

1.000

0.000

35

0.229

1.000

125.940

0.000

1.000

366.400

3.228

3.760

1.000

0.000

36

0.197

1.000

111.380

0.000

1.000

383.428

4.243

4.273

1.000

0.000

37

0.162

1.000

115.040

0.000

1.000

342.378

1.570

3.320

1.000

0.000

39

0.171

1.000

106.830

0.000

1.000

385.400

1.088

4.312

1.000

0.000

40

0.244

1.000

111.380

0.000

2.000

389.407

3.238

4.341

1.000

0.000

41

0.345

1.000

128.320

0.305

1.000

393.826

7.201

4.530

1.000

0.000

42

0.362

1.000

93.360

0.706

2.000

389.862

4.059

4.253

1.000

0.000

43

0.260

1.000

111.380

0.000

3.000

403.434

1.015

4.797

1.000

0.000

47

0.219

1.000

120.610

0.000

3.000

419.434

1.347

4.795

1.000

0.000

48

0.247

1.000

125.940

0.000

2.000

380.427

4.114

7.114

1.000

0.000

49

0.374

1.000

120.610

0.000

1.000

433.488

3.336

4.275

1.000

0.000

4a

0.355

1.000

143.720

0.000

4.000

518.593

3.462

6.372

1.000

0.000

4

0.252

1.000

120.610

0.000

2.000

371.417

4.906

3.760

1.000

0.000

8b

0.354

1.000

111.380

0.000

1.000

425.508

3.174

4.275

1.000

0.000

8c

0.262

1.000

77.240

0.000

1.000

293.325

3.877

3.159

0.000

0.000

9a

0.411

1.000

77.240

0.000

1.000

401.489

0.956

3.928

1.000

0.000

9

0.625

0.000

107.730

0.000

0.000

299.112

15.021

2.793

1.000

13.535

Selection of training and test set

The main objective of QSAR is to develop model robust enough to make accurate and reliable predictions of activities of new molecules. This necessitates the validation of developed QSAR models using external data set. However, in most of the cases, proper external data set is not available, thus original data set is divided into training and test sets. The robustness of the model in extrapolating beyond the chemistry space defined by the training set depends on the ability of the training set to represent unknown molecules. So, the selection of the training set is very important in QSAR analysis. Predictive potential of a model on the new data set is affected by the similarity between chemical nature of training and test set (Eriksson et al., 2003; Guha and Jurs, 2005; Leonard and Roy, 2006).

Several techniques are available for the partition of the data set into training and test sets including statistical molecular design, self-organizing map, clustering, Kennard–Stone selection, sphere exclusion, etc. (Roy, 2007).

In the present case, clustering technique was used for selection of training and test set (Everitt et al., 2001). Hierarchical clustering and nonhierarchical clustering represent the two broad categories of clustering techniques. One of the main nonhierarchical techniques is K-means clustering (Dougherty et al., 2002) which is used in this study. In this method, clusters are initiated randomly and their means are calculated in descriptor space. Molecules are reassigned to clusters whose means are nearer to the position of molecules. This is followed by the selection of test set molecules from each cluster since both test set and training set can represent all clusters and thus characteristics of the whole dataset. In our study, the whole data set was divided into five clusters based on K-means clustering (Table 3). From each of these five clusters, one molecule from near the centre was selected for the test set and the remaining for the training set (Table 4).
Table 3

K-means clustering of the compounds

Cluster

Compound

1

14a, 14b, 14c, 15a, 15b, 15c, 15d, 15e, 15f, 15g

2

2, 34, 35, 36, 37, 10a, 10, 11, 20, 19

3

39, 4, 4a, 8b, 8c, 9a, 9, 15, 16, 17, 18

4

40, 41, 42, 43, 47, 49

5

48, 12a, 16c, 16d, 17a, 19a

Table 4

Composition of training and test set

Training set

14a, 14c, 15a, 15b, 15c, 15d, 15e, 15f, 15g, 2, 35, 36, 37, 10a, 10, 11, 20, 19, 4, 4a, 8b, 8c, 9a, 9, 18, 17, 16, 15, 40, 42, 43, 47, 49, 12a,16c, 16d, 17a, 19a

Test set

14b, 34, 39, 41, 48

2D QSAR model development

Availability of thousands of descriptors presents the researchers with the mathematical problem of selecting subset of chemically and biologically relevant descriptors (d) from a much larger set (D). The search for the optimal set of descriptors may be guided by the minimization or maximization of a chosen statistical parameter; for example, one may be interested in a model that makes the standard deviation (SD) as small as possible. A full search (FS) of the variables is not viable because it requires great number of linear regressions. In the past replacement method (RM) (Duchowicz et al., 2006a, b; Helguera et al., 2006) and later the enhanced replacement method (ERM) (Mercader et al., 2008) were proposed that generate linear regression models quite close to the FS ones requiring much lesser computational work. Both of these techniques move toward the minimum value of SD by carefully taking into account the relative errors of the coefficients of the least-squares model given by a subset of descriptors. RM produced models with better statistical parameters than the forward stepwise regression procedure and variants of the genetic algorithms [Draper and Smith, 1981; So and Karplus, 1996; Leardi and Gonzalez, 1998; Caballero and Fernandez, 2008]. ERM leads to comparable or even better statistical parameters, however, require slightly more computational effort (Mercader et al.,2008a, b). The RM is a rapidly convergent iterative algorithm that produces linear regression models with small SD in comparatively short computational time (Duchowicz et al., 2007; Duchowicz et al., 2008, 2009; Goodarzi et al., 2009). However, in some complicated cases, the RM can get trapped in a local minimum of SD. The ERM follows the same idea but is less likely caught into local minima as well as less reliant on the initial solution.

2D QSAR model validation

QSAR model validation is necessary to recognize statistically robust models capable of making accurate and reliable predictions of activities of new molecules. Following approaches have been used to validate the QSAR equations.

Internal validation

Following methods were used for the internal validation of the developed models.

Fraction of the variance (R2)

The closer the value of R2 to unity better is the QSAR model. QSAR models were selected according to R2 values. According to the literature, the predictive QSAR model must have R2 > 0.6. (Golbraikh and Tropsha, 2002; Tropsha et al., 2003).

Cross-validation test

PRedictive Error Sum of Squares (PRESS) and \( R_{\text{cv}}^{ 2} \) obtained by using leave-one-out (L-O-O) process were used to test the robustness, stability and predictive power of QSAR equations. Model with a high \( R_{\text{cv}}^{ 2} \) value is considered to have high predictivity.

Standard deviation (SD)

The smaller the value of SD, the better is the QSAR model.

Fischer statistics (F)

Value of F greater than the tabulated value indicates that the QSAR equation is significant.

Y-scrambling

To guard against the possibility of having chance models, the method of Y-scrambling was used. In this method, models are fitted for randomly shuffled activity values and compared with the model obtained for the actual activity values. True values should lie sufficiently outside the background reference distribution for one to confidently say that there exist a real model on the given data and that it is not the same as models that were learned by chance (Selassie et al., 2005; Wold and Eriksson, 1995).

Lack of over-fitting

A model over-fits if it includes more descriptors than required. The lack of over-fitting for all the QSAR models was confirmed by using the following conditions:

Number of data points/number of descriptors ≤4

QSAR models were checked for their correlation with fewer descriptors than that of the original. None of them was found to be statistically significant.

External validation

The QSAR models were subjected to external validation by prediction of the activity of test set molecules. The predictive capacity of these models is judged from their predictive R2 (\( R_{\text{pred}}^{ 2} \)) values, which were calculated by the following equation:
$$ R_{\text{pred}}^{ 2} = 1- \sum \left( {Y_{{{\text{pred}}({\text{test}})}} - Y_{\text{test}} } \right)^{ 2} /\sum \left( {Y_{\text{test}} - Y_{\text{training}} } \right)^{ 2} $$

HQSAR model development

SYBYL-X 1.2 (Tripos, Inc., St. Louis, MO) running on a Pentium Dual-Core CPU and Microsoft Windows 7.0 operating system was used for HQSAR studies. In HQSAR, a molecule is described as a unique string of numbers or ‘bins’ (molecular hologram). The bins represent all of the unique fragments included within a particular molecule and are assigned by a cyclic redundancy check (CRC) algorithm. All linear, branched and overlapping structure fragments were used to generate HQSAR descriptors. The structure fragments from each original molecule consisted of a user-defined minimum and a maximum number of atoms, which are fragment-size parameters. The information in each fragment is defined by fragment distinction parameters, including atoms (A), bonds (B), connections (Con), hydrogen (H), chirality (Ch), and H donor or acceptor (DA). The generated fragments were then hashed into a fixed-length array to produce a molecular hologram. The fixed length was defined as hologram-length parameter.

The HQSAR module provides 12 default hologram lengths (53, 59, 61, 71, 83, 97, 151, 199, 257, 307, 353, and 401), which are prime numbers, to minimize the possibility of fragment collision. The particular nature of substructure fragments generated by HQSAR and, consequently, the information contained in the resultant molecular holograms was altered by adjusting these parameters. For hologram-generation process, different combinations of these parameters were considered using the fragment-size default (47). The HQSAR analysis was performed by screening 12 default series of hologram length values ranging from 53 to 401 bins. The patterns of fragment counts were then related to the measured biological activity of the training set.

Results and discussion

2D QSAR

A series of polysubstitued quinoline derivatives comprising of 43 molecules was selected for this study. The series was divided into training and test sets using k-means clustering as described previously. The test set comprised of molecules 14b, 34, 39, 41, and 48 while the training set comprised of remaining molecules. Training set molecules were used to develop QSAR models by applying forward stepwise multiple linear regression (FSMLR), RM and ERM using physicochemical properties of the molecules as the independent variables and their pIC50 values as the dependent variables. Adequate care was taken to prevent use of collinear variables in the same equation as it leads to false correlations. Out of the generated QSARs only those having up to five parameters were considered. Further selection of models was based on higher multiple correlation coefficient (R) or variance (R2), minimum inter-correlation among the descriptors found in the same model coupled with high Fischer ratio values (F) and low standard deviation values (SD). Another statistical parameter used in the study is the Kubinyi function (FIT). It is a statistical parameter that closely relates to the Fisher ratio (F). However, it is devoid of the main drawback of F that is too sensitive to changes in small d values, and poorly sensitive to changes in large d values. The greater the FIT value the better the linear equation.

The application of the FSMLR to the training set of 38 molecules resulted in several models; the best model (Eq. 1) was identified based on criteria discussed earlier.
$$ {\text{IC}}_{ 50} = 1. 4 2 8 7\left( { \pm 0.0. 20 7 1} \right){\text{ Chi4PathCluster }} + { 2}. 7 9 2 2 \left( { \pm 0. 4 4 9 8} \right){\text{ SsNH2Count }}-{ 4}. 4 20 6 4( \pm 0. 8 9 6 3){\text{ SsCIE}}{\text{-}}{\text{index }} + 1. 3 5 5 4 \left( {{ \pm }0. 3 7 9 8} \right){\text{ SulfursCount }}- 0. 1 7 3 9 \left( { \pm 0.0 8 1 4} \right){\text{ SdsCHE - index}}- 2.0 4 6 9\left( { \pm 1.0 5 60} \right) $$
(1)

R = 0.897, R2 = 0.804, SD = 0.379, F = 26.204, FIT = 2.080, \( R_{\text{cv}}^{2} = 0. 6 6 5 \), PRESS = 38.721, \( R_{\text{adj}}^{2} = 0. 7 7 3 \), RMSE(CV) = 0.451

Analysis of residuals obtained using Eq. 1 suggested that molecule 19 was an outlier. The analysis of other generated models also suggested that it was the molecule with highest error (>2Sigma). Surprisingly, the structure of this molecule is not significantly different from the rest of the molecules belonging to the training set. Since the quality of the input data will greatly influence the performance of the QSAR model, molecule 19 was taken out of the training set. The FSMLR and resulting 37-molecule training set were then used to calculate the best QSAR models with a value of d ≤ 5. Among numerous models developed by FSMLR, the best one selected on the basis of the parameters already discussed, turns out to be
$$ p{\text{IC}}_{ 50} = 1.3331\left( { \pm}0. 1 8 2 8 \right){\text{ Chi4PathCluster}} + 2. 9 30 8\left( { \pm 0. 3 9 4 3} \right){\text{ SsNH2Count}}-4. 4 1 70({\pm}0. 7 8 3 8){{\text{SsCIE}}{{\text-}}{\text{index}}} + 1. 3 9 5 2 { }\left( { \pm 0. 3 3 1 3} \right){\text{SulfursCount}}-0. 1 8 6 8 { }\left( { \pm }0.0 7 10 \right){\text{ SdsCHE - index}}- 1. 7 1 2 4\left({\pm}0. 9 2 5 9 \right) $$
(2)

R = 0.920, R2 = 0.847, SD = 0.354, F = 34.180, FIT = 2.576, \( R_{\text{cv}}^{2} = 0.717 \), PRESS = 30.762, \( R_{\text{adj}}^{2} = 0.822 \), \( R_{\text{pred}}^{2} = 0. 5 5 6 \), RMSE(CV) = 0.411

Here, the absolute errors of the regression coefficients are given in parentheses and \( R_{{_{\text{pred}} }}^{2} \) stands for variance of the test set. Above model represents a good quality of fit, evident by the R value, and higher values of Fischer statistics and Kubinyi function justify the statistical significance of the model, while the predictive power of model is justified by high values of \( R_{\text{cv}}^{2} \) and \( R_{\text{pred}}^{2} \).

While applying RM to the training set of 38 molecules the best model turns out to be
$$ p{\text{IC}}_{50} = 0.0 1 5 8\left( {\pm} 0.00 3 1 \right){\text{ Mol}}.{\text{Wt}}. + 0.2486\left( {\pm}0.0679 \right){\text{ DipoleMoment}}-3.6695\left( { \pm}0.8439 \right){\text{SsCIE-index}} +3.4012\left( { \pm }0. 4 5 20 \right){\text{SsNH2Count}}+0.4264\left({\pm}0.1344\right){\text{SsCH3Count}}-3.2936\left({\pm}1.3343\right)$$
(3)
R = 0.895, R2 = 0.800, SD = 0.320, F = 25.646, FIT = 2.035, \( R_{\text{cv}}^{2} = 0. 7 3 6 \), PRESS = 30.512, \( R_{\text{adj}}^{2} = 0.769 \), RMSE(CV) = 0.4136
Close examination of residuals obtained using above model resulted in identification of molecule 19 as outlier. Molecule 19 was thus eliminated from the training set and the resulting training set was then used to calculate the best QSAR model, which turns out to be
$$ p{\text{IC}}_{50} = 0.0 1 40\left( { \pm}0.00 2 7 \right){\text{ Mol}}.{\text{Wt}}.+ 0.2314\left( { \pm} 0.0596 \right){\text{ DipoleMoment}}-3.8150\left( {\pm}0.7397\right){\text{SsCIE-index}} + 3.5169\left( { \pm} 0.3970 \right){\text{SsNH2Count}} + 0.4631\left( { \pm}0.1181\right){\text{ SsCH3Count}}-2.5646\left( { \pm}1.1883 \right) $$
(4)
R = 0.918, R2 = 0.843, SD = 0.297, F = 33.191, FIT = 2.677, \( R_{\text{adj}}^{2} = 0.781 \), PRESS = 23.874, \( R_{\text{adj}}^{2} = 0.817 \), \( R_{\text{pred}}^{2} = 0. 4 7 9 \), RMSE(CV) = 0.381

All the statistical parameters of Eq. 4 are much better as compared to equation 2. The higher value of R indicated the better quality of fit achieved. The values of Fisher statistics and Kubinyi function are higher by several magnitudes as compared to that for Eq. 2, suggesting greater statistical significance of Eq. 4. The predictive power of Eq. 4 is much better as compared to Eq. 2 in cross validation which is indicated by the higher values of \( R_{\text{cv}}^{2} \). However, Eq. 2 predicts the test set marginally better as compared to Eq. 4 indicated by its slightly higher \( R_{\text{pred}}^{2} \) value.

Application of ERM to the training set of 38 molecules and filtering of developed models based on statistics resulted in identification of following as the best model
$$ p{\text{IC}}_{ 50} = { 6}. 9 4 4 4\left( { \pm 1. 6 60 1} \right){\text{ SKMostHydrophilic }} + { 4}. 2 3 4 9 { }\left( { \pm 0. 5 60 8} \right){\text{SsNH2Count}} + 0.0 3 8 1 8\left( { \pm 0.00 8 1} \right){\text{ PSAExcludingP}}\& {\text{S}} - 3. 2 2 2 5 { }\left( { \pm 0. 8 5 7 2} \right){\text{ SsCIE - index }} + 0. 4 8 1 3 { }( \pm 0. 1 1 8 4){\text{SsCH3Count}}- 3. 2 2 20( \pm 1. 2 2 4 3) $$
(5)
R = 0.904, R2 = 0.817, SD = 0.295, F = 28.566, FIT = 2.267, \( R_{\text{cv}}^{2} \) = 0.740, PRESS = 30.128, \( R_{\text{adj}}^{2} = 0.788 \), RMSE(CV) = 0.391
As in the case of RM and FSMLR molecule 19 was identified as outlier. Molecule 19 was thus eliminated from the training set and the resulting 37-molecule training set was then used to calculate the best QSAR model, which is
$$ p{\text{IC}}_{ 50} = { 5}. 5 30 1\left( { \pm 1. 5 2 7 3} \right){\text{ SKMostHydrophilic}} + 4.0 3 1 3 { }\left( { \pm 0. 4 9 7 4} \right){\text{SsNH2Count}} + 0.0 3 70\left( { \pm 0.00 7 2} \right){\text{ PSAExcludingP}}\& {\text{S}} - 3. 2 3 9 5 { }\left( { \pm 0. 7 5 9 4} \right){\text{ SsCIE - index}} + 0. 4 8 8 1 { }\left( { \pm 0. 10 4 3} \right){\text{SsCH3Count}}- 2. 40 2 4( \pm 1. 10 8 2) $$
(6)
R = 0.924, R2 = 0.854, SD = 0.272, F = 36.217, FIT = 2.921, \( R_{\text{cv}}^{2} \) = 0.788, PRESS = 23.076, \( R_{\text{adj}}^{2} = 0.830 \), \( R_{\text{pred}}^{2} = 0.627 \), RMSE(CV) = 0.328
All the linear models have acceptable predictive quality and present different type of descriptors. Each equation presents different descriptors because their distinct combination is optimal to predict the activity. By examining the statistical parameters calculated from the training and test sets it was concluded that the ERM produces better results over FSMLR and RM when exploring large sets of descriptor. With the purpose of demonstrating that Eqs. 2, 4, and 6 do not result from coincidence, a widely used approach was resorted to establish the model’s robustness: the so-called Y-scrambling. It consists of scrambling the experimental property in such a way that activities do not correspond to the respective molecules. 100 cases of Y-scrambling were analyzed, and the highest values of R2 = 0.386, 0.346, and 0.374 obtained were found to be considerably smaller than that obtained for true calibration R2 = 0.847, 0.843, and 0.854 for Eqs. 2, 4, and 6, respectively (Table 5). These results suggest that the models are robust, that the calibrations are not fortuitous correlations, and that a reliable structure–activity relationship have been derived.
Table 5

Y-scrambling data for Eqs. 2, 4, and 6

Number of scrambling

Equation 2

Equation 4

Equation 6

R2

\( R_{\text{cv}}^{2} \)

R2

\( R_{\text{cv}}^{2} \)

R2

\( R_{\text{cv}}^{2} \)

1

0.363

0.186

0.269

0.128

0.254

−0.167

2

0.278

−0.187

0.186

−0.136

0.323

−0.353

3

0.386

0.152

0.224

0.133

0.268

0.168

4

0.265

0.173

0.269

0.175

0.276

−0.246

5

0.279

0.124

0.276

−0.145

0.237

0.126

6

0.208

0.197

0.228

0.156

0.126

−0.257

7

0.265

0.144

0.238

0.149

0.126

−0.259

8

0.259

−0.161

0.232

−0.245

0.374

−0.277

9

0.245

0.155

0.346

−0.344

0.294

0.143

10

0.364

0.212

0.305

0.129

0.290

−0.215

The correlation matrices shown in Tables 6, 7, and 8 reveal that the descriptors of the linear models are not seriously inter-correlated (Rij < 0.599), which justifies the presence of all the parameters in Eqs. 2, 4, and 6. The predictive power of the linear model is satisfactory as revealed by its stability upon the inclusion or exclusion of molecules, measured by the values of statistical parameter \( R_{\text{cv}}^{2} \), 0.717, 0.781, and 0.788 for Eqs. 2, 4, and 6, respectively.
Table 6

Correlation matrix for descriptors used in Eq. 2

 

chi4pathCluster

SsNH2count

SsCIEIndex

SulfursCount

SdsCHEIndex

chi4pathCluster

1.000

0.295

−0.130

−0.279

−0.144

SsNH2count

0.295

1.000

0.094

−0.352

−0.287

SsCIEIndex

−0.130

0.094

1.000

0.183

−0.067

SulfursCount

−0.279

−0.352

0.183

1.000

0.345

SdsCHEIndex

−0.144

−0.287

−0.067

0.345

1.000

Table 7

Correlation matrix for descriptors used in Equation 4

 

Mol.Wt.

DipoleMoment

SsCIEIndex

SsNH2Count

SsCH3Count

Mol.wt.

1.000

−0.322

−0.105

0.205

0.330

DipoleMoment

−0.322

1.000

0.069

−0.298

−0.298

SsCIEIndex

−0.105

0.069

1.000

0.094

−0.030

SsNH2Count

0.205

−0.298

0.094

1.000

−0.128

SsCH3Count

0.330

−0.298

−0.030

−0.128

1.000

Table 8

Correlation matrix for descriptors used in Eq. 6

 

SkmostHydrophilic

SsNH2Count

PSAExcluding P&S

SsCIEIndex

SsCH3Count

SkmostHydrophilic

1.000

−0.365

−0.226

0.067

−0.030

SsNH2Count

−0.365

1.000

0.282

0.094

−0.128

PSAExcluding P&S

−0.226

0.282

1.000

−0.277

0.123

SsCIEIndex

0.067

0.094

−0.277

1.000

−0.030

SsCH3Count

−0.030

−0.128

0.123

−0.030

1.000

The plots of predicted versus experimental pIC50 is shown in Figs. 1, 2, and 3. Table 9 shows the predicted pIC50 given by Eqs. 2, 4, and 6 for the training and test sets. The behavior of the residuals in terms of the predictions illustrated in Fig. 4 shows normal distributions for both sets.
https://static-content.springer.com/image/art%3A10.1007%2Fs00044-011-9831-x/MediaObjects/44_2011_9831_Fig1_HTML.gif
Fig. 1

Experimental versus predicted pIC50 for training and test sets using Equation 2

https://static-content.springer.com/image/art%3A10.1007%2Fs00044-011-9831-x/MediaObjects/44_2011_9831_Fig2_HTML.gif
Fig. 2

Experimental versus predicted pIC50 for training and test sets using Equation 4

https://static-content.springer.com/image/art%3A10.1007%2Fs00044-011-9831-x/MediaObjects/44_2011_9831_Fig3_HTML.gif
Fig. 3

Experimental versus predicted pIC50 for training and test sets using Eq. 6

Table 9

Predicted pIC50 and Residuals for Eqs. 2, 4, 6 and HQSAR

Cpd

Equation 2

Equation 4

Equation 6

HQSAR

Predicted

Residual

Predicted

Residual

Predicted

Residual

Predicted

Residual

10a

7.619

−0.119

8.206

−0.706

7.935

−0.435

7.345

0.156

10

5.457

−0.757

5.081

−0.381

4.904

−0.204

5.136

−0.436

11a

7.433

−1.133

8.009

−1.709

7.173

−0.873

5.231

1.069

12a

7.706

−1.106

7.812

−1.212

7.653

−1.053

6.358

0.242

14a

5.382

−0.482

4.569

0.331

5.031

−0.131

4.892

0.008

14ba

8.313

0.387

8.520

0.180

8.648

0.052

8.913

−0.213

14c

8.536

0.564

8.614

0.486

8.400

0.700

9.313

−0.213

15a

8.313

−0.313

8.642

−0.642

7.996

0.004

8.002

−0.002

15b

8.313

0.187

7.971

0.529

8.204

0.296

8.581

−0.081

15c

7.726

0.474

7.831

0.369

7.387

0.813

8.194

0.006

15d

7.726

−0.326

7.822

−0.422

7.224

0.176

7.483

−0.083

15e

7.726

−0.326

8.067

−0.667

7.300

0.100

7.030

0.370

15f

9.137

−0.537

7.941

0.659

8.166

0.434

8.368

0.232

15g

8.213

−0.313

8.646

−0.746

8.214

−0.314

7.923

−0.023

15

4.789

0.711

4.972

0.528

4.454

1.046

5.870

−0.370

16c

8.970

0.930

9.186

0.714

8.805

1.095

9.736

0.164

16d

9.162

0.038

10.291

−1.091

9.900

−0.700

9.193

0.007

16

5.083

−0.383

5.339

−0.639

5.210

−0.510

4.386

0.314

17a

10.500

0.500

10.916

0.084

10.680

0.320

10.383

0.617

17

5.083

−0.283

5.424

−0.624

5.662

−0.862

4.829

−0.029

18

9.570

−0.770

8.632

0.168

9.904

−1.104

8.991

−0.191

19a

8.921

1.079

9.611

0.389

9.398

0.602

9.194

0.806

19

5.637

−0.537

20

9.578

1.122

9.539

1.161

9.942

0.758

10.837

−0.137

2

7.499

−0.499

7.364

−0.364

8.331

−1.331

7.329

−0.329

34a

7.047

0.753

6.674

1.126

7.011

0.789

7.973

−0.173

35

7.626

0.074

7.289

0.411

8.049

−0.349

7.998

−0.298

36

8.309

0.291

7.762

0.838

7.333

1.267

9.113

−0.513

37

7.040

−0.040

6.569

0.431

7.275

−0.275

6.235

0.766

39a

7.029

−1.729

7.063

−1.763

7.000

−1.700

5.375

−0.075

40

8.401

−1.301

8.076

−0.976

8.077

−0.977

6.944

0.557

41a

7.304

0.896

7.431

0.769

7.703

0.497

8.213

−0.013

42

5.166

0.834

5.580

0.420

5.775

0.225

5.344

0.656

43

9.009

0.491

8.221

1.279

8.652

0.848

9.938

−0.438

47

9.006

−0.706

8.522

−0.222

8.772

−0.472

8.524

−0.224

48a

8.234

1.166

8.851

0.549

8.614

0.786

9.294

0.106

49

8.313

0.487

8.253

0.547

8.649

0.151

8.244

0.557

4a

11.108

−0.008

10.862

0.238

10.863

0.237

10.992

0.108

4

7.626

0.774

8.210

0.190

8.466

−0.066

8.392

0.008

8b

8.313

0.187

8.103

0.397

8.197

0.303

8.392

0.108

8c

5.430

1.270

6.417

0.283

6.427

0.273

6.829

−0.129

9a

7.850

−1.050

7.254

−0.454

7.250plePara>

−0.450

7.160

−0.360

9

5.063

0.437

5.096

0.404

5.043

0.457

5.701

−0.201

aTest set compounds

https://static-content.springer.com/image/art%3A10.1007%2Fs00044-011-9831-x/MediaObjects/44_2011_9831_Fig4_HTML.gif
Fig. 4

Dispersion plot of residuals for Eqs. 2, 4, and 6

Molecular descriptors appearing in the models developed encode steric, electronic and topological information of the molecule and are discussed in greater details hereunder.
  • Chi4PathCluster signifies molecular connectivity index of 4th order pathcluster and describes structure information specifically on a branch point, emphasizing the immediate branch point environment. It is defined for the branched skeleton and positive contribution (Eq. 2) of this descriptor in the QSAR model demonstrates that increased branching on the substituents on quinoline nucleus particularly at R2 will lead to improved PDE4 inhibitory activity. This finding is also supported by studying the inhibitory potency of molecules in which branching were introduced at R2 (Molecules 10a, 14c, 16c, 16d, 17a, 18, 20, and 4a), suggesting that these molecules were suitable for further optimization with respect to their biological activities.

  • SsNH2Count defines the total number of –NH2 group connected with one single bond. The positive contribution of this descriptor (Eqs. 2, 4, and 6) describes the importance of –CONH2 at R4 for PDE4 inhibitory activity. The finding is also corroborated by the low activity of molecules lacking CONH2 at R4 (11a, 14a, 13, 16c, 16d, and 19) as compared to molecule with CONH2 at R4 and similar substituents at other positions.

  • SsClE-index is electrotopological state indices for number of chlorine connected with one single bond. The negative coefficient (Eqs. 2, 4 and 6) of this descriptor suggests that presence of chlorine atoms in the molecule lowers its PDE4 inhibitory activity, as indicated by the low activity of molecules having chlorine atoms (9, 10, 34, 41, and 42).

  • SdsCHE-index is electrotopological state index for number of –CH group connected with one double and one single bond, i.e., alkene atom types. It can be seen that this descriptor bears negative coefficient in (Eq. 2) thus molecule with fewer alkene type carbons are bestowed with higher PDE4 inhibitory activity while molecules with higher number of alkene type carbons (9, 15f, and 15g) have lower PDE4 inhibitory activity.

  • Mol.Wt., signifies molecular weight of a compound. The positive coefficient of Mol.Wt. (Eq. 4) signifies the importance of higher molecular weight for PDE4 inhibition. However, this finding should not distract from the fundamental rule of drug designing, i.e., the Lipinski rule (Mol.Wt. not more than 500).

  • DipoleMoment signifies dipole moment calculated from the partial charges of the molecule. Thus molecules with greater charge separation (i.e., greater number of electronegative atoms) have large values of DipoleMoment. Positive coefficient of this descriptor in Eq. 4 indicates that increase in the number of electronegative atoms and thus charge separation in molecules (4a and 20) is beneficial for PDE4 inhibitory activity.

  • SsCH3Count defines the total number of –CH3 group connected with single bond. The positive coefficient of this descriptor (Eqs. 4 and 6) signifies the importance of methyl group for PDE4 inhibition. Molecules having greater number of methyl groups have more potent PDE4 inhibitory activity. The higher activity of molecules 4a, 16d, and 20 over other molecules justifies this finding.

SKMostHydrophilic is the most hydrophilic value on the vdW surface (by Kellog Method using Slogp). This descriptor signifies the importance of having highly hydrophilic atom in the molecule for PDE4 inhibition. The positive coefficient of this descriptor (Eq. 6) indicates that the molecules having most hydrophilic atom is likely to have most potent PDE4 inhibitory activity. This is aptly exemplified by the higher activity of compounds 4a and 20.

PSAExcludingP&S signifies total polar surface area excluding phosphorous and sulpfur. The descriptor has positive correlation with PDE4 inhibitory activity of polysubstitued quinolines (Eq. 6) thus molecules with greater polar surface area will have greater PDE inhibitory activity. The polar surface of molecule will help it in establishing polar interactions with the active site residues. Highest activity of molecule 4a is clear evidence in support of this finding.

The standardization of the regression coefficients of Eq. 6, allows assigning a greater importance to the molecular descriptors that exhibit larger absolute standardized coefficients. The result is given as follows, with standardized coefficients shown in parentheses:
$$ {\text{SKMostHydrophilic}}\left( { 5. 5 30 1} \right) > {\text{SsNH2Count}}\left( { 4.0 3 1 3} \right) > {\text{SsCIE-index }}\left( { - 3. 2 3 9 5} \right) \, > {\text{SsCH3Count }}\left( {0. 4 8 8 1} \right) > {\text{PSAExcludingP}}\& {\text{S }}\left( {0.0 3 70} \right) $$
(7)

From this inequality, it is deduced that SKMostHydrophilic is the most relevant variable for the present set of molecules. As all of the molecular descriptors take positive numerical values for all the molecules, and considering the sign of the regression coefficients, a molecule would tend to exhibit a relatively higher binding affinity for higher numerical values of SKMostHydrophilic, SsNH2Count, SsCH3Count, PSAExcludingP&S, and lower values of SsCIE-index. Of course, mixing effects among the five variables would also lead to a high estimated potency for the molecules.

The accomplishment of the general tendency of descriptors’ importance as given by Eq. 6 can be checked from the numerical values taken by the variables in Table 2 and by the predictions given in Table 9. The most relevant descriptor SKMostHydrophilic a hydrophilic descriptor is expected to have a high dependence on the functional groups and thus atoms present in the molecule. The importance of having electronegative atoms in the molecules is also highlighted by the positive coefficients of DipoleMoment in equation in Eqs. 3 and 4.

HQSAR

Hologram quantitative structure–activity relationship calculations were carried out using three distinct parameters—the fragment size, the hologram length, and the fragment type (fragment distinction). The HQSAR models were first generated using the default fragment size (47) combined with various fragment types and various hologram lengths. Table 10 summarizes the results for different fragment types and hologram length. With the best fragment type parameters, PLS analyses were performed to investigate whether different fragment sizes could improve the statistical parameters.
Table 10

Results of HQSAR analyses for various fragment distinctions on the key statistical parameters using fragment-size default (47)a

Model

Fragment

\( R_{\text{cv}}^{2} \)

SEP

R2

SEE

HL

N

1

A/B

0.697

0.402

0.923

0.208

83

6

2

A/B/C

0.666

0.391

0.827

0.210

257

3

3

A/B/C/H

0.688

0.367

0.903

0.275

257

6

4

A/B/C/H/Ch

0.679

0.363

0.889

0.257

307

6

5

A/B/C/H/Ch/DA

0.747

0.369

0.907

0.250

257

5

6

A/B/C/Ch/DA

0.742

0.365

0.894

0.208

353

4

7

A/B/C/H/DA

0.735

0.376

0.899

0.237

199

5

8

A/B/C/Ch

0.664

0.323

0.835

0.257

401

3

9

A/B/C/DA

0.731

0.378

0.901

0.267

353

5

10

A/B/H/DA

0.659

0.358

0.845

0.286

61

4

11

A/B/H

0.635

0.399

0.867

0.243

353

6

12

A/C/H/DA

0.773

0.327

0.908

0.201

307

5

13

A/C/Ch/DA

0.742

0.340

0.894

0.246

353

4

14

A/C/DA

0.731

0.357

0.901

0.219

353

5

Bold values indicate the best model

HL hologram length, N optimal number of components; fragment distinction—A atom, B bond, C connection, H hydrogen, Ch chirality, DA donor and acceptor

Cross-validation was done by means of leave-one-out (L-O-O) procedure. The optimum number of components is obtained by performing L-O-O analysis with SAMPLS.30. Through this procedure, each molecule is systematically excluded once from the data set, after which its predicted activity is obtained by the model derived from the remaining molecules. The HQSAR results from the different fragment sizes are summarized in Table 11. The best model was obtained using a hologram length of 307, 5 optimum number of components (O.N.C) and Atom + Connectivity + Hydrogen + Donor and Acceptor as the fragment type (\( R_{\text{cv}}^{2} = 0. 7 7 3 \), R2 = 0.908). Larger fragment size was favored for improving the statistical data in the form of \( R_{\text{cv}}^{2} \) and R2. However, the increment in \( R_{\text{cv}}^{2} \) was not significant, when the fragment size changed from 2–5 to 7–10. To avoid over interpretation, we chose a model with a higher \( R_{\text{cv}}^{2} \) and a smaller number of components as the final HQSAR model. This HQSAR model was built using Atom + Connectivity + Hydrogen + Donor and Acceptor as the fragment type and 2–5 as the fragment size, with a hologram length of 151 (\( R_{\text{cv}}^{2} \) = 0.783, \( R_{\text{cv}}^{2} \) = 0.952, O.N.C = 5, \( R_{\text{pred}}^{2} \) = 0.993) as shown in Table 11. Observed and predicted pIC50 values of the training and test set molecules for the best HQSAR model are plotted in Fig. 5. The plot of residuals versus predicted pIC50 is shown in Fig. 6. The low residual values show that the HQSAR model obtained is highly reliable and can be used to predict the biological activity of novel molecules.
Table 11

HQSAR analyses for the influence of various fragment sizes on the key statistical parameters using the best fragment distinction (A/C/H/DA)

Fragment size

\( R_{\text{cv}}^{2} \)

SEP

R2

SEE

HL

N

25

0.783

0.308

0.952

0.200

151

5

3–6

0.755

0.342

0.909

0.213

257

4

4–7

0.773

0.327

0.908

0.201

307

5

5–8

0.752

0.339

0.913

0.239

401

5

6–9

0.764

0.342

0.917

0.244

401

5

7–10

0.761

0.337

0.931

0.253

83

5

Bold values indicate the best model

https://static-content.springer.com/image/art%3A10.1007%2Fs00044-011-9831-x/MediaObjects/44_2011_9831_Fig5_HTML.gif
Fig. 5

Experimental versus predicted pIC50 for training and test sets using for the HQSAR model

https://static-content.springer.com/image/art%3A10.1007%2Fs00044-011-9831-x/MediaObjects/44_2011_9831_Fig6_HTML.gif
Fig. 6

Dispersion plot of residuals for HQSAR

An attractive property of HQSAR technique is that it provides straightforward clues about the individual atomic contributions to the biological activities using different color codes. HQSAR color codes the individual atoms of the molecules depending upon their contribution toward the biological activity. Figures 7 and 8 depicts the individual atomic contribution of the most potent molecule 4a and, least potent molecule 10 to its molecular bioactivity. The colors at the red end of the spectrum (red, red-orange, and orange) reflect unfavorable (negative) contributions, while colors at the green end (yellow, green-blue, and green) indicate favorable (positive) contributions. Atoms with intermediate contributions are colored in white.
https://static-content.springer.com/image/art%3A10.1007%2Fs00044-011-9831-x/MediaObjects/44_2011_9831_Fig7_HTML.gif
Fig. 7

Individual atomic contribution of the most potent molecules 4a to bioactivity

https://static-content.springer.com/image/art%3A10.1007%2Fs00044-011-9831-x/MediaObjects/44_2011_9831_Fig8_HTML.gif
Fig. 8

Individual atomic contribution of the most potent molecules 10 to bioactivity

The quinoline ring invariant in all of the PDE4 inhibitors was colored white, green, and yellow indicating positive contributions for activity, since this ring serves as a structural scaffold for holding the pharmacophoric groups in suitable orientation for maximum complementarity with the catalytic site of PDE4. Many atoms are shown in orange color for molecule 10 while most of the atoms in molecule 4a are shown in green color.

The atoms of methyl group at R5 position are shown in green color in molecule 4a showing its maximum contribution while the hydrogen atom in molecules 10 and 16 are shown in white color indicating their intermediate contribution. Couple of atoms 3-chlorophenyl group at R1 in molecule 10 are shown in orange indicating toward the negative contribution of the group toward PDE4 inhibitory activity.

Design of new molecules

Ligand-based method such as 2D QSAR is widely used not only because it is computationally less intensive but it can also lead to the rapid generation of QSARs from which the biological activity of newly designed molecules can be predicted. In contrast, an accurate prediction of activity of untested molecules based on the computation of binding free energies is both complicated and lengthy. The developed 2D QSAR models could be a clear indicator to intuitionist medicinal chemist for predicting novel molecules with enhanced PDE4 inhibitory activity. Also, a consistent observation is that minor changes in the substitutions produce significant differences in activity. Hence, further design of new molecules was a challenging task. Critical interpretation of the 2D QSAR and HQSAR models resulted in the identification of key structural features which could be exploited for improving the potency of the reference molecule 4a.

Taking into consideration the information obtained from QSAR models, applying the principles of bioisosterism and considering the synthetic feasibility, substitutions were proposed on the quinoline ring system at different positions which may perhaps increase the activity. The proposed substitutions increased the values of SKMostHydrophilic, SsNH2Count, PSAExcludingP&S, and SsCH3Count without affecting the values of SsCIE-index. Thus, we can predict few molecules (S7–S12) that might be the next synthetic targets (Table 12). Moreover, the proposed molecules also fulfill the conditions of Lipinski’s rule of five for oral bioavailability. Predicted −log1/IC50 for these proposed molecules against PDE4 along with their ClogP, molecular weight, and the number of hydrogen bond acceptors and donors (conditions of Lipinski’s “rule of five”) are given in Table 12.
Table 12
Structure, predicted pIC50 and rule of five criteria for the proposed molecules
https://static-content.springer.com/image/art%3A10.1007%2Fs00044-011-9831-x/MediaObjects/44_2011_9831_Figa_HTML.gif

No.

R

pIC50 (predicted Eq. 6)

pIC50 (predicted HQSAR)

ClogP

MW

HBD

HBA

S1

4-Methylphenyl

11.601

11.921

4.640

475

2

7

S2

3-Methylphenyl

11.273

11.382

4.640

475

2

7

S3

3,5-Dimethylphenyl

11.232

11.288

5.130

489

2

7

S4

2,4-Dimethylphenyl

11.182

11.294

5.130

489

2

7

S5

2,5-Dimethylphenyl

11.098

11.192

5.130

489

2

7

S6

3,4-Dimethylphenyl

11.030

10.829

5.130

489

2

7

Conclusion

Predictable and statistically significant 2D QSAR and HQSAR models of polysubstituted quinoline derivatives as PDE4 inhibitors were developed. Among the 2D QSAR models, the best model was obtained with enhanced replacement method using combination of steric, electronic, polar and topological descriptors based on internal and external validation. The analysis of developed QSAR models for the series of polysubstitued quinoline derivatives revealed that PDE4 binding affinity of this class of molecules is greatly influenced by the functional groups attached to different positions of the basic skeleton. For the dataset of 43 molecules, polarity of the molecules seems to be the major governing factor for PDE4 receptor binding. Topological features of the molecules also seem to play important role in PDE4 receptor affinity. The predicted PDE4 inhibitory activity of the newly designed molecules was found to be quite similar based on both the 2D QSAR and HQSAR models. A successful HQSAR model should provide important information about molecular fragments directly related to the biological activity, apart from predicting the activities of the untested molecules. Further the present study succeeded in designing 2D QSAR and HQSAR models that will guide synthetic medicinal chemist to design and synthesize new molecules with increased biological activity than existing compounds.

Copyright information

© Springer Science+Business Media, LLC 2011