Asthma and chronic obstructive pulmonary disease (COPD) are the two most prevalent chronic airway diseases. COPD is a treatable and preventable disease but current predictions are that it will continue to increase as an important cause of mortality and morbidity worldwide [1–2]. Phosphodiesterases (PDEs) have been classified into at least 11 families (PDE 1–11) according to their substrate sensitivity, inhibitor selectivity, Ca²⁺/calmodulin requirement and amino acid sequences [3–4]. Phosphodiesterase-4 (PDE4) is a key enzyme in the hydrolysis of cAMP in mast cells, basophils, eosinophils, monocytes and lymphocytes, as well as areas in the brain and airway smooth muscle [5–6].

PDE4 plays a significant role in modulating the activity of cAMP, an important second messenger that mediates the relaxation of airway smooth muscle and suppresses inflammatory cell function, thereby attenuating the inflammatory response [7]. Increasing the intracellular concentration of cAMP in the airway tissues and cells suppresses inflammatory cell function and thus should be beneficial for treatment of asthma and COPD [8]. Over the last two decades pharmaceutical companies have placed numerous PDE4 inhibitors into clinical trials for asthma or COPD. Only a small number of these drugs have the potential to be approved for market [9–10].

Comparative molecular field analysis (CoMFA) is one of the well known 3D-QSAR descriptors which has been used regularly to produce the three dimensional models to indicate the regions that affect biological activity with a change in the chemical substitution [11]. The advantages of CoMFA are the ability to predict the biological activities of the molecules and to represent the relationships between steric/electrostatic property and biological activity in the form of contour maps gives key features on not only the ligand-receptor interaction but also the topology of the receptor [12].

We present here our 3D-QSAR studies using CoMFA method on a training set of 5,6-dihydro-(9H)-pyrazolo-[4,3-c]-1,2,4-triazolo-[4,3-α]-pyridine derivatives as PDE4 inhibitors by considering the steric and electrostatic influences. The model deduced from this investigation provides underlying structural requirements and good predictive ability, which could aid new PDE4 inhibitors prior to their synthesis.

Thirty-one molecules were randomly partitioned into a training set of 27 and a test set of four compounds with bias given to both chemical and biological diversity in both the training set and the test set molecules. Despite the ambiguity of drug-receptor interactions in general, a statistically significant model was obtained from the CoMFA study. A “cross-validated q²” may then be defined, completely analogously to the definition of the conventional q², as

where press is the standard errors of the cross-validated predictions and SD is the sum of squared deviations of each biological property value from their mean and press, or predictive sum of squares, is the sum, over all compounds, of the squared differences between the actual and “predicted” biological property values[15].

Often for QSARs developed with CoMFA a shift in the q² values is observed as the grid spacing is altered. To examine this possibility with these data, the different grid boxes with 1.0, 1.5, 2.0, 2.5, and 3.0 Å grid spacing, respectively, were used for the CoMFA calculations. The influence of the different grid spacing to CoMFA model is obvious. Only from the q² after leave-one-out cross-validation, the model with the grid spacing of 2.0 Å was selected as the best model (see Table 2).

The statistical parameters of CoMFA analysis is summarized in Table 3. The leave-one-out cross-validated PLS analysis of the best model gave rise to a cross-validated value (q²) of 0.741, suggesting that the model is a useful tool for predicting PDE4 inhibitory activity [16]. The correlation coefficient between the calculated and experimental activities, non-cross-validated value (r²) of 0.954 with standard error estimate 0.211. The respective relative contributions of steric and electrostatic fields were 0.915 and 0.085, indicating that steric field is more predominant. Then the condition without electrostatic were studied and the new q² and r² values were 0.739 and 0.953 respectively. In fact, the electrostatic contribution was nearly negligible. The actual and predicted values of the training set by the best model are given in Table 1, and the graph of observed activity versus predicted activities of training set molecules from CoMFA analysis is illustrated in Figure 3. The 3D-QSAR model was validated using a test set (in Table 1) of 4 compounds, which were not included in the development of the model. On the basis of the PLS statistics of CoMFA model, this is further validated by the residual values of the test set (Table 1). Figure 4 represents the graph of the actual versus predicted pIC₅₀ values of the test set molecules for CoMFA model.

The contour plot representations of the CoMFA results for PDE4 inhibitors are presented in Figures 5 and 6 using compound 24 as reference structure. The green-colored regions indicate areas where steric bulk enhances PDE4 inhibitory activity, while the yellow contours indicate regions where steric bulk is detrimental for the biological activity. Blue-colored regions show areas where electropositive charged groups enhance PDE4 inhibitory activity, while red regions represent where electronegative charged groups improve the activity.

The electrostatic contour map displayed in Figure 5 shows a region of red polyhedral space, indicating that the electron-rich groups are beneficial to the activity. Compounds 4 and 7 have higher inhibition activity than compound 10 because the chlorine atom is placed within the electron-rich charge red contour. Additionally, a blue polyhedron in the top left corner of Figure 5, indicates that electron-rich substituents will reduce the biological activity. Compound 11, with a strong electron withdrawing substituent, 4-trifluoromethylphenyl, can not fit into the electropositively charged blue contour. Thereby, compound 11 has lower activity than other compounds in the model.

The steric contour map is displayed in Figure 6. The plot shows the cyclobutyl group of molecule 24 placed between two big green polyhedrons. If a substituent, such as 3-pentyl group, is attached on molecule 28, it occupies the green contour and enhances the activity. In compounds 25 and 29, where the substituent group R is cyclopentyl and 1-methylcyclohex-1-yl, respectively, these fit into the green contour, and the activity of these compounds are higher. Compounds 20, 21 and 22, with methyl, ethyl and propyl substituents, show less activity than compound 28. Additionally, the contour plot shows a yellow polyhedron in the top left corner of Figure 6. If a bulky substituent occupies the yellow contour this will depress the biological activity. Compounds 8, 9 and 11, with 4-methoxyphenyl, 4-chlorophenyl and 4-trifluoromethylphenyl substituents, respectively, are very close to the yellow contour which represents the unfavored steric region. Consequently, these compounds almost have no activity.

3D QSAR studies were performed using CoMFA on a series of derivatives with inhibitory activity on phosphodiesterase-4. A satisfactory CoMFA model was obtained with LOO cross-validation q² and non-cross-validated r² values of 0.741 and 0.954 respectively. The developed model also possesses promising predictive ability as discerned by the testing on the external test set, and should be useful to elucidate the relationship between compound structures and biological activities and to facilitate design of more potent phosphodiesterase-4 inhibitors. For example, use of a p-trifluoromethyl substituent in a cyclobutyl maybe increase the biological activity, since a fluorine atom at that position participates in the electron-rich charge red contour and the trifluoromethyl will fit into the green contour. Similarly, other p-substituents on the cycylobutyl moiety might show even greater inhibitory power than a simple cyclobutyl.