# Polynitrogen Bicyclic and Tricyclic Compounds as PDE4 Inhibitors
## 3 Results and Discussion
### Molecular Modelling  
To further rationalise the biological results with regard to the presence of a methyl group in position 6 of the scaffold, a molecular modelling study on the two pairs of compounds with a tricyclic structure (Figure 5), namely 10**a/10b** (IC\({}_{50}\)= 62 nM and inactive, respectively) and **10d/10e** (inactive and IC\({}_{50}\) = 175.5 nM, respectively) has been performed. The 3D structures of the molecules were built with the 'DS ViewerPro 6.0' [25] and the lengths of the hydrogen bonds between the compounds and amino acids of the catalytic domain of human phosphodiesterase 4B2B (PDB-ID 3 GWT, resolution 1.75 A) [31] were searched and measured. For each compound, the best docking position (best binding energy) into the catalytic site was calculated with Autodock [26]. The ligand-enzyme complex structure was solvated and optimized through a complete minimization of the potential energy with GROMACS (version 2023) [27]. The lengths of the hydrogen bonds between the ligand and amino acids or with water that acts as a 'bridge' between ligands and residues are reported in Table 6, while Figures 6-9 show a visual representation of the pose of the molecules in the catalytic site and hydrogen bond interactions, respectively. Figure 5: Structures of selected compounds for molecular modelling studies. NA: not active. Figure 6: Orientation of **10a** (green) and **10b** (red) in the catalytic site. Figure 8: Orientation of **10d** (red) and **10e** (green) in the catalytic site. Figure 7: Hydrogen bond interactions for **10a** (**A**) and **10b** (**B**). Figure 9: Absence of hydrogen bond interactions for **10d** in the catalytic site (**A**). Hydrogen bond interactions for **10e** (**B**). Starting the discussion from the pair **10a** and **10b**, bearing at 1-position a diethyl carboxamide group and at 6-position a methyl or a hydrogen respectively (see Figure 6), we can notice a different'mode of accommodation' in the binding site (Figure 6, **10a** green, **10b** red) which could potentially help to explain the very different activity recorded for **10a** and **10b**. Specifically, compound **10a** can engage a three-point hydrogen bond between the carbonyl oxygen (O14, Table 6) of the pyridazinone ring, the pyrimidine-N5 (N16, Table 6), and the hydrogen of the side chain amino group of Glu443. In contrast, compound **10b** can form only one hydrogen bond interaction between the oxygen of the carbonyl (O7, Table 6) in the acetamido chain and the amino group of the side chain of the same Gln443. In the same way, compounds **10d** and **10e**, showing the methyl(benzyl)acetamido group at position 1 and methyl or hydrogen at the 6-position, respectively (see Figure 8), exhibit a different orientation of the scaffold in the catalytic site (Figure 8, **10d** red, **10e** green). Even in this case, the opposite accommodations are responsible for engaging hydrogen bond interactions. Compound **10e** interacts with the Gln433 by a strong hydrogen bond (length 1.98 A) through the oxygen atom (O11, Table 6) of the carbonyl group of the piridazinone ring. Moreover, the molecule is firmly anchored to a catalytic site by two other hydrogen bonds involving the carbonyl oxygen (O18, Table 6) of the acetamido chain and pyrimidine-N5 (N20, Table 6), water molecules (SOL508 and SOL528) bridging with Tyr233 and Asp392. Compound **10d** shows no interactions, which could explain the lack of activity (Figure 9). Interesting information arises from the evaluation of the whole volume occupied by the molecules (Figure 10), which adds further explanation for the difference in the inhibitory activity between the pairs **10a**/**10e** (active terms, mesh surface) and **10b**/**10d** (inactive terms, transparent surface). Nonetheless, molecular modelling results do not enable us to conclusively clarify the role of the methyl at position 6, which seems to be a discriminating factor for biological activity, although in opposite fashion for the two pairs of compounds.