Atom Pairs APs

Carhart et al developed the AP method of measuring molecular similarity. An AP is defined as a substructure consisting of two nonhydrogen atoms i and j and their interatomic separation  

The Lederle group has used the AP similarity method to compare chemicals in their data base. have used the AP method in selecting 

Kigure 4. Target chemical and five selected analogues using ED and AP methods from the starlist data base of chemicals. 

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Table 6.3. Sample molecules acetone and isobutene described by atom pair (ap) descriptors.

The atom pair, ap, and topological torsion, tt, descriptors are selected for illustrative purposes in the similarity searching context. 

MoBSS 14 Pfizer Min 441a PGVL 1.00E+13 2D ligand 2D Atom Pair (AP)... 

Cabrera et al. [50] modeled a set of 163 drugs using TOPS-MODE descriptors with a linear discriminant model to predict p-glycoprotein efflux. Model accuracy was 81% for the training set and 77.5% for a validation set of 40 molecules. A "combinatorial QSAR" approach was used by de Lima et al. [51] to test multiple model types (kNN, decision tree, binary QSAR, SVM) with multiple descriptor sets from various software packages (MolconnZ, Atom Pair, VoSurf, MOE) for the prediction of p-glycoprotein substrates for a dataset of 192 molecules. Best overall performance on a test set of 51 molecules was achieved with an SVM and AP or VolSurf descriptors (81% accuracy each). 

According to these definitions, each atom of a molecule is assigned to no, one or two PPPs. Since the descriptor is based on atom pairs, a pharmacophore matrix is built up. The entries py of the pharmacophore matrix P hold the PPP pair of vertex i and vertex j. If an atom is not a member of any PPP group, the row and column that correspond to the atom remain empty. A single atom can also belong to more than one PPP group. In this case, the entry py of the pharmacophore matrix P holds more than one PPP pair. All possible pairing combinations of the five PPPs result in 15 pairs (DD, DA, DP, DN, DL, AA, AP, AN, AL, PP, PN, PL, NN, NL, LL). 

The idea of using atom pairs as molecular features in structure-activity studies vas first proposed by Carhart et al. (84). AP descriptors are defined by their atom types and topological distance bins. An AP is a substructure defined by two atom types and the shortest path separation (or graph distance) between the atoms. The graph distance is defined as the smallest number of atoms along the path connecting two atoms in a molecular structure. The general form of an atom-pair descriptor is as follows ... 

By analogy with 2D atom-pair descriptors (Fig. 2.4), 3D AP descriptors can also be de-... 

Next, for a given scattering angle 6, one evaluates the (A, b) relative scattering angle 6, from eqs. (3.2.6) it follows that 6, = arcos [ - k Ikf + 2 k Ik) cos 6]). One then calculates the impact parameters py, / = 1, 2,..., that correspond to 6, i.e., the roots of t<,(P)l This equation is solved for the py by inverse interpolation based on the previously calculated table of Xb versus p typically, inverse-quadratic interpolation suffices for 1 eVs s 10 eV when the XbiP) tabulated in steps Ap 0.1 A. The smallest root pj, corresponds mostly to a direct rebound from the repulsive core of Ui, if Ui, exhibits a single well and 6 < 6, then there will exist two more roots (pj, and pj, ) due to the inward deflection caused by the attractive forces. The atom-pair transition amplitudes... 

Atom Pair FPs Pairs of atoms and the minimum number of bonds linking them constitute the substmctural components of APFs. Generally, only APs separated by seven or fewer bonds are considered. As described by Carhardt et al. [45], the general form of the substmcture of an APF is given by Eq. (1.5) ... 

Two other atomic properties have been used in the definition of atom type, thereby increasing its fuzziness relative to that in the ap and tt descriptors - atomic log P contribution (yielding hydrophobic pairs, hps, and torsions, hts) and partial atomic charges (charge pairs, cps, and charge torsions, cts). 

Writing the equation in the usual way directs too much attention to the atoms and not enough to the electrons We can remedy that by deleting any spec tator ions and by showing the unshared electron pairs and covalent bonds that are made and broken Both sodium hydroxide and sodium fluoride are com pletely ionized in water therefore Na" which ap pears on both sides of the equation is a spectator ion Hydrogen fluoride is a weak acid and exists as undissociated HF molecules in water... 

The synclinal conformation (sc) is appropriate for overlap of an oxygen nonbonded pair with the a C—Cl orbital. The preferred ap relationship, requires an antiperiplanar alignment of a lone-pair orbital with the bond to the electronegative substituent. Because of the donor-acceptor nature of the interaction it is enhanced in the order F < O < N for the donor (D) atom and N < O < F for the acceptor (A) atom. 

There are 2.56 d orbitals available for bond formation. To form 5.78 bonds these would hybridize with the s orbital and 2.22 of the less stable p orbitals. In copper, with one electron more than nickel, there is available an additional 0.39 electron after the hole in the atomic d orbitals is filled. This might take part in bond formation, with use of additional Ap orbital. However, the increase in interatomic distance from nickel to copper suggests that it forms part of an unshared pair with part of the bonding electrons, thus decreasing the effective number of bonds. 

Inspection of the second resonance structure reveals that this nitrogen atom is actually sp hybridized, not sp. It might look like it is sp hybridized in the first resonance structure, but it isn t. Here is the general rule a lone pair that participates in resonance must occupy ap orbital. In other words, the nitrogen atom in the compound above is sp hybridized. And as a result, this nitrogen atom is trigonal planar rather than trigonal pyramidal. 

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