Descriptor atom pair

The models developed for log D prediction usually aim at being global ones. This, however, does not work on practice. Sheridan et al. [109] noticed that the accuracy of log D prediction of molecules decreased approximately 2-3 times (RMSE = 0.75 versus 1.5-2) as the similarity of the test molecule to the molecules in the training set (using Dice definition with the atom pair descriptors) changed from 1 to 0 (most to least similar). Thus, if a test set molecule had a very similar molecule in the training set, it was possible to accurately predict its log D value. A detailed overview of state of the art methods to access the same problem was published elsewhere [117]. 

Sheridan, R.P., Miller, M.D., Underwood, D.J., and Kearsley, S.K. Chemical similarity using geometric atom pair descriptors. /. Chem. Inf. Comput. Sci. 1996, 36, 128-136. 

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-... 

Step 1. Multiple descriptors such as molecular connectivity indices or atom pair descriptors (cf Section 2.1) are generated initially for every compound in a data set. 

Some research groups have extended the atom-pair descriptors to three-point (triplets) and four-point (quartets) pharmacophore descriptors (35,37,76,81) as described in section 2. These descriptors have a potentially superior descriptive power, and a perceived advantage over atom pairs is the increased "shape" information (intrapharmacophore distance relationships) content of the individual descriptors (37a). The quartet (tetrahedral) four-point descriptors offer further potential 3D content by including information on volume and chirality (37a, 82), compared with the triplets that are components of the quartets and represent planes or "slices" through the 3D shapes. 

Similar to atom pairs descriptors, REX descriptors are codes defined by a pair of terminators and the link between them [Judson, 1992b] ... 

With respect to the atom pairs descriptors, REX descriptors use more generalized linear fragments, allowing more complex substructures to be dealt with. 

Unlike topological torsions, atom pairs are sensitive to long-range correlations between the atoms in molecules and therefore to small changes in one part of even large molecules. Atom pair descriptors usually are Boolean variables encoding the presence or absence of a particular atom pair in each molecule. 

Using the geometric distance in place of the topological distance between any pair of atom types, geometric atom pair descriptors were analogously defined [Sheridan, Nilakantan et al, 1989 Sheridan, Miller et al, 1996]. Atom types are defined here by the chemical element, number of heavy-atom cormections, number of n electron pairs, number of attached hydrogens, and formal charge. 

A structural feature is defined by nine numbers. The first four numbers (nl-n4) serve to identify the specific atom type, atom pair, or atom environment by means of a predefined set of properties, while the remaining five numbers (n5-n9) determine which bits of the whole key are set by the feature. Specifically, in the case of single atom descriptors, nl is 0 and n2 and n3 encode one or two properties of the atom for atom pair descriptors, nl encodes the number of bonds (topological distance) between the atoms, while nl and n3 encode the property values of the two atoms finally, for custom atom environment descriptors, nl is equal to 7, while n2 encodes the specific atom environment and n3 encodes the property of the atom in the center of that environment. The number n4 encodes the number of occurrences in the molecule of the considered feature. The number n5 is used to specify the number of bits that are set, while n6 is a flag indicating whether or not hashing is allowed the final three numbers, n7, n8, and n9 identify the bits in the structural key. 

Fig. 13.1-4 Atom-pairs and topological torsions, (a) Illustration of atom-types used in atom-pair descriptor calculation including atomic identities, pi-bonding, and molecular topology, (b) Distinct atom-types, some of which occur multiple times, make up the basic unit of atom-pair calculation.

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