Molecular Topology CATS

The derivation of the topological distance matrix from the molecular graph is followed by the assignment of PPPs to the nodes of the graph. The following list provides chemical definitions of the five PPP types that are implemented in the CATS descriptor. The upper-case letter in parentheses is the abbreviation of each PPP type. Additionally, a functional group description is paired with its corresponding SMARTS in square brackets  

These numbers also illustrate the visiting order of the algorithm during graph 

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). 

A particular property of the topological CATS descriptor is its speed of calculation. Thereby, the program qualifies for applications that deal with very large numbers of compounds, e.g. virtual screening campaigns in early stages of the drug discovery process. 

The main difference in the correlation vector representation of a 3D conformation in comparison with a topological representation of a molecule is that the distances between the atoms are no longer shortest paths. Instead, Euclidean distances between all atoms are used. Distances between atoms are not restricted to integer values, so the distances have to be partitioned into a set of 

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Fig. 3.1 The CATS family of descriptors CATS, CATS3D and SURFCATS. The degree of abstraction from the atomic molecular structure is assumed to be SURFCATS > CATS3D > CATS. All descriptors are based on a PPP-type description of the underlying molecule. For each descriptor, pairs ofPPPs are transformed into a correlation vector. CATS is calculated from the topological...

The CATS (chemically advanced template search) from Schneider et al. [23] was originally proposed as a ligand-based topological pharmacophore for scaffold hopping, a specific subset ofbioisosteric replacement, where the objective is to discover molecular scaffolds that are topologically different but retain the key functional requirements necessary for macromolecular recognition [24]. 

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