Molecular graph types

We begin with the way chemists perceive similarity between two molecules. This process involves, consciously or unconsciously, comparing several types of structural features present in the molecules. For example, considering the five aliphatic alcohols (represented by their H-suppressed molecular graphs) in Figure 1, we note both similarities and differences they are all four-carbon alcohols a, b, c and d are acyclic, whereas e has a ring a and b are primary alcohols, c and e are secondary alcohols and d is a tertiary alcohol b and c have the same skeleton, but for the labeling of points (atoms), while the other skeletons are distinct etc. 

Path-Type MCIs A path in a molecular graph is an ordered set of consecutive bonds (bi, b2, bi,..., bm) with the property that bond bk (1 < k < m) starts from the atom where bond bk-1 ends. The length of such a path is m. The order of a path equals its length m. The general formula for a path-type MCI is... 

Nowadays, more than 4000 types of descriptors are known.17 There exist different ways to classify them. With respect to the type of molecular representation used for their calculations—chemical formula, molecular graph, or spatial positions of atoms—one speaks about ID, 2D, and 3D descriptors, respectively. Descriptors can be global (describing the molecule as a whole) and local (only selected parts are considered). One could distinguish information-based descriptors, which tend to code the information stored in molecular structures, and knowledge-based (or semiempir-ical) descriptors issued from the consideration of the mechanism of action. Most of those descriptors can be obtained with the DRAGON, CODESSA PRO, and ISIDA programs. 

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 ... 

Fig. 3.2 Schematic of the CATS descriptor calculation, (a) The hydrogen-depleted two-dimensional molecular graph provides the input, (b) The graph is simplified for the distance matrix computation different bond orders are not considered (unweighted graph) and all element types are disregarded. The algorithm starts at an arbitrary chosen atom and visits all nodes of the graph in a breadth-first manner, thereby building up the distance matrix. The numbers at the vertices are used to reference individual atoms in the distance matrix.

Fig. 3.4 Definition of scaffold (Sc) and reduced scaffold (ReSc). In this work we defined the scaffold of a molecules as the side-chain depleted molecular graph without annotation of atom types. A reduced scaf-...

From the PDB and topological analysis, we construct a molecular graph with untyped bonds and recognized chemical rings. For correct chemical recognition, we need to determine hybridization states, from which we then try to derive correct bond types. 

Figure 12.7 presents the molecular graph of CLOH—HBeH complex where the intermolecular O-H—H-Be DHB exists. It was found that this structure corresponds to the stable energetic minimum [35], This is the shortest ever found theoretically intermolecular contact (H—H) since it amounts to only 1.049 A. On the other hand, such a short contact represents the proton-acceptor distance.9 It is worth mentioning that the other shortest contact was revealed for bifluoride (FHF)-ion. For this system, the H—F equivalent distances amount to 1.1—1.2 A. The exact value depends on the type of experimental measurements or the applied method of calculations [36]. 

D structures of drugs were converted into hydrogen-suppressed molecular graphs, where nodes are labeled with atom types except hydrogens and edges are labeled with bond types. 

Assign PPP atom types to the nodes of the molecular graph. 

In this section different types of fragments are classified with respect to their topology and the level of abstraction of molecular graphs. 

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