Molecular descriptors graph-based representations

Figure 4.1 Ligand-based virtual screening methods. The figure shows different computational methods for screening compound databases that take either a local or a global view on molecular structure. Molecular similarity methods that operate on molecular descriptors, histogram representations, superposition or (reduced) molecular graphs evaluate molecular structure globally. By contrast, local structural features are explored by substructure and pharmacophore searching or QSAR modeling.

Some molecular descriptors, called - determinant-based descriptors, are calculated as the determinant of a - matrix representation of a molecular structure. Moreover, permanents, short- and long-hafnians, calculated on the topological - distance matrix D, were used as graph invariants by Schultz and called per(D) index, shaf(D) index, lhaf(D) index [Schultz et al, 1992 Schultz and Schultz, 1992]. 

The two-dimensional representation of a molecule considers how the atoms are connected, i.e. it defines the connectivity of atoms in the molecule in terms of the presence and nature of chemical bonds. Approaches based on the -+ molecular graph allow a two-dimensional representation of a molecule, usually known as the topological representation. Molecular descriptors derived from the algorithms applied to a topological representation are called 2D-descriptors, i.e. they are the so-called - graph invariants. 

GAO is an orbital-based graph-theoretical representation of molecules from which the common graph invariants, such as connectivity, Zagreb, and Wiener indices, can be calculated, and thus it represents a source of orbital-based molecular descriptors, which can be generally called GAO descriptors. Note that orbital interaction graph of linked atoms is another representation of molecules, which accounts for atom orbitals. 

As previously mentioned, the acronym QSAR stands for the quantitative structure-activity relationship. However, there may be some ambiguity associated with the attribute quantitative. It does not necessarily follows that results expressed or having numerical representation are necessarily quantitative. Qualitative results can equally be numerically represented. Strictly speaking, we define and view QSAR models as quantitative only when the numerically expressed models allow meaningful interpretation of the numerical results obtained for the structure-activity relationship within the basic concepts of the particular model. This means that the physicochemical models should allow quantitative interpretation of the numerical physicochemical descriptors used and that the structure-mathematical models should allow quantitative interpretation of the numerical structure-mathematical descriptors used. We will use the symbol qsar and QSAR as the abbreviation for qualitative structure-activity relationship. Such are the relationships that are non-numerical and the relationships that may be numerical but the variables used are interrelated and thus do not allow unique interpretation of the MRA equations. Because all molecular descriptors hitherto used in QSAR, whether they are based on physicochemical properties, quantum mechanical calculations, or molecular graphs, are all interrelated, it follows that all such hitherto reported results, without further elaboration, remain essentially qualitative, being qsar rather than QSAR. 

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 latter scenario is sometimes referred to as scaffold or lead hopping [22-25]. This is a formidable challenge for the descriptor and the similarity measure. While avoiding the chemical graph and atom type-based molecular representation, the essential features required for activity have to be retained. By definition, such a task will be prone to picking out false positives and, therefore, requires a fast search in large and diverse databases together with a tunable level of similarity. 

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