Graph reduced

The descriptor uses readily calculable physicochemical properties from the topological structure. The descriptors used in this study were atomic weight, hydropho-bicity, molecular refractivity, atomic charge, polar surface area, hydrogen bond acceptors, and hydrogen bond donors. The authors note that Martin et al. [32] applied a similar approach for the design of diverse combinatorial libraries. 

Of the eight descriptors used in this analysis, the molecular weight and molar refractivity were demonstrated to be the most significant in improving the separation of experimentally observed bioisosteres from the nonbioisosteric data set. However, molecular weight and refractivity are highly correlated, so only one of these properties may be necessary to assist in the discrimination of these two data sets. 

Endcap groups are then identified as those that provide lateral hydrophobic features that consist of three atoms (e.g., isopropyl) and are abstracted as a single atom. Due to the size of the sulfur atom, thioethers are handled similarly although they contain only two atoms. These features are important for the overall size and shape of a molecule. 

The ErG representation was found to have competitive performance to Daylight fingerprints in 11 different virtual screening experiments using an updated variant of the Hert-Willett data set [34] defined from the MDDR database. However, what is 

The RG generation algorithm defined by Birchall et al. begins by fragmenting recursively a given molecule at all nonterminal, acydic single bonds with three exceptions acydic sp carbon to acyclic sp carbon bonds acyclic heteroatom to acyclic heteroatom bonds and acyclic heteroatom to acyclic sp bonds. 

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Delete all measured streams and search for cycles on the reduced graph. The cycles in the resulting graph represent indeterminable flows. 

The Morgan algorithm 5> is a device used by the Chemical Abstracts Service for assigning indices to the nodes of constitutional formulas whose H-atoms have been omitted, i. e. their reduced graphs. If the indices of all atoms are needed, e.g. for the representation of stereochemistry, an additional procedure is needed for establishing those for the H-atoms. Constitutional symmetry is not indicated directly by Morgan indices. 

Gillet, V.J., Willett, P., and Bradshaw, J. Similarity searching using reduced graphs./. Chem. Inf. Comput. Sci. 2003, 43, 338-345. 

Birchall, K., Gdlet, V.J., Harper, G. and Pickett, S.D. (2006) Training similarity measures for specific activities application to reduced graphs. Journal of Chemical Information and Modeling, 46 (2), 577-586. 

Fig. 5-4. An irreducible graph (first line) arid some reducible graphs (second line) yielding that graph after cutting off all reducible parts. The reducible parts are indicated by boxes...

Gillet, V.J., Downs, G.M., Holliday, J.D., Lynch, M.F., Dethlefsen, W. Computer storage and retrieval of generic chemical structures in patents. 13. Reduced graph generation. Journal of Chemical Information and Computer Science 1991, 31, 260-270. 

Barker, E. J., Gardiner, E.J., Gillet, V. J., Kitts, P., Moris, J., et al. Further development of reduced graphs for identifying bioactive compounds. Journal of Chemical Information and Computer Sciences 2003, 43, 346-356. 

For the screw characteristic curves presented in Fig. 4.12 and in Fig. 4.13 for a conventional and grooved fed extruder, respectively, the reduced graphs are shown in Fig. 4.14. As can be seen here, each type of extruder can be represented with a single curve for a whole range of rotational speeds. It is to be noted that in this representation the effect of viscous dissipation was not included, which may explain why some of the points fall somewhat outside the fitted lines. 

Fig. 14. Example of the reduced-graph expression of a chemical structure...

Figure 1.12. Examples of reduced graphs. Nodes corresponding to aromatic rings (Ar), aliphatic rings (R), functional groups (F) and linking groups (L) are shown (adapted from Gillet el al. 2003)...

For database searching, pharmacophores are best defined by all possible distances between chosen groups or features (pharmacophore points). Therefore, as illustrated in Figure 1.13, they are best represented as a molecular graph (similar to reduced graphs). In this case, different from conventional graphs, however, nodes correspond to points (or centroids) and edges to inter-point distances, rather than bonds. 

Gillet VJ, Willett P, Bradshaw J (2003) Similarity searching using reduced graphs. J Chem Inf Comput Sci 43 338-345. 

Figure 1.11 Examples of chemical structures corresponding to the same GWB reduced graph of type R/F (shown in center). (Adapted from ref 224.)...

Takahashi, Y, Sukekawa, M. and Sasaki, S.I. (1992). Automatic Identification Molecular Similarity Using Reduced-Graph Representation of Chemical Structure. J.Chem.Inf.Comput.ScL, 32, 639-643. 

The reduced graph may contain vertices representing the cyclic and acyclic portions of the molecule or contiguous groups of carbon or heteroatoms. 

An example of a reduced graph is a molecular graph composed of weighted edges and with vertex number equal to the number of functional groups perceived by using predefined rules [Takahashi, Sukekawa et al., 1992]. 

For the former case, the relationship is described in the overlap matrix, and for the latter, the relationship is described in the inclusion matrix to avoid the duplication of vertices in the reduced graph representation. They are used to determine the —> topological distance between functional groups. 

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