Canonicalization

The task is now to take one of the numberings as the standard one and to derive a unique code from it, which is called canonicalization. This can be accomplished by numbering the atoms of a molecule so that it is represented later by only one connection table or bond matrix. Such a unique and reproducible numbering or labeling of the atoms is obtained by a set of rules. 

Various methods have been developed for a unique and unambiguous numbering of the atoms of a molecule and thus for deriving a canonical code for this molecule [76]. Besides eigenvalues of adjacency matrices [77], it is mainly the Morgan Algorithm that is used [79]. 

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If the indexing of the atoms is changed, the CT will have a different appearance. Thus, the representation of a chemical structure in a CT is unambiguous but not unique, which can only be achieved by canonicalization (see below). 

Figure 2-77. Determination of parity value, a) First the structure is canonicalized. Only the Morgan numbers at the stereocenter are displayed here, b) The listing starts with the Morgan numbers of the atoms next to the stereocenter (1), according to certain rules. Then the parity value is determined by counting the number of permutations (odd = 1, even = 2).

The constitution can be represented in an unambiguous and unique manner by canonicalization (Morgan Algorithm). 

Sayle, R. and Delany, J. Canonicalization and enumeration of tautomers. EuroMug-99. Cambridge, UK, 28-29 October 1999, http //www.daylight. 

Algorithm I - Registration - Canonicalization of Connection Tables. A connection table for a chemical substance with n atoms can be numbered in as many as n different ways. The problem of generating a canonical form involves selecting a... 

To obtain a unique SMILES notation, computer programs such as the Toolkit include the CANGEN algorithm [1] which performs CANonicalization, resulting in unique enumeration of atoms, and then GENerates the unique SMILES notation for the canonical structure. In the case of pyridine, this is notation (III). Any molecular structure entered in the Toolkit is converted automatically into its unique representation. 

The chemical structure database and registration procedure play dual roles in an enterprise screening informatics environment. These components are essential to the transactional HTS informatics system and serve as the basis for cheminformatics data analysis. While capturing the chemical structures for association with the final screening endpoints, this system also captures and applies the organizational chemical business rules to validate and standardize chemical structures and canonicalize their representations. Structural representation is a critical prerequisite for any subsequent cheminformatics analysis. 

The preferred representation of the Figure 14.5 structure may be as a mixture of the E and Z geometric isomers because they can interconvert via other tautomeric intermediates. Related to tautomer canonicalization is the ability to identify tautomers by exact or substructure querying of the... 

FIGURE 14. 5 Example of tautomer structure canonicalization. In reality tautomers can exist as mixtures. 

Sayle, R. 1999. Canonicalization and Enumeration of Tautomers, http //www.dayhght.com/meetings/emug99/ Delany/taut html/index.htm. 

Equivalence Class. In the canonicalization of structures that have some element of symmetry, certain atoms that are topologically equivalent may yield the same canonical number. These atoms are considered to be in the same equivalence class. The concept of equivalence class is used, for example, in the Daylight Chemical Information Systems handling of reactions, to examine equivalent atoms when mapping reactant and product atoms. 

Canonicalize chemical structures, i.e., make all chemical structures quickly comparable for a computer. For example, canonical smiles or InChls can be used. 

Canonicalize the structures of actives against target A (Set 1), target B (Set 2), and all other compounds ever tested in safety profiling (Set 3). 

Create Function canonicalize() Returns Trigger As EOSQL ... 

Create Trigger canonicalize Before Insert Or Update On ctable For Each Row Execute Procedure canonicalize() ... 

This canonicalize function uses NEW to refer to the row being inserted or updated. NEW.cansmi refers to the value under question. The canonical SMILES is computed and compared to NEW. cansmi. If they are not the same, the NEW.smi value is replaced by the canonical SMILES value and the NEW row is returned. This NEW row is used by the RDBMS in place of the original row. The create trigger command causes this operation to be put into effect in the RDBMS. 

Next, by considering the energy, E, as a Hamiltonian operator, H, we introduce the coordinate, Qkvx and the momentum, Pkv. This is the process of canonicalization. 

The introduction of the electromagnetic potentials, A and 0, into Maxwell equations, the derivation of the wave function of A, and the canonicalization of the space consisting of this... 

The conversion of structural information to the Identifier is based on a set of lUPAC structure conventions, and rules for normalization and canonicalization (conversion to a single, predictable sequence) of an input structure representation. The resulting InChl is simply a series of characters that serve to uniquely identify the structure from which it was derived. The InChl uses a layered format to represent all available structural information relevant to compound identity. InChl layers are listed below. Each layer in an InChl representation contains a specific type of structural information. These layers, automatically extracted from the input structure, are designed so that each successive layer adds additional detail to the Identifier. The specific layers generated depend on the level of structural detail available and whether or not allowance is made for tautomerism. Of course, any ambiguities or uncertainties in the original structure wiU remain in the InChl. 

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