Molecules, structural descriptors

The estimations Equations (6.17a, b) of probabilities P Ak), P Ak D not only increase the algorithm s prediction accuracy but also open up new possibilities. For example, function fn A in the range [0,1] can be considered as a measure of molecule n belonging to a fuzzy set of molecules that reveal activity Ak- The descriptor weight gn Dd can be considered in the same manner, and then the molecule structure descriptors can be of arbitrary nature, e.g., such as in the refs. 51 and 52. 

A structure descriptor is a mathematical representation of a molecule resulting from a procedure transforming the structural information encoded within a symbolic representation of a molecule. This mathematical representation has to be invariant to the molecule s size and number of atoms, to allow model building with statistical methods and artificial neural networks. 

A structure descriptor is a mathematical representation of a molecule resulting from a procedure transforming the structural information encoded within a symbolic representation of a molecule. 

Molecules can be represented by structure descriptors in a hierarchical manner with respect to a) the descriptor data type, and b) the molecular representation of the compound. 

Further prerequisites depend on the chemical problem to be solved. Some chemical effects have an undesired influence on the structure descriptor if the experimental data to be processed do not account for them. A typical example is the conformational flexibility of a molecule, which has a profound influence on a 3D descriptor based on Cartesian coordinates. In particular, for the application of structure descriptors with structure-spectrum correlation problems in... 

On the other hand, there is considerable interest to quantify the similarities between different molecules, in particular, in pharmacology [7], For instance, the search for a new drug may include a comparative analysis of an active molecule with a large molecular library by using combinatorial chemistry. A computational comparison based on the similarity of empirical data (structural parameters, molecular surfaces, thermodynamical data, etc.) is often used as a prescreening. Because the DFT reactivity descriptors measure intrinsic properties of a molecular moiety, they are in fact chemical fingerprints of molecules. These descriptors establish a useful scale of similarity between the members of a large molecular family (see in particular Chapter 15) [18-21],... 

The model was claimed to compute 5000-6000 molecules per min. The predictive ability of the model was validated by four approaches. In the first approach, a set of 20 compounds was randomly selected as an initial validation test set. A model was developed from the remaining 86 compounds with an MAE of 0.33, from which the test set values were then predicted. The results of this test prediction were very good and provided momentum for support of the three structure descriptors. In the second approach, a full cross-validation test of the model was investigated. The data set of 102 compounds was divided... 

The second variant of QSAR is the use of actual structural descriptors, such as molecular orbital indices or topological codes, to define numerically the structure of a molecule and to find linear relationships with numerical biological data (Kier and Hall, 1976, 1992). 

A physical model usually predisposes to physicochemical descriptors, such as p/Ca, log P or molar volume for the whole molecule, or the equivalent descriptors for substituents on a common molecular framework. But different structures can have the same or similar property values, and we are interested in designing structures. So at some stage we must choose structural descriptors (atom types, substructural fragments, connections, or indices from molecular orbital calculations) or at least relate structure to property in order to design the appropriate structure. 

First, a list of unique scaffolds was derived and sorted by complexity. The complexity was calculated from four structural descriptors, namely number of rings in the smallest set of smallest rings, number of heavy atoms, number of bonds and the sum of heavy atomic numbers in the scaffold. Each scaffold or class center in the list was assigned an ID that corresponded to its position in the list. How much a molecule resembled its class center was determined by the number of side-chains attached to the scaffold. Fewer side-chains will give a closer resemblance to the class center. The similarity of a drug with the class center was reflected in the membership value. The membership value was based on the sum of heavy atomic numbers, the number of rotating bonds, the number of one and two nodes and the number of double and triple bonds in a molecule compared with its scaffold. Since the membership value indicated the contribution of rings in the class center for a certain... 

Spatial autocorrelation is a quantitative measure of the probability of finding objects of defined properties within a distance of interest [9, 10]. The concept of autocorrelation is mainly applied in fields such as geography, economics, ecology or meteorology to describe the spatial distribution of features. The idea of a molecular descriptor based on the autocorrelation concept was first introduced into the field of cheminformatics by Moreau and Broto in 1980 [11] with the ATS (autocorrelation of a topological structure) descriptor. For this approach, the atoms of a molecule were represented by properties such as atomic mass or partial charge. The distance between atoms was measured as the number of bonds between the respective atoms (topological distance). 

Carhart et al. [15] described a generalized structural descriptor called an atom pair which is defined in terms of the atomic environments of, and shortest path separation between, all pairs of atoms in the topological representation of a chemical structure. A similar descriptor has been suggested by Klopman [16]. More recently, Judson [20] described a more sophisticated approach to analyze structural feature of molecules for structure-activity studies. 

Toxicity, as with all forms of biological activity, is a result of the molecular structure of the chemical concerned. Given that fact, the computational chemist is presented with a problem that is, at least theoretically, soluble. The tools that have been applied so successfully to rationalizing biological activity in terms of chemical structure can also be used for correlating toxicity with various structural parameters.24 Such structural descriptors may be physicochemical values,25 functions of molecular size and shape, molecular connectivity, and numbers of atoms, or they may be quantum-chemical parameters relating to electronic distribution within the molecule.26-27... 

The diversity of a library of compounds denotes the degree of heterogeneity, structural range or dissimilarity within the set of compounds. A number of different diversity metrics have been suggested and all are based, either directly or indirectly, on the concept of intermolecular similarity or distance. Determining the (dis)similarity between two molecules requires firstly that the molecules are represented by appropriate structural descriptors and secondly that a quantitative method of determining the degree of resemblance between the two sets of descriptors exists. 

Many different structural descriptors have been developed for similarity searching in chemical databases [4] including 2D fragment based descriptors, 3D descriptors, and descriptors that are based on the physical properties of molecules. More recently, attention has focused on diversity studies and many of the descriptors applied in similarity searching are now being applied in diversity studies. Structural descriptors are basically numerical representations of structures that allow pairwise (dis)similarities between structures to be measured through the use of similarity coefficients. Many diversity metrics have been devised that are based on calculating structural (dis)similarities, some of these are described below. 

One of the most commonly used structural descriptors in similarity and diversity studies is that of the 2D fragment bitstring where a molecule is represented by a vector of binary values that indicate the presence or absence of structural features, or fragments, within the molecule. Many different similarity measures or coefficients have been developed to quantify the degree of similarity between such vector based descriptors [5-7]. Usually, the values that can be taken by a coefficient lie in the range 0..1, or they can be normalised to be within this range. A similarity coefficient of 1 indicates that the two molecules are identical with respect to the structural descriptors and a value of 0 indicates that the two molecules are maximally different... 

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