Descriptors structural

The formulation of informative QSPR models adequate for multicomponent disordered systems is anything but trivial and their predictive and interpretative power depends critically on the information content of the descriptors utilized [22], The selection of descriptors for meaningful QSPR models implies the knowledge of what features of the stmcture are measured by a given descriptor and of how the microscopic properties influence the macroscopic (measured) properties in a mechanistic way. Without this knowledge it is hard to apply a reverse QSPR approach to optimize materials directly. 

Having introduced these two principal characteristics of similarity measures, we shall now focus upon the three main components of a measure. These are the structural descriptors that are used to characterize the molecules, the weighting scheme that is used to differentiate more important features from less important features, and the similarity coefficient that is used to quantify the degree of similarity between pairs of molecules. 

The first topological index to be published was the Wiener index, W, which is half the sum of the bond-by-bond path lengths between each pair of atoms. The Wiener index has some interesting mathematical properties and can correlate well with chemical properties such as melting point and viscosity. It can be calculated from each off-diagonal element of the path length matrix, Djj, of a structure  

The value is largest for linear structures and smallest for compact structures (e.g., multibranched and/or cyclic molecules). 

The Balaban index is also calculated from the distance matrix of a structure and is otherwise known as the average distance sum connectivity index. Each distance sum, D, is the sum of the elements of the /th row of the distance matrix. The index is normalized by the numbers of bonds, B, and rings, C, and is calculated from  

The large number of topological indices that can be calculated for a structure raises the question as to which should be used in a particular application, especially as it can be difficult to relate many of the highei order indices to 

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Inductive methods for establishing a correlation between chemical compounds and their properties are the theme of Chapter 9. In many cases, the structure of chemical compounds has to be pre-processed in order to make it amenable to inductive learning methods. This is usually achieved by means of structure descriptors, methods for the calculation of which are outlined in Chapter 8. 

Over and beyond the representations of chemical structures presented so far, there are others for specific applications. Some of the representations discussed in this section, e.g., fragment coding or hash coding, can also be seen as structure descriptors, but this is a more philosophical question. Structure descriptors are introduced in Chapter 8. 

To understand the recommendations for structure descriptors in order to be able to apply them in QSAR or drug design in conjunction with statistical methods or machine learning techniques. 

In this chapter the focus is on structure descriptors. After a definition of this term their properties are described and an oveiwiew is given of some frequently used structure descriptors. 

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. 

The information content of a structure descriptor depends on two major factors a) the molecular representation of the compound b) the algorithm which is used for the calculation of the descriptor. 

Structure descriptors can be distinguished by the data type Table 8-1) of the descriptor and the molecular representation of the compound (Table 8-2). 

Another, probably more broadly applicable, technique is to represent a chemical compound by some of its properties. Figure 8-15 is an extension of Figure 8-1 and shows that when no structure descriptors can be derived because the structure is not known, thcji a compound can be represented by a second property (2) or. better, a series of properties, in order to predict the property 1 of interest. 

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. 

There arc some prerequisites for a 3D structure descriptor. It should be ... 

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... 

Dunn W J III, S Wold, U Edlund, S Hellberg and J Gasteiger 1984. Multivariate Structure-Activib Relationships Between Data from a Battery of Biological Tests and an Ensemble of Structur Descriptors The PLS Method. Quantitative Structure-Activity Relationships 3 131-137. 

With the development of accurate computational methods for generating 3D conformations of chemical structures, QSAR approaches that employ 3D descriptors have been developed to address the problems of 2D QSAR techniques, that is, their inability to distinguish stereoisomers. Examples of 3D QSAR include molecular shape analysis (MSA) [26], distance geometry,and Voronoi techniques [27]. The MSA method utilizes shape descriptors and MLR analysis, whereas the other two approaches apply atomic refractivity as structural descriptor and the solution of mathematical inequalities to obtain the quantitative relationships. These methods have been applied to study structure-activity relationships of many data sets by Hopfinger and Crippen, respectively. Perhaps the most popular example of the 3D QSAR is the com-... 

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