Calculation of Structure Descriptors

Chemainformatics A Textbook. Edited by Johann Gasieiger and Thomas Engel Copyright 2003 Wiley-VCH Verlag GmbH Co. KGaA. 

s method of cstabli.shing a rclation.ship between a molcculai structure and it.s properties is inductive. It depends on a set of compounds with know n properties or activities whicli is used for model building. 

Iteration of the steps, descriptor selection, model building, and model validation in combination with an optimi ation algorithm allows one to select a descriptor subset having maximum predictivity. 

The method of building predictive models in QSPR/QSAR can also be applied to the modeling of materials without a unique, clearly defined structure. Instead of the connection table, physicochemical data as well as spectra reflecting the compound s structure can be used as molecular descriptors for model building, 

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. 

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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. 

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. 

In eq. 14.3.2, 1xv is the index for the heteroatom-containing molecule and (1Xv) p is the index for the corresponding, nonpolar (np) hydrocarbon equivalent. Bahnick and Doucette [20] demonstrate the calculation of these descriptors for 2-chloroacetani-lide. A ]xv accounts for nondispersive molecular interaction. Testing this model on a validation set of 40 structurally diverse compounds resulted in a standard deviation for the experimental versus estimated values of 0.37. The comparison of this value with the standard error of estimate (5 = 0.34) from the regression model suggests this model can be used confidently within the range of these structures. 

Matrices are the most common mathematical tool to encode structural information of molecules. They usually are the starting point for the calculation of many molecular descriptors and graph invariants moreover, they constitute the mathematical form used as the molecule input in the majority of software packages for calculation of molecular descriptors. 

Descriptors are atomic or molecular parameters or even molecular properties that contain information about the energy of each type of intermolecular interaction. They can be classified into two broad categories empirical and theoretical. Empirical descriptors depend on experimental measurements thus, they are available for a limited number of solutes (16). Theoretical descriptors are derived from the solute structure they are usually based on ab initio or semiempirical quantum chemistry calculations or on the connectivity of atoms in the molecule. With the proper use of dedicated software, the number of structural descriptors that can be assigned to a given solute is practically unlimited. Comprehensive compilations of the literature (17,18) register over 2000 known theoretical descriptors. 

As an alternative to ab initio methods, the semi-empirical quantum-chemical methods are fast and applicable for the calculation of molecular descriptors of long series of structurally complex and large molecules. Most of these methods have been developed within the mathematical framework of the molecular orbital theory (SCF MO), but use a number of simplifications and approximations in the computational procedure that reduce dramatically the computer time [6]. The most popular semi-empirical methods are Austin Model 1 (AMI) [7] and Parametric Model 3 (PM3) [8]. The results produced by different semi-empirical methods are generally not comparable, but they often do reproduce similar trends. For example, the electronic net charges calculated by the AMI, MNDO (modified neglect of diatomic overlap), and INDO (intermediate neglect of diatomic overlap) methods were found to be quite different in their absolute values, but were consistent in their trends. Intermediate between the ab initio and semi-empirical methods in terms of the demand in computational resources are algorithms based on density functional theory (DFT) [9]. 

For some appUcations it suffices to use descriptors that describe the topology of structures only (see e.g. Section 7.4). However, there ene many molecular properties that depend on the 3D shape of the molecules (see Section 7.5). Descriptors that take this information into account are called geometrical descriptors or geometrical indices. To allow calculation of geometrical descriptors, the atoms of the molecular graph M M have to be given 3D coordinates (iR ) (see Subsection 2.63). Various methods are available for this task [271,272], we use an empirical force field method similar to [5]. 

This parametric approach to spectral simulation was developed and utilized by Grant and Paul and Lindeman and Adams in their studies of linear and branched alkanes. These initial studies involved the calculation of simple topological parameters to be used as descriptions of the local structural environments of carbon atoms. This approach has been implemented more extensively and effectively with an interactive computer system that handles the calculation and manipulation of large numbers of structural descriptors. Topological, geometric, and electronic representations of local atomic environments can be encoded as descriptors. This computational methodology has been successfully applied to several structural classes of compounds cydo-hexanols and decanols, steroids, cyclopentanes and cyclopentanols, nor-bornanols, decalones, and carbohydrates. ... 

The large pool of calculated molecular structure descriptors was de-... 

Calculate molecular structure descriptors for each molecule. The descriptors are derived directly from the stored topological representations of the structures or from the 3D molecular models ... 

Many of the descriptors which can be calculated from the 2D structure rely upon the molecular graph representation because of the need for rapid calculations. Kier and Hall have developed a large number of topological indices, each of which characterises the molecular structure as a single number [Hall and Kier 1991]. Every non-hydrogen atom ir the molecule is characterised by two delta values, the simple delta Si and the valence delta SJ ... 

Chemoinformatics (or cheminformatics) deals with the storage, retrieval, and analysis of chemical and biological data. Specifically, it involves the development and application of software systems for the management of combinatorial chemical projects, rational design of chemical libraries, and analysis of the obtained chemical and biological data. The major research topics of chemoinformatics involve QSAR and diversity analysis. The researchers should address several important issues. First, chemical structures should be characterized by calculable molecular descriptors that provide quantitative representation of chemical structures. Second, special measures should be developed on the basis of these descriptors in order to quantify structural similarities between pairs of molecules. Finally, adequate computational methods should be established for the efficient sampling of the huge combinatorial structural space of chemical libraries. 

The similarity matrices are constructed by one in-house program developed inside CHIRBASE using the application development kit of ISIS. They contain the similarity coefficients as expressed by the Tanimoto method. In ISIS, the Tanimoto coefficients are calculated from a set of binary descriptors or molecular keys coding the structural fragments of the molecules. 

The concept of property space, which was coined to quanhtahvely describe the phenomena in social sciences [11, 12], has found many appUcahons in computational chemistry to characterize chemical space, i.e. the range in structure and properhes covered by a large collechon of different compounds [13]. The usual methods to approach a quantitahve descriphon of chemical space is first to calculate a number of molecular descriptors for each compound and then to use multivariate analyses such as principal component analysis (PCA) to build a multidimensional hyperspace where each compound is characterized by a single set of coordinates. 

Graphs may be represented in algebraic form as matrices [3-5]. This numerical description of the structure of chemical compounds is essential for the computer manipulation of molecules and for the calculation of various topological indices and graph descriptors [6]. The computation of the E-state indices is based on the adjacency and distance matrices. 

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