Calculation of descriptors

Well over 300 structure-based chemodescriptors are typically calculated for use in our modeling studies using various software programs. From POLLY 

Information index for the magnitudes of distances between all possible pairs of vertices of a graph 

Wiener index = half-sum of the off-diagonal elements of the distance matrix 

Information content of the distance matrix partitioned by frequency of occurrences of distance h 

Triplet index from distance matrix, square of graph order, and distance sum operation y = 1-5 

By using the 3D arrangement of atoms in a molecule and the calculated physicochemical properties of these atoms, it is possible to calculate molecular descriptors. Since the descriptor is typically a mathematical vector of a fixed length, we can use it for a fast search in a database, provided that the database contains the equivalent descriptor for each data set and that the descriptor is calculated for the query. We have seen before that particularly similarity and diversity can be excellently expressed with molecular descriptors. 

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Ease of calculation of descriptors is desirable so that the models derived can be conveniently used by medicinal chemists. Descriptors that can be calculated from 2D chemical structures without the use of software are recommended. 

The most commonly used methods for calculation of descriptor similarities are the Tanimoto coefficient, the Euclidean distance, and the Mahalanobis distance (Fig. 12). 

Distance matrices may also be calculated for real three-dimensional (Euclidean) distances between atoms using the Cartesian coordinates of the atom positions (Figure 4.1c). These matrices allow the calculation of descriptors that account for the shape and conformation of atoms. If conformation is not required or desired, the bond... 

Radial distribution functions can be adapted quite flexibly to the desired representation of molecules. The RDF functions developed can be divided into several groups regarding the basic function type, the distance range of calculation, the type of distance information, the dimensionality, and the postprocessing steps. Most of the varieties of RDF descriptors introduced in this chapter can be combined arbitrarily to fit to the required task. As a consequence, more than 1,400 useful descriptors can be derived from radial functions [1], The molecules used for the calculation of descriptors are shown in the figures. 

ARC allows descriptor settings to be dehned in various ways. The code method dehnes the general method for the calculation of descriptors. Available methods are... 

Product-based selection is much more computationally demanding than reagent-based selection. Typically, it requires the computational enumeration of the full virtual combinatorial library and calculation of the descriptors for all possible products, prior to the application of a subset selection method. Consider a three-component reaction with 100 reagents available at each substituent position and assume that the aim is to build a 10 x 10 x 10 combinatorial library. In reagent-based selection, this requires the calculation of descriptors for 300 compounds (100 + 100 + 100). In product-based design, however, the full library of 1 million compounds (100 x 100 x 100) must be enumerated and descriptors must be calculated for each product molecule. 

The size of a virtual library can be reduced by applying filters to eliminate reagents that are known to be undesirable [67]. However, in some cases, the virtual library may still be too large to allow full enumeration, and thus full product-based design is infeasible. (Although the need for full enumeration may not be necessary in the future, for example, Barnard et al. [82] have recently developed a method for the rapid calculation of descriptors for the products in a virtual combinatorial library that avoids the need for enumeration.)... 

As we have seen, molecular descriptors constitute information about steric and electronic constraints conferred by chemical structure [104, 105]. Molecular descriptors underlie both pharmacophore models [106, 107] and analyses of similarity or diversity among compound collections [108,109]. The calculation of descriptors therefore serves as a starting point in the analyses of small-molecule relationships assessed prior to compound synthesis, before selecting compounds for HTS, and in the interpretation of biological measurements of small-molecule perturbation. 

In principle, there are three main steps required to carry out diversity-based subset selections (1) the calculation of descriptors representing the compound structures, (2) a quantitative method to describe the similarity or dissimilarity of molecules in relationship to each other, and (3) selection methods to identify compounds based on their similarity or dissimilarity values that best represent the entire compound set. In the following, the three steps are described in more detail. 

The focus of this chapter is ligand-based virtual screening. The underlying principle is the assumption that similar molecules should exhibit similar binding properties with respect to a given target [11[. Molecular similarities are based on descriptors and similarity measures. Section 3.2 introduces the calculation of descriptors. Some selected descriptors are discussed in detail. The choice of descriptors does not mean an assessment however, it is driven by the experience of the authors. 

Embedding a molecule in space yields further descriptors. Examples include the chirality of a molecule in 3D space, the symmetry group, the van der Waals volume, etc. As embeddings are local energy minima obtained via optimization, they do not describe ideal tetrahedra or other ideal geometric shapes but rue often somewhat deformed, such that calculation of descriptors of embeddings still has many unsolved problems. 

In cases in which the active site structure is known, an alternative approach would be geometry optimization and calculation of descriptors for the effector molecule-active site ensemble. Docking of the effector molecule in the active site can be done manually using computer-generated structures (Murcia et al. 2006 Huey et al. 2007 Weber et al. 2006 Tucinardi et al. 2007). 

Following are some examples of calculation of descriptors for organometallic complexes in which the ligand has low molecular weight. Descriptors were chosen whose values seem to be more sensitive to the presence and type of metal atom, as well as to the number, shape, and size of ligands. Some of the analyzed complexes have been synthesized and have various practical applications. 

The extremes of data distributions are depicted in Figure 2 along with an arbitrary midpoint in a calculation of descriptor entropy. 

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