Numerical descriptors

A challenging task in material science as well as in pharmaceutical research is to custom tailor a compound s properties. George S. Hammond stated that the most fundamental and lasting objective of synthesis is not production of new compounds, but production of properties (Norris Award Lecture, 1968). The molecular structure of an organic or inorganic compound determines its properties. Nevertheless, methods for the direct prediction of a compound s properties based on its molecular structure are usually not available (Figure 8-1). Therefore, the establishment of Quantitative Structure-Property Relationships (QSPRs) and Quantitative Structure-Activity Relationships (QSARs) uses an indirect approach in order to tackle this problem. In the first step, numerical descriptors encoding information about the molecular structure are calculated for a set of compounds. Secondly, statistical and artificial neural network models are used to predict the property or activity of interest based on these descriptors or a suitable subset. 

Propellants may be of a number of different types CFCs, hydrofluoroalkanes (HFAs), or alkanes. The composition impacts upon performance. A numerical system is employed to identify fluorinated propellants. The rules governing this numbering system allow the molecular structure to be derived from the numerical descriptor. The rules may be listed as follows ... 

D-molecular descriptors, alignment-independent and based on molecular interaction, called GRIND have been developed. These are autocorrelation transforms that are independent of the orientation of the molecules in 3D space. The original descriptors can be extracted from the autocorrelation transform with the ALMOND program. The basic idea is to compress the information present in 3D maps into a few 2D numerical descriptors which are very simple to understand and interpret. 

In a standard cell-based method, the range of each of k numerical descriptors is subdivided into m bins, yielding mk cells. To select a representative set of molecules from a database, one molecule is selected at random from each cell... 

As discussed in Subheading 1., the primary design criterion is often based on either similarity or diversity. Quantifying these measures requires that the compounds are represented by numerical descriptors that enable pairwise molecular similarities or distances to be calculated or that allow the definition of a multidimensional property space in which the molecules can be placed. 

Fragment- or substructure-based descriptors include maximum common substructures (MSC) or combinations of scaffolds or subscaffolds. Simple numeric descriptors include calculated LogP,... 

We discuss how the size of a library can he drastically reduced without loss of information or decreases in the chances of finding a lead compound. The approach is based on the use of statistical molecular design (SMD) for the selection oflibrary compounds to synthesise and test, followed by the use of quantitative structure activity relationships (QSARs) for the evaluation of the resulting test data. The use of SMD and QSAR is, in turn, critically dependent on an appropriate translation of the molecular structure to numerical descriptors, the recognition of inhomogeneities (clusters) in both the structural... 

To this class belong the discrete numerical descriptors that describe the basic molecular structure, e.g., molecular weight, number of atoms, number of rings, etc. 

From Sergio I learned the correct ways to produce mathematical models, and the tricks to interpret them. However, it was immediately dear that Chemometrics (and cheminformatics as well) can do very little when the numerical descriptors are poor or not related to the phenomena under study. 

In the next step, computational algorithms are applied to derive numerical descriptors that describe structural properties of all compounds in the library [11]. These descriptors are used for the following comparison of all molecules and the subsequent selection of building blocks for synthesis. 

Fig. 4 The diversity computation bypass. A direct description of molecular diversity is not possible - therefore diversity and similarity are assessed in numerical descriptor space.

Fig. 5 Structural formulas are the best representation of molecules for chemists - numerical descriptors are preferred by computers.

The first and most important step is to choose properties that describe the molecules as numerical values. In the following text these numerical representations of some molecular properties tvill be denoted as descriptors . The use of numeric descriptors prepares the problem for subsequent computer processing (Fig. 5). AU subsequent steps of a study look at the descriptors instead at the molecules themselves. Therefore, diversity or similarity is defined in the descriptor space instead of the chemical space. The relevance of descriptor similarity for the similarity of the molecules must be ensured by appropriate choice of the descriptor set [16, 17]. Obviously, it is very important to know the characteristics and appUcability of various descriptor sets. 

Table S18 MFP scheme for encoding the three numerical descriptors.

Kauffman, G.W. and Jurs, P.C. (2001b) QSAR and k-nearest neighbor classification analysis of selective cyclooxygenase-2 inhibitors using topologically-based numerical descriptors./. Chem. Inf. Comput. Sci., 41, 1553-1560. 

Nandy A. and Basak, S.C. (2005) Simple numerical descriptor for quantifying effect of toxic substances on DNA sequences. J. Che-m. Inf. Comput. Sci., 40, 915-919. 

Xue, L., Godden, J.W., Stahura, F.L. and Bajorath, J. (2003c) Profile scaling increases the similarity search performance of molecular fingerprints containing numerical descriptors and structural keys./, Chem, Inf, Comput, Sci, 43, 1218-1225. 

QSARs are based on the assumption that the structure of a molecule (for example, its geometric, steric, and electronic properties) must contain features responsible for its physical, chemical, and biological properties and on the ability to capture these features into one or more numerical descriptors. By QSAR models, the biological activity (or property, reactivity, etc.) of a new designed or untested chemical can be inferred from the molecular structure of similar compounds whose activities (properties, reactivities, etc.) have already been assessed. 

Given these numerous descriptors and selection techniques, the question arises, whether chemical diversity can be correlated to biological diversity. This section summarizes own and many published validation studies for selected diversity descriptors. Several physico-chemical descriptors were investigated in different studies to uncover the relationship between 2D/3D similarity and biological activity. 

Virtual screening techniques require the definition of a chemistry space in order that the similarity (and distance) between compounds within the space can be quantified. Once a space has been defined, a diverse subset is one that covers the chemistry space well, whereas a focused subset is one that is restricted to a localized region within the space. A chemistry space is defined through the use of numerical descriptors, which can be calculated for molecules, as shown schematically in Fig. 1. The similarity (and... 

Figure 1 Numerical descriptors are used to define a chemistry space, and the similarity (or distance) between molecules is determined using a similarity coefficient applied to the descriptor representations of the molecules.

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