Molecular descriptors definition

The Handbook of Molecular Descriptors collects the definitions, formulas and short comments of molecular descriptors known in chemical literature, our intention being to consider all the known molecular descriptors. The definitions of technical terms, around 1800 in all, are organized in alphabetical order. The importance of a molecular descriptor definition is not related to its length. Only a few old descriptors, abandoned... 

We must now mention, that traditionally it is the custom, especially in chemo-metrics, for outliers to have a different definition, and even a different interpretation. Suppose that we have a fc-dimensional characteristic vector, i.e., k different molecular descriptors are used. If we imagine a fe-dimensional hyperspace, then the dataset objects will find different places. Some of them will tend to group together, while others will be allocated to more remote regions. One can by convention define a margin beyond which there starts the realm of strong outliers. "Moderate outliers stay near this margin. 

Each of these columns of this symmetrical matrix may be seen as representing a molecule in the subspace formed by the density functions of the N molecules that constitute the set. Such a vector may also be seen as a molecular descriptor, where the infinite dimensionality of the electron density has been reduced to just N scalars that are real and positive definite. Furthermore, once chosen a certain operator in the MQSM, the descriptor is unbiased. A different way of looking at Z is to consider it as an iV-dimensional representation of the operator within a set of density functions. Every molecule then corresponds to a point in this /V-dimensional space. For the collection of all points, one can construct the so-called point clouds, which allow one to graphically represent the similarity between molecules and to investigate possible relations between molecules and their properties [23-28]. 

Symbols, Definitions and Classification of Calculated Molecular Descriptors... 

This homogeneity does depend both on the level of the molecular description and on the definition of the ad hoc molecular descriptors. 

Since the definition of chemical reference spaces very much depends on the choice of molecular descriptors, we begin the description with a brief overview of some commonly used types of descriptors, as summarized in Table 1. 

In our study we compare two diversity-driven design methods (uniform cell coverage and clustering), two analysis methods motivated by similarity (cell-based analysis and cluster-classification), and two descriptor sets (BCUT and constitutional). Thus, our study addresses some of the many questions arising in a sequential screen how to choose the initial screen, how to analyze the structure-activity data, and what molecular descriptor set to use. The study is limited to one assay and thus cannot be definitive, but it at least provides preliminary insights and reveals some trends. 

Applications of molecular descriptors are as diverse as their definitions. The important classes of applications include QSAR and/or QSPR, similarity, diversity, predictive models for virtual screening and/or data mining, data visualization. We will discuss briefly some of these applications in the next sections. 

There are literally thousands of molecular descriptors available for various applications. We have only mentioned a few of them in previous paragraphs. Interested readers can find a more complete coverage of molecular descriptors in reference (15), which gives definitions for 3,300 molecular descriptors. Many software, or subroutines as an integral part of other programs, are available to generate various types of molecular descriptors. Table 2.2 lists a few of these software. 

The quantification of molecular similarity generally involves three components molecular descriptors to characterize the molecules, weighting factors to differentiate more important characteristics from less important ones, and the similarity coefficient to quantify the degree of similarity between pairs of molecules (20, 21). The first two components are related to the definition of chemical space as discussed in Section 2.4. Therefore, it is natural to assume that structurally similar molecules should cluster together in a chemical space, and to define the similarity coefficient of a pair of molecules to be the distance between them in the chemical space. The shorter the distance is the more similar the pair is. 

Table 2.5 defines the 40 molecular descriptors and provides their values. Figure 2.1 provides further definition of the different types of molecular fragments used while Figure 2.2 provides further definition of the hydrogen bonding and biphenyl ring corrections. Simamora and Yalkowsky (1994) consider the values in parentheses in Table 2.5 insignificant, based on the statistical analysis used to derive the molecular descriptor values. 

Molecular descriptors and chemical spaces. The majority of chemoinformatics methods depend on the generation of chemical reference spaces into which molecular data sets are projected and where analysis or design is carried out. The definition of chemical spaces critically depends on the use of computational descriptors of molecular structure, physical or chemical properties, or pharmacophores. Essentially, any comparison of molecular characteristics that goes beyond simple structural comparison requires the calculation of property values and the application... 

The measurement of molecular diversity requires the definition of a chemical space. This A-dimensional chemical space is represented by a group of selected molecular descriptors. Each compound in a collection can be assigned coordinates based on the measurement of its descriptor values. Increasing distance, within the dimensions of the assigned coordinate space, should correlate with increasing diversity (or decreasing similarity) between compounds. 

The dimensionality of chemical structure space exceeds that of known biological functional space. The dimensionality of biological functional space has increased in recent years due to the discovery of a multitude of genes, largely from the Human Genome Project. This chapter, however, will focus on chemical diversity rather than functional diversity. Quantification of chemical diversity involves two areas first, the predefmition of a chemical space, accomplished by selection of a diversity metric and a compound representation (i.e., molecular descriptors) and second, a rational subset selection, or classification, method dependent on efficient dimensionality reduction. Here, we describe these methods, prerequisites for a definition... 

The power of the solvation equation approach is that it can characterise various partition systems and lipophilicity scales by five molecular descriptors (dispersivity, size, polarisability-dipolarity, H-bond acidity and basicity). All of the five descriptors should be included into the linear regression equations by definition. When one or two coefficients are not significantly different from zero, it means that that particular property does not play a significant role in the partition. 

From the eccentricity definition, a graph Q can be immediately characterized by two - molecular descriptors known as topological radius R and topological diameter D. The topological radius of a molecule is defined as the minimum atom eccentricity and the topological diameter is defined as the maximum atom eccentricity, according to the following... 

Local or global molecular descriptors related to the electronic distribution in the molecule they are fundamental to many chemical reactions, physico-chemical properties, and ligand-macromolecule interactions. The theory of electronic density is based on a quantum-mechanical approach however, - electronegativity and charges, which are not physical observables, are also important quantities for the definition of several electronic descriptors. 

By the definition given above, molecular descriptors are divided into two main classes -+ experimental measurements, such as - logP, - molar refractivity, - dipole moment, -> polarizability, and theoretical molecular descriptors, which are derived from a symbolic representation of the molecule and can be further classified according to the different types of molecular representation. 

Estrada, E. and Ramirez, A. (1996). Edge Adjacency Relationships and Molecular Topographic Descriptors. Definition and QSAR Applications. J.Chem.Inf Comput.ScL, 36, 837-843. 

Plavsic, D. (1999). On the Definition and Calculation of the Molecular Descriptor R lR. Chem. Phys.Lett, 304,111-116. 

Some basic concepts and definitions of statistics, chemometrics, algebra, graph theory, similarity/diversity, which are fundamental tools in the development and application of molecular descriptors, are also presented in the Handbook in some detail. More attention has been paid to information content, multivariate correlation, model complexity, variable selection, and parameters for model quality estimation, as these are the characteristic components of modern QSAR/QSPR modelling. 

According to the previous definition, molecular descriptors represent properties of a molecule. The most important issue is to eliminate properties that are not relevant for the task to be solved. This is similar to analytical methodology, where unwanted effects are eliminated or suppressed by using chemical or physical methods, like chemical modifiers in chromatography or background compensation in spectroscopy. 

Atomic properties P are physics and chemical observables characterizing each chemical element. They play a fundamental role in the definition of most of the molecular descriptors, being physico-chemical properties, as well as biological, toxicological, and environmental properties, deeply determined by the chemical elements constituting the molecule itself. 

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