Descriptors, molecular

Substructure and 3D pharmacophore searching involve the specification of a precise query, which is then used to search a database in order to identify molecules for screening. In such an approach, either a molecule matches the query or it does not Similarity searching offers a complementary approach, in that the query is typically an entire molecule. This query molecule is compared to all molecules in the database and a similarity coefficient calculated. The top-scoring database molecules (based on the similarity coefficient) are the hits from the search. In a typical scenario the query molecule would be known to possess some desirable activity and the objective would be to identify molecules which will hopefully show the same activity. We therefore require some method for deciding how to compute the similarity between two molecules. In order to achieve this we need to choose a set of molecular descriptors for the compounds. These descriptors are then used to compute the similarity coefficient. 

A very popular descriptor is logP, the logarithm of the partition coefficient, most commonly for the partition between 1-octanol and water (the logarithm converts the 

Descriptor Information typically required for calculation Comments 

Hashed fingerprints, structural keys 2D structure See Section 12.2 

Counts of specific atonts, rings or other 2D structure Typically based on 

This chapter will try to answer some of these questions and investigate various approaches to derive statistically sound, robust, and predictive in silico models. 

Among the advantages with 2D-based descriptors are their rapid speed of computation for large sets of compounds and that they do not require 3D structures. Thus, these descriptors avoid the problem and compute times associated with 3D structure generation and conformational analysis, even though there are programs available that generate reliable 3D structures, for example, CORINA [5]. 

The 2 D-based descriptors are sometimes divided into different types of descriptors such as constitutional, fragment, and functional group-based as well as topological descriptors. 

A significant advantage of using constitutional descriptors is the ease of interpretation. It is straightforward for a researcher to understand the impact of these descriptors on derived statistical structure-property models. 

In graph theory, graphs are defined by an ordered pair consisting of two sets, V and R  

Three different variables are used for calculating molecular descriptors indicator variable, count variable, and graph-theoretical indices, as described below. Molecular 

One of the main aims of computer simulation in chemistry is the prediction of physical, chemical, biological or pharmaceutical properties of chemical compounds using malecular descriptars. We distinguish various kinds of such invariants of molecule graphs, here are a few obvious ones  

In order to define a general notion of moleculeir descriptor, we first briefly recall the basic definition of molecular graph. 

Consider a set of chemical elements, eind assume a set Zg of admissible atom states for the elements in , Zg = Uxec Iciheled molecular graph on n atoms in with atom states contained in Zg is a triple M = (e, y), where ° = (e(0). e(n - 1)) is a sequence of length n of (labeled) atoms e(i) , for 

The corresponding unlabeled molecular graphs with n atoms in are the orbits of the action 

The orbit S (M) of M is denoted by M. We denote the set of the labeled molecular graphs with n atoms by M euid use this notation to introduce the following sets  

FIGURE 2.17 Spectrum-like structure representation (b) of the 6-OH,5,7,4 -NO flavonoid derivative as obtained from the XY projection of oriented 3-D structure (a). 

The Wiener index [86] can be expressed in terms of the distance matrix [87] and equals the half-sum of all distance matrix entries. Randi(5 [88] and Kier and Hall indices of order 0-3 [89] are calculated from coordination numbers of atoms or from values of atomic connectivity. The Kier shape index (order 1-3) [90] depends on the number of skeletal atoms, molecular branching, and the ratio of the atomic radius and the radius of the carbon atom in the sp hybridization state. The Kier flexibility index [90] is derived from the Kier shape index. The Balaban index depends on the row sums of the entries of the distance matrix and the cyclomatic number [92,93]. The information content index and its derivatives (order 0-2) are based on the Shannon information theory [95]. Modifications of the information content index are structural information content, complementary information content, and bond information content [96], 

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Let us start with a classic example. We had a dataset of 31 steroids. The spatial autocorrelation vector (more about autocorrelation vectors can be found in Chapter 8) stood as the set of molecular descriptors. The task was to model the Corticosteroid Ringing Globulin (CBG) affinity of the steroids. A feed-forward multilayer neural network trained with the back-propagation learning rule was employed as the learning method. The dataset itself was available in electronic form. More details can be found in Ref. [2]. 

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. 

The profits from using this approach are dear. Any neural network applied as a mapping device between independent variables and responses requires more computational time and resources than PCR or PLS. Therefore, an increase in the dimensionality of the input (characteristic) vector results in a significant increase in computation time. As our observations have shown, the same is not the case with PLS. Therefore, SVD as a data transformation technique enables one to apply as many molecular descriptors as are at one s disposal, but finally to use latent variables as an input vector of much lower dimensionality for training neural networks. Again, SVD concentrates most of the relevant information (very often about 95 %) in a few initial columns of die scores matrix. 

There was a time when one could use only a few molecular descriptors, which were simple topological indices. The 1990s brought myriads of new descriptors [11]. Now it is difficult even to have an idea of how many molecular desaiptors are at one s disposal. Therefore, the crucial problem is the choice of the optimal subset among those available. 

It has often been mentioned in this chapter that many molecular descriptors can well be highly intcr-corrclatcd. Therefore, any significant information content of a... 

R. Todeschini, V Consonni, Handbook of Molecular Descriptors. Wiley-VCH, Weinheim, 2002. 

To find out how to distinguish between the different kinds of molecular descriptors. 

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,... 

Table 8-1. Classification of molecular descriptors by descriptor s data type.

The concept of feature trees as molecular descriptors was introduced by Rarey and Dixon [12]. A similarity value for two molecules can be calculated, based on molecular profiles and a rough mapping. In this section only the basic concepts are described. More detailed information is available in Ref. [12]. 

WHIM descriptors Weighted Holistic Invariant Molecular descriptors) are discussed in detail in the Handbook, Chapter XIII, Section 2 [48, 49]. 

A comprehensive overview of spatial molecular descriptors is given by Todeschini and Consormi [15]. 

R. Todeschini, V Consormi, Handbook of Molecular Descriptors, in Methods and Principles in Medicinal Chemistry, Vol. 11, R. Mannhold, H. Kubinyi, H. Timmerman (eds.), Wiley-VCH, Weinheim, 2000. 

For example, the objects may be chemical compounds. The individual components of a data vector are called features and may, for example, be molecular descriptors (see Chapter 8) specifying the chemical structure of an object. For statistical data analysis, these objects and features are represented by a matrix X which has a row for each object and a column for each feature. In addition, each object win have one or more properties that are to be investigated, e.g., a biological activity of the structure or a class membership. This property or properties are merged into a matrix Y Thus, the data matrix X contains the independent variables whereas the matrix Ycontains the dependent ones. Figure 9-3 shows a typical multivariate data matrix. 

D descriptors), the 3D structure, or the molecular surface (3D descriptors) of a structure. Which kind of descriptors should or can be used is primarily dependent on the si2e of the data set to be studied and the required accuracy for example, if a QSPR model is intended to be used for hundreds of thousands of compounds, a somehow reduced accuracy will probably be acceptable for the benefit of short processing times. Chapter 8 gives a detailed introduction to the calculation methods for molecular descriptors. 

Molecules are usually represented as 2D formulas or 3D molecular models. WhOe the 3D coordinates of atoms in a molecule are sufficient to describe the spatial arrangement of atoms, they exhibit two major disadvantages as molecular descriptors they depend on the size of a molecule and they do not describe additional properties (e.g., atomic properties). The first feature is most important for computational analysis of data. Even a simple statistical function, e.g., a correlation, requires the information to be represented in equally sized vectors of a fixed dimension. The solution to this problem is a mathematical transformation of the Cartesian coordinates of a molecule into a vector of fixed length. The second point can... 

Multivariate data analysis usually starts with generating a set of spectra and the corresponding chemical structures as a result of a spectrum similarity search in a spectrum database. The peak data are transformed into a set of spectral features and the chemical structures are encoded into molecular descriptors [80]. A spectral feature is a property that can be automatically computed from a mass spectrum. Typical spectral features are the peak intensity at a particular mass/charge value, or logarithmic intensity ratios. The goal of transformation of peak data into spectral features is to obtain descriptors of spectral properties that are more suitable than the original peak list data. 

Spectral features and their corresponding molecular descriptors are then applied to mathematical techniques of multivariate data analysis, such as principal component analysis (PCA) for exploratory data analysis or multivariate classification for the development of spectral classifiers [84-87]. Principal component analysis results in a scatter plot that exhibits spectra-structure relationships by clustering similarities in spectral and/or structural features [88, 89]. 

Molecular descriptors must then be computed. Any numerical value that describes the molecule could be used. Many descriptors are obtained from molecular mechanics or semiempirical calculations. Energies, population analysis, and vibrational frequency analysis with its associated thermodynamic quantities are often obtained this way. Ah initio results can be used reliably, but are often avoided due to the large amount of computation necessary. The largest percentage of descriptors are easily determined values, such as molecular weights, topological indexes, moments of inertia, and so on. Table 30.1 lists some of the descriptors that have been found to be useful in previous studies. These are discussed in more detail in the review articles listed in the bibliography. 

CODESSA can compute or import over 500 molecular descriptors. These can be categorized into constitutional, topological, geometric, electrostatic, quantum chemical, and thermodynamic descriptors. There are automated procedures that will omit missing or bad descriptors. Alternatively, the user can manually define any subset of structures or descriptors to be used. 

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. 

Todeschini R, Consonni V. Handbook of molecular descriptors. Berlin Wiley-VCH, 2000. 

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