Spatial descriptors

Defining spatial descriptors for freely tumbling particles is considerably more difficult, and consequently, the use of a number of derivative particle descriptors... 

The molecular surface area (Area) descriptor is a 3D spatial descriptor that describes the van der Waals area of a molecule. The molecular surface area determines the extent to which a molecule exposes itself to the external environment. This descriptor is related to the binding, transport properties and the solubility of compounds. 

The molecular volume (Vm) is a 3D spatial descriptor that defines the molecular volume inside the contact surface. The molecular volume is calculated as a function of conformation. Molecular volume is related to the binding and transport properties of compounds. 

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]. 

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

Breindl et. al. published a model based on semi-empirical quantum mechanical descriptors and back-propagation neural networks [14]. The training data set consisted of 1085 compounds, and 36 descriptors were derived from AMI and PM3 calculations describing electronic and spatial effects. The best results with a standard deviation of 0.41 were obtained with the AMl-based descriptors and a net architecture 16-25-1, corresponding to 451 adjustable parameters and a ratio of 2.17 to the number of input data. For a test data set a standard deviation of 0.53 was reported, which is quite close to the training model. 

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... 

Once the molecules are aligned, a molecular field is computed on a grid of points in space around the molecule. This field must provide a description of how each molecule will tend to bind in the active site. Field descriptors typically consist of a sum of one or more spatial properties, such as steric factors, van der Waals parameters, or the electrostatic potential. The choice of grid points will also affect the quality of the final results. 

Thus, a molecule can be characterized in terms of its potential hydrogen bonding, polar, hydrophobic and ionic interactions in 3D space. The size and the spatial distribution of these molecular interaction contours is translated into a quantitative scheme, the VolSurf descriptors, without the need to align the molecules in 3D space [8, 9] (Fig. 17.1). 

Three-dimensional (3-D) descriptors of molecules quantify their shape, size, and other structural characteristics which arise out of the 3-D disposition and orientation of atoms and functional groups of molecules in space. A special class of 3-D indices is quantitative descriptors of chirality. If a molecule has one or more chiral centers, the spatial disposition of atoms can produce enantiomers, many of which will have the same magnitude of calculated and experimental physicochemical properties having, at the same time, distinct bioactivity profiles. Basak and coworkers [22] have developed quantitative chirality indices to discriminate such isomers according to their structural invariants which are based on the Cahn-Ingold-Prelog (CIP) rules. 

The key descriptors used to predict the likelihood of a CYP inhibition are incredibly vast. Descriptors can, for example, be defined as spatial, electronic or conformational. Some of the key structural properties include lipophilicity, pKa and PSA and are relatively easy to interpret, while others are more complex. For further information on descriptors used in DDI modeling, please refer to De Groot et al. [6]. 

In contrast to a chemical property which can be measured, a molecular descriptor is computed from the molecular structure. Contained in the structural information are the atoms making up the molecule and their spatial arrangement. From the coordinates of the atoms, the geometric attributes (i.e., the size and shape of the molecule) can be deduced. A straightforward example is the molecular mass, which is computed by adding up the masses of the individual atoms making up the molecule and indicated in the elemental composition. The result is accurate since the atomic masses are independent of the chemical bonds with which they are involved. However, the molecular mass reflects few of the geometrical and chemical attributes of a compound and M is therefore a poor predictor for most properties. 

Nowadays, more than 4000 types of descriptors are known.17 There exist different ways to classify them. With respect to the type of molecular representation used for their calculations—chemical formula, molecular graph, or spatial positions of atoms—one speaks about ID, 2D, and 3D descriptors, respectively. Descriptors can be global (describing the molecule as a whole) and local (only selected parts are considered). One could distinguish information-based descriptors, which tend to code the information stored in molecular structures, and knowledge-based (or semiempir-ical) descriptors issued from the consideration of the mechanism of action. Most of those descriptors can be obtained with the DRAGON, CODESSA PRO, and ISIDA programs. 

Spatial autocorrelation is a quantitative measure of the probability of finding objects of defined properties within a distance of interest [9, 10]. The concept of autocorrelation is mainly applied in fields such as geography, economics, ecology or meteorology to describe the spatial distribution of features. The idea of a molecular descriptor based on the autocorrelation concept was first introduced into the field of cheminformatics by Moreau and Broto in 1980 [11] with the ATS (autocorrelation of a topological structure) descriptor. For this approach, the atoms of a molecule were represented by properties such as atomic mass or partial charge. The distance between atoms was measured as the number of bonds between the respective atoms (topological distance). 

The following discussion considers three PPP pair descriptors CATS (topological PPP pairs), CATS3D (spatial PPP pairs) and SURFCATS (surface PPP pairs). Figure 3.1 provides a graphical overview. 

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