Three dimension molecular descriptors

D-QSAR. Since compounds are active in three dimensions and their shape and surface properties are major determinants of their activity, the attractiveness of 3D-QSAR methods is intuitively clear. Here conformations of active molecules must be generated and their features captured by use of conformation-dependent descriptors. Despite its conceptual attractiveness, 3D-QSAR faces two major challenges. First, since bioactive conformations are in many cases not known from experiment, they must be predicted. This is often done by systematic conformational analysis and identification of preferred low energy conformations, which presents one of the major uncertainties in 3D-QSAR analysis. In fact, to date there is no computational method available to reliably and routinely predict bioactive molecular conformations. Thus, conformational analysis often only generates a crude approximation of active conformations. In order to at least partly compensate for these difficulties, information from active sites in target proteins is taken into account, if available (receptor-dependent QSAR). Second, once conformations are modeled, they must be correctly aligned in three dimensions, which is another major source of errors in the system set-up for 3D-QSAR studies. 

Given a graph-theoretical square matrix M of dimension N x N, three families of molecular descriptors are calculated from the kth power of the matrix M. These are... 

For convenience, we shall classify the molecular models according to their topological dimensionality, p. A molecular conformation defined by the set of nuclear position vectors is a zero-dimensional (OD) model. A one-dimensional (ID) model corresponds to a molecular skeleton, defined by the set of nuclear positions and their connectivity (bond) matrix. Contour surfaces of one-particle molecular properties such as electron density or electrostatic potential are topologically two-dimensional (2D) models embedded in three dimensions. Finally, we find a true three-dimensional (3D) model whenever an entire one-electron property over all space is involved. This model can be regarded as the continuum of all 2D isoproperty surfaces. The difference among the models is summarized in Figure 1. We shall deal with pD models in this work (p = 0,1, 2, 3). Each of them requires a different type of shape descriptor. 

One may observe that the relations (15.27) and (15.29) are the same. Consequently, the two-dimensional (2D) ovality molecular vdW descriptor, 2d, is identical with the ovahty index, O. The relations (15.30) and (15.32) extend the index O so that one can also measure the deviation of a molecule from the spherical shape on one- (ID) and on three-dimensions (3D) of the vdW space. 

Theoretically, optimum separation is achieved when the sample dimensionality and system dimensionality are equivalent, resulting in an ordered separation (Figure 3). In the above example, only one separation dimension would be required to analyze the alkane sample. If, however, the dimensionality of the sample exceeds that of the system, sample components will not be resolved in an orderly fashion, but rather a disordered or chaotic separation will result. In Figure 3, three descriptors are required to define the sample - shape, pattern, and size. In a chemical sense, these might be molar mass, polarity, and molecular shape. As more dimensions of separation are applied, greater definition of the mixture components is achieved. Unfortunately, for very complex samples, the sample dimensionality will be... 

Prior to van t Hoff and Le Bel, chemistry was two-dimensional. Since 1874, however, we have had to deal with the third dimension in molecular models, projection formulae, configurational descriptors and, most recently, computer algorithms used to describe and specify configuration. The problem is complicated because chirality, an important aspect of three-dimensional structure, is an attribute of the molecule as a whole whereas the commonly used Cahn-Ingold-Prelog configurational descriptors require factorisation of chirality into individual chiral elements. This paper deals with the history of chirality and the present status of describing it. 

---