Geometry-based descriptors

Geometry-based approach from a geometrical point of view, a cavity is a concave empty space that can be described using 2D (surface) or 3D shape descriptors (19-21). We consider three regions in the protein environment the protein bulk, the bulk solvent and the cavity space. The protein bulk is the space filled by the protein atoms. The bulk solvent is the space outside the protein which differentiates from the space inside the protein which defines the cavity where the drug-like molecule is supposed to bind. The identification of protein pockets by numerical methods suppose the capacity to discriminate first the protein bulk from the rest... 

Let us consider instead the possibility of a geometry-based description. In this framework, a thermodynamic variable is identified with a vector of the geometrical space, designated Ms, describing the equilibrium state S of interest. To distinguish this vector aspect notationally, we employ the Dirac ket symbol F) to denote the abstract geometrical vector that corresponds to (double-headed arrow) the calculus-based descriptors of the variable,... 

Bodor and Huang correlated the octanol/water partition coefficient, Po/w (unitless) at 298 K for a set of 302 compounds with a set of 58 descriptors to obtain Eq. [49]. These parameters include seven QM based descriptors that were calculated with the AMI method. The dipole moment is p(D) Qo and Qn are the square roots of the sum of the squares of charges on the O and N atoms, respectively. The parameter Qon is the sum of absolute values of charges on the O and N atoms, and ABSQ is the sum of the absolute values of the charges on all atoms. In addition to these QM descriptors, the surface area, A (A ), and the ovality, O, were calculated from the QM-optimized geometry. The ovality is defined by actual area/area as a sphere, O = A/[4ti(3V/ 4ti) ]. The molecular mass, M, and two indicator variables, Ngik and Nq, for alkanes and carbon atoms, respectively, were also employed. 

From the geometry matrix, the usual -> graph invariants can be calculated such as -t characteristic polynomial, -> eigenvalue-based descriptors, -> path counts, - ID numbers, -> 3D-Balaban index, -> 3D-Schultz index and so forth [Randic, 1988b Nikolic et al, 1991]. It is noteworthy that all these indices are sensitive to molecular geometry. Moreover, the geometry matrix is used for the calculation of size descriptors and - 3D-MoRSE descriptors. 

In conclusion, we have to admit that the geometry-dependent descriptors do not lead to as good a correlation as that based on % and L/B. The reason is that /) are global molecular descriptors, while % is a local, bond additive descriptor, which apparently better reflects the structure-chromatographic retention relationship. However, the index /) can help us to clarify the question ... 

Another important problem should be emphasized here. Since aromaticity is a phenomenon defined by convention, then we should be well aware of the fact that a geometry-based description of aromaticity may not always be in line with other descriptors, although qualitatively it usually remains in agreement with them. - ... 

In principle, the integrand in (13.10) might be evaluated with Taylor series expansions such as (12.96), based on successively higher derivatives of the initial state. In practice, however, direct experimental evaluation of the functional dependence of each My on path variables would be needed to evaluate C along extended paths. Further discussion of global curvature or other descriptors of the Riemannian geometry of real substances therefore awaits acquisition of appropriate experimental data, well beyond that required to describe individual points on a reversible path. 

Often, all alignment-based methods and molecular field and potential calculations are classified as pharmacophore perception techniques. We will include most of these methods in this review however, when using the term pharmacophore model, we will be referring mainly to one specific type of perception, namely three-dimensional feature-based pharmacophore models represented by geometry or location constraints, qualitative or quantitative. An extrapolation of the pharmacophore approach to a set of multi-dimensional descriptors (pharmacophore fingerprints) has been developed mostly for library design and focusing purposes [3-8]. 

In addition to the VolSurf treatment of the GRID fields, the information from the MIF can also be transformed to obtain a pharmacophoric type of representation, which is useful in the modeling of metabolic stability, cytochrome inhibition or even the direct study of the ADME related proteins (Fig. 10.3). The Almond software [17] transforms the MIF into a distance-based representation of the molecule interaction. These parameters describe the geometry of the interaction and QSAR models can be derived where the interaction with a protein is essential. Detailed information on these descriptors is presented elsewhere in this book. 

Autocorrelation descriptors calculated for 3D-spatial molecular geometry are based on interatomic distances collected in the -> geometry matrix and the property function is defined by the set of atomic properties. 

By calculating molecular descriptors based on 3D geometry without a common orientation frame, the Comparative Molecular Moment Analysis overcomes the problems due to the molecular alignment. 

A nonlinear 18-parameter model based on 10 molecular descriptors calculated by semi-empirical quantum-chemistry methods, starting from optimized 3D geometries [Bodor et al, 1989 Bodor and Huang, 1992b Huang and Bodor, 1994] ... 

The stereoelectronic representation (or lattice representation) of a molecule is a molecular description related to those molecular properties arising from electron distribution - interaction of the molecule with probes characterizing the space surrounding them (e.g. - molecular interaction fields). This representation is typical of - grid-based QSAR techniques. Descriptors at this level can be considered 4D-descriptors, being characterized by a scalar field, i.e. a lattice of scalar numbers associated with the 3D - molecular geometry. 

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