Geometrical molecular descriptors

Basak, S.C., Grunwald, G.D. and Niemi, G.J. (1997a). Use of Graph-Theoretic and Geometrical Molecular Descriptors in Structure-Activity Relationships. In From Chemical Topology to Three-Dimensional Geometry (Balaban, A.T., ed.). Plenum Press, New York (NY), pp. 73-116. 

MODEL Molecular Descriptor Lab (MODEL) (http //jing.cz3.nus.edu.sg/ cgi-bin/model/model.cgi) is a free Web-based server for computing a comprehensive set of 3778 molecular descriptors, which can be divided into 6 classes constitutional descriptors, electronic descriptors, physical chemistry properties, topological indexes, geometrical molecular descriptors, and quantum chemistry descriptors [73], Compounds can be provided to the server in various molecular formats such as PDB, MDL, MOL2, and COR, and the computed molecular descriptors are displayed in a few seconds or less. Cross-links to the relevant sections of the reference manual page are also provided for some of the descriptors and descriptor classes. 

Use of Graph-Theoretic and Geometrical Molecular Descriptors in Structure-Activity Relationships... 

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. 

Three classes of calculated molecular descriptors, viz., topological and substruc-tural descriptors, geometrical (3-D) indices, and quantum chemical (QC) indices, have been extensively used in QSAR studies pertaining to drug discovery and environmental toxicology [8-12],... 

In order to apply the SA protocol, one of the keys is to design a mathematical function that adequately measures the diversity of a subset of selected molecules. Because each molecule is represented by molecular descriptors, geometrically it is mapped to a point in a multidimensional space. The distance between two points, such as Euclidean distance, Tanimoto distance, and Mahalanobis distance, then measures the dissimilarity between any two molecules. Thus, the diversity function to be designed should be based on all pairwise distances between molecules in the subset. One of the functions is as follows ... 

Therefore, similar to the attempts made to estimate vapor pressure (Section 4.4) there have been a series of quite promising approaches to derive topological, geometric, and electronic molecular descriptors for prediction of aqueous activity coefficients from chemical structure (e.g., Mitchell and Jurs, 1998 Huibers and Katritzky, 1998). The advantage of such quantitative structure property relationships (QSPRs) is, of course, that they can be applied to any compound for which the structure is known. The disadvantages are that these methods require sophisticated computer software, and that they are not very transparent for the user. Furthermore, at the present stage, it remains to be seen how good the actual predictive capabilities of these QSPRs are. 

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. 

Geometric Volume- Boiling Point Relationships Bhattacharjee and Dasgupta [12,13] introduced the geometric volume, Vg, as molecular descriptor for alkanes, halomethanes, and haloethanes. A bilinear relationship has been reported for alkanes... 

Nelson and Jurs [41] have developed models for three sets of compounds (1) hydrocarbons, (2) halogenated hydrocarbons, and (3) alcohols and ethers. Each model correlates log[C (mol L-1)] with nine molecular descriptors that represent topological, geometrical, and electronic molecule properties. The standard error for the individual models is 0.17 log unit and for a fourth model that combines all three compound sets, the standard error is 0.37 log unit. 

Recent progress in computational hardware and the development of efficient algorithms have assisted the routine development of molecular quantum-mechanical calculations. New semiempirical methods calculate realistic quantum-chemical molecular quantities in a relatively short computational time frame. Quantum-chemical calculations are thus an attractive source for molecular descriptors that can express all of the electronic and geometric properties of molecules and their interactions. Quantum-chemical methods can be applied to QSARs by direct derivation of electronic descriptors from the molecular wave function. 

Although various computational approaches for the prediction of intestinal drug permeability and solubility have been reported [219], recent computer-based absorption models utilize a large number of topological, electronic, and geometric descriptors in an effort to take both aqueous drug solubility and permeability into account. Thus, descriptors of partitioned total surface areas [168], Abraham molecular descriptors [220,221], and a variety of structural descriptors in combination with neural networks [222] have been shown to be determinants of oral drug absorption. 

Yalkowsky and Banerjee have pubhshed an extensive review of methods for estimating aqueous water solubility of organic compounds. Many methods have been developed based on measured properties such as partition coefficients, chromatographic parameters, and activity coefficients. " Purely in silico methods are based on LFER, and a variety of geometric, electronic, and topological molecular descriptors. ... 

Geometric and mass centres of a molecule are not molecular descriptors, but they are used to translate the molecule at the centre, thus providing a unique reference origin which allows invariance to translation and separation between translational and rotational motions. 

Both molecular descriptors are able to discriminate among groups having the same number of valence electrons but with different hybridization and different chemical environments. Moreover, they show high sensitivity to geometric isomers, conformations, and heteroatoms. 

However, when molecular descriptors are derived from molecular graphs, cis/trans isomerism is not usually recognized and some molecular descriptors were proposed in order to discriminate between cis/trans isomers, such as the - corrected electron charge density connectivity index, and - periphery codes. - Weighted matrices were also devised for obtaining the -> geometric modification number that is added to any topological index in order to discriminate cis/trans isomers. 

Molecular descriptors defined in several different ways but always derived from the three-dimensional structure of the molecule. Generally, geometrical descriptors are... 

Figure G-1. Scheme of the molecular descriptors classified as geometrical descriptors.

The three-dimensional representation views a molecule as a rigid geometrical object in space and allows a representation not only of the nature and connectivity of the atoms, but also the overall spatial configuration of the molecule. This representation of a molecule is called geometrical representation, and molecular descriptors derived from this representation are called 3D-descriptors. Examples of 3D-descrip-tors are -> geometrical descriptors, several -> steric descriptors, and -+ size descriptors. 

Important derived matrices are the powers of the geometry matrix, used to define - molecular profiles descriptors, and the -> distance/distance matrix DD, which unifies the topological and geometric molecular information. 

A geometrical shape descriptor based on the radii of three spheres centred at the barycentre of the molecule [Meyer, 1986a], The first sphere of radius Ri has volume equal to the -> van der Waals volume-, the second sphere of radius Rz has volume equal to the -> molecular volume, and the third sphere of radius R3 is defined as the sphere embedding the whole molecule. The shape descriptor is then defined as ... 

Description WebSite Calculation of several sets of molecular descriptors from molecular geometries (topological, geometrical, WHIM, 3D-MoRSE, molecular profiles, etc.). http //www.disat.unimib.it/chm/... 

Katritzky, A.R. and Gordeeva, E.V. (1993). Traditional Topological Indices vs Electronic, Geometrical, and Combined Molecular Descriptors in QSAR/QSPR Research. J.Chem.Inf.Com-putSci., 33,835-857. 

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