Other Molecular Descriptors

The electronic, steric, and hydrophobic descriptors described above are rooted in the physical chemistry of intermolecular interactions. It is also possible to calculate molecular descriptors that are not based on physical chemistry, but rather are just a consideration of the 2D structure of the molecule. Because the physical properties may be calculated from the 2D structure of the molecule, it follows that the structure contains this information and that consideration of 

Structure alone should give a reliable QSAR. The problem is that it may be impossible to interpret such a model in terms of physical chemistry. 

At approximately the same time as the original QSAR publications appeared, Free and Wilson published a regression analysis that quantified traditional SAR thinking the constancy of the contribution to potency of a particular substituent at a particular position on a parent molecule. The contribution is assumed to be independent of the efibcts of varying other substituents at other positions. For example, if substitution of a hydrogen by a chlorine atom increases potency 3-fold in one analog, it is assumed that such a substitution at this position will always increase potency 3-fold. However, it is also assumed that the contribution to potency of a particular substituent does depend on the position of substitution. These assumptions result in an equation that has, for each position of substitution, (n - 1) terms, where n is the number of substituents at that position. Hence the number of terms in the equation for p positions of substitution is given by equation (3.14). 

The data is fitted by multiple regression analysis using a computer. The Free-Wilson equation for the erythromycin esters is shown in equation (3.15).  

In equation (3.15), A refers to a hydroxyl group at position 12, FO to a formyl ester, AC to an acetyl ester, PR to a propionyl ester, and the number to the position of substitution. The low value of x suggests that this relationship might over-fit the data because it is much lower than the standard deviation of replicate measurements. 

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The idea of ligand efficiency was extended by considering other molecular descriptors. Abad-Zapatero and Metz [56] introduced a percentage efficiency index, a binding efficiency index and a surface-binding efficiency index by normalizing... 

Other molecular descriptors have been utilized to describe the molecular shape of constrained solutes (Figure 5.2b,c). Yan and Martire [38,39] have described a... 

For this task, easily accessible properties of mixtures or pure metabolites are compared with literature data. This may be the biological activity spectrum against a variety of test organisms. Widely used also is the comparison of UV [90] or MS data and HPLC retention times with appropriate reference data collections, a method which needs only minimal amounts and affords reliable results. Finally, there are databases where substructures, NMR or UV data and a variety of other molecular descriptors can be searched using computers [91]. The most comprehensive data collection of natural compounds is the Dictionary of Natural Products (DNP) [92], which compiles metabolites from all natural sources, also from plants. More appropriate for dereplication of microbial products, however, is our own data collection (AntiBase [93]) that allows rapid identification using combined structural features and spectroscopic data, tools that are not available in the DNP. 

Tel. 218-720-4279, fax 218-720-4219, e-mail sbasak ua.d.umn.edu Generation of connectivity and other molecular descriptors for use in QSAR and similarity/dissimilarity analysis. Silicon Graphics and PCs. 

The most well-known complexity indices are listed below. Other molecular descriptors which give information about molecular complexity are the indices of neighbourhood symmetry and the - total adjacency index. The latter was proposed by Bonchev and Polansky [Bonchev and Polansky, 1987] as a simple measure of topological complexity, being a measure of the degree of connectedness of molecular graph. 

A QSAR approach based on a set of methods that combines molecular shape similarity and commonality measures with other - molecular descriptors both to search for similarities among molecules and to build QSAR models [Hopfinger, 1980 Burke and Hopfinger, 1993], The term molecular shape similarity refers to molecular similarity on the basis of a comparison of three-dimensional molecular shapes represented by some property of the atoms composing the molecule, such as the van der Waals spheres. TTie molecular shape commonality is the measure of molecular similarity when conformational energy and molecular shape are simultaneously considered [Hopfinger and Burke, 1990]. 

Tlie main assumption of this approach is that the shape of the molecule is closely related to the shape of the - binding site cavity and, as a consequence, to the biological activity. Therefore, a shape reference compound is chosen which represents the binding site cavity, and the similarity (or commonality) measured between the reference shape and the shape of other compounds is used to determine the biological activity of these compounds. As well as the shape similarity measures, other molecular descriptors such as those in - Hansch analysis can be used to evaluate the biological response. The MSA model is thus defined as ... 

Other molecular descriptors derived from the charge density matrix are the average atom charge density Pi and the average bond charge density P2, defined as ... 

Correlation with Other Molecular Descriptors — This applies mainly to artificial descriptors. A correlation with experimental descriptors is helpful to produce missing experimental data. 

In contrast to most other molecular descriptors, affinity fingerprints are not directly derived from molecular structures. 

Other molecular descriptors based on atom eccentricity values combined with other —> local vertex invariants are the eccentric connectivity index, the —> eccentric distance sum, the connective eccentricity index, the eccentric adjacency topochemical indices, the superadjacency index, and the —> eccentricity-hased Madan indices. 

Moreover, two other molecular descriptors, called RDSQ index and RDCHI index, respectively, were defined, based on a Randic-like formula [Ivanciuc, Balaban et al., 1993b] ... 

Some other molecular descriptors related to the charge density matrix have been proposed [Salem, 1966 Mayer, 2007]. Some of them are listed below. 

B and C are the number of vertices and the cyclomatic number, respectively, and ay the elements of the adjacency matrix, taking values equal to 1 for pairs of adjacent vertices, and zero otherwise. Other molecular descriptors were calculated by applying several different matrix operators [Ivanciuc, 2000h], such as spectral indices, Hosoya-like indices, and Balaban-like information indices. 

Spectral moments of the matrix M(w) are other molecular descriptors defined in terms of the kth power of the eigenvalues ... 

Marrero-Ponce, Y. (2004b) Total and local (atom and atom type) molecular quadratic indices significance interpretation, comparison to other molecular descriptors, and QSPR/QSAR applications. Bioorg. Med. Chem., 12, 6351-6369. 

Statistical analysis requires a large number of observations, each of which is described by a set of well-defined attributes. The presence of a co-crystal structure in the CSD serves as an observation in our case. The structure is evidence that the constituent molecules can form a co-crystal with each other. Molecular descriptors, similar to those used in QSAR/QSPR studies, " were calculated for pairs of co-crystallising molecules. These paired molecular descriptors provided the numerical attributes for statistical analysis. 

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