Molecular descriptor information content descriptors

It has often been mentioned in this chapter that many molecular descriptors can well be highly intcr-corrclatcd. Therefore, any significant information content of a... 

The information content of a structure descriptor depends on two major factors a) the molecular representation of the compound b) the algorithm which is used for the calculation of the descriptor. 

The SlogP, SMR, and PEOE VSA descriptors have rich information content and can be used in place of many traditional descriptors (13-17). Figure 5 presents the results of a collection of 64 linear models each of which approximates a traditional descriptor as a linear combination of the VSA descriptors (trained on approx 2,000 small molecules). Out of the 64 descriptors, 32 showed an r2 of 0.90 or better and 49 had an r2 of 0.80 or better, and 61 showed an r2 of 0.5 or better. Descriptors related to flexibility are poorly modeled. In particular, the Lipinksi parameters log/5, acceptor count, donor count, and molecular weight are... 

Average molecular weight and -> relative atom-type count are simple molecular descriptors that encode information on atomic composition. Other important descriptors of the atomic composition are based on the -> total information content and the - mean information content, defined as ... 

The nuclear information content /nucl is a molecular descriptor calculated as the sum of information on the proton-neutron composition of all the nuclei of the molecule ... 

Information content is a fundamental measure derived from the partitioning of elements into equivalence classes several - molecular descriptors are derived as -t information indices. 

This descriptor calculated for the - H-depleted molecular graph coincides with the -> vertex orbital information content in the case of atoms of the same chemical element and maximal order of neighbourhood ... 

To accoimt for steric effects in molecule-receptor interactions, the weighted information indices by volume have been proposed [Ray et al, 1985]. These molecular descriptors are calculated in the same way as the indices of neighbourhood symmetry defined above using the atomic van der Waals volumes to get the probabilities of the equivalence classes. In other words, the van der Waals voliunes of the atoms belonging to each equivalent class are summed to give a molecule subvolume, then divided by the total molecule volume. For example, the weighted information content by volume is defined as ... 

Both total and mean information content are widely used as molecular descriptors and are called - information indices. 

Molecular descriptors calculated as - information content of molecules. Different criteria are used for defining - equivalence classes, i.e. equivalency of atoms in a molecule such as chemical identity, ways of bonding through space, molecular topology and symmetry, - local vertex invariants [Bonchev, 1983]. 

A molecular descriptor derived from the - cardinality layer matrix LC of a molecular graph (7 defined as - mean information content [Konstantinova, 1996] ... 

As the values of the leverage matrix are sensitive to the whole molecule structure, they automatically contain information about the molecular complexity, which is a function of the size, symmetry, elemental molecular composition, molecular branching, and centricity. Thus, 3D complexity descriptors can be obtained from this matrix as total and standardized information content ... 

The above considerations also hold for different hierarchical descriptions of a system at a given level, i.e. the same level is traversed by an inner hierarchical organization because of different descriptions of the same elements. The molecular representations are hierarchical descriptions of the molecular system, therefore, derived from the different representations of the molecular structure several - molecular descriptors are calculated with different chemical information contents. 

A molecular symmetry descriptor calculated as - total information content ... 

Some basic concepts and definitions of statistics, chemometrics, algebra, graph theory, similarity/diversity, which are fundamental tools in the development and application of molecular descriptors, are also presented in the Handbook in some detail. More attention has been paid to information content, multivariate correlation, model complexity, variable selection, and parameters for model quality estimation, as these are the characteristic components of modern QSAR/QSPR modelling. 

These descriptors mainly encode information on molecular symmetry if all the atoms have different leverage values, that is, the molecule does not show any element of symmetry, 7th = Ao log Ao and 7sh = 1 otherwise, if all the atoms have equal leverage values (a perfectly symmetric theoretical case), 7th =0 and 7sh = 0. The total information content on the leverage equality 7xh is more discriminating than 7sh because of its dependence on molecular size, and thus it could be thought of as a measure of molecular complexity. These indices were demonstrated to be useful in modeling physico-chemical properties related to entropy and symmetry [Consonni, Todeschini et al, 2002b]. 

The Shannon s entropy is also largely applied to the analysis of the information content of molecular descriptors vithin data sets of molecules and to assess the diversity of chemical libraries [Lin, 1996b Bajorath, 2001]. 

Information content and Shannon s entropy of molecular descriptors were extensively studied by Bajorath, Godden, and coworkers in several papers [Godden, Stahura et al., 2000 Godden and Bajorath, 2000, 2002, 2003]. 

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