Descriptors scaling

Practical problems in the estimation of the lipophilicity of araliphatic and aliphatic compoimds led to the / hydrophobicity scales of Rekker and Leo/Hansch. However, all such descriptor scales depend on experimental determinations. New molecular descriptors were developed from scratch, starting with the work of Randic, Kier and Hall, i.e. the various molecular connectivity parameters %. Later the electrotopological state parameters and the Todeschini WHIM parameters were added. Whereas topological descriptors are mathematical constructs that have no unique chemical meaning, they are clearly related to some physicochemical properties and are suited to the description of compound similarities in a quantitative manner. Thus, despite several critical comments in the past, they are now relatively widely used in QSAR studies. Only a meaningless and excessive application in quantitative models, as far as the number of tested and included variables is concerned, still deserves criticism. 

Pomona College Medicinal Chemistry Project database (. Sigma resonance (Oj ) values were derived from Op - Oj. Sterlc descriptors scaled to van der Waals radii (Charton s u) were selected from the literature (20, 21). 

For each s pificant descriptor set, obtained in the previous step, an additional noncoUinear descriptor scale was added, and the appropriate (n + l)-parameter regression treatment was performed. When the Fisher criterion at the given probability level, F (or the cross-validated correlation coefficient for leave-one-out Rcv(Q). obtained for any of these correlations was smaller than that for the best correlation of the previous rank, the latter was designated as the final result and the search was terminated. Otherwise, the descriptor sets with the highest regression... 

Table 2.11 Descriptor scales for the 20 natural amino acids (from Hellberg et al. 1987, copyright (1987) American Chemical Society)...

Steinhauer and Gasteiger [30] developed a new 3D descriptor based on the idea of radial distribution functions (RDFs), which is well known in physics and physico-chemistry in general and in X-ray diffraction in particular [31], The radial distribution function code (RDF code) is closely related to the 3D-MoRSE code. The RDF code is calculated by Eq. (25), where/is a scaling factor, N is the number of atoms in the molecule, p/ and pj are properties of the atoms i and/ B is a smoothing parameter, and Tij is the distance between the atoms i and j g(r) is usually calculated at a number of discrete points within defined intervals [32, 33]. 

If the descriptors are on different scales then those which naturally occupy a larger scale may be given more weight in the subsequent analysis, simply because of their natura units. In autoscaling the descriptors are scaled to zero mean and a standard deviatior of 1. 

The term fine chemicals is widely used (abused ) as a descriptor for an enormous array of chemicals produced at small scale and is frequently assumed to infer a significant added value of the product derived from the degree of complexity (number of functional groups, geometric isomers, and enantiomers) and precision in their manufacture. Whether the term fine chemicals refers to the finesse of the chemistry or to the small scale of manufacture is far from clear. However, in order to assist our discussion the following division can be adopted [2] ... 

One of the advantages of the as molecnlar descriptor to characterise the steric properties of ligands is its generality. This has allowed the placement of tertiary phosphines and NHCs on the same scale. The valnes reported in Fig. 1.18 for two of the most classical phosphines indicate that the less bnUcy PPhj compares with NHCs of intermediate bulkiness, snch as those presenting p-tolyl N-substitnents, while the bulkier PCyj compares with the bulky IPr and SlPr NHCs. Finally, farther refinement of the model was recently disclosed in the form of the dihedral angles ( )j and( )2 (Fig. 1.20). 

The %HIA, on a scale between 0 and 100%, for the same dataset was modeled by Deconinck et al. with multivariate adaptive regression splines (MARS) and a derived method two-step MARS (TMARS) [38]. Among other Dragon descriptors, the TMARS model included the Tig E-state topological parameter [25], and MARS included the maximal E-state negative variation. The average prediction error, which is 15.4% for MARS and 20.03% for TMARS, shows that the MARS model is more robust in modeling %H1A. 

Sarmders, R. A., Platts, J. A. Scaled polar surface area descriptors development and application to three sets of partition... 

Lipophilicity is intuitively felt to be a key parameter in predicting and interpreting permeability and thus the number of types of lipophilicity systems under study has grown enormously over the years to increase the chances of finding good mimics of biomembrane models. However, the relationship between lipophilicity descriptors and the membrane permeation process is not clear. Membrane permeation is due to two main components the partition rate constant between the lipid leaflet and the aqueous environment and the flip-flop rate constant between the two lipid leaflets in the bilayer [13]. Since the flip-flop is supposed to be rate limiting in the permeation process, permeation is determined by the partition coefficient between the lipid and the aqueous phase (which can easily be determined by log D) and the flip-flop rate constant, which may or may not depend on lipophilicity and if it does so depend, on which lipophilicity scale should it be based ... 

However, Clog P and, more generally, Hpophilidty descriptors referring to octanol-water are not the only lipophilicity parameters to be taken into account As mentioned above, isotropic and anisotropic Hpophilidty values gave rise to two different Hpophilidty scales for ionized compounds and thus it is recommended to test both of them (after checking the absence of any coHnearity) when looking for a QSAR model involving ions. 

For years, the reigning paradigm for the unfolded state has been the random coil, whose properties are given by statistical descriptors appropriate to a freely jointed chain. Is this the most useful description of the unfolded population for polypeptide length scales of biological interest The answer given by this volume is clear there is more to learn. But first a word about the occasion that prompted this volume. 

QSAR studies are a fertile area for ANNs and numerous papers have been published in the field. Katritzky s group has a range of interests in this area, particularly related to compounds of biological importance see for example Reference 6. Some QSAR studies have been on a heroic scale. Molnar s group has used training sets of around 13,000 compounds and a total database containing around 30,000 to try to develop meaningful links between cytotoxicity and molecular descriptors.7... 

There is still a long way to go in the harmonisation of indices, applicability of new techniques and standardisation. These are essential steps in order to advance in the detection of the stressor effects by means of structural descriptors. However, even if these questions might be solved, the ability of structural descriptors to detect effects is limited. Many stressors occur in low concentrations, in acute episodes, or have side effects that are not reflected in the structure (composition, abundance) of the biofilm. In these cases where chronic effects would not occur, or are hidden, a finer scale of detection is required. 

Structure and function need to be jointly considered in the assessment of effects of stressors on river systems. It has been shown that the two sets of parameters offer complementary information since they cover different time scales and responses. This being shown in the case of biofilms is not a unique characteristic of them, but it might be applied to all other biological communities (e.g. macroinvertebrates, fish). These differ from the biofilm in its higher size and life span, and therefore in their integrative capacity to reflect effects in one part of the ecosystem. Higher traffic levels in addition to biofilms should be considered to study the whole ecosystem. In all of these biological compartments, the combined use of descriptors may amplify our ability to predict the effect of stressors on river basins. 

When the experimental values of I and A are known, one can determine through these expressions the values of /a and tj. Since for atoms and molecules, the trends shown by these values of /a and tj are, in general, in line with those provided by several empirical scales constructed intuitively by chemists, the identification of these global DFT descriptors with their associated chemical concepts is strengthened. In other words, the quantity (I+A)/2 shows, in general, the same behavior as that of the electronegativity concept, while the quantity (I—A) shows, also in general, the same behavior as that of the chemical hardness concept. 

On the other hand, there is considerable interest to quantify the similarities between different molecules, in particular, in pharmacology [7], For instance, the search for a new drug may include a comparative analysis of an active molecule with a large molecular library by using combinatorial chemistry. A computational comparison based on the similarity of empirical data (structural parameters, molecular surfaces, thermodynamical data, etc.) is often used as a prescreening. Because the DFT reactivity descriptors measure intrinsic properties of a molecular moiety, they are in fact chemical fingerprints of molecules. These descriptors establish a useful scale of similarity between the members of a large molecular family (see in particular Chapter 15) [18-21],... 

Decision Trees are also a well-known technique in the field [151]. They arrange a subset of the descriptor components in a hierarchical fashion (a binary tree) such that on a particular node in the tree a classification on a single descriptor component decides whether the left or the right branch underneath is followed. The leaves of the tree determine the overall classification label. Decision trees have been found useful, especially on large-scale descriptors like binary pharmacophore descriptors [152]. 

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