Relative descriptors

Relative descriptors are usually defined with respect to a reference structure. In some applications, this reference is an experimental conformation or a minimum energy conformer (a OD or ID model). The relative descriptors allow one to quantify the deviations from the desired structure and thus establish a measure of conformational stability.In applications relevant to molecular similarity, the reference structure can be another compound (e.g., a lead in drug design27) or a particular array of atoms (e.g., the pharmacophore ) against which any new molecule is compared. In this latter case, the analysis involves 2D or 3D models. 

Relative descriptors, which usually are less discriminating than the absolute descriptors, are somewhat limited in their usefulness. For example, a given value of rms deviation between two structures may be the result of a number of completely unrelated conformations, sizes, and shape features. A detailed characterization of shape must employ absolute descriptors or at least the simultaneous use of two or more independent relative descriptors. 

Relative and absolute descriptors also differ from each other at a more fundamental level. If we compare two molecules (either their nuclear geometries or their electron densities), the result will normally depend on how they are oriented relative to each other. In contrast to absolute descriptors, relative descriptors are not invariant if one of the molecules compared is rigidly translated or rotated. Therefore, the proper use of relative descriptors must be accompanied by some sort of optimization in the superposition between two structures. Yet, a maximum superposition (e.g., by minimizing the rms deviation of paired atoms) may not produce a relative orientation that is most relevant in a given comparison of molecular shapes. This is a problem with no unique solution and is still under much research. [See discussions in Ref. 27.]... 

A measurement of compactness for lattice polymers is based on a similar idea.213,216 in this case, the parameter Q is defined as the ratio N/Nq, where N/ is the number of nearest-neighbor (nonbonded) contacts in the polymer and No its expected value for a compact global minimum. Another compactness parameter, based on residue contacts, is also used to classify folding features.223 Note that these relative descriptors explicitly use the molecular connectivity that is, they characterize molecular ID models. 

The relative descriptor C(R, 0) provides a criterion with which to obtain the optimum molecular alignment. Although the problem of achieving a maximized alignment is encountered routinely in computer-assisted drug design, a completely satisfactory solution is elusive. Improved solutions have been stud-ied232-239 and continue to be developed. 

The third stage of conversion will translate the nomenclature stereodescriptor to an atom/bond specific parity descriptor. This process is straightforward for R S, R fS and E/Z because only a single stereocentre is involved. Translating the relative ring descriptors (e.g., cis, a or ejco) is somewhat more complex because it requires identifying the ring plane and the substituents referred to by the relative descriptor. 

Detailed restrictions on the use of the various types of relative descriptors are given in Chemical Abstracts Index Guide, Appendix IV, 1989, pp. 1811-1831. 

Two other atomic properties have been used in the definition of atom type, thereby increasing its fuzziness relative to that in the ap and tt descriptors - atomic log P contribution (yielding hydrophobic pairs, hps, and torsions, hts) and partial atomic charges (charge pairs, cps, and charge torsions, cts). 

If the binary descriptors for the objects s and t are substructure keys the Hamming distance Eq. (6)) gives the number of different substructures in s and t (components that are 1 in either s or but not in both). On the other hand, the Tanimoto coefficient (Eq. (7)) is a measure of the number of substructures that s and t have in common (i.e., the frequency a) relative to the total number of substructures they could share (given by the number of components that are 1 in either s or t). 

The solubility of a compound is thus affected by many factors the state of the solute, the relative aromatic and aliphatic degree of the molecules, the size and shape of the molecules, the polarity of the molecule, steric effects, and the ability of some groups to participate in hydrogen bonding. In order to predict solubility accurately, all these factors correlated with solubility should be represented numerically by descriptors derived from the structure of the molecule or from experimental observations. 

The water-vapor transmission rate (WVTR) is another descriptor of barrier polymers. Strictly, it is not a permeabihty coefficient. The dimensions are quantity times thickness in the numerator and area times a time interval in the denominator. These dimensions do not have a pressure dimension in the denominator as does the permeabihty. Common commercial units for WVTR are (gmil)/(100 in. d). Table 2 contains conversion factors for several common units for WVTR. This text uses the preferred nmol/(m-s). The WVTR describes the rate that water molecules move through a film when one side has a humid environment and the other side is dry. The WVTR is a strong function of temperature because both the water content of the air and the permeabihty are direcdy related to temperature. Eor the WVTR to be useful, the water-vapor pressure difference for the value must be reported. Both these facts are recognized by specifying the relative humidity and temperature for the WVTR value. This enables the user to calculate the water-vapor pressure difference. Eor example, the common conditions are 90% relative humidity (rh) at 37.8°C, which means the pressure difference is 5.89 kPa (44 mm Hg). 

In contrast to SOMs, nonlinear maps (NLMs) represent relative distances between all pairs of compounds in the descriptor space of a 2D map. The distance between two points on the map directly reflects the similarity of the... 

In general, the described techniques provide an effective, flexible, and relatively fast solution for library design based on analysis of bioscreening data. The quantitative relationships, based on the assessment of contribution values of various molecular descriptors, not only permit the estimation of potential biological activity of candidate compounds before synthesis but also provide information concerning the modification of the structural features necessary for this activity. Usually these techniques are applied in the form of computational filters for constraining the size of virtual combinatorial libraries and... 

A large variety of techniques are available to develop predictive models for toxicity. These range from relatively simple techniques to relate quantitative levels of potency with one or more descriptors to more multivariate techniques and ultimately the so-called expert systems that lead the user directly from an input of structure to a prediction. These are outlined briefly below. 

A QSAR for which the standard error of each descriptor is given concerns the bradycardic effect of a series of tetraalkylbispidines [47]. The QSAR models the selectivity between the desired bradycardic effect and the adverse contractile effect. It is important, in assessing and modeling drug toxicity, that the toxic effect is assessed relative to the desired effect as described above. The QSAR developed for the selectivity of the tetraalkylbispidines was ... 

Purdy [91] used the technique to predict the carcinogenicity of organic chemicals in rodents, although his model was based on physicochemical and molecular orbital-based descriptors as well as on substructural features and it used only a relatively small number of compounds. His decision tree, which was manual rather than computer based, was trained on 306 compounds and tested on 301 different compounds it achieved 96% correct classification for the training set and 90% correct classification for the test set. 

Our basic methods have been detailed In previous reports (11, 12). In summary, however, our approach Is basically the same as that used by Hansch and co-workers (20-22) A set of compounds, which can reasonably be expected to elicit their carcinogenic response via the same general mechanism. Is chosen, and their relative biological activities, along with a set of molecular descriptors. Is entered Into a computer. The computer, using the relative biological response as the dependent variable, then performs stepwise multiple regression anayses (23) to select... 

These descriptors include relative partition coefficients (tt), ... 

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