Appropriate Descriptors

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. 

Methods of analyzing the diversity of the selected subset ensure that an appropriate chemical space is covered. Descriptors such as fingerprints, and 2D, and 3D descriptors, as well as molecular surface properties, which can be... 

The simplest shape for the cavity is a sphere or possibly an ellipsoid. This has the advantage that the electrostatic interaction between M and the dielectric medium may be calculated analytically. More realistic models employ moleculai shaped cavities, generated for example by interlocking spheres located on each nuclei. Taking the atomic radius as a suitable factor (typical value is 1.2) times a van der Waals radius defines a van der Waals surface. Such a surface may have small pockets where no solvent molecules can enter, and a more appropriate descriptor may be defined as the surface traced out by a spherical particle of a given radius rolling on the van der Waals surface. This is denoted the Solvent Accessible Surface (SAS) and illustrated in Figm e 16.7. 

Oligosaccharide and polysaccharide structures occur not only in free form but often as parts of glycopeptides or glycoproteins [11] or of glycolipids [21]. It can be cumbersome to designate their structures by using the recommendations of 2-Carb-37. The use of three-letter symbols for monosaccharide residues is therefore recommended. With appropriate locants and anomeric descriptors, long sequences can thus be adequately described in abbreviated form. 

The process of defining any QSPR model involves three fundamental components (i) a set of descriptors, (ii) a method to select the most appropriate descriptors, and (iii) the experimental data to train and test the model. It is important to note here that none of these components are unique and many models can be... 

The question of selecting the most appropriate method for any one compound has been addressed recently by Kiihne et al. [52]. Initially several different methods are used to predict the solubility of a reference library of compounds. A subset of compounds from this reference library that are most similar to the compound of interest is identified and the method with the smallest sum of errors in the predicted solubility for this subset is chosen to predict the solubility. Dearden [3] considered whether a consensus approach could improve prediction over any one method. While the predictions from certain pairs of methods could be combined with improved results, some combinations led to poorer performance than either method alone. Chen et al. [53] were able to achieve improved correlation with their QSPR model using different QSPRs for different classes of compounds. Thus, while each QSPR used the same set of eight descriptors, the contribution of each descriptor changed according to the compound type. Each group had 82-101 compounds and achieved an of 0.86-0.92. 

Because of the large number of chemicals of actual and potential concern, the difficulties and cost of experimental determinations, and scientific interest in elucidating the fundamental molecular determinants of physical-chemical properties, considerable effort has been devoted to generating quantitative structure-property relationships (QSPRs). This concept of structure-property relationships or structure-activity relationships (QSARs) is based on observations of linear free-energy relationships, and usually takes the form of a plot or regression of the property of interest as a function of an appropriate molecular descriptor which can be calculated using only a knowledge of molecular structure or a readily accessible molecular property. 

The usual approach is to compile data for the property in question for a series of structurally similar molecules and plot the logarithm of this property versus molecular descriptors, on a trial-and-error basis seeking the descriptor which best characterizes the variation in the property. It may be appropriate to use a training set to obtain a relationship and test this relationship on another set. Generally a set of at least ten data points is necessary before a reliable QSPR can be developed. 

Fig. 16. Panorama of values in the literature for diffusion coefficients of hydrogen in silicon and for other diffusion-related descriptors. Black symbols represent what can plausibly be argued to be diffusion coefficients of a single species or of a mixture of species appropriate to intrinsic conditions. Other points are effective diffusion coefficients dependent on doping and hydrogenation conditions polygons represent values inferred from passivation profiles [i.e., similar to the Dapp = L2/t of Eq. (95) and the ensuing discussion] pluses and crosses represent other quantities that have been called diffusion coefficients. The full line is a rough estimation for H+, drawn assuming the top points to refer mainly to this species otherwise the line should be higher at this end. The dashed line is drawn parallel a factor 2 lower to illustrate a plausible order of magnitude of the difference between 2H and H.

RR, PCR, and PLS are appropriate methodologies when the number of descriptors exceeds the number of observations, and they are designed to utilize all available descriptors in order to produce an unbiased model whose predictive ability is accurately reflected by q2, regardless of the number of independent variables in the model. 

A relevant aspect in QSAR studies and pharmacophore modeling is the choice of the most appropriate molecular descriptors with respect to both the molecular series... 

Chemical structures are often characterized by binary vectors in which each vector component (with value 0 or 1) indicates absence or presence of a certain substructure (binary substructure descriptors). An appropriate and widely used similarity measure for such binary vectors is the Tanimoto index (Willett 1987), also called Jaccard similarity coefficient (Vandeginste et al. 1998). Let xA and xB be binary vectors with m components for two chemical structures A and B, respectively. The Tanimoto index fAB is given by... 

Present rules also can generate anomalous descriptors if tetragonal or octahedral centers are ligated with enantiomorphic ligands. This can be prevented by measures analogous to those just described, namely the appropriate use of capital and lowercase descriptors and restrictions on applying enantiomorphic preferences such as R > S. 

Alternative names are shown in some cases this should emphasize that there is often no unique correct name. Sometimes, it can be advantageous to bend the rules a little so as to provide a neat name rather than a fully systematic one. Typically, this might mean adopting a lower priority functional group as the suffix name. It is important to view nomenclature as a means of conveying an acceptable unambiguous stmc-ture rather than a rather meaningless scholastic exercise. Other examples will occur in subsequent chapters, and specialized aspects, e.g. heterocyclic nomenclature, will be treated in more detail at the appropriate time (see Chapter 11). Stereochemical descriptors are omitted here, but will be discussed under stereochemistry (see Sections 3.4.2 and 3.4.3). 

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