Shape similarity, of molecules

Based on this "ID number" approach, the shape similarity of molecules can be evaluated by numerical comparisons of shape codes [2]. The same technique of similarity evaluation, originally developed for complete molecules, can also be applied, in identical form, to the shape codes of functional groups as discussed in earlier parts of this report. 

In such a case, the electron density fragment additivity principle provides a simple approach for analyzing and evaluating local shape similarity of molecules. The fragment electron densities F are well defined within any LCAO-based quantum chemical electron density, and it is simple to consider the family of MIDCOs, their shape groups, as well as their shape codes in a manner entirely analogous to the... 

One very useful approach in rational drug design is the study of the local shapes and local shape similarities of molecules showing similar biochemical activities, and the technique of shape groups offers an algorithmic approach to this problem. 

Both indices have been applied to other molecular properties, e.g. electrostatic potentials and fields, and to describe the shape similarity of molecules [1068, 1069]. 

This set F(G,n) provides an absolute shape characterization of G and the body B enclosed by it. By analogy with the two-dimensional case, we may use these F(G,n) sets to introduce a relative measure for shape similarity of two molecular contour surfaces Gi and G2. These surfaces may belong to two different molecules, or... 

This Centrally Inverted Map Method (CIMM) of molecular shape complementarity analysis allows one to use the techniques of similarity measures. In fact, the problem of shape complementarity is converted into a problem of similarity between the original (a,b) parameter map of shape groups HP (a,b) of molecule M] and the centrally inverted (a,b) parameter map of the complementary HP2-ii(a,b) shape groups of molecule M2. 

There is, however, an alternative (but still indirect) way to view these molecules. It involves studies of crystalline solids and the use of the phenomenon of diffraction. The radiation used is either X rays, with a wavelength on the order of 10 cm, or neutrons of similar wavelengths. The result of analyses by these diffraction techniques, described in this volume, is a complete three-dimensional elucidation of the arrangement of atoms in the crystal under study. The information is obtained as atomic positional coordinates and atomic displacement parameters. The coordinates indicate the position of each atom in a repeat unit within the crystal, while the displacement parameters indicate the extent of atomic motion or disorder in the molecule. From atomic coordinates, it is possible to calculate, with high precision, interatomic distances and angles of the atomic components of the crystal and to learn about the shape (conformation) of molecules in the crystalline state. 

Although the literature shows abundant example of studies of quantum similarity of molecules [45], analogous investigations on atoms are nearly nonexistent. Below we briefly describe how a shape function-based approach may lead to results which are more appealing than those on the density giving a first example of the advantage of using cr(r) as an alternative to p(r). 

At the molecular level, shape is now reali d to be one of the most fundamental concepts of chemistry, even though it may be difficult to quantify [67], In 1980 the first quantum-mechanical measure of shape similarity for molecules was put forward by Carbo et al. [68]. This measure, which was intended to be of special use in molecular design studies, proved to be of seminal influence. For any two molecules, M and N, the similarity, S ns was defined as the ratio... 

Often, the shape comparisons of local regions of molecules are of interest, which, in many instances, may appear more important than the evaluation of the global similarities of molecules. 

An important fact has been pointed out by Parr and Berk the bare nuclear potential Vn(r) shows many similarities with the electronic density function p(r). The computed isopotential contours of the composite nuclearpotential VnC lwere remarkably similar to some of the molecular isodensity contours (MIDCOs) of the electronic ground states in several simple molecules. One may regard the composite nuclear potential as the harbinger of electronic density, and isopotential contours of the composite nuclear potential V (r) can serve as surprisingly good approximations of MIDCOs. The nuclear potential contours (NUPCOs) are suitable for an inexpensive, approximate shape representation of molecules. 

Ultrafast shape recognition (USR) [19] is a recent and unusually rapid descriptor-based shape similarity technique. USR is based on the observation that the shape of a molecule is determined by the relative positions of its atoms. This 3D spatial arrangement of atoms is accurately described by a set of distributions of interatomic distances measured from four strategically located reference points, which are in turn characterized by its first three statistical moments. The shape similarity of two molecules is Anally calculated through an inverse of the sum of least absolute differences in their respective descriptors (full details about this recent technique along with applications can be found in a recent review [20]). 

Overlay of Chemical Structures (ROCS) program, which has become very popular in recent years [146, 147]. It also includes pharmacophore features by assigning a color force field to the atoms based on the work of Mills and Dean [148]. A number of successful applications have been published [149]. For instance Bostrom et al. reported a new series of CBl receptor antagonists based on replacing the methylpyr-azole scaffold in Rimonabant [150]. EON [151] is an extension of ROCS in that way that it determines the similarity of molecules not just on the basis of shape, but takes the electrostatic potential of a molecule into account as well. 

In chemistry the similarity of molecules plays a central role. Indeed, comparable molecules, usually molecules with a similar shape, are expected to show similar chemical properties and reactivity patterns. Specifically, there chemical behavior is expected to be similar [34]. The concept of functional groups is extensively used in organic chemistry [35], through which certain properties are transferable (to a certain extent) from one molecule to another, and the intense QSAR investigations in pharmaceutical chemistry [36] are illustrations of the attempts to master and exploit similarity in structure, physicochemical properties and reactivity of molecular systems. 

In eq 24, PI5Q = -log I50 where I is the molarity causing 50% inhibition, n is the number of carbon atoms in an alkyl chain, A is an electronic factor, B a hydrophobic parameter, and C is the contribution to activity of the parent portion of the molecule. Amoore i continues to make progress in quantitatively correlating the shape of organic compounds with their odor. The similarity of molecules is compared by scanning their molecular silhouettes with a computerized pattern recognition machine. 

Spectral lines are fiirther broadened by collisions. To a first approximation, collisions can be drought of as just reducing the lifetime of the excited state. For example, collisions of molecules will connnonly change the rotational state. That will reduce the lifetime of a given state. Even if die state is not changed, the collision will cause a phase shift in the light wave being absorbed or emitted and that will have a similar effect. The line shapes of collisionally broadened lines are similar to the natural line shape of equation (B1.1.20) with a lifetime related to the mean time between collisions. The details will depend on the nature of the intemrolecular forces. We will not pursue the subject fiirther here. 

Phosphorus trifluoride is a colourless gas the molecule has a shape similar to that of phosphine. Although it would not be expected to be an electron donor at all (since the electronegative... 

In connection with electronic strucmre metlrods (i.e. a quantal description of M), the term SCRF is quite generic, and it does not by itself indicate a specific model. Typically, however, the term is used for models where the cavity is either spherical or ellipsoidal, the charge distribution is represented as a multipole expansion, often terminated at quite low orders (for example only including the charge and dipole terms), and the cavity/ dispersion contributions are neglected. Such a treatment can only be used for a qualitative estimate of the solvent effect, although relative values may be reasonably accurate if the molecules are fairly polar (dominance of the dipole electrostatic term) and sufficiently similar in size and shape (cancellation of the cavity/dispersion terms). 

The present review intends to be illustrative rather than comprehensive, and focuses on the results of this study leading to the hypothesis 9 — the three-dimensional shape similarity between interacting groups in reacting molecules is responsible for more specific and precise molecular recognition than would otherwise be achieved — and on the explanation of biological recognition on this basis. 

A receptor is a surface membrane component, usually a protein, which regulates some biological event in response to reversible binding of a relatively small molecule40 . The precise three-dimensional structures of the binding sites of receptors still remain unknown today. Thus, this section mainly describes the correlation of shape similarity between the molecules which would bind to a given receptor with their biological activity. 

A theoretical treatment, similar to that given above for spherical nuclei, may be provided for disc-shaped nuclei of only one or two molecules thickness (5jc) on reactant surfaces. For these... 

The first half of our story builds up to reactions, and we learn about the characteristics of molecules that help us understand reactions. We begin by looking at atoms, the building blocks of molecules, and what happens when they combine to form bonds. We focus on special bonds between certain atoms, and we see how the nature of bonds can affect the shape and stability of molecules. At this point, we need a vocabulary to start talking about molecules, so we learn how to draw and name molecules. We see how molecules move around in space, and we explore the relationships between similar types of molecules. At this point, we know the important characteristics of molecules, and we are ready to use our knowledge to explore reactions. 

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