Relative shape similarity

Relative shape similarity in molecular 2D and 3D models can be assessed by using one of several approaches. The first of such procedures was introduced by Carbo and co-workers for the analysis of the entire electron density.226 Many variations of the original procedure have been proposed,227-23i 35 as various practical implementations.232-235... 

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. 

Calixarene and their resorcinarene relatives are similar to CDs with respect to their ability to form a concave cavity in which guests can bind. Calixarenes are conformationally more flexible than the resorcinarenes, and depending on the substituents attached to their wider upper rim or to the narrower lower rim they may exist in a highly-symmetric bowl-shaped, so-called cone conformation or in several other conformations that do not exhibit an as perfect cavity as does the cone conformation (Scheme 9). Cationic guests, such as alkali metal or ammonium ions. 

The USR (Ultrafast Shape Recognition) Method. This method was reported by Ballester and Richards (53) for compound database search on the basis of molecular shape similarity. It was reportedly capable of screening billions of compounds for similar shapes on a single computer. The method is based on the notion that the relative position of the atoms in a molecule is completely determined by inter-atomic distances. Instead of using all inter-atomic distances, USR uses a subset of distances, reducing the computational costs. Specifically, the distances between all atoms of a molecule to each of four strategic points are calculated. Each set of distances forms a distribution, and the three moments (mean, variance, and skewness) of the four distributions are calculated. Thus, for each molecule, 12 USR descriptors are calculated. The inverse of the translated and scaled Manhattan distance between two shape descriptors is used to measure the similarity between the two molecules. A value of 1 corresponds to maximum similarity and a value of 0 corresponds to minimum similarity. 

Accepting that the relative shapes of the (T°(pH) curves are well established, the question follows as to what extent the shapes of (pH) curves vary between different oxides. To that end, the sets of curves are displaced horizontally till the zero points coincide. Figure 3.59 gives an example where a striking similarity is observed, which could even be Improved by slightly adjusting the specific area. 

By contrast, relative shape analysis and relative shape descriptors can change for each molecule, depending on the other molecule used for comparison. For n molecules there are n(n-l)/2 molecule pairs, hence n(n-l)/2 families of relative shape descriptors of the given type. Consequently, in the study of shape similarities in large molecular families, the quadratic dependence of the number of relative shape descriptors on the number of molecules is a disadvantage and the use of relative shape descriptors is often impractical. Shape similarity measures based on relative shape descriptors are called similarity measures of the second kind. 

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... 

Arteca, G.A., Jammal, V.B., Mezey, P.G., Yadav, J.S., Hermsmeier, M.A. and Gund, T.M. (1988b). Shape Group Studies of Molecular Similarity Relative Shapes of Van der Waals and Electrostatic Potential Surfaces of Nicotinic Agonists. J.Mol.Graphics, 6,45-53. 

Arteca GA, Jammal YB, Mezey PG, Yadav JS, Hermsmeiers MA, Gund TM. Shape group studies of molecular similarity relative shapes of van der Waals and electrostatic potential surfaces of nicotinic agonists. J Mol Graph 1988 6 45-53. 

The isotherm of the parent SBA-15 (not shown) was of type fV with possessing a HI hysteresis loop [8], characterized by adsorption and desorption branches nearly parallel to the abscissa at high relative pressure. Similarly to SBA-15, sample WO also shows an isotherm of type fV with a HI hysteresis loop, indicating that it contains mesopores with a narrow radius distribution [8]. With increasing water content in the glycerol, the slope of the adsorption and desorption branches at high relative pressure (P/Po > 0.8) increases, which might indicate the formation of slit-shaped pores [8]. While for samples WIO and W15 still type IV isotherms are observed, indicative for mesoporous materials, the isotherms of samples W30 and W40 are intermediates between type IV and type I, the latter indicative for the presence of micropores [8]. 

You have three covalent compounds with three very different boiling points. All of the compounds have similar molar mass and relative shape. Explain how these three compounds could have very different boiling points. 

A relative shape descriptor is a d-dimensional function associated with a pair of molecules (in their p-dimensional models). These functions measure relative molecular similarity instead of the absolute (i.e., nonrelative) shape of the corresponding model. In this category we find, among others, root-mean-square (rms) deviations, °-2 quantum similarity measures, and some polymer compactness measures. 

Relative shape descriptors are defined in terms of a reference structure, which may be an experimental X-ray or NMR structure. Similarly, we can use a molecular mechanics conformational energy minimum as the initial structure for a dynamics simulation. The reference can also be a target conformation with desired shape features—for example, being maximally compact i -aie or... 

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]). 

This highlights the good feature map, but poor shape similarity for this compound. Without the benefit of stmctural information, it is difficult to know the relative importance of these attributes. 

Talc is a hydrated magnesium silicate, which has a platy shape, similar to clays. Unlike clays, the mineral does not possess a significant level of surface hydroxyl groups, which is the primary reason for the application differences between the two minerals. Talcs have a surface that interacts poorly with rubber (it has a characteristic slippery feel), is basic in character, and is relatively hydrophobic. Good sources of talc are relatively scarce. This has ensured that the cost of talc is relatively high. 

The above database results can be translated into simple qualitative rules for selecting co-crystal formers. Choosing co-formers with similar shapes, similar fractional polarities and similar dipole moments to the API should increase the chances of successful co-crystal formation. Because of the relative weakness of the underlying trends, a large number of experiments is required to demonstrate convincingly that consideration of these factors improves the success rate of cocrystal screening experiments. 

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