Shape similarity

One application of kappa indexes is quantitation of shape similarity in contrast to the absolute quantitation of size. The kappa values permit a rational prediction of which molecules have a high degree of shape similarity. Thus, n-pentane, diethylether, and diethylamine have similar kappa values. Electronic structure is information to be encoded into other indexes. The kappa values predict that these three molecules have very similar shape. 

A comparison of cyclic and acyclic values is illuminating. The values for cyclohexane and 2,.1-dimethylbutane are identical. Two-dimensional traces of Dreiding models of these two molecules reveal a high degree of superimposabil-ity. This is a consequence of comparable shape, from values, and comparable size, from A values. Identical values for durene (1,2,4,5-tetramethylbenzene) and naphthalene correspond to a high degree of superimposability, due a similar shape and size A = 10 for both). 

With all orders of kappa values, a more comprehensive description of molecular shape is possible. This should permit a useful quantitation of shape similarity. 

A second application of the index is its use to predict candidate molecules to fill molecular cavities. With the increasing use of molecular graphics, the fit, docking, or intercalation of molecules into cavities in macromolecular simulations becomes an important consideration in drug design. The visualizations of proposed receptor sites, enzyme active sites, and other cavities and spaces of interest in macromolecules make it possible to make measurements of the dimensions of a cavity. Of course, the validity of these images depends on the quality of the input data and the assumptions attending the calculations. If the visualized details of a cavity are to be believed, then there is certainly some interest in what molecules may fit that cavity or some part of it. 

The dimensions of a computer-visualized cavity are readily accessible. From these dimensions a generalized shape may be quantitated and a prediction made as to which molecules should be considered as candidates for fitting the cavity. To transfer information from linear measurements of cavity dimensions to values of shape, some approximate relationship must be established between these two metrics. The most convenient approach is to recognize that a cavity is of irregular shape hence rectangular dimensions are nor universally appropriate. We can, however, take advantage of the fact that values for cycles are very similar to values of acyclic molecules that have similar shapes on a two-dimensional trace. The identical values for cyclohexane and 2,3- 

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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... 

When the bulk containing the binder is uniform, it is compressed on pneumatic, hydraulic, or ram-type presses. Compression can be carried out in presses provided with suitably designed cavities or in metallic pans. The pans ate filled with the powder mass, and a plunger with a cross-sectional shape similar to that of the pan is used to compress the tablet. The resulting tablets ate commonly used with powder puffs or cosmetic bmshes. 

The shape of the converging section is a smooth trumpet shape similar to the simple converging nozzle. However, special shapes of the diverging section are required to produce the maximum supersonic-exit velocity. Shocks result if the divergence is too rapid and excessive boundary layer friction occurs if the divergence is too shallow. See Liepmann and Roshko (Elements of Gas Dynamic.s, Wiley, New York, 1957, p. 284). If the nozzle is to be used as a thrust device, the diverg-... 

The Role of Molecular Shape Similarity in Specific Molecular Recognition... 

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. 

The problem of molecular recognition has attracted biologically oriented chemists since Emil Fischer s lock-and-key theory l0). Within the last two decades, many model compounds have been developed micelle-forming detergents11, modified cyclodextrins 12), many kinds of crown-type compounds13) including podands, coronands, cryptands, and spherands. Very extensive studies using these compounds have, however, not been made from a point of view of whether or not shape similarity affects the discrimination. 

Another example of the shape similarity effect on molecular recognition involves the similarity between the structures of the binding sites. Investigation was made for four reaction systems I-IV each consisting of a 1 1 mixture of thiols HS—X and HS—Y... 

In this Section, possible factors influencing the selectivity other than shape similarity and shape-specific weak interactions (Sect. 2.4) are discussed. These mainly include intermolecular association, exchange reactions, and hydrophobic interaction. In connection with intermolecular association and crystalline 1 1 complex formation (Sect. 2.3), tetrameric intermediates are also discussed. 

This provides substantial evidence for shape similarity effect on the specific recognition. 

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. 

The similarity recognition hypothesis presented here would be applicable to the specific and precise discrimination in chemical and biological systems. It is hoped that this review will serve to stimulate further work on the physicochemical origin of the shape-similarity effect on specific molecular recognition, for example, work on weak interactions specific for the three-dimensional shape of interacting groups. 

Sorptometei measurements ran higher in 8 of the 12 lots of A1 tested, apparently reflecting the area measurements of the pores, cracks and capillaries of the material and irregular shapes Similar comparisons obtained with samples of Ammonium Perchlorate are summarized in Table 13... 

Many experimenters have adopted the practice of feeding a preformed mixture of steam and water to their test sections, either out of interest in this type of system or else to avoid the power demanded by long channels. The CISE Laboratories in Italy have produced a considerable amount of data of this kind (S4), and a typical example of their results is shown in Fig. 13. The curves have a characteristic swan-neck shape similar to the Russian data for unstable flow conditions shown in Fig. 9, and the burn-out flux values are generally below those for normal steady-flow conditions. 

The field of synthetic enzyme models encompasses attempts to prepare enzymelike functional macromolecules by chemical synthesis [30]. One particularly relevant approach to such enzyme mimics concerns dendrimers, which are treelike synthetic macromolecules with a globular shape similar to a folded protein, and useful in a range of applications including catalysis [31]. Peptide dendrimers, which, like proteins, are composed of amino acids, are particularly well suited as mimics for proteins and enzymes [32]. These dendrimers can be prepared using combinatorial chemistry methods on solid support [33], similar to those used in the context of catalyst and ligand discovery programs in chemistry [34]. Peptide dendrimers used multivalency effects at the dendrimer surface to trigger cooperativity between amino acids, as has been observed in various esterase enzyme models [35]. 

The characteristic derivative-shaped feature at g 1.94 first observed in mitochondrial membranes has long been considered as the sole EPR fingerprint of iron-sulfur centers. The EPR spectrum exhibited by [4Fe-4S] centers generally reflects a ground state with S = I and is characterized by g values and a spectral shape similar to those displayed by [2Fe-2S] centers (Fig. 6c). Proteins containing [4Fe-4S] centers, which are sometimes called HIPIP, essentially act as electron carriers in the photoinduced cyclic electron transfer of purple bacteria (106), although they have also been discovered in nonphotosynthetic bacteria (107). Their EPR spectrum exhibits an axial shape that varies little from one protein to another with g// 2.11-2.14 and gi 2.03-2.04 (106-108), plus extra features indicative of some heterogeneous characteristics (Pig. 6d). 

Andrews KM, Cramer RD. Toward general methods of targeted library design topomer shape similarity searching with diverse structures as queries. / Med Chem 2000 43 1723-40. 

Molecular similarity has also been used directly to model toxicity. Bartlett et al. [63] found that the incidence of cutaneous rash from oral penicillins was a function of shape similarity to benzylpenicillin, and Basak et al. [64] used molecular similarity to model the mutagenicity of aromatic and heteroaromatic amines. 

The latter method, the template method, involves a reaction to produce a transition state similar to the desired product using a template. The template should have a shape similar to the space of the product. The template interacts with the substrate by forming noncovalent bonds such as coordination bonds (Fig. 3). The representative and most successful examples are found in crown ether chemistry. In the chemistry, alkali metals act as templates to create a crown-ether-like transition state with an ethylene glycol substrate by using metal-oxygen coordination bonds. 

Permeability-pH profiles, log Pe - pH curves in arhficial membrane models (log Pjpp - pH in cehular models), generally have sigmoidal shape, similar to that of log Dod - pH cf. Fig. 3.1). However, one feature is unique to permeabihty profiles the upper horizontal part of the sigmoidal curves may be verhcally depressed, due to the drug transport resistance arising from the aqueous boundary layer (ABL) adjacent to the two sides of the membrane barrier. Hence, the true membrane contribution to transport may be obscured when water is the rate-limiting resistance to transport. This is especially true if sparingly soluble molecules are considered and if the solutions on either or both sides of the membrane barrier are poorly stirred (often a problem with 96-well microhter plate formats). 

Mezey, P.G. (1995) Methods of molecular shape-similarity analysis and topological shape design. 

Cellular fossils can be studied under the microscope, and more recently, laser Raman spectroscopy has been used (see below). The platelets often show cells with sizes, shapes, cell structure and colony shapes similar to those of today s microorganisms. These properties could not have survived if the rocks had been heated to temperatures above 420 K, and the fossils also would not have withstood high pressures. 

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