Alpha shapes

Edelsbrunner, H. and Mucke, E. (1994) Three dimensional alpha shapes. ACM Trans. Graphics 13, 43-72. 

The influence of atoms other than carbons in a sp3 hybrid state on the molecular shape is accounted for by the Kappa alpha shape indices. They can be obtained by modifying each a and mp, in Equation 5.19 to Equation 5.22, with a value ... 

Communication of text and graphics files between computers using World-Wide-Webb (WWW) servers. UNIX, PC, and Macintosh versions available via NCSA anonymous ftp from ftp.ncsa.uiuc.edu (141.142.20.50). Alternative anonymous ftp sources for Mosaic include sunsite.unc.edu (all versions), ftp.sunet.se (all versions), and ftp.Iuth.se (Macintosh version). Alvis (Alpha Shape Visualizer) for construction and rendering of objects from x,y,z coordinates in 3D space. Poly view for graphics rendering. Silicon Graphics. 

Another acceptable QSAR was obtained between the Ae. aegypti larvae and a series of trisipara-substituted-phenyl)tins. The toxicity of the compounds correlated well with the kappa shape index (kl) and the kappa alpha shape index (ka2), which is a modified version of the kappa shape index. Both of these indices are attributes related to the molecular shape encoded in the molecule." ... 

Liang, J., Edelsbrunner, H., Fu, E, Sudhakar, P. V, and Subramaniam, S., Analytical shape computation of macromolecules. 1. Molecular area and volume through alpha shape. Proteins 33,1 (1998). 

Alpha shapes General geometry package usable to analyse packing and accessibility http // alpha.geomagic.com/ alpha/ NCSA, H. Edelsbrunner ... 

Alpha Shape Visualizer for construction and rendering of objects from x,y,z coordinates in 3D space. Polyview for graphics rendering. Available via anonymous ftp from ftp.ncsa.uiuc.edu (141.142.20.50). Silicon Graphics. 

As with the molecular connectivity indices, higher-order shape indices have also been defined. The kappa indices themselves do not include any information about the identity of the atoms. This is the role of the kappa-alpha indices. Tlie alpha value for each atom is a measure of its size relative to some standard (chosen to be the sp -hybridised carbon) ... 

Because of the high rate of emission of alpha particles and the element being specifically absorbed on bone the surface and collected in the liver, plutonium, as well as all of the other transuranium elements except neptunium, are radiological poisons and must be handled with very special equipment and precautions. Plutonium is a very dangerous radiological hazard. Precautions must also be taken to prevent the unintentional formulation of a critical mass. Plutonium in liquid solution is more likely to become critical than solid plutonium. The shape of the mass must also be considered where criticality is concerned. 

Platelets adherent to collagen change shape and spread out on the subendothelium. They release the contents of their storage granules (the dense granules and the alpha granules) secretion is also stimulated by thrombin. 

Dazhu Y, Yongjun Z, Mobius S. 1991. Rapid method for alpha counting with extractive scintillator and pulse shape analysis. J Radioanal Nucl Chem 147(1) 177-189. 

Normal hemoglobin molecules are complex, three-dimensional structures consisting of four chains of amino acids known as polypeptide chains. Two of these chains are known as alpha subunits with 141 amino acid residues each, and the remaining polypeptide chains are the beta subunits with 146 amino acid residues each. The sequences of amino acids in the alpha and beta subunits are different, but fold up via noncovalent interactions to form similar three-dimensional structures. When a polypeptide chain arranges itself in space, i.e., when it folds, amino acids that were far apart in the chain are brought closer in proximity. The final overall shape of the protein molecule is influenced by (1) the amino acids in the chain, and (2) the interactions that are possible between distant amino acids. 

The indicators were not tested for their suitability for taxometric analyses, but the authors reported that the composite was reasonably reliable (alpha =. 76). Whisman and Pinto performed a MAMBAC analysis, and both curves had a clear peak (although it was substantially shifted to the right), indicating a taxon with the base rate of about. 25. The actual base rate estimate was. 44, but the inconsistency between the shape and the estimate was probably due to high nuisance correlations. The authors, however, concluded that the inconsistency indicated dimensionality and did not pursue the issue further. It appears that this conclusion is mistaken. Although the plots are somewhat ambiguous, and there are only two of them, no firm inference can be drawn from this study. 

The hydrolysis curves for the three alpha amylases considered in this review are all similar in shape. They show a rapid hydrolysis in the early stages with a slow secondary stage of hydrolysis which cannot be explained as due either to inactivation of the enzymes or to the influence of products formed during the hydrolysis. The extent of the hydrolysis and the position of the break in the hydrolysis curve depend upon the concentration of enzyme the break in the hydrolysis curve does not appear to be a fixed point characteristic of any one enzyme. With each of the alpha amylases discussed here the slowing down of the hydrolysis appears to be due largely to the replacement of the original substrate by products for which the amylase has relatively low affinity. 

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