Distance geometry cluster analysis

Abstract. A smooth empirical potential is constructed for use in off-lattice protein folding studies. Our potential is a function of the amino acid labels and of the distances between the Ca atoms of a protein. The potential is a sum of smooth surface potential terms that model solvent interactions and of pair potentials that are functions of a distance, with a smooth cutoff at 12 Angstrom. Techniques include the use of a fully automatic and reliable estimator for smooth densities, of cluster analysis to group together amino acid pairs with similar distance distributions, and of quadratic progrmnming to find appropriate weights with which the various terms enter the total potential. For nine small test proteins, the new potential has local minima within 1.3-4.7A of the PDB geometry, with one exception that has an error of S.SA. 

Proceeding with the large-R analysis of the ionization matrix element, (f V i), we find that at large Kr2-X separations it decreases as 1/R r2 x. As a result, the contribution of the two-electron recombination - ionization pathway to the decay width depends on the cluster geometry as l/-R r Kr Kr2-x-Since the decomposition of the (Kr+)2X cluster along the Kr+-Kr+ coordinate automatically means elongation of the Kr2-X distance as well, the power law exponents are effectively summed, resulting in the l/R Kr dependence. A detailed analysis shows that this type of power law is characteristic of all the possible decay pathways. 

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