Coarse-grained elastic network models have been successful in determining functionally relevant collective motions. The level of coarse-graining, however, has usually focused on the level of one point per residue. In this work, we compare the applicability of elastic network models over a broader range of representational scales. We apply normal mode analysis for multiple scales on a highresolution protein data set using various cutoff radii to define the residues considered to be interacting, or the extent of cooperativity of their motions. These scales include the residue-, atomic-, proton-, and explicit solvent-levels. Interestingly, atomic, proton, and explicit solvent level calculations all provide similar results at the same cutoff value, with the computed mean-square fluctuations showing only a slightly higher correlation (0.61) with the experimental temperature factors from crystallography than the results of the residue-level coarse-graining. The qualitative behavior of each level of coarse graining is similar at different cutoff values. The correlations between these fluctuations and the number of internal contacts improve with increased cutoff values. Our results demonstrate that atomic level elastic network models provide an improved representation for the collective motions of proteins compared to the coarse-grained models.

SynopsisThe Pace-Datyner theory for diffusion of penetrant molecules in polymers has been analyzed. I t has been found that the correct solution of the problem they pose is possible only at 0 K, since then the separation of two chains at x = m is equal to the minimum of the DiBenedetto potential for their interaction. Otherwise the energy of symmetrical separation is infinite. By using the linearization method to solve the differential equation, Pace and Datyner neglected the problem of unnatural boundary conditions at x = 00 for temperatures above 0 K. The exact numerical solutions of differential equations at temperature 0 K were therefore compared with the results of the Pace-Datyner linear approximation. For temperatures different from 0 K the solution of the problem is possible only when the proper cutoff is imposed. The analytical expression for the coefficients in the DiBenedetto potential has been found, and the potential can be written as

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Three types of reactants were used to introduce cross-links into the starch-ether polymers, specifically hexamethylene diisocyanate, a hydridosilane, and a silanol-terminated oligosiloxane. The resulting cross-linked starch-ether films in the dry state were extremely brittle (as they are in their un-cross-linked states), with glass transition temperatures between 30 and 40 °C. The desired chain orientations were therefore carried out in the swollen state, with an externally applied mechanical force, focusing on the diisocyanate-cured triethylamylose films. The solvents were removed from these materials while they were in the stretched state, either uniaxial or biaxial, and the improvements in the mechanical properties thus achieved were determined as a function of this stretch ratio. It was found that the tensile strengths, tensile moduli, and elongations at break increased monotonically and frequently dramatically with increase in orientation, as gauged by this ratio. In addition, two solvent-removal processes were investigated, drying in air and coagulation in a suitable nonsolvent. Films obtained from the coagulation processes showed smaller improvements in mechanical properties and rougher surfaces than those obtained by air-drying.