Rubin chain

Panels c and d illustrate the sequence of residual spectral densities fff, which clearly tend towards an Ohmic spectral density (with cut-off) as the order of the effective-mode decomposition increases. The cutoff frequency (Or has to be larger than any frequency of interest (i.e., J (o) 0 for m > cor) here, we have chosen (Or = 4,000cm . The quasi-Ohmlc spectral density towards which the successive TJf s converge coincides with the spectral density generated by the Rubin chain model [12,34,39] with mode frequency fitR/v. The convergence of the sequence towards the Rubin limit follows from the limiting behavior —> 2 that can be... 

Fu, H., Sadis, S., Rubin, D. M., Glickman, M., van Nocker, S., Finley, D., and Vierstra, R. D. Multiubiquitin chain binding and protein degradation are mediated by distinct domains within the 26 S proteasome subunit Mcbl./. Biol. Chem. 1998, 273, 1970-1981. 

Komuniecki R, McCrury J, Thissen J, Rubin N (1989) Electron-transfer flavoprotein from anaerobic Ascaris suum mitochondria and its role in NADH-dependent 2-methyl branched-chain enoyl-CoA reduction. Biochim Biophys Acta 975 127-131 Komuniecki R, Harris BG (1995) Carbohydrate and energy metabolism in helminths. In Marr JJ, Muller M (eds) Biochemistry and molecular biology of parasites. Academic, London, pp 49-66... 

The work of DiMarzio and Rubin (DiMarzio, 1965 Rubin, 1965 DiMarzio and Rubin, 1971) began the development of a related but more powerful approach. Rather than calculating microstructural details from a presumed architecture, Rubin s matrix method concentrates on the effect of local interactions on the propagation of the chain, thereby deriving the statistical properties of the random walk and the structure of the entire chain. This formalism is the foundation for several subsequent models, so some details are reviewed here. The notation is transposed into a form consistent with the contemporary models discussed below. 

DiMarzio and Rubin s predictions (Rubin, 1965 DiMarzio and Rubin, 1971) confirm earlier results (Hoeve et al., 1965 Silberberg, 1967 Roe, 1965, 1966) and provide new ones. The entropy per segment is zero for xs < Xso but decreases considerably as chains lose configurational freedom upon adsorption for Xs > Xsc- The force between surfaces is monotonically repulsive for Xs < Xsc and increases as xs decreases. For Xs > Xsc. monotonic attraction is predicted, although its strength at fixed separation passes through a maximum and then falls as Xs increases. These predictions, however, do not allow for exchange of polymer with the bulk solution. 

Consequently, a third segment (two steps from the first) may occasionally take the same position as the first segment. For Isolated molecules near a surface, steps towards or within the surface layer are biased with a weighting factor exp( ), all other steps are random, l.e., their weighting factor is unity. Since the DlMarzlo-Rubin single-chain model forms the basis of more sophisticated theories, we return to it in sec. 5.5a. 

In recent years a number of authors have reported the specific enzymatic cleavage of the cross-links in collagen (Barkin and Oneson, 1961 High-berger, 1961b Kiihn et al., 1961 Nishihara, 1962 Schmitt, 1963 Kiihn et al., 1963a Rubin et al., 1963 Hafter and Hermann, 1963). The enzymes used include pepsin, ficin, trypsin, and unpurified pancreas extracts of these pepsin is the most effective. As pepsin has no esterase or other nonproteolytic activity it appears that the cross-links include, even if they are not entirely, sections of peptide chains. 

Involvement of esters in the intermolecular cross-links accounts for the dissolution of mature collagen by hydroxylamine, hydrazine or alkali in the presence of hydrogen-bond breakers. Similarly, the participation of hexoses accounts for the dissolution of collagen by periodic acid and a hydrogen-bond breaker. Recently, it has been shown that collagen can be completely dissolved by some proteolytic enzymes (see Section II). These enzymes also cleave the intramolecular cross-links (Kiihn et al, 1963a Rubin et al., 1963). It appears therefore that either the crosslinks include a peptide chain or the chain close to the cross-links contains pepsin- and trypsin-sensitive bonds. 

Any disturbance from secular equilibrium decays back toward secular equilibrium through the decay of the shorter-lived supported chains. If the chains have significantly different decay rates, they are reasonably well decoupled and can be used to date processes comparable to the lifetimes of each chain (e.g., Condomines et al., 1988 Rubin et al., 1994 Thompson et al., 2003). As a useful rule of thumb, the time taken for a parent-daughter pair to return to approximate secular equilibrium, is about five half-lives of the shorter lived nuclide. In five half-lives, —97% of initial disequilibrium has decayed. Whether any detectable disequilibrium actually remains depends on the precision of measurements and degree of initial disequilibrium. 

In this chapter, we discuss the rheological properties of main-chain nematic LCPs. Rheological data for side-chain nematics can be found in Zentel and Wu (1986), Gu et al. (1993), Colby et al. (1993), Kannan et al. (1993, 1994), and Rubin et al. (1995). Other, excellent... 

Gelman A, Rubin DB. Markov chain Monte Carlo methods in biostatistics. Stat Meth Med Res 1996 5 339-55. 

A more objective method is to investigate the Gelman-Rubin diagnostics for chain convergence. This procedure is automated within WinBUGS. This method compares the between-chains and within-chain variability in a similar spirit to an analysis of variance. Samples are required from at least two chains that are started... 

Rubin, J., Brennan, T., and Sundaralingam, M. (1972) Crystal and molecular structure of a naturally occurring dinucleoside monophosphate. Uridylyl-(3 -5 )-adenosine hemihydrate. Conformational rigidity of the nucleotide unit and models for polynucleotide chain folding, Biochem. 11, 3112-3128. 

Komuniecki, R., Campbell, T. and Rubin, N. (1987) Anaerobic metabolism in Ascaris suum acyl CoA intermediates in isolated mitochondria synthesizing 2-methyl branched-chain fatty acids. Mol. Biochem. Parasitol. 24 147-154. 

S. Laureti, F. Forini, A. Cosentino et al. (2000). Autoantibodies against recombinant human steroidogenic enzymes 21-hydroxylase, side-chain cleavage and 17a-hydroxylase in Addison s disease and autoimmune polyendocrine syndrome type 111. Ear. J. Endocrinol. 142, 187-194. Simpson, E.R., C. Clyne, G. Rubin, W.C. Boon,... 

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