Statistical subunits

To explain the behavior of polymer solutions in the overlapped regime, it is necessary to adopt a picture of the structure of these systems. The chain molecule is represented as a string of m statistical subunits with mean-squared end-to-end vectors R12 The average concentration inside a statistical subunit can be expressed as ... 

As the screening length decreases in a good solvent, the chain dimensions should also decrease until the screening length is comparable to the statistical subunit length. 

The chain is modeled as a system of beads and springs undergoing Brownian motion in a viscous medium. The other polymer chains provide the viscous medium for any individual chain. The inherent dynamics can be represented in terms of N relaxation modes, where N is the number of statistical subunits in the chain. The shear relaxation modulus G(f) is given by ... 

When the ionic strength increases to the point where the Debye length is comparable to the size of a statistical subunit, the polyelectrolyte problem can be approached in the same manner as the normal excluded-volume problem. The limiting form for Equation 10.11 becomes ... 

A complete set of intermolecular potential functions has been developed for use in computer simulations of proteins in their native environment. Parameters have been reported for 25 peptide residues as well as the common neutral and charged terminal groups. The potential functions have the simple Coulomb plus Lennard-Jones form and are compatible with the widely used models for water, TIP4P, TIP3P and SPC. The parameters were obtained and tested primarily in conjunction with Monte Carlo statistical mechanics simulations of 36 pure organic liquids and numerous aqueous solutions of organic ions representative of subunits in the side chains and backbones of proteins... 

The VWA domains in some integrin a subunits are readily apparent from their sequences. Although much functional evidence (reviewed in Loftus and Liddington, 1997) supports a hypothesis that integrin (3 subunits also contain a VWA domain (Lee et al., 1995 Bajt and Loftus, 1994 Tozer et al., 1996 Tuckwell and Humphries, 1997), there has been no statistical evidence for significant sequence similarity. 

The liver enzyme exists in two forms, E and S, which differ only by some six residues in their amino acid sequence.13 Only the S is active toward 3-/3-hydroxysteroids, but both forms are active toward ethanol. None of the known amino acid differences is located in the subunit interfaces. Accordingly, E and S chains combine in statistical ratios to form EE, SS, and ES dimers. These different species are termed isozymes, which means that they are multiple molecular forms of the same enzyme. When it is isolated from liver, the enzyme consists of about 40 to 60% of the EE dimer, the remainder being SS and ES. 

ECB deacylase is an 81-83-kDa heterodimer consisting of 63- and 18-20-kDa subunits. Penicillin G acylase from Escherichia coli is an 87-kDa heterodimer with 65- and 22-kDa subunits [32], For comparison, cephalosporin acylase from a Pseudomonas strain is an 83-kDa heterodimer consisting of 57- and 26-kDa subunits [33], The essential absence of any external catalytic requirement, cofactor stimulation, or product inhibition of ECB deacylase is also an intrinsic property of penicillin acylase [34], Based on the amino-terminal sequences of the two subunits of ECB deacylase, a 48% sequence similarity has been observed between the small subunit of ECB deacylase and a penicillin acylase [25]. This statistically significant albeit moderate sequence similarity from two short segments of the enzymes suggests an evolutionary relationship between ECB deacylase and peni-... 

The structure of a-chitin was refined by using automatic, rigid, subunit, least-squares refinement and the difference-Fourier method. Two distinct types of statistical modification could be present in the structure, both of which would allow complete, intersheet hydrogenbonding between OH-6 groups within the general framework of Carlstrom s structure.56 The R factor is 22%. 

This section of the review of DOM in freshwaters will examine its isolation by XAD resins and by membranes, the molecular weight distribution of DOM, its elemental composition, its acidic functional groups, its distribution of carbon among structural subunits, and the low-molecular-weight molecules (amino acids, sugars, and lignin-derived phenols) that are liberated from DOM by hydrolysis or oxidative degradation. For each of these subtopics, a statistical summary of published data will be presented. 

A statistical summary of more than 82 reintegrated NMR spectra of FAs, HAs, and NOM is given in Figure 7. The results are striking. Freshwater FAs, HAs, and NOM have remarkably similar distributions of carbon among the five structural subunits. For all three materials, organic carbon is distributed in the following order of abundance alkyl > alkoxy— aromatic > carboxyl carbonyl. 

Mahieu et al. (1999) conducted a similar statistical survey of the NMR spectra of several hundred whole soils and soil size fractions, soil-derived HAs and FAs, and aquatic FAs. They used four structural subunits carbonyl— 160-220 ppm aromatic—110-160 ppm O-alkyl—50-110 ppm and alkyl—0-50 ppm. Their carbonyl subunit includes the carbonyl and carboxyl structural subunits used in this review, and their boundary between alkyl and 0-alkyl subunits is 50 ppm, rather than 60 ppm. For the 31 aquatic FAs in that study, the mean percentages of carbonyl, aromatic, O-alkyl, and alkyl carbon were 24%, 21%, 20%, and 35%, respectively. These percentages are very close to the mean values in Figure 7 for FAs in freshwaters (21%, 25%, 23%, and 32%, respectively). The degree to... 

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