Loop length distribution

In this section we give a selection of theoretical and experimental results for homopolymer adsorption. For a meaningful comparison between theory and experiment it is mandatory that the experimental system Is well defined, with as many parameters known as possible (chain length and chain-length distribution, solvency, adsorbent properties, etc.). Wherever feasible, we shall discuss theoretical predictions In combination with experimental data. However, this correspondence cannot be malnteiined in all cases there are useful theoretical predictions that, as yet, cannot be checked experimentally (for example, the relative contributions of loops and tails), whereas for some measurable quantities no quantitative theory has yet been developed (for example, most kinetic data). 

For each set of loops, all examples were extracted from the Brookhaven Data Bank [7] and characterized according to loop length, 0, y/ conformation, sequence and structural superposition. The distribution of loop lengths (Figure 15.4) shows that nearly 70% have five or less residues. The loops that form structural families are indicated by shading in Figure 15.4 and summarized in Table 15.2. As expected, the families occur in the very short loops, where the number of possible conformations is small. These families are described in detail by Thornton and coworkers [22], and here we present just one family from each supersecondary group, as an example of the sorts of pattern observed. 

The best method of modelling this behaviour is using a model called diagonal quasi-independence, and corresponds to a probability mixture model in which with probability a, the loops lengths are constrained to be the same, and with probability (1-a), they are independent. This method gives the relationship shown below, where Nik is the predicted count with first loop length i and third loop length k, (3 - and (3y are the two independent distributions. 

The partition function for the loop part of the amorphous fraction is obtained by integrating over all possible distributions of individual loop lengths... 

The interdiffusion of polymer chains occurs by two basic processes. When the joint is first made chain loops between entanglements cross the interface but this motion is restricted by the entanglements and independent of molecular weight. Whole chains also start to cross the interface by reptation, but this is a rather slower process and requires that the diffusion of the chain across the interface is led by a chain end. The initial rate of this process is thus strongly influenced by the distribution of the chain ends close to the interface. Although these diffusion processes are fairly well understood, it is clear from the discussion above on immiscible polymers that the relationships between the failure stress of the interface and the interface structure are less understood. The most common assumptions used have been that the interface can bear a stress that is either proportional to the length of chain that has reptated across the interface or proportional to some measure of the density of cross interface entanglements or loops. Each of these criteria can be used with the micro-mechanical models but it is unclear which, if either, assumption is correct. 

Most devices are designed for a constant potential and, as a result, power is usually distributed to loads at constant potential. Two possible configurations for delivering a constant potential to multiple loads are illustrated in Figure 2-73. In the parallel circuit, the potential across the load decreases as the distance from the source increases. For the loop circuit, potentials are more nearly equal along the length of the circuit. 

At this point a third intermediate approach deserves mentioning. It is due to Allegra [43] who proposed that polymer crystallization is controlled by a metastable equilibrium distribution of intramolecular clusters, the so-called bundles , forming in the liquid phase. These subsequently aggregate to the side surfaces of the crystals, driven by van der Waals interactions. The lamellar thickness is determined by the average contour length of the loops within the bundles. Although the model can... 

The 4TM receptors are pentameric complexes composed of subunits of 420 to 550 amino acids. The subunits exhibit sequence identities from 25 to 75%, with a similar distribution of hydrophobic and hydrophilic domains (Table 3.1). The hydrophilic 210 to 230 amino-acid N-terminal domain is followed by three closely spaced hydrophobic and putative transmembrane domains, then a variable-length intracellular loop, and finally a fourth putative transmembrane region shortly before the C-terminus (Figure 3.1). Of the four candidate transmembrane regions, evidence suggests that TM2 forms an a-helix, while the other hydrophobic regions more likely are folded as (3-sheets. 

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