Coil model

In addition to an array of experimental methods, we also consider a more diverse assortment of polymeric systems than has been true in other chapters. Besides synthetic polymer solutions, we also consider aqueous protein solutions. The former polymers are well represented by the random coil model the latter are approximated by rigid ellipsoids or spheres. For random coils changes in the goodness of the solvent affects coil dimensions. For aqueous proteins the solvent-solute interaction results in various degrees of hydration, which also changes the size of the molecules. Hence the methods we discuss are all potential sources of information about these interactions between polymers and their solvent environments. 

Peterlin168 has shown that the viscometric data for potato amylose acetate in chloroform solution can be readily interpreted in terms of a random-coil model for the molecule, in which there is hindered rotation at the oxygen atom of the glucosidic linkage. 

Hadley, E. B. Geltman, S. H. An antiparallel a-helical coiled-coil model system for rapid assessment of side-chain recognition at the hydrophobic interface. J. Am. Chem. Soc. 2006,128,16444-16445. 

Polymeric solids such as polystyrene are most often noncrystalline. The random coil model would be most appropriate to describe such solids. In many polymers, both crystalline and amorphous regions are present in such materials, well-defined coiled regions are embedded in a randomly coiled matrix. 

Current investigations on dilute polymer solutions are still largely limited to the class of macromolecular solutes that assume randomly coiled conformation. It is therefore natural that there should be a growing interest in expanding the scope of polymer solution study to macromolecular solutes whose conformations cannot be described by the conventional random-coil model. The present paper aims at describing one of the recent studies made under such impetus. It deals with a nonrandom-coil conformation usually referred to as interrupted helix or partial helix. This conformation is a hybrid of random-coil and helix precisely, a linear alternation of randomly coiled and helical sequences of repeat units. It has become available for experimental studies through the discovery of helix-coil transition phenomena in synthetic polypeptides. 

Hoffman (37) has offered a variety of circumstantial evidence supporting the random coil model. In A-B block copolymers of styrene and butadiene, for instance, the characteristic dimension of the dispersed phase particles depends on the molecular weight of blocks in the dispersed phase according to ... 

Aharoni has stated that the observed rates of crystallization in polymers are inconsistent with the times required for random-coil molecules to separate themselves from the melt, and claims this as support for the collapsed coil model (43). No numerical comparisons are given, and it is difficult therefore to judge the basis for his assertion. 

More quantitative chemical evidence for random coil configuration comes from cyclization equilibria in chain molecules (49). According to the random coil model there must be a very definite relationship among the concentrations of x-mer rings in an equilibrated system, since the cyclization equilibrium constant Kx should depend on configurational entropy and therefore on equilibrium chain and ring dimensions. Values of /Af deduced from experimental values on Kx for polydimethylsiloxane, both in bulk and in concentrated solution, agree very well with unperturbed dimensions deduced from dilute solution measurements(49). 

From the point of view that the statistically coiled model chain is built up of rigid rods (random links), it seems that eq. (5.10) must be truncated, as eq. (5.11a). 

What follows are selected applications of frequently employed biophysical approaches to characterization of coiled coils. Thus, although different coiled-coil models, either native or de novo designed, may require varying techniques and/or technique conditions specific to the coiled coil for full characterization, the principles and usefulness of these approaches are made clear. 

In Fig. 23, d is plotted against MB, the molecular weight of dimethylsiloxane blocks, for various dispersions. As can be seen, above MB = 10 x 103 d falls between the two limiting lines corresponding to the fully stretched chain model and the random coil model, while below MB = 10 x 103, 6 is closer to the former model than to the latter. 

Fig. 7. Schematic diagram of the canine femoral artery copper coil model of thrombolysis. A thrombogenic copper coil is advanced to either femoral artery via the left carotid artery. By virtue of the favorable anatomical angles of attachment, a hollow polyurethane catheter advanced down the left carotid artery nearly always enters the descending aorta, and with further advancement, into either femoral artery without fluoroscopic guidance. A flexible, Teflon-coated guidewire is then inserted through the hollow catheter and the latter is removed. A copper coil is then slipped over the guidewire and advanced to the femoral artery (see inset). Femoral artery flow velocity is measured directly and continuously with a Doppler flow probe placed just proximal to the thrombogenic coil and distal to a prominent sidebranch, which is left patent to dissipate any dead space between the coil and the next proximal sidebranch. Femoral artery blood flow declines progressively to total occlusion over the next 10-12 mm after coil insertion.

Matlab computer codes for the helix-coil model are given below. First, we introduce a function that computes and returns the vector [1, v, v, u2] M, given the inputs v, w, and k ... 

An important feature of the diffraction pattern predicted by these models is the occurrence of a series of meridional reflections which are orders of a 10.33 A periodicity. This periodicity is associated with the axial projection of the asymmetric unit, which consists of seven residues. Astbury and Bell (1939) had noted such a periodicity in a-keratin and given spacings for the first four orders, whereas a spacing of 1.49 A, close to the seventh order, had been noted by MacArthur (1943). More recently, meridional scatter in the vicinity of the fifth, ninth, and eleventh orders has been reported (Fraser and MacRae, 1961b). In a field where structural models had been considered plausible if they predicted one reflection the suggestion of the coiled-coil models was thus a very significant advance. 

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