Chain stiffness, measure

The measurements of chain stiffness of denatured proteins are made in the presence of a strong denaturant, such as 8 M urea or 6 M GdmCl, in which peptide H-bonds are weak and peptide helices unfold (Scholtz et al., 1995 Smith and Scholtz, 1996), and the possible presence of (/-helices or /3-hairpins is not an issue in these denaturants. The careful and thorough measurements of intrinsic viscosities made by Tanford and co-workers (1968), discussed above, yield a substantially lower estimate for chain stiffness than the work of Flory and co-workers. A comparison is made by Tanford (1968) between the proportionality coefficient... 

The analysis described above is useful for modelling colligative properties but does not address polyelectrolyte conformations. Polyelectrolyte conformations in dilute solution have been calculated using the worm-like chain model [103,104], Here, the polymer conformation is characterized by a persistence length (a measure of the local chain stiffness) [96]. One consequence of the... 

Now at present we have no means of applying a known force to a particular chain and measuring its extension. What can be done is to measure the vibrations of chains in various situations and relate these directly via normal mode analysis, or indirectly via continuum (rod) models to a set of stiffnesses. 

Relaxation curves can be measured by simple NMR experiments. On the other hand, information about cross-link density and chain stiffness can be retrieved by exploiting... 

Note that the Kuhn length is comparable to the persistence length lp, which is an alternative measure of the chain stiffness (see Sect. 3.2). For DNA (more generally, chains with worm-like elasticity), l = 2lp. 

Some examples of stiff-chain polymers able to form a liquid-crystalline phase in the solution are listed in Table l1. The ratio of the statistical segment length1 of a polymer chain, 1, to its width, d, (last column of Table 1) measures the degree of chain stiffness. For flexible macromolecules fid 1 stiff-chain macromolecules are those for which fid t> 1. 

This equation tells us that, since is proportional to the molar salt concentration (see, for example, [3.5.7]), the electrostatic persistence length (or chain stiffness) decreases Inversely proportionally with Increasing salt concentration. In fig. 5.5 we present, as an experimental example, the salt dependence of for DNA, as measured by several techniques. For comparison, the theoretical dependence based on [5.2.24] is also shown. 

The models just discussed apply to chains in an ideal or 0 solvent, in which excluded volume interactions are absent. In practice, solution properties are more often determined in good solvents in which long-range excluded volume interactions lead to an increase in . These long-range interactions increase with M, so that equation lb is no longer valid. Excluded volume interactions and chain stiffness can be difficult to distinguish without measurements in a 0 solvent. 

It is very probable that the energetics favoring the left-handed helix are also effective when the molecule is in solution. These forces, therefore, would also affect the contribution of chain stiffness and form to the optical rotation. The relation between these two phenomena and the conformation revealed by x-rays remains to be explored. A preliminary attempt at relating the conformation of /3-d-(l— 4)-linked polysaccharides to simple conformational concepts in carbohydrate chemistry has focused on the carbon-oxygen bond sequence between the residues (see Fig. 22) that form the well-known molecule methylal. Measurements of dipole moments of methylal show that the conformation shown in Fig. 22A is favored here, the group moments are in partial opposition, and the O-C-4 bond is gauche, relative to C-1-0-5. This is exactly the con-... 

Values of the imperturbed dimension can be obtained experimentally from dilute solution measurements made either directly in a theta solvent (see Chapter 9, Section 9.7) or by using indirect measurements in nonideal solvents and employing an extrapolation procedure. The geometry of each chain allows the calculation of ( and results are expressed either as o or as the characteristic ratio = (r )o/ F. Both provide a measure of chain stiffness in dilute solution. The range of values normally foimd for o is from about 1.5 to 2.5, as shown in Table 10.1. 

The parameter Zo is a measure of chain stiffness. In the statistical segment model, the greater the number of monomers in a segment, the fewer the segments for a given length and the stiffer the chain [16] (Chapter 2.6). 

It can be shown that q is equal to the average projection of R, the end distance vector, of an infinitely long wormlike chain onto the tangent vector at the chain end. Hence, on average, an infinite wormlike chain with a larger q is more extended in the direction of its end tangent vector. This suggests that q can be taken as a measure of chain stiffness. 

Equation 2.15 may be considered to be another definition of the persistence length (note that its original definition is eq 2.2). It states that the persistence length is a measure of chain stiffness associated with bending. Some authors prefer the notation (2A) to q, but we use the latter throughout this book. 

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