Conformation average

The tetraoxahydrospirophosphorane (57) has been isolated in 66% yield from the reaction of (55) with triethylammonium perfluor-opinacolate (56). Hexafluoroacetone inserts into the P-H bond of (57) to form (58) which may also be obtained from (59) as shown1 1. The 1H and 19F n.m.r. spectra of the phosphoranes reveal rapid pseudorotational processes and a time-averaged conformation of a flattened chair for the six-membered rings. 

Mezey, P.G. (1998) Averaged Electron Densities for averaged conformations, J. Comput. Chem., 19 1337. 

The potential of mean torque, parameterized by the local interaction tensors Xa and Xc (assume to be cylindrical) for the aromatic core and the C C segment, respectively, can be mapped out at each temperature by fitting the observed quadrupolar splittings in the mesophase. Furthermore, the order matrix of an average conformer of the molecule can also be calculated.17 Now pn is needed to describe the internal dynamics. 

This is supported by our data obtained for TGF-fi3 dynamics in solution [14], according to which the average conformation of the TGF-fi3 dimer is less extended than its conformation in crystal [51], as evidenced by the... 

Limited, X-ray diffraction evidence suggested that the chain is a 2(1.52) helix, with an uncoordinated variation about this average conformation. As the projected height of the trisaccharide repeat-unit is 1.52 nm, the average advance per saccharide is 0.507 nm, similar to that in cellulose and D-mannan. 

Any discussion of the conformation-dependent properties of macromolecular solutions must start with a consideration of the physical parameters required for quantitative description of the average conformation of the solute molecule in solution. As shown below, three parameters, N, s, and a, are necessary and sufficient for helix-forming homopolypeptides. Here N is the degree of polymerization of the polypeptide molecule, and s and tr have the meanings described in Chapter B. 

The average conformation of an a-helix-forming polypeptide was formulated first by Zimm and Bragg (4) and then by several authors (5-9). A comprehensive survey of these theories can be found in a book by Poland and Scheraga 10) or in our companion review article (//). In this section, we outline the formulation of Nagai (5). For convenience of presentation, a peptide residue (-CO-HC R-NH-) is called helix unit when distorted to the a-helical conformation, while it is called random-coil unit when allowed to rotate about the bonds C C and C -N. These units are designated h and c. Thus a particular conformation of an a-helix-forming polypeptide chain is represented by a sequence of h and c. 

From the above discussion it is clear that the average conformation of a polypeptide in solution depends on both the chain length N and the co-operativity parameter a, even if the helical fraction is fixed. In particular, it has been shown that, when compared at the same fN and N, the average number of helical sequences, gN, becomes smaller as a is lowered. Thus for fixed fN and N there exist a variety of different interrupted helical conformations, depending on the magnitude of a. Figure 4 illustrates two typical examples of such conformations. This theoretical prediction makes a study of the conformation-dependent properties of synthetic polypeptides rather inviting. 

In Chapter B it has been shown that, if the restrictions that N> 1, a112 < 1, and No112 > 2 are imposed, very useful approximate expressions can be derived for the quantities characterizing the average conformation of a polypeptide molecule. Teramoto et al. (i4) have simplified Nagai s expressions for by imposing the same restrictions. Their results read... 

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