Zimm and Bragg

Because unidimensional NMR spectra of denatured proteins lack resonance dispersion and resemble spectra of mixtures of free amino acids, it was assumed that the denatured state behaves as a random coil (McDonald and Phillips, 1969). Calculations (Brant et al., 1967 Zimm and Bragg, 1959) and spectroscopic measurements on... 

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. 

The helical fraction has here been defined as the number of helix units present in the chain under consideration relative to the total number of residues in the same chain that can assume a-helical conformation, i.e. N — 2. It should be noted that this way of defining fN differs from that of Zimm and Bragg (4), who adopted the number of hydrogen bonds formed in the chain. The difference, however, becomes important only for short chains. 

Go et al. (1968) have recently shown how the data of Sections IXB and IXD may be used to compute the parameters [e.g. a and s of Zimm and Bragg (1959)] of the helix-coil transition in polyamino acids. Heretofore, it had been necessary to rely on a comparison of the results of the statistical mechanical theory with experimental data in order to obtain these parameters. However, with the aid of the aforementioned calculations of the conformational energies of dipeptides and helices, it has been possible to formulate a theory for computing a and s. It remains to be seen how well the computed values of these parameters agree with those evaluated from experimental data on the melting of polyamino acid helices. 

The theoretical treatment of Zimm and Bragg has also been applied to the shallow thermal transition of poly-L-lysine, in which the variation of helical content as a function of temperature has been obtained from rotatory dispersion measurements (Applequist and Doty, 1961). If one assumes that the parameter o- is the same as for poly-y-benzyl-L-glutamate, it is then possible to obtain the heat per residue for the formation of the helix of poly-L-lysine. The small magnitude of this result, between —50 and —80 cal/mole near pH 10, as compared to the enthalpy of the hydrogen bond estimated... 

Zimm and Bragg showed that the fraction of segments in a helical conformation exhibits a sharp cooperative transition as s is increased, which is equivalent to increasing the interaction energy e or decreasing the temperature. The interaction energy is designed into the system based on the chemical... 

An early term, s-values (Zimm and Bragg, 1959) for these tendencies, is rarely used now. 

Polarimetric (or indeed, any optical) data alone can yield only two thermodynamic parameters describing the thermal transition, Tc and AH. To proceed further, it becomes desirable to use one of the statistical mechanical treatments of one-dimensional cooperative transitions which have been recently formulated to treat this and more generalized problems (S, 15). In the present work we use the theory of Zimm and Bragg (18, 19) and extensions of this by Applequist (2). The theory predicts all the major features of the transition found experimentally in terms of a parameter, <7, which in our nomenclature is given by... 

In order to carry out complete calculations, we employ the simplest form of Zimm and Bragg [56,57]... 

Lehman and McTague have treated both single-molecule and ensemble averaged properties of DNA using the MI model. Their notation follows that of Zimm and Bragg. Since it differs from that previously employed, we give the relationship between the two notations and briefly outline the approach of Lehman and McTague. 

Theoretical prediction and experimental measurement of the thermodynamic stability of a-helix has been one of the central issues in biophysical research. Pioneering work was done by Zimm and Bragg [38] which was then improved by Lifson and Roig [39]. Much work has since been and is currently being done with vigorous use of statistical mechanics, molecular dynamics, and other types of computer simulation. Only a few examples are cited here [40-45]. Since the statistical mechanical treatment of helix stability has been developed primarily on a few... 

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