Zimm-Bragg theory

The titration curves of the three polypeptides can be analyzed by adapting the Zimm-Bragg theory for the helix-coil transition " to the cooperative binding of the surfactant to the polypeptide, provided that the thermodynamic contribution of any conformational change accompanying the binding is comparatively small and that the electrical potential on the surface of the polypeptide molecule can be regarded to be constant. The theory defines two parameters the equilibrium constant s and an initiator a. If the polypeptide sequence is schematically written as... 

According to the Zimm-Bragg theory, the degree of binding x = Cb/Cp, where Cp is the polypeptide residue concentration, becomes... 

Since the Zimm-Bragg parameters o and s of the naturally occurring amino acids (In water) cannot be obtained from studies of the helix-coil transition in homopolymers, because of experimental difficulties, a technique Is developed to circumvent these problems. It involves the study of the thermally induced transition curves for random copolymers of "guest amino acid residues in a water-soluble host" po y(amino acid). The data may be interpreted with the aid of suitable theories for the helix-coil transition in random copolymers to obtain a and s for the "guest" residues. It is shown in this paper that, for the usual ranges of parameters found for polylamino acids), one of the two lowest order approximations (corresponding to earlier treatments by Lifson and Allegra) is completely adequate. In essence, the low-order approximations hoid if o and s for the two constituents of the copolymer do not differ appreciably from each other. 

Water-soluble random copolymers containing u-phenylalanine and A -O-hydroxypropylR-glutamine are prepared. The thermally induced helix-coil transition in these copolymers in water is studied. The incorporation of (.-phenylalanine is found to increase the helix-content of the host polymer. The Zimm-Bragg parameters cr and s for the helix-coil transition in poly(L-phenylaianine) in water are deduced from an analysis of the melting curves of the copolymers. The values of s, computed from both the Lifson and Allegra theories are (Ufson/Allegra a 0.0018) s 1.056/1.061 (273 K), 1.078/1,086 (293 K), 1.041/1.047 (313 K), 1.000/1.003 (333 K). 

Helical growth (HG) occurs when a sequence of linear steps according to MSOA leads to a critical concentration C at which cooperative helical growth begins (Fig. 2b). Because more bonds per unimer are expected in the helical than in the linear chain, the sudden increase of DP at C > C is described by a constant K] > K and by the familiar Zimm-Bragg cooperativity parameter."." The original theory was developed by Oosawa for the nucleus schematized in Fig. lb and applied to the G- -F transformation of actin. A recent extension by van der Schoot and coworkers,"" applied to helical assemblies of discotic molecules, does not require the specification of the critical nucleus. 

Regarding the theoretical considerations for the possibilities of a reentrant isotropic phase in the polypeptide LC, Lin et al. proposed a theory based on the Flory-Matheson lattice model in which the free energy change for the helix-coil transition has been incorporated into the lattice scheme [80]. Some assumptions were also adopted. First, the molecular cOTiformation in the isotropic phase was considered to be temperature-dependent and follow a modified Zimm-Bragg notion... 

Zimm-Bragg helix-coil theory for N = 4 chain units. 

B. H. Zimm and J. K. Bragg. Theory of phase transition between helix and random coil in polypeptide chains. J. Chem. Phys., 31 (1959) 526-535. 

In considering the cooperative behavior of linear chain molecules consisting of identical monomeric units, a particularly simple situation arises if cooperative interactions occur only between immediately adjacent monomeric units. This corresponds to the linear Ising lattice model [18] which is the basis for the Zimm-Bragg thermodynamic theory of the cooperative helix coil conformational transition of linear polymers [3]. Considering the processes in a simple chain of = 4... 

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. 

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