Helix-random coil equilibrium

It remains for us to discuss the dimensions of polypeptides and other helix-forming chain molecules. Most of the theoretical works on models of such chains have been primarily concerned with the equilibrium of the helix-random coil transition and have not specifically treated the chain dimensions. An exception is found in the work of Nagai (195 ), who combined his theory of the transition with a very simple model of the chain dimensions. It amounts to the assumption that each helical sequence behaves like a rigid statistical chain element without correlation in direction with the randomly coiled sections which are adjacent to it. Then, if a fraction f of the monomer units are members of helical sequences, we may at once write... 

Chapter E is devoted to the mean-square dipole moment and mean rotational relaxation time derived from dielectric dispersion measurements. Typical data, both in helieogenic solvents and in the helix-coil transition region, are presented and interpreted in terms of existing theories. At thermodynamic equilibrium, helical and randomly coiled sequences in a polypeptide chain are fluctuating from moment to moment about certain averages. These fluctuations involve local interconversions of helix and random-coil residues. Recently, it has been shown that certain mean relaxation times of such local processes can be estimated by dielectric dispersion experiment. Chapter E also discusses the underlying theory of this possibility. 

In a dilute protein solution, the nano length scale or the molecular structure of protein molecules determines the thermodynamic equilibrium between protein-protein and protein-water interactions. The consequent surface and hydrodynamic properties of proteins are resulted from the proportion of hydrophobic, hydrophilic, and charged amino acid residues. For example, caseins could adopt a random coil structure due to their flexible structure as a result of phosphorylated serine residues caseins indeed lack the ordered structures of a-helix, 3-sheet, and 3-turn found in globular proteins. This gives rise to better multifunctionality of caseins over globular proteins. 

For all atoms located within the a helices of hPrP, the resonances show the expected downfield shifts relative to the random coil values, but smaller values of A5( C ) indicate for the C-terminal two turns of each of the helices 2 and 3 that the a-helical structure is in equilibrium with unfolded forms of the polypeptide. This was corroborated by the observation that all amide protons in the hydrogen bonds of the helices 2 and 3 were measurably protected against exchange, except for the residues 187-194 in helix 2, and the residues 225-228 in helix 3 (Zahn et al., 2000). 

Fig. 2. The molecular description which suggested the use ctf the lattice model The random coil has to form a turn of a-helix (A). Favorable intnactions stabilizing the helix occur only when the rotations about six bonds are frozen (B. The tozm rotations are shown with one rf tte bvorable interactions is the NH—OC hydrogen bond, indicated with a dashed line when it occurs.) Subsequent freezing of the rotations about only two bonds will produce the same favorable contacts upon goii from B to C (cf. Pauling and Cor (56% for the stmcture of the a-helix). TIk equilibrium constant for the reaaion coil A is much less than unity, while that for the reactions At B and B C is near unity...

About 75% of hemoglobin is in the form of an a-helix and 25% is a random coil form. Certain amino acid substitutions could shift the equilibrium between the a-helix and the random coil, thereby altering tertiary structure (Chou and Fasman, 1974). One such substitution is proline, which cannot participate in an a-helix (except as one of the first three residues). Hemoglobins Duarte and Madrid have a proline substitution for alanine, while eight other hemoglobins substitute proline for leucine. 

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