Abstract
Analogous with the Potts model that describes the helix‐coil transition in the isolated polypeptide chain (a Hamiltonian model allowing for the energy U of hydrogen bond formation) the number Q of conformational states of a repeating unit of the chain and the topology of Δ = 3 hydrogen bond formation (the hydrogen bond fixing three pairs of φψ chain rotations) has been constructed and the corresponding transfer‐matrix has been obtained. In the thermodynamical limit, the partition function is expressed through the principal root of the cubic equation. The degree of helicity, the transition point and range, the correlation length, the number of junctions between the helical and coiling sections as well as the mean length of helical and coiling sections are calculated. Empirically introduced parameters of the Zimm–Bragg theory, constants of hydrogen bond formation s, and the cooperativity parameter σ as functions of microscopic parameters U, Q, and Δ are obtained by direct calculations. The behavior of this model was investigated at other topologies of the hydrogen‐bond closing Δ = 2 and Δ = 4, and it was suggested that the actual polypeptide chain (Δ = 3) provides the optimum correlation of helical structure of the order of globule dimensions. An expression was obtained for the maximum correlation length of the order ξ ∼ Q^(Δ‐1)/2^. For a System with solvent competing for the formation of hydrogen bonds with peptide groups a Hamiltonian model was constructed that took account of the energy E of the formation of hydrogen bond with the solvent and the number q of orientations of a solvent molecule about the peptide groups. It is shown that by the redefinition of the temperature parameter, the model with solvent reduces to the model of an isolated chain. Aside from the definition relationship that exists between the parameters of the theory U < 2__E__ < U~q~ and the ordinary helix‐coil transitions (“melting”), the model also describes the transition from the coiling state to the helical one (“arrangement”) under heating. The change in temperature and transition range with solvent parameters was discussed and it was shown, that despite the difference in Δ__T__ for the given polypeptide chain (Q = constant) with different solvent parameters, at “melting” and “arrangement,” the transition occurred at the same correlation length (the same cooperativity).