On the Helix-Coil Equilibrium in Polypeptides

The Zimm—Bragg model for helix-coil transitions in polypeptides is discussed. An exact general form for the partition function is derived by Ising's method. Approximations for long chains lead to simple equations describing the transition in the critical region. These are compared for the cases where the minimum size of a nonbonded sequence is one and three residues, respectively, the latter being applicable to α-helical polypeptides. The nature of the helix-coil equilibrium is discussed in terms of the surface representing the populations of molecular states. Fluctuations in degree of bonding are discussed, and shown to be related to the sharpness of the transition. Some experimental data on polypeptides are compared with the theory, and yield values for the heat and entropy of helix formation per mole of residues.