Theory of the cooperative transition between two ordered conformations of poly(L-proline). I. Phenomenological theory

The states of three residues are correlated in a nearest-neighbor Ising model matrix treatment of a one-dimensional phase transition, in which nucleation is assumed to differ at each end of a regular sequence (asymmetric nucleation). The correlation of the states of three residues requires a 4 X 4 matrix, which cannot be reduced in size because of the asymmetric nature of the nucleation. Also, because of the asymmetry, at least four independent parameters for a homopolymer (rather than the two usually encountered in the helix-coil transition), ant at least five for a specific-sequence copolymer, are required to describe the transition behavior. The most important current interest in such a treatment (for a homopolymer) is its applicability to the poly(L-proline) form I in equilibrium form II interconversion. The earlier treatment of Schwarz, using the nearest-neighbor Ising model (with correlation of only two residues), is identical with the above treatment, and requires only a 2 X 2 matrix which greatly simplifies numerical computations, which are presented in the next two papers of this series. However, the 4 X 4 matrix treatment is required in order to make the asymmetric nature of the nucleation explicit and physically understandable, for a homopolymer; for a specific-sequence copolymer, such as a protein, it is essential in order to show how the asymmetric nature of helix nucleation differs from one amino acid to another.