A hierarchical "nesting" approach to describe the stability of alpha helices with side-chain interactions

A straightforward hierarchical statistical-mechanical approach is shown to enable one to describe the stability of the alpha helix in the presence of side-chain interactions. The formulation can be used with even the simple nearest-neighbor models and it is demonstrated explicitly with the popular 2 x 2 Zimm-Bragg model [B. H. Zimm and J. K. Bragg (1959) J. Chem. Physics 31, 526-535]. It involves a conceptual dissection of the polypeptide chain into interacting blocks; the behavior of any block with side-chain interactions is treated then with conventional binding polynomial techniques. This dissection is a manifestation of "nesting," which is a hierarchical framework for the description of the behavior of complex macromolecules [C. H. Robert, H. Decker, B. Richey, S. J. Gill, and J. Wyman (1987) Proc. Natl. Acad. Sci. 84, 1891-1895]. The method is demonstrated through applications to existing, detailed data for the pH and salt dependences of the helix-coil transition in the S peptide and in synthetic peptides.