A theoretical study on the origin of cooperativity in the formation of 3(10)- and alpha-helices.

By using a simple repeating unit method, we have conducted a theoretical study which delineates the preferences for beta-strand, 2(7)-ribbon, 3(10)-helix, and alpha-helix formation for a series of polyglycine models up to 14 amino acid residues (Ac-(Gly)(n), n = 0, 1, 2,., 14). Interactions among residues, which result in cooperativity, are clearly indicated by variations in calculated energies of the residues. Whereas no cooperativity is found in the formation of beta-strands and 2(7)-ribbons, there is a significant cooperativity in the formation of 3(10)- and alpha-helices, especially for the latter. In the case of alpha-helices, the 14th residue is more stable than the 3rd by about 3 kcal/mol. A good correlation between calculated residue energy and residue dipole moment was uncovered, indicating the importance of long-range electrostatic interactions to the cooperativity. The results of our calculations are compared with those of the AMBER and PM3 methods, and indicate that both methods, AMBER and PM3, need further development in the cooperative view of electrostatic interactions. The result should be of importance in providing insight into protein folding and formation of helical structures in a variety of polymeric compounds. This also suggests a strategy for the development of more consistent molecular mechanics force fields.