Free Energy Determinants of Secondary Structure Formation: I. α-Helices

The Zimm-Bragg parameters s and sigma are calculated for the helix-coil transition of poly-L-alanine. The theoretical approach involves evaluating gas phase conformational energies for both coil and helical states using the CHARMM potential function and accounting for solvation effects with various continuum solvation models. Conformational free energies are then incorporated into a formalism developed by Go et al. for the calculation of s and sigma. Calculated values for both s and sigma as well as the enthalpy change associated with helix formation are in good agreement with experimental data when the Finite Difference Poisson-Boltzmann (FDPB) method is used to treat solvent effects. The driving force for the helix-coil transition is analyzed in terms of individual free energy components. Hydrogen bond formation is found to contribute little to helix stability because the internal hydrogen bonding energy is largely canceled by the large free energy cost associated with removing polar groups from water. The entropic cost associated with fixing backbone dihedral angles in the helical conformation is found to be approximately 7 e.u./residue (about 2 kcal/mol at room temperature). The major driving force favoring helix formation can be associated with interactions including enhanced van der Waals interactions in the close-packed helix conformation and the hydrophobic effect. These contribute about 2 kcal/mol favoring the helical state. The differences in helical propensities between alanine and glycine are attributed primarily to hydrophobic and packing interactions involving the C beta with a smaller contribution arising from increased conformational freedom for glycine in the coil state. The description of helix formation presented here is consistent with previous conclusions regarding tertiary structure formation which suggest that hydrophobic and close-packed interactions provide stability while hydrogen bond formation constitutes a structural constraint imposed by the high free energy cost associated with burying unsatisfied hydrogen bonding groups. alpha-Helix formation may thus be viewed as a form of hydrophobic collapse constrained by the requirement that polar groups be either exposed to solvent or form hydrogen bonds. More generally it appears from this study that for a folding model to be a realistic, it must properly account for the chemical nature of the polypeptide chain, particularly the solvation energetics of amide groups.