Addition of side-chain interactions to 3(10)-helix/coil and alpha-helix/3(10)-helix/coil theory

An increasing number of experimental and theoretical studies have demonstrated the importance of the 3(10)-helix/ alpha-helix/coil equilibrium for the structure and folding of peptides and proteins. One way to perturb this equilibrium is to introduce side-chain interactions that stabilize or destabilize one helix. For example, an attractive i, i + 4 interaction, present only in the alpha-helix, will favor the alpha-helix over 3(10), while an i, i + 4 repulsion will favor the 3(10)-helix over alpha. To quantify the 3(10)/alpha/coil equilibrium, it is essential to use a helix/coil theory that considers the stability of every possible conformation of a peptide. We have previously developed models for the 3(10)-helix/coil and 3(10)-helix/alpha-helix/ coil equilibria. Here we extend this work by adding i, i + 3 and i, i + 4 side-chain interaction energies to the models. The theory is based on classifying residues into alpha-helical, 3(10)-helical, or nonhelical (coil) conformations. Statistical weights are assigned to residues in a helical conformation with an associated helical hydrogen bond, a helical conformation with no hydrogen bond, an N-cap position, a C-cap position, or the reference coil conformation plus i, i + 3 and i, i + 4 side-chain interactions. This work may provide a framework for quantitatively rationalizing experimental work on isolated 3(10)-helices and mixed 3(10)-/alpha-helices and for predicting the locations and stabilities of these structures in peptides and proteins. We conclude that strong i, i + 4 side-chain interactions favor alpha-helix formation, while the 3(10)-helix population is maximized when weaker i, i + 4 side-chain interactions are present.