Models for the 3₁₀‐helix/coil, π‐helix/coil, and α‐helix/3₁₀‐helix/coil transitions in isolated peptides

Models for the 3(10)-helix/coil and pi-helix/coil equilibria have been derived. The theory is based on classifying residues into 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. The models for alpha-helix formation and 3(10)-helix formation have also been combined to describe a three-state equilibrium in which alpha-helical, 3(10)-helical, and coil conformations are populated. The results are compared with the modified Lifson-Roig theory for the alpha-helix/coil equilibrium. The comparison accounts for the experimental observations that 3(10)-helices tend to be short and pi-helices are not favored for any length. This work may provide a framework for quantitatively rationalizing experimental work on isolated 3(10)-helices and mixed 3(10)-/alpha-helices.