The Alpha Helix: Geometry, Hydrogen Bonding, and Stability

Pauling's Prediction

The right-handed α-helix was described by Linus Pauling, Robert Corey, and Herman Branson in 1951, before definitive crystallographic verification was available. ^[4] Their approach was model building constrained by the chemical logic established in earlier work: the peptide bond is planar, the bond lengths and angles are fixed, and the only permitted backbone conformation is one in which all amide groups form hydrogen bonds. Working with scale models and applying these constraints, they arrived at a helical geometry with 3.6 residues per turn, a hydrogen bond between the carbonyl oxygen of residue i and the amide NH of residue i+4, and a right-handed sense of rotation. The prediction proved correct in every geometric detail when X-ray crystallography of proteins became adequate to resolve secondary structure elements. The α-helix is one of the great examples in structural biology of model building guided by chemical reasoning reaching a correct answer before experiment could confirm it.

The Geometry of the Alpha Helix

The idealized right-handed α-helix has the following geometric parameters: φ = −57° and ψ = −47° per residue; 3.6 residues per turn; a rise per residue along the helix axis of 1.5 Å; a pitch (the axial distance per full turn) of 5.4 Å; and a helix radius (measured to the Cα atoms) of approximately 2.3 Å. The side chains project outward and slightly downward from the helix axis, accessible to solvent and binding partners. The helix interior is formed entirely by the backbone atoms, which pack with van der Waals contacts between atoms of adjacent turns.

The 3.6-residue periodicity has a consequence that is important for understanding helical peptide function: a residue at position i on a helix faces roughly the same direction as the residue at position i+3 or i+4, because 3.6 residues correspond to approximately one full turn. Residues spaced by 3 to 4 positions in sequence are on the same face of the helix. Residues spaced by 7 positions are on almost exactly the same face, because 7 positions correspond to approximately two turns (7/3.6 = 1.94 turns). This periodicity underlies the design of amphipathic helices, leucine zippers, and coiled coils.

The Hydrogen Bond Pattern

The structural stability of the α-helix is provided by a ladder of backbone hydrogen bonds, each formed between the carbonyl oxygen of residue i and the amide NH of residue i+4. Every residue in the helix interior participates in four hydrogen bonds: as the donor NH in two bonds (with carbonyls at i−4 and i−3) and as the acceptor carbonyl in two bonds (with NHs at i+3 and i+4). Only the first four N-terminal residues and the last four C-terminal residues of a helix lack the full complement of hydrogen bonds, which is why helical propensity measurements typically focus on internal positions and why the ends of helices are conformationally more labile than the interior.

The four-residue cap positions, N1 to N4 at the N-terminus and C1 to C4 at the C-terminus, are partially unsatisfied hydrogen bond donors and acceptors respectively. These unsatisfied groups are frequently compensated by capping interactions with polar side chains or water molecules, and the identities of residues at cap positions significantly influence helix stability. Asparagine, aspartate, serine, and threonine are common N-cap residues that donate hydrogen bonds to the unsatisfied backbone NH groups of the helix N-terminus; glycine is a common C-cap residue.

Helix Propensity by Residue

Not all amino acids stabilize helical conformations equally. The intrinsic helix propensity of each residue, defined as the free energy difference between the helical and coil states in a host-guest model peptide system, varies across the twenty canonical amino acids. Alanine is the strongest helix former among non-ionic residues, with a free energy preference for helix of approximately 0.4 kcal/mol relative to glycine as a reference. ^[5] Leucine, methionine, glutamate, lysine, and arginine are moderate helix formers. Valine and isoleucine, with their β-branched side chains, are weak helix formers because the branching creates steric conflict with the helical backbone geometry. Proline is a helix breaker: it cannot donate an NH hydrogen bond, and the pyrrolidine ring restricts φ to values incompatible with the helical region. Glycine, by virtue of its expanded conformational freedom and lack of a side chain to stabilize the helical conformation through hydrophobic packing, is also a relatively poor helix former.

These propensity differences are real but modest in magnitude, typically less than 1 kcal/mol. They are insufficient on their own to determine whether a given sequence will form a helix in solution; helix formation requires a cooperative accumulation of propensity along the sequence. A helix of twelve residues with average propensity accumulates more stability than any individual residue can provide, and the context of flanking residues, tertiary packing, and electrostatic interactions all contribute to the overall stability. Helix propensity scales are most useful for comparative design decisions, not for absolute prediction of helical content.

Variants: The 3⊂1⊂0 Helix and the π-Helix

Two other helical secondary structures are observed in peptides and proteins, though far less commonly than the α-helix. The 3₁₀-helix forms i to i+3 hydrogen bonds rather than i to i+4, giving it 3.0 residues per turn, a tighter core, and a more elongated appearance. Its (φ, ψ) values of approximately −49° and −26° place it at the edge of the Ramachandran helical region. It is found mainly in short segments of one to two turns at the termini of α-helices and in some isolated short helices. The α-methylated amino acid Aib strongly promotes 3₁₀ helix formation and is a common building block in designed helical peptides.

The π-helix forms i to i+5 hydrogen bonds, giving it 4.4 residues per turn and a wider, flatter structure than the α-helix. It is rare, found in less than 10 percent of proteins and almost exclusively in short segments embedded within α-helices. Its wider core creates a cavity along the helix axis that has been associated with functional roles in specific protein families. The π-helix is sometimes described as an insertion of a single residue into an α-helix, a model supported by comparative analyses of related protein structures.

The Helix Macrodipole and Its Functional Consequences

As established in Article 2.2, the peptide bond carries a substantial dipole moment directed from nitrogen toward oxygen. In an α-helix, all peptide bond dipoles are aligned roughly parallel to the helix axis, creating a cumulative macrodipole with a partial positive charge at the N-terminus and a partial negative charge at the C-terminus. This macrodipole is not merely a geometric curiosity. It influences the binding of charged ligands near the helix termini, stabilizes anionic groups at the N-terminal end and cationic groups at the C-terminal end, and perturbs the pKa values of ionizable residues within approximately four positions of the termini. In enzyme active sites, the strategic placement of helix N-termini creates positive electrostatic environments that stabilize negatively charged transition states and reaction intermediates. In peptide design, helix macrodipoles are accounted for in the placement of charged residues and in the orientation of helices relative to membranes and binding partners.