Fig. 1: Exo-helical symmetries of the α-helix defined by amino acid periodical repetition patterns.

A Helical wheel with Ω = 100°. Exo-helical rotational angles (χ) for the first 18 repetition patterns (i, i + x) are shown. P exo-helices in shades of red on the right half of the wheel and M exo-helices in shades of blue on the left wheel side. B Representation of the helical symmetries for the α-helix first 18 residues in a χ vs. Δ plot. C Side view of the exo-helices generated by the first seven repetition patterns (x = 1–7 for (i, i + x)). Helical types are displayed for all cases together with the calculated P, Δ, and number of units per helical turn (N). The first repetition pattern (i, i + 1) describes an exo-helix (dark red) with the same structural parameters as the α-helix. For (i, i + 2) pattern, the pattern helix is shown in light blue and as a double (i, i + 4) helix in dark brown. Exo-helices are expressed by the formula ±R/T, where (±) defines the right (+, P) or left (−, M) helical sense. R indicates the total number of helical monomer repeats per turn, and T the total number of turns.