**Rules for recognition and selection of a helical pair for a peptide fragment**

- Analysis of the secondary structure of the amino acid chain is carried out using the Dictionary for Secondary Structure of Protein. Search for sections of helixes of the following types: α-, 310-, and π- helix.
- A helical pair is a portion of the protein structure that is formed by two helixes adjacent to the polypeptide chain connected by an unstructured fragment (coil) of arbitrary length and configuration.
- The following types of helical pairs are found in proteins: α-α-corner, α-α-hairpin, and V- and L-structures.
- Each helix of a pair can be inscribed in a cylinder. The cylinder axis is determined by the least squares method with the minimum deviation of the helix parameters from the ideal helix.
- Two axes of the helixes determine the spatial structure of the helical pair. The spatial structure of the helical pair is determined by the interplanar distance (d) and the projections of the axes of the helixes on the plane.
- The polygon area (S) of the intersection of the projections of the helixes depends on the relative position of the helixes (geometry) and the diameter of the cylinders of the helixes. The cylinder diameter is determined by the type of helix and the average size of the side chain.

**Distinctive properties of types of helical pairs**

**1. α-α corner**

- dense orthogonal packing of helixes;
- the projections of the helixes and the axis of the helixes intersect;
- the values of the interplanar distance and the minimum distance are equal (d = r);
- the intercoil distance within d ≈ (9-11) Å;
- the area and perimeter of the intersection of the projections of the helixes are larger than the other two- helix motifs;
- torsion θ and flat ϕ inter helix angles have values of 70-110°;
- the length of the waist (Np) is usually 4-5 amino acids.

**2. α-α-hairpin**

- dense antiparallel packing of helixes;
- the projections of the helixes intersect, but the axes of the helixes do not intersect;
- the range of the intercoil distance, d, is wider than that of the α-α corner;
- interhelix angles 0-30°;
- the length of the waist (Np) may vary;
- usually consists of two long helixes.

**3. L-shaped structure**

- dense bevelled packaging of helixes;
- the projections of the helixes and the axes of the helixes do not intersect (S ≈ 0 Å2, P ≈ 0 Å);
- interhelix angle has a value ϕ ≈ 90°;
- The waist length (Np) may vary.

**4. V-shaped structure**

- dense bevelled packaging of helixes;
- the projections of the helixes (most often) and the axes of the helixes do not intersect;
- area, S, and perimeter have values close to zero;
- area, S, and perimeter have values close to zero;
- coil (Np), as a rule, consists of one amino acid;
- length of the helixes, as a rule, does not exceed three to four turns..