Dihedral angle Totally Explained

Everything about Dihedral Angle totally explained

ť In aerospace engineering, the dihedral is the angle between the two wings; see dihedral.

In geometry, the angle between two planes is called their dihedral or torsion angle.

The dihedral angle of two planes can be seen by looking at the planes "edge on", for example, along their line of intersection. The dihedral angle

phi_

(blue). When the fourth atom eclipses the first atom, the dihedral angle is zero; when the atoms are exactly opposite (as in Figure 2), the dihedral angle is 180°.

Dihedral angles of biological molecules

The backbone dihedral angles of proteins are called φ (phi, involving the backbone atoms C'-N-C^α-C'), ψ (psi, involving the backbone atoms N-C^α-C'-N) and ω (omega, involving the backbone atoms C^α-C'-N-C^α). Thus, φ controls the C'-C' distance, ψ controls the N-N distance and ω controls the C^α-C^α distance.
The planarity of the peptide bond usually restricts

omega

to be 180° (the typical trans case) or 0° (the rare cis case). The distance between the C^α atoms in the trans and cis isomers is approximately 3.8 and 2.9 Å, respectively. The cis isomer is mainly observed in Xaa-Pro peptide bonds (where Xaa is any amino acid).
   The sidechain dihedral angles of proteins are denoted as χ₁-χ₅, depending on the distance up the sidechain. The χ₁ dihedral angle is defined by atoms N-C^α-C^β-C^γ, the χ₂ dihedral angle is defined by atoms C^α-C^β-C^γ-C^δ, and so on.
   The sidechain dihedral angles tend to cluster near 180°, 60°, and -60°, which are called the trans, gauche⁺, and gauche^- conformations. The choice of sidechain dihedral angles is affected by the neighbouring backbone and sidechain dihedrals; for example, the gauche⁺ conformation is rarely followed by the gauche⁺ conformation (and vice versa) because of the increased likelihood of atomic collisions.
   Dihedral angles have also been defined by the IUPAC for other molecules, such as the nucleic acids (DNA and RNA) and for polysaccharides.

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