Torsion angle: omega.

[electronicsbyjulie]

This is the angle of the peptide bond, normally stuck in the trans position but typically distorted by steric effects from other atoms in the strand.

From https://en.wikipedia.org/wiki/Pi_helix:

The general formula for the rotation angle Ω per residue of any polypeptide helix with trans isomers is given by the equation

So the function in the Protein class that creates helices should make use of the above equation to rotate the omega bond according to the specified phi and psi angles. This can be done by applying a rotation to the whole amino acids, about the axis of the omega bond, without having to rotate any bonds within any amino acid.

[electronicsbyjulie]

Because the equation image in the original post looks like &$%# in dark mode.

[electronicsbyjulie]

The formula gives incorrect results:

float omega(float phi, float psi)
{
	float f = (phi+psi)/2;
	f = pow(cos(f), 2)*4;
	f = (1.0-f)/3;
	float g = acos(f);
	return g;
}

Omega for alpha helix: 99.3832 degrees. ❌
Omega for beta sheet: 171.839 degrees.
Omega for 3.10 helix: 120.39 degrees.
Omega for pi helix: 87.1885 degrees. ❌
Omega for polyproline II helix: 124.149 degrees.
Omega for polyproline I helix: 113.044 degrees.
Omega for straight strand: 180 degrees.

The alpha and pi helices should have angles near 180 degrees.