Dihedral angles from coordinates. Get dihedral angles from protein backbone coordinates. Calculate Phi, Psi from 3D coordinates of (N-term, C-alpha and C-term)

dihedral_angle_from_coordinates.py

""" Dihedral angles from coordinates. Get dihedral angles from 
    protein backbone coordinates.
    This script takes 4 vectors representing 4 points as input
    and returns the dihedral angle between them.
    
    The script was originally developed to calculate dihedral angles (phi,psi)
    from protein backbone atoms' coordinates in 3D (N-term, C-alhpa, Cterm).
"""

import numpy as np

def calc_dihedral(u1, u2, u3, u4):
    """ Calculate dihedral angle method. From bioPython.PDB
    (adapted to np.array)

    Calculate the dihedral angle between 4 vectors
    representing 4 connected points. The angle is in
    [-pi, pi].

    """

    a1 = u2 - u1
    a2 = u3 - u2
    a3 = u4 - u3

    v1 = np.cross(a1, a2)
    v1 = v1 / (v1 * v1).sum(-1)**0.5
    v2 = np.cross(a2, a3)
    v2 = v2 / (v2 * v2).sum(-1)**0.5
    porm = np.sign((v1 * a3).sum(-1))
    rad = np.arccos((v1*v2).sum(-1) / ((v1**2).sum(-1) * (v2**2).sum(-1))**0.5)
    if not porm == 0:
        rad = rad * porm

    return rad
    
a = np.array([1219.7, 4106.1, -7366.7])
b = np.array([1277.1, 4016.6, -7447.1])
c = np.array([1398.6, 3944.8, -7407.8])
d = np.array([1501.2, 3943.2, -7521.3])

alpha = calc_dihedral(a,b,c,d)
print("Dihedral angle in radians:", alpha, "and degrees:", alpha*180/np.pi)