model/coords6d.py

import numpy as np
import scipy
import scipy.spatial

# calculate dihedral angles defined by 4 sets of points
def get_dihedrals(a, b, c, d):

    b0 = -1.0*(b - a)
    b1 = c - b
    b2 = d - c

    b1 /= np.linalg.norm(b1, axis=-1)[:,None]

    v = b0 - np.sum(b0*b1, axis=-1)[:,None]*b1
    w = b2 - np.sum(b2*b1, axis=-1)[:,None]*b1

    x = np.sum(v*w, axis=-1)
    y = np.sum(np.cross(b1, v)*w, axis=-1)

    return np.arctan2(y, x)

# calculate planar angles defined by 3 sets of points
def get_angles(a, b, c):

    v = a - b
    v /= np.linalg.norm(v, axis=-1)[:,None]

    w = c - b
    w /= np.linalg.norm(w, axis=-1)[:,None]

    x = np.sum(v*w, axis=1)

    #return np.arccos(x)
    return np.arccos(np.clip(x, -1.0, 1.0))

# get 6d coordinates from x,y,z coords of N,Ca,C atoms
def get_coords6d(xyz, dmax):

    nres = xyz.shape[1]

    # three anchor atoms
    N  = xyz[0]
    Ca = xyz[1]
    C  = xyz[2]

    # recreate Cb given N,Ca,C
    b = Ca - N
    c = C - Ca
    a = np.cross(b, c)
    Cb = -0.58273431*a + 0.56802827*b - 0.54067466*c + Ca

    # fast neighbors search to collect all
    # Cb-Cb pairs within dmax
    kdCb = scipy.spatial.cKDTree(Cb)
    indices = kdCb.query_ball_tree(kdCb, dmax)

    # indices of contacting residues
    idx = np.array([[i,j] for i in range(len(indices)) for j in indices[i] if i != j]).T
    idx0 = idx[0]
    idx1 = idx[1]

    # Cb-Cb distance matrix
    dist6d = np.full((nres, nres),999.9, dtype=np.float32)
    dist6d[idx0,idx1] = np.linalg.norm(Cb[idx1]-Cb[idx0], axis=-1)

    # matrix of Ca-Cb-Cb-Ca dihedrals
    omega6d = np.zeros((nres, nres), dtype=np.float32)
    omega6d[idx0,idx1] = get_dihedrals(Ca[idx0], Cb[idx0], Cb[idx1], Ca[idx1])

    # matrix of polar coord theta
    theta6d = np.zeros((nres, nres), dtype=np.float32)
    theta6d[idx0,idx1] = get_dihedrals(N[idx0], Ca[idx0], Cb[idx0], Cb[idx1])

    # matrix of polar coord phi
    phi6d = np.zeros((nres, nres), dtype=np.float32)
    phi6d[idx0,idx1] = get_angles(Ca[idx0], Cb[idx0], Cb[idx1])

    mask = np.zeros((nres, nres), dtype=np.float32)
    mask[idx0, idx1] = 1.0
    return dist6d, omega6d, theta6d, phi6d, mask