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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
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