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import numpy as np
import torch
from chemical import INIT_CRDS
PARAMS = {
"DMIN" : 2.0,
"DMAX" : 20.0,
"DBINS" : 36,
"ABINS" : 36,
}
# ============================================================
def get_pair_dist(a, b):
"""calculate pair distances between two sets of points
Parameters
----------
a,b : pytorch tensors of shape [batch,nres,3]
store Cartesian coordinates of two sets of atoms
Returns
-------
dist : pytorch tensor of shape [batch,nres,nres]
stores paitwise distances between atoms in a and b
"""
dist = torch.cdist(a, b, p=2)
return dist
# ============================================================
def get_ang(a, b, c):
"""calculate planar angles for all consecutive triples (a[i],b[i],c[i])
from Cartesian coordinates of three sets of atoms a,b,c
Parameters
----------
a,b,c : pytorch tensors of shape [batch,nres,3]
store Cartesian coordinates of three sets of atoms
Returns
-------
ang : pytorch tensor of shape [batch,nres]
stores resulting planar angles
"""
v = a - b
w = c - b
v /= torch.norm(v, dim=-1, keepdim=True)
w /= torch.norm(w, dim=-1, keepdim=True)
vw = torch.sum(v*w, dim=-1)
return torch.acos(vw)
# ============================================================
def get_dih(a, b, c, d):
"""calculate dihedral angles for all consecutive quadruples (a[i],b[i],c[i],d[i])
given Cartesian coordinates of four sets of atoms a,b,c,d
Parameters
----------
a,b,c,d : pytorch tensors of shape [batch,nres,3]
store Cartesian coordinates of four sets of atoms
Returns
-------
dih : pytorch tensor of shape [batch,nres]
stores resulting dihedrals
"""
b0 = a - b
b1 = c - b
b2 = d - c
b1 /= torch.norm(b1, dim=-1, keepdim=True)
v = b0 - torch.sum(b0*b1, dim=-1, keepdim=True)*b1
w = b2 - torch.sum(b2*b1, dim=-1, keepdim=True)*b1
x = torch.sum(v*w, dim=-1)
y = torch.sum(torch.cross(b1,v,dim=-1)*w, dim=-1)
return torch.atan2(y, x)
# ============================================================
def xyz_to_c6d(xyz, params=PARAMS):
"""convert cartesian coordinates into 2d distance
and orientation maps
Parameters
----------
xyz : pytorch tensor of shape [batch,nres,3,3]
stores Cartesian coordinates of backbone N,Ca,C atoms
Returns
-------
c6d : pytorch tensor of shape [batch,nres,nres,4]
stores stacked dist,omega,theta,phi 2D maps
"""
batch = xyz.shape[0]
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 = torch.cross(b, c, dim=-1)
Cb = -0.58273431*a + 0.56802827*b - 0.54067466*c + Ca
# 6d coordinates order: (dist,omega,theta,phi)
c6d = torch.zeros([batch,nres,nres,4],dtype=xyz.dtype,device=xyz.device)
dist = get_pair_dist(Cb,Cb)
dist[torch.isnan(dist)] = 999.9
c6d[...,0] = dist + 999.9*torch.eye(nres,device=xyz.device)[None,...]
b,i,j = torch.where(c6d[...,0]<params['DMAX'])
c6d[b,i,j,torch.full_like(b,1)] = get_dih(Ca[b,i], Cb[b,i], Cb[b,j], Ca[b,j])
c6d[b,i,j,torch.full_like(b,2)] = get_dih(N[b,i], Ca[b,i], Cb[b,i], Cb[b,j])
c6d[b,i,j,torch.full_like(b,3)] = get_ang(Ca[b,i], Cb[b,i], Cb[b,j])
# fix long-range distances
c6d[...,0][c6d[...,0]>=params['DMAX']] = 999.9
mask = torch.zeros((batch, nres,nres), dtype=xyz.dtype, device=xyz.device)
mask[b,i,j] = 1.0
return c6d, mask
def xyz_to_t2d(xyz_t, params=PARAMS):
"""convert template cartesian coordinates into 2d distance
and orientation maps
Parameters
----------
xyz_t : pytorch tensor of shape [batch,templ,nres,3,3]
stores Cartesian coordinates of template backbone N,Ca,C atoms
Returns
-------
t2d : pytorch tensor of shape [batch,nres,nres,37+6+3]
stores stacked dist,omega,theta,phi 2D maps
"""
B, T, L = xyz_t.shape[:3]
c6d, mask = xyz_to_c6d(xyz_t[:,:,:,:3].view(B*T,L,3,3), params=params)
c6d = c6d.view(B, T, L, L, 4)
mask = mask.view(B, T, L, L, 1)
#
# dist to one-hot encoded
dist = dist_to_onehot(c6d[...,0], params)
orien = torch.cat((torch.sin(c6d[...,1:]), torch.cos(c6d[...,1:])), dim=-1)*mask # (B, T, L, L, 6)
#
mask = ~torch.isnan(c6d[:,:,:,:,0]) # (B, T, L, L)
t2d = torch.cat((dist, orien, mask.unsqueeze(-1)), dim=-1)
t2d[torch.isnan(t2d)] = 0.0
return t2d
def xyz_to_chi1(xyz_t):
'''convert template cartesian coordinates into chi1 angles
Parameters
----------
xyz_t: pytorch tensor of shape [batch, templ, nres, 14, 3]
stores Cartesian coordinates of template atoms. For missing atoms, it should be NaN
Returns
-------
chi1 : pytorch tensor of shape [batch, templ, nres, 2]
stores cos and sin chi1 angle
'''
B, T, L = xyz_t.shape[:3]
xyz_t = xyz_t.reshape(B*T, L, 14, 3)
# chi1 angle: N, CA, CB, CG
chi1 = get_dih(xyz_t[:,:,0], xyz_t[:,:,1], xyz_t[:,:,4], xyz_t[:,:,5]) # (B*T, L)
cos_chi1 = torch.cos(chi1)
sin_chi1 = torch.sin(chi1)
mask_chi1 = ~torch.isnan(chi1)
chi1 = torch.stack((cos_chi1, sin_chi1, mask_chi1), dim=-1) # (B*T, L, 3)
chi1[torch.isnan(chi1)] = 0.0
chi1 = chi1.reshape(B, T, L, 3)
return chi1
def xyz_to_bbtor(xyz, params=PARAMS):
batch = xyz.shape[0]
nres = xyz.shape[1]
# three anchor atoms
N = xyz[:,:,0]
Ca = xyz[:,:,1]
C = xyz[:,:,2]
# recreate Cb given N,Ca,C
next_N = torch.roll(N, -1, dims=1)
prev_C = torch.roll(C, 1, dims=1)
phi = get_dih(prev_C, N, Ca, C)
psi = get_dih(N, Ca, C, next_N)
#
phi[:,0] = 0.0
psi[:,-1] = 0.0
#
astep = 2.0*np.pi / params['ABINS']
phi_bin = torch.round((phi+np.pi-astep/2)/astep)
psi_bin = torch.round((psi+np.pi-astep/2)/astep)
return torch.stack([phi_bin, psi_bin], axis=-1).long()
# ============================================================
def dist_to_onehot(dist, params=PARAMS):
dist[torch.isnan(dist)] = 999.9
dstep = (params['DMAX'] - params['DMIN']) / params['DBINS']
dbins = torch.linspace(params['DMIN']+dstep, params['DMAX'], params['DBINS'],dtype=dist.dtype,device=dist.device)
db = torch.bucketize(dist.contiguous(),dbins).long()
dist = torch.nn.functional.one_hot(db, num_classes=params['DBINS']+1).float()
return dist
def c6d_to_bins(c6d,params=PARAMS):
"""bin 2d distance and orientation maps
"""
dstep = (params['DMAX'] - params['DMIN']) / params['DBINS']
astep = 2.0*np.pi / params['ABINS']
dbins = torch.linspace(params['DMIN']+dstep, params['DMAX'], params['DBINS'],dtype=c6d.dtype,device=c6d.device)
ab360 = torch.linspace(-np.pi+astep, np.pi, params['ABINS'],dtype=c6d.dtype,device=c6d.device)
ab180 = torch.linspace(astep, np.pi, params['ABINS']//2,dtype=c6d.dtype,device=c6d.device)
db = torch.bucketize(c6d[...,0].contiguous(),dbins)
ob = torch.bucketize(c6d[...,1].contiguous(),ab360)
tb = torch.bucketize(c6d[...,2].contiguous(),ab360)
pb = torch.bucketize(c6d[...,3].contiguous(),ab180)
ob[db==params['DBINS']] = params['ABINS']
tb[db==params['DBINS']] = params['ABINS']
pb[db==params['DBINS']] = params['ABINS']//2
return torch.stack([db,ob,tb,pb],axis=-1).to(torch.uint8)
# ============================================================
def dist_to_bins(dist,params=PARAMS):
"""bin 2d distance maps
"""
dstep = (params['DMAX'] - params['DMIN']) / params['DBINS']
db = torch.round((dist-params['DMIN']-dstep/2)/dstep)
db[db<0] = 0
db[db>params['DBINS']] = params['DBINS']
return db.long()
# ============================================================
def c6d_to_bins2(c6d, same_chain, negative=False, params=PARAMS):
"""bin 2d distance and orientation maps
"""
dstep = (params['DMAX'] - params['DMIN']) / params['DBINS']
astep = 2.0*np.pi / params['ABINS']
db = torch.round((c6d[...,0]-params['DMIN']-dstep/2)/dstep)
ob = torch.round((c6d[...,1]+np.pi-astep/2)/astep)
tb = torch.round((c6d[...,2]+np.pi-astep/2)/astep)
pb = torch.round((c6d[...,3]-astep/2)/astep)
# put all d<dmin into one bin
db[db<0] = 0
# synchronize no-contact bins
db[db>params['DBINS']] = params['DBINS']
ob[db==params['DBINS']] = params['ABINS']
tb[db==params['DBINS']] = params['ABINS']
pb[db==params['DBINS']] = params['ABINS']//2
if negative:
db = torch.where(same_chain.bool(), db.long(), params['DBINS'])
ob = torch.where(same_chain.bool(), ob.long(), params['ABINS'])
tb = torch.where(same_chain.bool(), tb.long(), params['ABINS'])
pb = torch.where(same_chain.bool(), pb.long(), params['ABINS']//2)
return torch.stack([db,ob,tb,pb],axis=-1).long()
def get_init_xyz(xyz_t):
# input: xyz_t (B, T, L, 14, 3)
# ouput: xyz (B, T, L, 14, 3)
B, T, L = xyz_t.shape[:3]
init = INIT_CRDS.to(xyz_t.device).reshape(1,1,1,27,3).repeat(B,T,L,1,1)
if torch.isnan(xyz_t).all():
return init
mask = torch.isnan(xyz_t[:,:,:,:3]).any(dim=-1).any(dim=-1) # (B, T, L)
#
center_CA = ((~mask[:,:,:,None]) * torch.nan_to_num(xyz_t[:,:,:,1,:])).sum(dim=2) / ((~mask[:,:,:,None]).sum(dim=2)+1e-4) # (B, T, 3)
xyz_t = xyz_t - center_CA.view(B,T,1,1,3)
#
idx_s = list()
for i_b in range(B):
for i_T in range(T):
if mask[i_b, i_T].all():
continue
exist_in_templ = torch.where(~mask[i_b, i_T])[0] # (L_sub)
seqmap = (torch.arange(L, device=xyz_t.device)[:,None] - exist_in_templ[None,:]).abs() # (L, L_sub)
seqmap = torch.argmin(seqmap, dim=-1) # (L)
idx = torch.gather(exist_in_templ, -1, seqmap) # (L)
offset_CA = torch.gather(xyz_t[i_b, i_T, :, 1, :], 0, idx.reshape(L,1).expand(-1,3))
init[i_b,i_T] += offset_CA.reshape(L,1,3)
#
xyz = torch.where(mask.view(B, T, L, 1, 1), init, xyz_t)
return xyz
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