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Utilities for calculating all atom representations.
"""
import torch
from src.common import residue_constants as rc
from src.common.data_transforms import atom37_to_torsion_angles
from src.common.rigid_utils import Rigid, Rotation
# Residue Constants from OpenFold/AlphaFold2.
IDEALIZED_POS37 = torch.tensor(rc.restype_atom37_rigid_group_positions)
IDEALIZED_POS37_MASK = torch.any(IDEALIZED_POS37, axis=-1)
IDEALIZED_POS = torch.tensor(rc.restype_atom14_rigid_group_positions)
DEFAULT_FRAMES = torch.tensor(rc.restype_rigid_group_default_frame)
ATOM_MASK = torch.tensor(rc.restype_atom14_mask)
GROUP_IDX = torch.tensor(rc.restype_atom14_to_rigid_group)
def torsion_angles_to_frames(
r: Rigid,
alpha: torch.Tensor,
aatype: torch.Tensor,
):
# [*, N, 8, 4, 4]
default_4x4 = DEFAULT_FRAMES[aatype, ...].to(r.device)
# [*, N, 8] transformations, i.e.
# One [*, N, 8, 3, 3] rotation matrix and
# One [*, N, 8, 3] translation matrix
default_r = r.from_tensor_4x4(default_4x4)
bb_rot = alpha.new_zeros((*((1,) * len(alpha.shape[:-1])), 2))
bb_rot[..., 1] = 1
# [*, N, 8, 2]
alpha = torch.cat(
[bb_rot.expand(*alpha.shape[:-2], -1, -1), alpha], dim=-2
)
# [*, N, 8, 3, 3]
# Produces rotation matrices of the form:
# [
# [1, 0 , 0 ],
# [0, a_2,-a_1],
# [0, a_1, a_2]
# ]
# This follows the original code rather than the supplement, which uses
# different indices.
all_rots = alpha.new_zeros(default_r.get_rots().get_rot_mats().shape)
all_rots[..., 0, 0] = 1
all_rots[..., 1, 1] = alpha[..., 1]
all_rots[..., 1, 2] = -alpha[..., 0]
all_rots[..., 2, 1:] = alpha
all_rots = Rigid(Rotation(rot_mats=all_rots), None)
all_frames = default_r.compose(all_rots)
chi2_frame_to_frame = all_frames[..., 5]
chi3_frame_to_frame = all_frames[..., 6]
chi4_frame_to_frame = all_frames[..., 7]
chi1_frame_to_bb = all_frames[..., 4]
chi2_frame_to_bb = chi1_frame_to_bb.compose(chi2_frame_to_frame)
chi3_frame_to_bb = chi2_frame_to_bb.compose(chi3_frame_to_frame)
chi4_frame_to_bb = chi3_frame_to_bb.compose(chi4_frame_to_frame)
all_frames_to_bb = Rigid.cat(
[
all_frames[..., :5],
chi2_frame_to_bb.unsqueeze(-1),
chi3_frame_to_bb.unsqueeze(-1),
chi4_frame_to_bb.unsqueeze(-1),
],
dim=-1,
)
all_frames_to_global = r[..., None].compose(all_frames_to_bb)
return all_frames_to_global
def prot_to_torsion_angles(aatype, atom37, atom37_mask):
"""Calculate torsion angle features from protein features."""
prot_feats = {
'aatype': aatype,
'all_atom_positions': atom37,
'all_atom_mask': atom37_mask,
}
torsion_angles_feats = atom37_to_torsion_angles()(prot_feats)
torsion_angles = torsion_angles_feats['torsion_angles_sin_cos']
torsion_mask = torsion_angles_feats['torsion_angles_mask']
return torsion_angles, torsion_mask
def frames_to_atom14_pos(
r: Rigid,
aatype: torch.Tensor,
):
"""Convert frames to their idealized all atom representation.
Args:
r: All rigid groups. [..., N, 8, 3]
aatype: Residue types. [..., N]
Returns:
"""
# [*, N, 14]
group_mask = GROUP_IDX[aatype, ...]
# [*, N, 14, 8]
group_mask = torch.nn.functional.one_hot(
group_mask,
num_classes=DEFAULT_FRAMES.shape[-3],
).to(r.device)
# [*, N, 14, 8]
t_atoms_to_global = r[..., None, :] * group_mask
# [*, N, 14]
t_atoms_to_global = t_atoms_to_global.map_tensor_fn(
lambda x: torch.sum(x, dim=-1)
)
# [*, N, 14, 1]
frame_atom_mask = ATOM_MASK[aatype, ...].unsqueeze(-1).to(r.device)
# [*, N, 14, 3]
frame_null_pos = IDEALIZED_POS[aatype, ...].to(r.device)
pred_positions = t_atoms_to_global.apply(frame_null_pos)
pred_positions = pred_positions * frame_atom_mask
return pred_positions
def compute_backbone(bb_rigids, psi_torsions, aatype=None, device=None):
if device is None:
device = bb_rigids.device
torsion_angles = torch.tile(
psi_torsions[..., None, :],
tuple([1 for _ in range(len(bb_rigids.shape))]) + (7, 1)
).to(device)
# aatype must be on cpu for initializing the tensor by indexing
if aatype is None:
aatype = torch.zeros_like(bb_rigids).cpu().long()
else:
aatype = aatype.cpu()
all_frames = torsion_angles_to_frames(
bb_rigids,
torsion_angles,
aatype,
)
atom14_pos = frames_to_atom14_pos(
all_frames,
aatype,
)
atom37_bb_pos = torch.zeros(bb_rigids.shape + (37, 3), device=device)
# atom14 bb order = ['N', 'CA', 'C', 'O', 'CB']
# atom37 bb order = ['N', 'CA', 'C', 'CB', 'O']
atom37_bb_pos[..., :3, :] = atom14_pos[..., :3, :]
atom37_bb_pos[..., 3, :] = atom14_pos[..., 4, :]
atom37_bb_pos[..., 4, :] = atom14_pos[..., 3, :]
atom37_mask = torch.any(atom37_bb_pos, axis=-1)
return atom37_bb_pos, atom37_mask, aatype.to(device), atom14_pos
def calculate_neighbor_angles(R_ac, R_ab):
"""Calculate angles between atoms c <- a -> b.
Parameters
----------
R_ac: Tensor, shape = (N,3)
Vector from atom a to c.
R_ab: Tensor, shape = (N,3)
Vector from atom a to b.
Returns
-------
angle_cab: Tensor, shape = (N,)
Angle between atoms c <- a -> b.
"""
# cos(alpha) = (u * v) / (|u|*|v|)
x = torch.sum(R_ac * R_ab, dim=1) # shape = (N,)
# sin(alpha) = |u x v| / (|u|*|v|)
y = torch.cross(R_ac, R_ab).norm(dim=-1) # shape = (N,)
# avoid that for y == (0,0,0) the gradient wrt. y becomes NaN
y = torch.max(y, torch.tensor(1e-9))
angle = torch.atan2(y, x)
return angle
def vector_projection(R_ab, P_n):
"""
Project the vector R_ab onto a plane with normal vector P_n.
Parameters
----------
R_ab: Tensor, shape = (N,3)
Vector from atom a to b.
P_n: Tensor, shape = (N,3)
Normal vector of a plane onto which to project R_ab.
Returns
-------
R_ab_proj: Tensor, shape = (N,3)
Projected vector (orthogonal to P_n).
"""
a_x_b = torch.sum(R_ab * P_n, dim=-1)
b_x_b = torch.sum(P_n * P_n, dim=-1)
return R_ab - (a_x_b / b_x_b)[:, None] * P_n
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