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#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
"""
This script implements protein structure alignment (CA atoms) using the
Kabsch algorithm to compute optimal rotation and RMSD.
References:
- Kabsch W. (1976, 1978) A solution for the best rotation to relate two sets of vectors. Acta Crystallographica A.
"""
import numpy as np
from Bio import PDB
def get_coordinates(structure, chain_id=None):
"""
Extract the coordinates of alpha carbon (CA) atoms from a protein structure.
Args:
structure (Bio.PDB.Structure.Structure): A protein structure object parsed by Bio.PDB.PDBParser.
chain_id (str, optional): The ID of the specific protein chain to extract coordinates from.
If None, coordinates are extracted from all chains. Defaults to None.
Returns:
numpy.ndarray: A 2D array where each row represents the 3D coordinates of a CA atom.
"""
coords = []
for model in structure:
for chain in model:
if chain_id is not None and chain.id != chain_id:
continue
for residue in chain:
for atom in residue:
if atom.get_name() == "CA":
coords.append(atom.get_coord())
return np.array(coords)
def kabsch_algorithm(P, Q):
"""
Apply the Kabsch algorithm to find the optimal rotation matrix that aligns two sets of points.
Args:
P (numpy.ndarray): The first set of points with shape (N, 3)
Q (numpy.ndarray): The second set of points with shape (N, 3)
Returns:
tuple: A tuple containing the rotation matrix (R), centroid of P (C_P), and centroid of Q (C_Q).
"""
# Centroid of P and Q
C_P = np.mean(P, axis=0)
C_Q = np.mean(Q, axis=0)
# Center the points
P_centered = P - C_P
Q_centered = Q - C_Q
# Covariance matrix
H = np.dot(P_centered.T, Q_centered)
try:
# Singular value decomposition
U, S, Vt = np.linalg.svd(H)
# Rotation matrix
R = np.dot(Vt.T, U.T)
# Special reflection case
if np.linalg.det(R) < 0:
Vt[-1, :] *= -1
R = np.dot(Vt.T, U.T)
except np.linalg.LinAlgError:
print("Warning: SVD did not converge. Returning identity rotation.")
R = np.eye(3) # Fallback to identity rotation
return R, C_P, C_Q
def calculate_rmsd(P, Q):
diff = P - Q
return np.sqrt(np.sum(diff * diff) / len(P))
def _is_standard_residue(residue):
hetflag = residue.id[0] # ' '=standard, 'H_'=hetero/water/ligand
return hetflag == " "
def _choose_altloc(atom_list):
"""Pick one altloc variant for a duplicated atom (e.g., CA).
Preference order: highest occupancy; tie-breaker: altloc 'A' or blank.
"""
if len(atom_list) == 1:
return atom_list[0]
best = max(
atom_list,
key=lambda a: (
a.get_occupancy() or 0.0,
1 if a.get_altloc() in ("A", " ") else 0,
),
)
return best
def _residue_key(chain, residue):
"""Build a stable residue key using (chain_id, resseq, icode)."""
het, resseq, icode = residue.get_id()
return (chain.id, int(resseq), (icode or "").strip())
def _collect_ca_coords(structure, chain_ids=None):
"""
Collect CA coordinates keyed by (chain_id, resseq, icode).
Returns
-------
dict[(chain_id, resseq, icode)] -> np.ndarray shape (3,), float64
Parameters
----------
structure : Bio.PDB.Structure.Structure
chain_ids : Iterable[str] | None Select multiple chains.
"""
chain_id_set = set(chain_ids) if chain_ids is not None else None
idx = {}
for model in structure:
for chain in model:
if chain_id_set is not None:
if chain.id not in chain_id_set:
continue
for res in chain:
if not _is_standard_residue(res):
continue
ca_atoms = [a for a in res if a.get_name() == "CA"]
if not ca_atoms:
continue
ca = _choose_altloc(ca_atoms)
key = _residue_key(chain, res)
idx[key] = ca.get_coord().astype(np.float64)
return idx
def align_and_calculate_rmsd(file1, file2):
"""
Align two protein structures based on their CA atoms and calculate RMSD.
Args:
file1 (str): Path to the first PDB file.
file2 (str): Path to the second PDB file.
Returns:
float or None: The RMSD value between the aligned structures.
Returns None if the number of CA atoms in the two structures differs.
"""
parser = PDB.PDBParser(QUIET=True)
structure1 = parser.get_structure("structure1", file1)
structure2 = parser.get_structure("structure2", file2)
coords1 = get_coordinates(structure1)
coords2 = get_coordinates(structure2)
if len(coords1) != len(coords2):
print(
"[WARNING] The lengths of coord1 and coord2 are different. There may exist missing atoms!"
)
orig_num_atoms = len(coords1), len(coords2)
coords1 = _collect_ca_coords(structure1)
coords2 = _collect_ca_coords(structure2)
# Use only residues present in BOTH structures
common_keys = sorted(set(coords1.keys()) & set(coords2.keys()))
if len(common_keys) < 3:
print(f"[WARNING] common CA pairs < 3 (got {len(common_keys)}). ")
return None
coords1 = np.vstack([coords1[k] for k in common_keys])
coords2 = np.vstack([coords2[k] for k in common_keys])
matched_num_atoms = len(coords1), len(coords2)
print(
f"Orig num atoms: {orig_num_atoms} Matched num atoms: {matched_num_atoms}"
)
R, C_P, C_Q = kabsch_algorithm(coords1, coords2)
# Apply rotation and translation
coords2_aligned = np.dot(coords2 - C_Q, R) + C_P
rmsd = calculate_rmsd(coords1, coords2_aligned)
return rmsd
def Binder_align_and_calculate_rmsd(file1, file2, chain_id):
"""
Align two protein structures based on their CA atoms, with one structure's specific chain, and calculate RMSD.
Args:
file1 (str): Path to the first PDB file.
file2 (str): Path to the second PDB file.
chain_id (str): The ID of the specific protein chain to extract coordinates from.
Returns:
float or None: The RMSD value between the aligned structures.
Returns None if the number of CA atoms in the two structures differs.
"""
parser = PDB.PDBParser(QUIET=True)
structure1 = parser.get_structure("structure1", file1)
structure2 = parser.get_structure("structure2", file2)
coords1 = get_coordinates(structure1)
coords2 = get_coordinates(structure2, chain_id)
if len(coords1) != len(coords2):
print(
"[WARNING] The lengths of coord1 and coord2 are different. There may exist missing atoms!"
)
return None
R, C_P, C_Q = kabsch_algorithm(coords1, coords2)
# Apply rotation and translation
coords2_aligned = np.dot(coords2 - C_Q, R) + C_P
rmsd = calculate_rmsd(coords1, coords2_aligned)
return rmsd
def _list_chain_ids(structure):
"""Return chain IDs in file order (first model only)."""
model = next(structure.get_models())
return [ch.id for ch in model]
def _coords_for_chain_ids(structure, chain_ids):
"""Stack CA coords for the given chain IDs (skip empty chains safely)."""
chunks = []
for cid in chain_ids:
arr = get_coordinates(structure, chain_id=cid)
if arr.size:
chunks.append(arr)
if not chunks:
return np.empty((0, 3), dtype=float)
return np.vstack(chunks)
def align_and_calculate_target_rmsd(file1, file2, n=None):
parser = PDB.PDBParser(QUIET=True)
structure1 = parser.get_structure("structure1", file1)
structure2 = parser.get_structure("structure2", file2)
chains1 = _list_chain_ids(structure1)
chains2 = _list_chain_ids(structure2)
if n is None:
n = len(chains1)
if n > len(chains2):
print(f"[WARNING] file2 has only {len(chains2)} chains; capping n to that.")
n = len(chains2)
ids1 = chains1[:n]
ids2 = chains2[:n]
coords1 = _coords_for_chain_ids(structure1, ids1)
coords2 = _coords_for_chain_ids(structure2, ids2)
if len(coords1) != len(coords2):
print(
"[WARNING] The lengths of coord1 and coord2 are different. "
"Trying residue-key matching fallback."
)
idx1 = _collect_ca_coords(structure1, chain_ids=ids1)
idx2 = _collect_ca_coords(structure2, chain_ids=ids2)
common_keys = sorted(set(idx1.keys()) & set(idx2.keys()))
if len(common_keys) < 3:
print(f"[WARNING] common CA pairs < 3 (got {len(common_keys)}).")
return None
coords1 = np.vstack([idx1[k] for k in common_keys])
coords2 = np.vstack([idx2[k] for k in common_keys])
print(f"Matched num CA atoms after fallback: {(len(coords1), len(coords2))}")
R, C_P, C_Q = kabsch_algorithm(coords1, coords2)
# Apply rotation and translation
coords2_aligned = np.dot(coords2 - C_Q, R) + C_P
rmsd = calculate_rmsd(coords1, coords2_aligned)
return rmsd
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