bio-pdb-geometric-analysis

Measure distances, angles, and dihedrals. Superimpose structures and calculate RMSD. Find neighbor atoms and contacts.

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Install skill "bio-pdb-geometric-analysis" with this command: npx skills add gptomics/bioskills/gptomics-bioskills-bio-pdb-geometric-analysis

Geometric Analysis

Measure distances, angles, and dihedrals. Superimpose structures and calculate RMSD. Find neighbor atoms and contacts.

Required Imports

from Bio.PDB import PDBParser, NeighborSearch, Superimposer from Bio.PDB import calc_angle, calc_dihedral import numpy as np

Distance Between Atoms

from Bio.PDB import PDBParser

parser = PDBParser(QUIET=True) structure = parser.get_structure('protein', 'protein.pdb')

chain = structure[0]['A'] atom1 = chain[100]['CA'] atom2 = chain[200]['CA']

Direct subtraction gives distance

distance = atom1 - atom2 print(f'Distance: {distance:.2f} Angstroms')

Or use numpy

import numpy as np distance = np.linalg.norm(atom1.coord - atom2.coord)

Distance Matrix

import numpy as np from Bio.PDB import PDBParser

parser = PDBParser(QUIET=True) structure = parser.get_structure('protein', 'protein.pdb')

ca_atoms = [r['CA'] for r in structure.get_residues() if r.has_id('CA') and r.id[0] == ' '] n = len(ca_atoms)

dist_matrix = np.zeros((n, n)) for i in range(n): for j in range(i + 1, n): dist = ca_atoms[i] - ca_atoms[j] dist_matrix[i, j] = dist dist_matrix[j, i] = dist

print(f'Distance matrix shape: {dist_matrix.shape}')

Angle Between Three Atoms

from Bio.PDB import PDBParser, calc_angle

parser = PDBParser(QUIET=True) structure = parser.get_structure('protein', 'protein.pdb')

residue = structure[0]['A'][100] n = residue['N'] ca = residue['CA'] c = residue['C']

calc_angle takes Vector objects (atom.coord returns array, use atom.get_vector())

angle_rad = calc_angle(n.get_vector(), ca.get_vector(), c.get_vector()) angle_deg = np.degrees(angle_rad) print(f'N-CA-C angle: {angle_deg:.1f} degrees')

Dihedral Angles

from Bio.PDB import PDBParser, calc_dihedral import numpy as np

parser = PDBParser(QUIET=True) structure = parser.get_structure('protein', 'protein.pdb')

chain = structure[0]['A']

Calculate phi angle (C-N-CA-C)

res_prev = chain[99] res_curr = chain[100]

phi = calc_dihedral( res_prev['C'].get_vector(), res_curr['N'].get_vector(), res_curr['CA'].get_vector(), res_curr['C'].get_vector() ) print(f'Phi: {np.degrees(phi):.1f} degrees')

Calculate psi angle (N-CA-C-N)

res_next = chain[101] psi = calc_dihedral( res_curr['N'].get_vector(), res_curr['CA'].get_vector(), res_curr['C'].get_vector(), res_next['N'].get_vector() ) print(f'Psi: {np.degrees(psi):.1f} degrees')

Ramachandran Angles for All Residues

from Bio.PDB import PDBParser, PPBuilder, calc_dihedral import numpy as np

parser = PDBParser(QUIET=True) structure = parser.get_structure('protein', 'protein.pdb')

ppb = PPBuilder() phi_psi = []

for pp in ppb.build_peptides(structure): angles = pp.get_phi_psi_list() for residue, (phi, psi) in zip(pp, angles): if phi is not None and psi is not None: phi_psi.append((residue.resname, np.degrees(phi), np.degrees(psi)))

for name, phi, psi in phi_psi[:10]: print(f'{name}: phi={phi:.1f}, psi={psi:.1f}')

Finding Neighbor Atoms

from Bio.PDB import PDBParser, NeighborSearch

parser = PDBParser(QUIET=True) structure = parser.get_structure('protein', 'protein.pdb')

Build search tree from all atoms

all_atoms = list(structure.get_atoms()) ns = NeighborSearch(all_atoms)

Find atoms within radius of a point

center = structure[0]['A'][100]['CA'].coord radius = 5.0 # Angstroms neighbors = ns.search(center, radius) print(f'Found {len(neighbors)} atoms within {radius}A')

Find atoms within radius of another atom

ca_atom = structure[0]['A'][100]['CA'] neighbors = ns.search(ca_atom.coord, 5.0)

Finding Residue Contacts

from Bio.PDB import PDBParser, NeighborSearch

parser = PDBParser(QUIET=True) structure = parser.get_structure('protein', 'protein.pdb')

all_atoms = list(structure.get_atoms()) ns = NeighborSearch(all_atoms)

Find all atom pairs within distance

contact_distance = 4.0 contacts = ns.search_all(contact_distance, level='R') # R = residue level

print(f'Found {len(contacts)} residue contacts within {contact_distance}A') for res1, res2 in contacts[:10]: print(f' {res1.resname}{res1.id[1]} - {res2.resname}{res2.id[1]}')

Contact Levels

from Bio.PDB import NeighborSearch

search_all returns pairs at specified level

Level codes: A=atom, R=residue, C=chain, M=model, S=structure

atom_contacts = ns.search_all(4.0, level='A') # Atom pairs residue_contacts = ns.search_all(4.0, level='R') # Residue pairs chain_contacts = ns.search_all(10.0, level='C') # Chain pairs

Superimposing Structures

from Bio.PDB import PDBParser, Superimposer

parser = PDBParser(QUIET=True) ref_structure = parser.get_structure('ref', 'reference.pdb') mobile_structure = parser.get_structure('mobile', 'mobile.pdb')

Get CA atoms from both structures

ref_atoms = [r['CA'] for r in ref_structure.get_residues() if r.has_id('CA') and r.id[0] == ' '] mobile_atoms = [r['CA'] for r in mobile_structure.get_residues() if r.has_id('CA') and r.id[0] == ' ']

Ensure same number of atoms

n = min(len(ref_atoms), len(mobile_atoms)) ref_atoms = ref_atoms[:n] mobile_atoms = mobile_atoms[:n]

Superimpose

sup = Superimposer() sup.set_atoms(ref_atoms, mobile_atoms) print(f'RMSD before: {sup.rms:.2f} Angstroms')

Apply transformation to all atoms in mobile structure

sup.apply(mobile_structure.get_atoms())

Calculating RMSD

from Bio.PDB import PDBParser, Superimposer import numpy as np

parser = PDBParser(QUIET=True) struct1 = parser.get_structure('s1', 'structure1.pdb') struct2 = parser.get_structure('s2', 'structure2.pdb')

atoms1 = [r['CA'] for r in struct1.get_residues() if r.has_id('CA') and r.id[0] == ' '] atoms2 = [r['CA'] for r in struct2.get_residues() if r.has_id('CA') and r.id[0] == ' ']

Using Superimposer (with alignment)

sup = Superimposer() sup.set_atoms(atoms1, atoms2) rmsd_aligned = sup.rms print(f'RMSD (aligned): {rmsd_aligned:.2f} A')

Raw RMSD (no alignment)

coords1 = np.array([a.coord for a in atoms1]) coords2 = np.array([a.coord for a in atoms2]) rmsd_raw = np.sqrt(np.mean(np.sum((coords1 - coords2) ** 2, axis=1))) print(f'RMSD (raw): {rmsd_raw:.2f} A')

CEAligner for Dissimilar Structures

from Bio.PDB import PDBParser, CEAligner

parser = PDBParser(QUIET=True) ref = parser.get_structure('ref', 'reference.pdb') mobile = parser.get_structure('mobile', 'query.pdb')

CE alignment works for structures with different sequences

aligner = CEAligner() aligner.set_reference(ref) aligner.align(mobile)

print(f'RMSD: {aligner.rms:.2f} A')

CEAligner automatically modifies mobile structure coordinates

Center of Mass

from Bio.PDB import PDBParser import numpy as np

parser = PDBParser(QUIET=True) structure = parser.get_structure('protein', 'protein.pdb')

Unweighted center (geometric center)

coords = np.array([a.coord for a in structure.get_atoms()]) center = coords.mean(axis=0) print(f'Geometric center: {center}')

Mass-weighted center (approximate - uses atom count)

For accurate mass-weighted, use element masses

atoms = list(structure.get_atoms()) masses = {'C': 12.0, 'N': 14.0, 'O': 16.0, 'S': 32.0, 'H': 1.0} total_mass = 0 weighted_sum = np.zeros(3) for atom in atoms: mass = masses.get(atom.element, 12.0) weighted_sum += mass * atom.coord total_mass += mass center_of_mass = weighted_sum / total_mass print(f'Center of mass: {center_of_mass}')

Radius of Gyration

import numpy as np from Bio.PDB import PDBParser

parser = PDBParser(QUIET=True) structure = parser.get_structure('protein', 'protein.pdb')

coords = np.array([a.coord for a in structure.get_atoms()]) center = coords.mean(axis=0)

Radius of gyration

rg = np.sqrt(np.mean(np.sum((coords - center) ** 2, axis=1))) print(f'Radius of gyration: {rg:.2f} A')

Finding Surface Residues

from Bio.PDB import PDBParser, NeighborSearch

parser = PDBParser(QUIET=True) structure = parser.get_structure('protein', 'protein.pdb')

Simple approach: residues with few neighbors

all_atoms = list(structure.get_atoms()) ns = NeighborSearch(all_atoms)

surface_residues = [] for residue in structure.get_residues(): if residue.id[0] != ' ': continue if not residue.has_id('CA'): continue

ca = residue['CA']
neighbors = ns.search(ca.coord, 10.0, level='R')
if len(neighbors) < 15:  # Threshold for surface
    surface_residues.append(residue)

print(f'Surface residues: {len(surface_residues)}')

Vector Operations

from Bio.PDB import PDBParser from Bio.PDB.vectors import Vector, rotaxis

parser = PDBParser(QUIET=True) structure = parser.get_structure('protein', 'protein.pdb')

Get vectors from atoms

atom1 = structure[0]['A'][100]['CA'] atom2 = structure[0]['A'][101]['CA']

v1 = atom1.get_vector() v2 = atom2.get_vector()

Vector operations

diff = v2 - v1 print(f'Distance vector: {diff}') print(f'Length: {diff.norm():.2f}')

Normalize

unit = diff.normalized()

Cross product

cross = v1 ** v2

Dot product

dot = v1 * v2

Chi Angles (Sidechain Dihedrals)

from Bio.PDB import PDBParser, calc_dihedral import numpy as np

parser = PDBParser(QUIET=True) structure = parser.get_structure('protein', 'protein.pdb')

Chi1 angle for a residue (N-CA-CB-CG)

residue = structure[0]['A'][100]

if residue.has_id('CB') and residue.has_id('CG'): chi1 = calc_dihedral( residue['N'].get_vector(), residue['CA'].get_vector(), residue['CB'].get_vector(), residue['CG'].get_vector() ) print(f'Chi1: {np.degrees(chi1):.1f} degrees')

Solvent Accessible Surface Area (SASA)

from Bio.PDB import PDBParser from Bio.PDB.SASA import ShrakeRupley

parser = PDBParser(QUIET=True) structure = parser.get_structure('protein', 'protein.pdb')

Calculate SASA using Shrake-Rupley algorithm

sr = ShrakeRupley() sr.compute(structure, level='S') # S=structure, M=model, C=chain, R=residue, A=atom

Access total SASA

print(f'Total SASA: {structure.sasa:.2f} A^2')

Access per-residue SASA

for residue in structure.get_residues(): if hasattr(residue, 'sasa'): print(f'{residue.resname}{residue.id[1]}: {residue.sasa:.2f} A^2')

SASA with Custom Parameters

from Bio.PDB import PDBParser from Bio.PDB.SASA import ShrakeRupley

parser = PDBParser(QUIET=True) structure = parser.get_structure('protein', 'protein.pdb')

Higher precision (more points = slower but more accurate)

sr = ShrakeRupley(probe_radius=1.4, n_points=960) sr.compute(structure, level='R')

Per-atom SASA

for atom in structure.get_atoms(): print(f'{atom.name}: {atom.sasa:.2f} A^2')

Identifying Buried vs Exposed Residues

from Bio.PDB import PDBParser from Bio.PDB.SASA import ShrakeRupley

parser = PDBParser(QUIET=True) structure = parser.get_structure('protein', 'protein.pdb')

sr = ShrakeRupley() sr.compute(structure, level='R')

buried = [] exposed = [] for residue in structure.get_residues(): if residue.id[0] != ' ': continue if hasattr(residue, 'sasa'): if residue.sasa < 10.0: # Threshold in A^2 buried.append(residue) else: exposed.append(residue)

print(f'Buried: {len(buried)}, Exposed: {len(exposed)}')

Related Skills

  • structure-io - Parse and write structure files

  • structure-navigation - Access chains, residues, atoms

  • structure-modification - Transform coordinates, modify structures

  • alignment - Sequence alignment for structure comparison

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