Get dihedral angles#

Calculating dihedral and torsional angles from atom quartets.

The function molsysmt.structure.get_dihedral_angles() calculates dihedral angles defined by four consecutively bonded atoms \((A, B, C, D)\), measuring the angle between planes \((A, B, C)\) and \((B, C, D)\).

Added in version 1.0.0.

API documentation

Follow this link for a detailed description of the input arguments, raised errors, and returned objects of this function: molsysmt.structure.get_dihedral_angles().

Basic usage#

Let’s measure the backbone \(\phi\) dihedral angles of Met-enkephalin:

import molsysmt as msm
import pyunitwizard as puw
import matplotlib.pyplot as plt

molsys = msm.convert(msm.systems['Met-enkephalin']['met_enkephalin.h5msm'])

Note

Demo Systems Catalog

This tutorial uses demonstration datasets provided by MolSysMT. To explore the full catalog of bundled systems, forms, and file paths, visit the Demo Systems guide.

We query the backbone \(\phi\) atom quartets using molsysmt.topology.get_dihedral_quartets() and calculate their angles:

phi_quartets = msm.topology.get_dihedral_quartets(molsys, phi=True)
phi_angles = msm.structure.get_dihedral_angles(molsys, dihedral_quartets=phi_quartets)
print('Phi angles (degrees):', puw.convert(phi_angles, to_unit='degrees'))

Phi angles (degrees): [[-179.99977050951892 -179.9997685580422 -179.99976916196186  -179.99977065567504]] degree

Measuring sidechain dihedral angles#

In addition to backbone angles, sidechain torsional angles (such as \(\chi_1, \chi_2\)) or custom quartets can be queried and evaluated:

chi1_quartets = msm.topology.get_dihedral_quartets(molsys, chi1=True)
chi1_angles = msm.structure.get_dihedral_angles(molsys, dihedral_quartets=chi1_quartets)
print(f'Identified {len(chi1_quartets)} chi1 quartets.')
print('Chi1 dihedral angles (degrees):', puw.convert(chi1_angles, to_unit='degrees'))

Identified 3 chi1 quartets.

Chi1 dihedral angles (degrees): [[-179.99988816868782 -179.99988283064798 -179.99992497471675]] degree

Ramachandran conformational distribution across structural ensembles#

By computing backbone \(\phi\) and \(\psi\) dihedral angles across an ensemble of structures, we can map the conformational space onto a classic 2D Ramachandran plot:

traj = msm.convert(msm.systems['pentalanine']['traj_pentalanine.h5msm'])
phi_q = msm.topology.get_dihedral_quartets(traj, phi=True)
psi_q = msm.topology.get_dihedral_quartets(traj, psi=True)

phi_vals = msm.structure.get_dihedral_angles(traj, dihedral_quartets=phi_q[1])
psi_vals = msm.structure.get_dihedral_angles(traj, dihedral_quartets=psi_q[1])

phi_deg = puw.get_value(puw.convert(phi_vals[:, 0], to_unit='degrees'))
psi_deg = puw.get_value(puw.convert(psi_vals[:, 0], to_unit='degrees'))

fig, ax = plt.subplots(figsize=(5, 5))
ax.scatter(phi_deg, psi_deg, alpha=0.3, s=10, c='navy')
ax.set_xlim(-180, 180)
ax.set_ylim(-180, 180)
ax.set_xlabel('$\\phi$ (degrees)')
ax.set_ylabel('$\\psi$ (degrees)')
ax.set_title('Ramachandran Plot (Residue 2)')
ax.grid(True, linestyle='--', alpha=0.5)
plt.tight_layout()
plt.show()

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