4.8.1.2. HELANAL — analysis of protein helices

Author:

Lily Wang

Year:

2020

Copyright:

Lesser GNU Public License v2.1+

New in version 2.0.0.

This module contains code to analyse protein helices using the HELANAL algorithm ([Bansal2000] , [Sugeta1967] ).

HELANAL quantifies the geometry of helices in proteins on the basis of their Cα atoms. It can determine local structural features such as the local helical twist and rise, virtual torsion angle, local helix origins and bending angles between successive local helix axes.

[Sugeta1967]

Sugeta, H. and Miyazawa, T. 1967. General method for calculating helical parameters of polymer chains from bond lengths, bond angles and internal rotation angles. Biopolymers 5 673 - 679

[Bansal2000]

Bansal M, Kumar S, Velavan R. 2000. HELANAL - A program to characterise helix geometry in proteins. J Biomol Struct Dyn. 17(5):811-819.

4.8.1.2.1. Example use

You can pass in a single selection:

import MDAnalysis as mda
from MDAnalysis.tests.datafiles import PSF, DCD
from MDAnalysis.analysis import helix_analysis as hel
u = mda.Universe(PSF, DCD)
helanal = hel.HELANAL(u, select='name CA and resnum 161-187')
helanal.run()

All computed properties are available in .results:

print(helanal.results.summary)

Alternatively, you can analyse several helices at once by passing in multiple selection strings:

helanal2 = hel.HELANAL(u, select=('name CA and resnum 100-160',
                                  'name CA and resnum 200-230'))

The helix_analysis() function will carry out helix analysis on atom positions, treating each row of coordinates as an alpha-carbon equivalent:

hel_xyz = hel.helix_analysis(u.atoms.positions, ref_axis=[0, 0, 1])

4.8.1.2.2. Classes

class MDAnalysis.analysis.helix_analysis.HELANAL(universe, select='name CA', ref_axis=(0, 0, 1), verbose=False, flatten_single_helix=True, split_residue_sequences=True)[source]

Perform HELANAL helix analysis on your trajectory.

Parameters:

  • universe (Universe or AtomGroup) – The Universe or AtomGroup to apply the analysis to.

  • select (str or iterable of str, optional) – The selection string to create an atom selection that the HELANAL analysis is applied to. Note that HELANAL is designed to work on the alpha-carbon atoms of protein residues. If you pass in multiple selections, the selections will be analysed separately.

  • ref_axis (array-like of length 3, optional) – The reference axis used to calculate the tilt of the vector of best fit, and the local screw angles.

  • flatten_single_helix (bool, optional) – Whether to flatten results if only one selection is passed.

  • split_residue_sequences (bool, optional) – Whether to split the residue sequence into individual helices. This keyword only applies if a residue gap is present in the AtomGroup generated by a select string. If False, the residues will be analysed as a single helix. If True, each group of consecutive residues will be treated as a separate helix.

  • verbose (bool, optional) – Turn on more logging and debugging.

results.local_twists

The local twist angle from atom i+1 to i+2. Each array has shape (n_frames, n_residues-3)

Type:

array or list of arrays

results.local_nres_per_turn

Number of residues per turn, based on local_twist. Each array has shape (n_frames, n_residues-3)

Type:

array or list of arrays

results.local_axes

The length-wise helix axis of the local window. Each array has shape (n_frames, n_residues-3, 3)

Type:

array or list of arrays

results.local_heights

The rise of each local helix. Each array has shape (n_frames, n_residues-3)

Type:

array or list of arrays

results.local_helix_directions

The unit vector from each local origin to atom i+1. Each array has shape (n_frames, n_residues-2, 3)

Type:

array or list of arrays

results.local_origins

The projected origin for each helix. Each array has shape (n_frames, n_residues-2, 3)

Type:

array or list of arrays

results.local_screw_angles

The local screw angle for each helix. Each array has shape (n_frames, n_residues-2)

Type:

array or list of arrays

results.local_bends

The angles between local helix axes, 3 windows apart. Each array has shape (n_frames, n_residues-6)

Type:

array or list of arrays

results.all_bends

The angles between local helix axes. Each array has shape (n_frames, n_residues-3, n_residues-3)

Type:

array or list of arrays

results.global_axis

The length-wise axis for the overall helix. This points at the first helix window in the helix, so it runs opposite to the direction of the residue numbers. Each array has shape (n_frames, 3)

Type:

array or list of arrays

results.global_tilts

The angle between the global axis and the reference axis. Each array has shape (n_frames,)

Type:

array or list of arrays

results.summary

Summary of stats for each property: the mean, the sample standard deviation, and the mean absolute deviation.

Type:

dict or list of dicts

4.8.1.2.3. Functions

MDAnalysis.analysis.helix_analysis.helix_analysis(positions: ndarray[tuple[int, ...], dtype[float64]], ref_axis: Tuple[float, float, float] | ndarray[tuple[int, ...], dtype[float64]] = (0, 0, 1)) → Dict[str, ndarray[tuple[int, ...], dtype[_ScalarType_co]]][source]

Calculate detailed helix properties from atomic coordinates using a sliding window approach.

This function implements the HELANAL algorithm to analyze protein helices based on their Cα atom coordinates. It calculates various geometric properties including local twists, bends, and screw angles that characterize the helix structure.

Parameters:

  • positions (NDArray[float64], shape (N, 3)) – Atomic coordinates of Cα atoms in the helix. Must contain at least 9 atoms for meaningful analysis.

  • ref_axis (array-like, shape (3,), optional) – Reference axis used for calculating tilt and screw angles. Default is z-axis (0, 0, 1).

Returns:

Dictionary containing the following keys: - ‘local_twists’ : NDArray[float64], shape (N-3,)

Local twist angle (in degrees) between consecutive residues (i+1 to i+2).

  • ’local_nres_per_turn’NDArray[float64], shape (N-3,)

    Number of residues per turn, calculated as 360° / local_twist.

  • ’local_axes’NDArray[float64], shape (N-3, 3)

    Local helix axis vectors for each window.

  • ’local_bends’NDArray[float64], shape (N-6,)

    Angles (in degrees) between local helix axes 3 windows apart.

  • ’local_heights’NDArray[float64], shape (N-3,)

    Rise per residue (in Å) along the local helix axis.

  • ’local_helix_directions’NDArray[float64], shape (N-2, 3)

    Unit vectors from each local origin to the next Cα atom.

  • ’local_origins’NDArray[float64], shape (N-2, 3)

    Projected origins for each local helix window.

  • ’all_bends’NDArray[float64], shape (N-3, N-3)

    Matrix of angles between all pairs of local helix axes.

  • ’global_axis’NDArray[float64], shape (3,)

    Best-fit axis through all helix origins.

  • ’local_screw_angles’NDArray[float64], shape (N-2,)

    Azimuthal angles (in degrees) in the plane perpendicular to global_axis.

Return type:

dict

Notes

The algorithm uses a sliding window of 4 consecutive Cα atoms to calculate local helix properties. For a helix with N residues, the function returns properties for N-3 windows.

The reference axis is used to define the zero angle for screw angle calculations. By default, this is along the z-axis (0, 0, 1).

References

Examples

>>> import numpy as np
>>> from MDAnalysis.analysis import helix_analysis
>>> # Generate a simple alpha-helix
>>> t = np.linspace(0, 4*np.pi, 12)  # 12 residues
>>> x = np.cos(t)
>>> y = np.sin(t)
>>> z = t / (4*np.pi) * 16  # ~1.5Å rise per residue
>>> positions = np.column_stack((x, y, z))
>>> # Analyze helix properties
>>> results = helix_analysis(positions)
>>> # Get average twist angle
>>> avg_twist = results['local_twists'].mean()
>>> print(f"Average twist angle: {avg_twist:.1f}°")
MDAnalysis.analysis.helix_analysis.vector_of_best_fit(coordinates)[source]

Fit vector through the centered coordinates, pointing to the first coordinate (i.e. upside-down).

Parameters:

coordinates (numpy.ndarray of shape (N, 3)) –

Returns:

Vector of best fit.

Return type:

numpy.ndarray of shape (3,)

MDAnalysis.analysis.helix_analysis.local_screw_angles(global_axis, ref_axis, helix_directions)[source]

Cylindrical azimuth angles between the local direction vectors, as projected onto the cross-section of the helix, from (-pi, pi]. The origin (angle=0) is set to the plane of global_axis and ref_axis.

Parameters:

  • global_axis (numpy.ndarray of shape (3,)) – Vector of best fit. Screw angles are calculated perpendicular to this axis.

  • ref_axis (numpy.ndarray of shape (3,)) – Reference length-wise axis. One of the reference vectors is orthogonal to this axis.

  • helix_directions (numpy.ndarray of shape (N, 3)) – array of vectors representing the local direction of each helix window.

Returns:

Array of screw angles.

Return type:

numpy.ndarray of shape (N,)