menger.analysis.mengercurvature

This module contains functionality for calculating Menger curvature along trajectories.

The Menger curvature provides information about local geometry by calculating the reciprocal radius of the circumscribed circle passing through three points.

The module contains: - menger_curvature(): numba function to compute curvature for a single frame - MengerCurvature: Analysis class that processes trajectories to extract curvature information

The analysis can be applied to any set of points, but is particularly useful for analyzing protein backbone conformations using C-alpha atoms.

Examples

Calculate Menger curvature for the chain A of a tubulin protein trajectory in serial mode:

>>> import MDAnalysis as mda
>>> from menger.analysis.mengercurvature import MengerCurvature
>>> from menger.tests.utils import make_universe
>>> md_name = "tubulin_chain_a"
>>> u = make_universe(
...     topology_name=f"{md_name}.pdb",
...     trajectory_name=f"{md_name}.dcd",
... )
>>> menger_analyser = MengerCurvature(
...     u,
...     select="name CA and chainID A",
...     spacing=2
... )
>>> menger_analyser.run()
>>> average_curvature = menger_analyser.results.local_curvatures
>>> flexibility = menger_analyser.results.local_flexibilities
>>> menger_curvature = menger_analyser.results.curvature_array

Calculate Menger curvature for the chain A of a tubulin protein trajectory in parallel mode:

>>> import MDAnalysis as mda
>>> from menger.analysis.mengercurvature import MengerCurvature
>>> from menger.tests.utils import make_universe
>>> md_name = "tubulin_chain_a"
>>> u = make_universe(
...     topology_name=f"{md_name}.pdb",
...     trajectory_name=f"{md_name}.dcd",
... )
>>> menger_analyser = MengerCurvature(
...     u,
...     select="name CA and chainID A",
...     spacing=2,
...     n_workers=4
... )
>>> menger_analyser.run(backend="multiprocessing", n_workers=4)
>>> average_curvature = menger_analyser.results.local_curvatures
>>> flexibility = menger_analyser.results.local_flexibilities
>>> menger_curvature = menger_analyser.results.curvature_array

See also

MDAnalysis.analysis.base.AnalysisBase: Base class for analysis

References

[1] Menger, Karl. Géométrie générale. 1954. <http://eudml.org/doc/192644>

[2] J. C. Léger. Menger Curvature and Rectifiability. Annals of Mathematics. 1999, 149, 831-869, DOI: 10.2307/121074

[3] Marien J, Prévost C, Sacquin-Mora S. nP-Collabs: Investigating Counterion-Mediated Bridges in the Multiply Phosphorylated Tau-R2 Repeat. J Chem Inf Model. 2024 Aug 26; 64(16):6570-6582. doi: 10.1021/acs.jcim.4c00742

Functions

`check_select`(universe, select)	Check if the selection string is valid for the universe. Args: universe (MDAnalysis.core.universe.Universe): Universe object. select (str): Selection string.
`check_spacing`(spacing, n_atoms)	Check if the spacing is valid given the number of atoms.
`compute_triangle_area`(edges_norm)	Calculate the area of a triangle given the norm of its edges.
`compute_triangle_edges`(frame, i, spacing)	Calculate the norm of the edges of a triangle given three vertices from a frame.
`menger_curvature`(frame, spacing)	Calculate the Menger Curvature for residues in [spacing+1:N-spacing] in a trajectory.
`menger_curvature_wrapper`(frame_index, ...)	Wrapper function for parallel computation of Menger curvature

Classes

MengerCurvature(universe_or_atomgroup[, ...])

This class calculates the Menger curvature for a trajectory of atoms or molecules.