Welcome to MembraneCurvature’s Documentation

Minimum MDAnalysis version: 2.4.0

Last updated: Jun 03, 2026

The MDAnalysis MembraneCurvature tool module calculates the Gaussian and mean curvature from Molecular Dynamics (MD) simulations.

MembraneCurvature derives 2D curvature profiles of a surface of reference. To suit the needs of your system, we offer flexible atom selection that will enable you to use the most convenient AtomGroup to extract curvature from your MD simulations!

This is an example on how to use MembraneCurvature:

import MDAnalysis as mda
from membrane_curvature.base import MembraneCurvature

u = mda.Universe(coordinates, trajectory)
mc = MembraneCurvature(u).run()

surface =  mc.results.average_z_surface
mean_curvature =  mc.results.average_mean_curvature
gaussian_curvature = mc.results.average_gaussian_curvature

You can find more details on how to use MembraneCurvature in the Usage page.

Features

MembraneCurvature allows you to:

• Calculate mean and Gaussian curvature from MD simulations.

• Derive 2D curvature profiles from atoms of reference with two different methods: binning or Fourier-based.

• Get per-frame or averaged results for surface, mean and Gaussian curvature.

Why MembraneCurvature?

MembraneCurvature is a user-friendly, actively-maintained, well-documented tool in Python 3 to derive 2D maps of membrane curvature from MD Simulations, using the most recent version of MDAnalysis Are you interested in calculating mean and Gaussian curvature from MD simulations? This tool is for you!

Installation

MembraneCurvature is available via pip, conda, and uv. Please refer to the Installation section in the Getting Started page for detailed installation instructions.

Contents:

• Getting Started
  • Installation
    • 1. Via pip
    • 2. Via conda
    • 3. With uv (recommended for development)
• MembraneCurvature’s API Documentation
  • MembraneCurvature
  • MembraneCurvature
  • Curvature
    • Functions
  • fourier_curvature()
  • gaussian_curvature()
  • gaussian_curvature_monge()
  • mean_curvature()
  • mean_curvature_monge()
  • Binning Surface
    • Functions
  • derive_surface()
  • get_z_surface()
  • normalized_grid()
  • Fourier Surface
    • Functions
  • fourier_mode_list()
  • n_fourier_parameters()
  • _compute_wavevector()
  • _build_fourier_matrix()
  • _solve_design_least_squares_svd()
  • _unpack_coefficients()
  • _fourier_fit_from_atoms()
  • _harmonic_height_and_phi_derivatives()
  • _eval_fourier_surface()
  • _bin_centre_mesh()
  • fourier_height_from_atoms()
  • fourier_height_derivatives_from_atoms()
  • Fourier Validators
  • _coerce_positions()
  • validate_positions()
  • validate_positive_domain_widths()
  • validate_positive_bin_counts()
• Algorithm
  • Overview
  • 1. Select atoms of reference
  • 2. Choose surface method
  • 2.1 Fourier method
    • 2.1.1 Choose Fourier modes
    • 2.1.2 Compute wavevectors
    • 2.1.3 Build design matrix
    • 2.1.4 Solve least-squares system
  • 2.2. Binning method
    • 2.2.1. Set grid
    • 2.2.2. Populate grid
  • 3. Derive surface and calculate surface derivatives
    • 3.1. Derive surface
    • 3.2. Calculate derivatives
    • 3.2a. Binning + finite differences (surface_method='binning')
    • 3.2b. Fourier fit + analytic derivatives (surface_method='fourier')
    • 3.3. Mean curvature
    • 3.4. Gaussian curvature
  • 4. Average over frames
• Usage
  • 1. Surface derivation methods
  • 2. Examples of how to use MembraneCurvature to derive curvature profiles
    • 2.1. Membrane-only systems
    • 2.2 Membrane-protein systems
• Visualization
  • 1. imshow
  • 2. contourf
• Tutorials
  • Membrane-only systems
    • POPC:POPE:CHOL bilayer (Coarse-Grained).
  • Membrane-protein systems
    • NhaA membrane protein in a POPE:POPG lipid bilayer (all atom)
    • References

License

Source code included in this project is available under the GNU Public License v3 from github.com/MDAnalysis/membrane_curvature.

Indices and tables

• Index

• Module Index

• Search Page