CATpie: A Python tool for quantifying membrane curvature, area, and geometrically faithful normal-line thickness from...

Area of Science:

• Computational biophysics
• Biomolecular simulations
• Membrane biophysics

Background:

• Membrane shape is crucial for bilayer mechanics and protein interactions.
• Existing methods for analyzing simulated membrane geometry have limitations, especially under periodic boundary conditions.
• Accurate geometric characterization is essential for understanding membrane behavior.

Purpose of the Study:

• To introduce CATpie, a Python framework for unified geometric analysis of simulated membranes.
• To provide accurate and resolution-independent measurements of membrane curvature, area, and thickness.
• To enable systematic geometric characterization of molecular dynamics simulations.

Main Methods:

• CATpie represents membranes as smooth leaflet height fields over a periodic domain.
• It fits real Fourier series to leaflet surfaces to construct the mid-surface.
• Mean and Gaussian curvature, real area, and normal-line thickness are evaluated from analytic expressions.

Main Results:

• CATpie accurately recovers curvature fields, real areas, and leaflet separation on benchmark surfaces.
• Application to a POPC/POPS bilayer reveals quantification of local deformations and thickness modulations.
• The T_norm/D_zz ratio highlights discrepancies between normal-line and vertical separation due to membrane tilt.

Conclusions:

• CATpie offers a robust and accurate method for geometric analysis of simulated membranes.
• It overcomes limitations of grid-based smoothing methods, providing geometrically controlled measures.
• The framework supports various simulation types and enables detailed characterization of membrane geometry.