Topological Approach to Measuring the Gaussian Curvature Modulus of Lipid Membranes in Simulation

Area of Science:

• Biophysics
• Computational Biology
• Materials Science

Background:

• Lipid membrane fission and fusion are essential cellular processes involving shape transformations.
• These events are governed by the Gaussian curvature modulus (κ), a parameter difficult to measure experimentally due to its topological nature.
• Existing methods face complications, often requiring open membrane edges that violate topological constraints.

Purpose of the Study:

• To introduce a novel computational method for determining the Gaussian curvature modulus (κ) of lipid membranes.
• To overcome the experimental challenges associated with measuring κ by avoiding open membrane edges.

Main Methods:

• Simulating triply periodic minimal surfaces (TPMS).
• Measuring the excess curvature energy (E) of these surfaces.
• Inferring the free energy (F) using a thermodynamic argument based on the temperature dependence of E and E/F.

Main Results:

• Successfully determined the Gaussian curvature modulus (κ) for a coarse-grained lipid model.
• Observed changes in κ and its ratio to the ordinary bending modulus across various temperatures and lipid shapes.
• Results align with established theoretical expectations for membrane behavior.

Conclusions:

• The proposed computational method provides a robust approach to determine the Gaussian curvature modulus (κ) of lipid membranes.
• This method circumvents limitations of previous techniques by utilizing TPMS simulations.
• The findings validate the method and offer insights into lipid membrane mechanics and thermodynamics.