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Mem3DG: Modeling membrane mechanochemical dynamics in 3D using discrete differential geometry.

Cuncheng Zhu¹, Christopher T Lee¹, Padmini Rangamani¹

¹Department of Mechanical and Aerospace Engineering, University of California San Diego, La Jolla CA 92093.

Biophysical Reports

|September 26, 2022

Summary

This study introduces Mem3DG, a computational framework using discrete differential geometry to model 3D membrane dynamics. It resolves inconsistencies in discrete models, enabling accurate simulation of cell membrane shape transformations.

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Area of Science:

Computational biology
Biophysics
Cell biology

Background:

Biomembranes exhibit diverse morphologies crucial for cellular functions.
Computational modeling is widely used to understand mechanochemical factors influencing membrane shape.
Discrete mesh models offer flexibility for simulating complex 3D shapes and physics but lack theoretical consensus.

Purpose of the Study:

To present Mem3DG, an extensible framework for modeling 3D membrane mechanochemical dynamics.
To resolve ambiguities in discrete geometric definitions and establish a link between discrete and smooth theories.
To provide a unifying perspective on relating discrete and smooth energy and forces in membrane modeling.

Main Methods:

Utilizes discrete differential geometry (DDG) on triangulated meshes.
Develops an extensible framework (Mem3DG) for simulating membrane dynamics.
Applies DDG formalism to unify discrete and smooth geometric theories.

Main Results:

Successfully models classical membrane shape transformations (biconcave disk, dumbbell, unduloid).
Simulates spherical bud formation on different membrane types.
Investigates the coupled effects of membrane mechanics and protein mobility on phase and shape transformation.

Conclusions:

Mem3DG provides a theoretically consistent and numerically efficient approach to 3D membrane modeling.
The framework unifies discrete and smooth geometric theories for energy and force calculations.
Mem3DG is poised to become an end-to-end tool for simulating realistic cell geometries with advancing 3D imaging technologies.