Continuum modeling of non-conservative fluid membrane for simulating long-term cell dynamics

Area of Science:

• Computational biology
• Biophysics
• Cellular dynamics

Background:

• Living cells exhibit active 3D deformation and movement over long timescales (minutes to days).
• Cell membrane dynamics, including endocytosis and exocytosis, are critical for large cell deformations but lack computational models for non-conservative membranes.
• Existing models struggle to simulate long-term cell dynamics with membrane turnover.

Purpose of the Study:

• To propose and validate a novel computational framework for simulating long-term 3D cell dynamics.
• To incorporate non-conservative fluidic membrane behavior into cell dynamics simulations.
• To enable quantitative analysis of cell shaping and movement influenced by membrane turnover.

Main Methods:

• Developed a computational framework treating the cell surface membrane as a viscous, non-conservative fluid.
• Discretized cell shape using a triangular mesh with dynamics governed by energy and dissipation functions.
• Implemented a modified dynamic remeshing method to optimize mesh structure during simulations.
• Validated the framework through numerical simulations of membrane flow and cell migration.

Main Results:

• The framework accurately reproduces physically consistent membrane flow.
• Artificial effects from the remeshing method were found to be negligible.
• Simulations of cell migration, driven by polarized surface tension (Marangoni effect), matched analytical solutions.
• The model quantitatively reproduces long-term active cell dynamics including membrane turnover.

Conclusions:

• The proposed computational framework effectively simulates long-term 3D cell dynamics with membrane turnover.
• This framework provides a valuable tool for analyzing cell shaping and movement mechanisms.
• It lays the groundwork for understanding various cellular processes involving dynamic membrane changes.