Absolute vs Convective Instabilities and Front Propagation in Lipid Membrane Tubes

Area of Science:

• Biophysics
• Fluid Dynamics
• Cell Biology

Background:

• Biological membrane tubes exhibit complex dynamics influenced by internal and external factors.
• Understanding membrane tube stability is crucial for processes like cell division and intracellular transport.

Purpose of the Study:

• To analyze the stability of biological membrane tubes under varying conditions.
• To investigate the role of base flow and tension in membrane tube dynamics.
• To elucidate the mechanisms behind axonal retraction and atrophy.

Main Methods:

• Analysis of membrane tube stability using dimensionless numbers: Föppl-von Kármán number (Γ) for tension and Scriven-Love number (SL) for flow speed.
• Nonlinear simulations of unstable membrane tubes.
• Weakly nonlinear analysis to approximate membrane dynamics with extended Fisher-Kolmogorov equations.

Main Results:

• Membrane dynamics are determined by Γ and SL.
• SL dictates the nature of instability (absolute vs. convective).
• Simulations show instabilities form propagating fronts, leaving thin, atrophied tubes, with shape transitions dependent on Γ.

Conclusions:

• The study provides insights into pattern selection mechanisms in axonal shapes.
• Findings are consistent with experimental observations of axonal retraction.
• Membrane dynamics can be modeled by extended Fisher-Kolmogorov equations, highlighting two Lifshitz points for bifurcations.