Absolute vs Convective Instabilities and Front Propagation in Lipid Membrane Tubes

Abstract

We analyze the stability of biological membrane tubes, with and without a base flow of lipids. Membrane dynamics are completely specified by two dimensionless numbers: the well-known Föppl--von Kármán number $\Gamma$ and the recently introduced Scriven--Love number $SL$, respectively quantifying the base tension and base flow speed. For unstable tubes, the growth rate of a local perturbation depends only on $\Gamma$, whereas $SL$ governs the absolute or convective nature of the instability. Furthermore, nonlinear simulations of unstable tubes reveal an initially localized disturbance results in propagating fronts, which leave a thin atrophied tube in their wake. Depending on the value of $\Gamma$, the thin tube is connected to the unperturbed regions via oscillatory or monotonic shape transitions -- reminiscent of recent experimental observations on the retraction and atrophy of axons. We elucidate our findings through a weakly nonlinear analysis, which shows membrane dynamics may be approximated by a model of the class of extended Fisher--Kolmogorov equations. Our study sheds light on the pattern selection mechanism in axonal shapes by recognizing the existence of two Lifshitz points, at which the front dynamics undergo steady-to-oscillatory bifurcations.

arXiv comment6 pages, 4 figures

References in corpus (14)

• Front propagation into unstable states
• Virus shapes and buckling transitions in spherical shells
• Dynamic Theory of Pearling Instability in Cylindrical Vesicles
• Membrane Viscosity Determined from Shear-Driven Flow in Giant Vesicles
• Osmotically Driven Shape Transformations in Axons
• Pearling and Pinching: Propagation of Rayleigh Instabilities
• Propagation of a Topological Transition: the Rayleigh Instability
• Front Propagation in the Pearling Instability of Tubular Vesicles
• The irreversible thermodynamics of curved lipid membranes
• Arbitrary Lagrangian--Eulerian finite element method for curved and deforming surfaces. I. General theory and application to fluid interfaces
• Geometry and dynamics of lipid membranes: The Scriven--Love number
• Hydro-osmotic instabilities in active membrane tubes
• Shear-driven instabilities of membrane tubes and dynamin-induced scission
• Dynamics of passive and active membrane tubes

Cited by in corpus (2)

• Morphodynamics of Active Nematic Fluid Surfaces
• The irreversible thermodynamics of curved lipid membranes II: Permeability and osmosis