(250i) Absolute/Convective Instabilities and Front Propagation in Lipid Membrane Tubes

Biological lipid membranes make up the boundary of the cell and many of its internal organelles, and are often found in cylindrical configurations. For example, membrane tethers are pulled along microtubules by various proteins, thin tubes can shoot suddenly from the endoplasmic reticulum into the cell cytoplasm, and axonal flows bring lipids from the growth cone of a neuron to its cell body. Such systems involve lipids flowing in-plane as a two-dimensional fluid, while the membrane bends out-of-plane as an elastic shell; moreover, these two behaviors are coupled [1,2]. Interestingly, membrane tubes undergo a pearling instability and form a so-called 'beads on a string' configuration, as observed in a variety of experiments. In this work, we investigate the stability of membrane tubes with and without a base flow of lipids. We confirm the well-known result that tubes are stable at low tensions and unstable at high tensions, yet for unstable tubes we find increasing the base flow velocity changes the nature of the instability from absolute to convective. In the former case, an initially local perturbation will grow faster than it is convected downstream, such that it eventually invades the entire domain. In the latter case, the perturbation is convected faster than it spreads, and at long times a stationary observer will see no disturbance---despite the perturbation continuing to grow. We confirm our theoretical predictions with nonlinear simulations of unstable membrane systems, which reveal qualitatively different long-time behaviors of tubes with different base tensions and velocities. We end by investigating the dynamics of propagating fronts, which arise as the initial perturbation invades the unperturbed yet unstable region. Our results may be relevant in understanding various biological situations, in particular lipid flows along the body of a neuron and the ensuing response to local disturbances.

[1] A. Sahu, ..., K.K. Mandadapu. "Irreversible thermodynamics of curved lipid membranes." Physical Review E (2017), arXiv:1701.06495

[2] A. Sahu, A. Glisman, J. Tchoufag, K.K. Mandadapu. "Geometry and dynamics of lipid membranes: The Scriven--Love number." Physical Review E (2020), arXiv:1910.10693