Absolute vs Convective Instabilities and Front Propagation in Lipid Membrane Tubes

Tchoufag, Joël; Sahu, Amaresh; Mandadapu, Kranthi K.

doi:10.1103/physrevlett.128.068101

Title: Absolute vs Convective Instabilities and Front Propagation in Lipid Membrane Tubes

Journal Article · 11 February 2022 · Physical Review Letters

DOI: https://doi.org/10.1103/physrevlett.128.068101 · OSTI ID:1891283

Tchoufag, Joël ^[1];

^[1]; Mandadapu, Kranthi K. ^[2]

Univ. of California, Berkeley, CA (United States)
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)

Here 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 Γ 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 Γ, whereas SL governs the absolute versus convective nature of the instability. Furthermore, nonlinear simulations of unstable tubes reveal an initially localized disturbance result in propagating fronts, which leave a thin atrophied tube in their wake. Depending on the value of Γ, 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.

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Research Organization:: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES)

Grant/Contract Number:: AC02-05CH11231

OSTI ID:: 1891283

Journal Information:: Physical Review Letters, Journal Name: Physical Review Letters Journal Issue: 6 Vol. 128; ISSN 0031-9007

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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