Breathing and moving vesicles in a geometric mechanochemical model
Abstract
We consider a geometric mechanochemical model of vesicles which couples the Helfrich flow for the shape of a lipid bilayer vesicle membrane X with a reaction-diffusion equations for a single ``morphogen'' ϕ on X. The Helfrich flow is the L2 gradient flow of the elastic bending energy E(X)=∫X (H−c0)2 dS of X, typically supplemented by area or volume constraints, or both. The morphogen ϕ adsorbs/desorbs at places of high/low mean curvature H, i.e., the kinetics of ϕ depend on H, and conversely ϕ modifies the spontaneous curvature c0 on X. The flow is no longer gradient, and hence allows for more complicated dynamics, including time periodic orbits, e.g., ``breathing and moving'' vesicle shapes. We show how to compute bifurcation diagrams for such solution branches via numerical continuation and bifurcation methods. We mostly focus on ``planar'' vesicles (1D closed curves) but also give an outlook on 3D vesicles (2D closed membranes).
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BibTeX
@misc{meiners2026breathing,
title = {{Breathing and moving vesicles in a geometric mechanochemical model}},
author = {Alexander Meiners and Hannes Uecker},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.09360},
eprint = {2609.09360},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.09360},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Breathing and moving vesicles in a geometric mechanochemical model
AU - Alexander Meiners
AU - Hannes Uecker
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2609.09360
UR - https://arxiv.org/abs/2609.09360
AB - We consider a geometric mechanochemical model of vesicles which couples the Helfrich flow for the shape of a lipid bilayer vesicle membrane X with a reaction-diffusion equations for a single ``morphogen'' ϕ on X. The Helfrich flow is the L^2 gradient flow of the elastic bending energy E(X)=∫_X (H−c_0)^2 dS of X, typically supplemented by area or volume constraints, or both. The morphogen ϕ adsorbs/desorbs at places of high/low mean curvature H, i.e., the kinetics of ϕ depend on H, and conversely ϕ modifies the spontaneous curvature c_0 on X. The flow is no longer gradient, and hence allows for more complicated dynamics, including time periodic orbits, e.g., ``breathing and moving'' vesicle shapes. We show how to compute bifurcation diagrams for such solution branches via numerical continuation and bifurcation methods. We mostly focus on ``planar'' vesicles (1D closed curves) but also give an outlook on 3D vesicles (2D closed membranes).
ER -