The Helfrich functional, denoted by Hc0, is a mathematical expression proposed by Helfrich (1973) for the natural free energy carried by an elastic phospholipid bilayer. Helfrich theorises that idealised elastic phospholipid bilayers minimise Hc0 among all possible configurations. The functional integrates a spontaneous curvature parameter c0 together with the mean curvature of the bilayer and constraints on area and volume, either through an inclusion of osmotic pressure difference and tensile stress or otherwise. Using the mathematical concept of embedded orientable surface to represent the configuration of the bilayer, one might expect to be able to adapt methods from differential geometry and the calculus of variations to perform a fine analysis of bilayer configurations in terms of the parameters that it depends upon. In this article we focus upon the case of spherical red blood cells with a view to better understanding spherocytes and spherocytosis. We provide a complete classification of spherical solutions in terms of the parameters in the Helfrich model. We additionally present some further analysis on the rigidity and stability of spherocytes.
1
ETH Zentrum, Zürich, Switzerland
2
University of Wollongong, Australia
Yann Bernard; Glen Wheeler; Valentina-Mira Wheeler. Rigidity and stability of spheres in the Helfrich model. Interfaces and free boundaries, Tome 19 (2017) no. 4, pp. 495-523. doi: 10.4171/ifb/390
@article{10_4171_ifb_390,
author = {Yann Bernard and Glen Wheeler and Valentina-Mira Wheeler},
title = {Rigidity and stability of spheres in the {Helfrich} model},
journal = {Interfaces and free boundaries},
pages = {495--523},
year = {2017},
volume = {19},
number = {4},
doi = {10.4171/ifb/390},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/390/}
}
TY - JOUR
AU - Yann Bernard
AU - Glen Wheeler
AU - Valentina-Mira Wheeler
TI - Rigidity and stability of spheres in the Helfrich model
JO - Interfaces and free boundaries
PY - 2017
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EP - 523
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DO - 10.4171/ifb/390
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