Is red blood cell a simple capsule?
Résumé
Like other cells, the red blood cell membrane is composed of a lipid bilayer and a cytoskeleton, connected by protein junction complexes, with possible sliding. Despite this biological reality, it is most often modelled as a one-layer capsule or as a vesicle. An alternative is to consider a two-layers membrane, each mimicking either the lipid bilayer or the cytoskeleton. The in-plane elastic part brought by the cytoskeleton is modelled by a continuous constitutive law (capsule) or a discrete spring network. Considering four regimes representing the dynamics in shear flow, we computationally asses all the strategies with couplings such as capsule-capsule or capsule-network and vesicle-capsule or vesicle-network. The anisotropy artificially introduced by a discrete spring network is a source of numerical instability, especially for the coupling with a vesicle. Though the capsule-capsule and vesicle-capsule models show similarity in behaviour, considering fluidity and surface incompressibility when using a vesicle to represent the bilayer is not without consequences. Rigorous area conservation provides noticeable additional stiffness and fluidity allows lipid recirculation. Overall, our results suggest that modelling the membrane closer to the biological reality is more impactful than the largely debated issue about the stress-free shape for the cytoskeleton. Now, our results when comparing the capsule and the capsule-capsule models in tank-treading regime providentially highlight a new indicator of the right stress-free shape motivating new experimental investigations.
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