Multiscale simulation of erythrocyte membranes

Zhangli Peng, Robert J. Asaro, and Qiang Zhu

To quantitatively predict the mechanical response and mechanically induced remodeling of red blood cells, we developed a multiscale method to correlate distributions of internal stress with overall cell deformation. This method consists of three models at different length scales: in the complete cell level the membrane is modeled as two distinct layers of continuum shells using finite element method (Level III), in which the skeleton-bilayer interactions are depicted as a slide in the lateral (i.e., in-plane) direction (caused by the mobility of the skeleton-bilayer pinning points) and a normal contact force; the constitutive laws of the inner layer (the protein skeleton) are obtained from a molecular-based model (Level II); the mechanical properties of the spectrin (Sp, a key component of the skeleton), including its folding/unfolding reactions, are obtained with a stress-strain model (Level I). Model verification is achieved through comparisons with existing numerical and experimental studies in terms of the resting shape of the cell as well as cell deformations induced by micropipettes and optical tweezers. Detailed distributions of the interaction force between the lipid bilayer and the skeleton that may cause their dissociation and lead to phenomena such as vesiculation are predicted. Specifically, our model predicts correlation between the occurrence of Sp unfolding and increase in the mechanical load upon individual skeleton-bilayer pinning points. Finally a simulation of the necking process after skeleton-bilayer dissociation, a precursor of vesiculation, is conducted.

DOI