### A Discrete Model of the Red Blood Cell Cytoskeleton and its Use in Immersed Boundary Method Simulations

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Thomas Fai, New York University
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The red blood cell cytoskeleton, which is anchored to the lipid bilayer membrane, is an elastic structure that helps the cell recover from the large deformations it experiences while circulating through the body. The cytoskeleton has an intricate three-dimensional structure, as shown in recent tomographic images [1], but it may be modeled simply as a graph of actin-based junctional complexes (nodes) connected by spectrin polymers (edges).
Our discrete model of the cytoskeleton incorporates statistical properties, such as the distributions of edge length and the number of neighbors of a given node, that are gathered directly from the tomograph data. To model the network elasticity, we treat the spectrin polymers as entropic springs. We show that the spring constant obtained from a well-known model of entropic springs is in reasonable agreement with the experimentally determined shear modulus. In previous work, a variable viscosity and variable density immersed boundary method was used to simulate the dynamics of red cells [2]. In those simulations, we used a continuum elastic model to approximate the cytoskeletonâ€™s response to in-plane shear. Here, we describe the effect of replacing the continuum model with the more realistic discrete model with its approximately 40,000 nodes.
**References**
[1] A. Nans, N. Mohandas, and D. L. Stokes. Native Ultrastructure of the Red Cell Cytoskeleton by Cryo-Electron Tomography. Biophysical Journal, 101:23412350, 2011.
[2] T.G. Fai, B.E. Griffith, Y. Mori, and C.S. Peskin. Immersed Boundary Method for Variable Viscosity and Variable Density Problems using Fast Constant-Coefficient Linear Solvers I: Numerical Method and Results. Submitted.

**Abstract Author(s): **Thomas Fai, Alejandra Leo-Macias, David Stokes, and Charles Peskin