# Mathematical Biology Seminar

### Thomas Fai

Courant Institute

#### A discrete model of the red blood cell cytoskeleton and its use in immersed boundary method simulations

#### Wednesday, January 22, 2014, at 3:05pm

LCB 219

The red blood cell cytoskeleton, which is anchored to a lipid bilayer membrane, is an elastic network that helps red cells recover from large deformations as they circulate through the body. Although the cytoskeleton has a convoluted structure, as shown in recent tomographic images, it may be modeled simply as a graph of actin-based junctional complexes (nodes) connected by spectrin polymers (edges).
We have developed a discrete cytoskeleton model that incorporates statistical properties
of the cytoskeleton such as the edge length and node degree distributions. A specialized
image processing technique is used to gather these distributions directly from tomograms.
The network elasticity comes from treating 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. By simulating the
behavior of red blood cells in shear flow using a variable viscosity and variable density
immersed boundary method, we have begun to compare this discrete model with its
approximately 40,000 nodes to more commonly-used continuum ones. We hope this model may
be useful for studying the mystery of what causes red cell aging. This is joint work with
Alejandra Leo-Macias, David Stokes, and Charles Peskin.