### Thomas Fai

Doctoral Candidate

Courant Institute of Mathematical Sciences

New York University

November 20, 2012

A discrete model of the red blood cell cytoskeleton and its use in Immersed Boundary method simulations

The red 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 can be thought of as a graph of spectrin polymers
(edges) connected at actin-based junctional complexes (nodes). In this
talk, we discuss an algorithm to generate a random graph on the surface
of a model red blood cell with the physiologically observed statistical
properties, such as the distributions of edge length and the number of
neighbors of a given node. To model the network elasticity, we treat
these edges 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 of the
continuum model of the cytoskeleton. Lastly, we present results from
Immersed Boundary simulations of the red cell under shear flow,
including the discrete cytoskeleton and its ~40,000 nodes. This is joint
work with Alejandra Leo-Macias, David Stokes, and Charles Peskin.