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Mathematical Biology seminar
Viktoria Hsu
University of Washington
"Electro-Diffusion in Cell Membranes, a Quasi Steady-State Approach"
Wednesday, January 28, 2004
3:05 pm LCB 225
Most mathematical models for signal generation in single neurons, such
as the classic Hodgkin-Huxley model, assume the single neuron is
bathed in an infinite buffer solution. Thus the composition of the
bath never changes. This assumption is appropriate for the comparison
of model results to in vitro studies, because in these studies the
cell preparation is actually bathed in a relatively fixed
environment. In their current state, such models are not able to take
into account large changes in the external environment of a cell, as
occur when metabolite levels are depleted (ischemia). Ischemia have
been linked to ailments like epileptic seizures and heart attacks. My
goal is to improve current neuron models such that changing
extracellular conditions can be taken into account in a single-cell
micro-environment. In this talk, I lay the foundation for a physically
consistent model for signal generation and ion transport, which is
based on the quasi steady-state approximation to an electrodiffusion
system. In the first part of the presentation, an efficient numerical
method for the solution of 1D Poisson-Nernst-Planck (PNP) systems is
introduced. In the second part of the talk, this numerical method is
applied to solving the consecutive steady-state dynamics of a
two-compartment system of ions. The results of this approach are
compared to the full PDE in order to demonstrate the sensibility of
the steady-state assumption. Finally, the quasi steady-state approach
is compared to a Hodgkin-Huxley type model for a cell with intact
gated channels (passive transport) but no ion pumps (active
transport). In the near future of this project, I shall incorporate
active ion transport, applied currents, and cell volume dynamics. In
the long term, I would like to consider tissues (networks of cells),
and incorporate connections between ion transport and other signaling
mechanisms.
For more information contact J. Keener, 1-6089
E-mail:
keener@math.utah.edu
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