Mathematical Biology Program

University of Utah
Department of Mathematics

Mathematical Biology Program


Program of Study


Weekly Schedule

Mathbiology Seminar

Journal Club







Contact Us

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