Speaker: Viktoria R. T. Hsu, Applied Mathematics
Title:
Date: Thursday, November 6, 2003
Time: 3:30 - 4:20pm
Place: Guggenheim Room 408d
Abstract. Most mathematical models for signal generation in single neurons, such as the classic Hodgkin- Huxley model, assume that 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 during ischemia. It is my goal to improve current neuron models so that the changing extracellular conditions can be taken into account in a single cell micro environment. The main challenges in this endeavor are due to the necessity of creating a finite extracellular compartment. This requires considering mass conservation and electroneutrality.
In this talk, I lay the foundation for a physically consistent model based on a quasi-steady- state approximation. In the first part of the presentation, an efficient numerical method for the solution of 1D Poisson-Nernst-Planck (PNP) systems is developed. 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 my approach are compared to the full PDE in order to confirm 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 but no ion pumps to maintain homeostasis. In the future, I would like to incorporate active ion transport, applied currents, and cell volume dynamics into my model.
Everyone welcome!