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Special Semester on Quantitative Biology analyzed by Mathematical Methods
Linz, October 1, 2007 - January 27, 2008
Inverse Problems related to Ion Channels

Workshop on Ion Channels, Wed, 10 Oct, 2007

Speaker: Kattrin Arning

Abstract

Ion channels are proteins with a hole down their middle that allow
ions to move across otherwise impermeable cell membranes, thereby
controlling many important physiological functions, such as conduc-
ting electrical signals down nerve fibres and initiating muscle contrac-
tion.
We look at mathematical models describing the ion transport pro-
cess through membrane channels. One important class of models is
based on the Poisson-Nernst-Planck equations, a set of partial dif-
ferential equations. Starting from this model we derive a simplified
surrogate model to approximate current-voltage relationships and fur-
thermore investigate inverse problems related to the structure of the
underlying channel. Numerical examples will be given using a one-
dimensional approximation of the system.

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