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A Geometric Comparison of Single Chain Multi-State Models of Ion Channel Gating

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Title: A Geometric Comparison of Single Chain Multi-State Models of Ion Channel Gating
Author: Willms, Allan R.; Nelson, Dominic
Abstract: Multi-state models of ion channel gating have been used extensively, but choosing optimally small yet sufficiently complex models to describe particular experimental data remains a difficult task. In order to provide some insight into appropriate model selection, this paper presents some basic results about the behavior of solutions of multi-state models, particularly those arranged in a chain formation. Some properties of the eigenvalues and eigenvectors of constant-rate multi-state models are presented. A geometric description of a three-state chain is given and, in particular, differences between a chain equivalent to an Hodgkin--Huxley model and a chain with identical rates are analyzed. One distinguishing feature between these two types of systems is that decay from the open state in the Hodgkin--Huxley model is dominated by the most negative eigenvalue while the identical rate chain displays a mix of modes over all eigenvalues.
URI: http://hdl.handle.net/10214/6607
Date: 2008-05-30
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Citation: Bull. Math. Biol. 70 (5) (2008) 1503-1524.


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