A geometric comparison of single chain multi-state models of ion channel gating

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.