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.