# A Tale of Two Topologies: Canonical Forms for Ion Channel Data Analysis

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In this talk I will introduce the manifest interconductance rank (MIR) form and contrast it to another long-known canonical form used in the

data-driven identification of ion channel gating kinetics: the uncoupled model (UCM). (The UCM has every open state connected to every closed state and vice versa). MIR form has significantly fewer parameters and provides more insight into gating kinetics than the uncoupled model. Beyond the new canonical form the principle results to be presented are

(1)All topologies with interconductance rank=1 and with the same number of open and closed states result in identical steady-state statistics

(2)detailed balance is preserved under transformation to either UCM or MIR forms and

(3) a general detailed balance preserving transformation. These results should facilitate maximum likelihood methods for finding models that best fit a given data set.