Analysing ion channels with hidden Markov models

Abstract

Ion channel current amplitudes (μ) and open probabilities (P _o) have been analysed so far by defining a 50% threshold to distinguish between open and closed states of the channels. With this standard method (SM) it is very difficult or even impossible to analyse channels of different size in one membrane patch correctly. A stochastical model, named the hidden Markov model (HMM), separates between observation noise and the stochastic process of opening and closing of ion channels. The HMM allows the independent analysis of μ, P _o, and mean dwell times (τ) of different channels in one membrane patch, without defining threshold levels. Using this method errors in the analysis are not summarized like in the SM because all different analysing procedures (e. g. filtering, setting of threshold, fitting processes) are done in one step. Two different K⁺ channels in excised basolateral membranes of the cortical collecting duct of rat (CCD) were analysed by the SM and the HMM. The μ value of the intermediate-conductance K⁺ channel (i-K⁺) was 3.9±0.1 pA (SM) and 3.8±0.2 pA (HMM) for 11 observations. The P _o value of this channel was 10.2±4.2% (SM) and 10.1±4.0% (HMM). The mean τ values were 5.4±0.6 ms for the open state and 9.6±2.2 ms and 145±21 ms for the closed states (SM) and 7.8±1.1 ms, 7.7±0.9 ms and 148±24 ms (HMM), respectively. For seven small-conductance K⁺ (s-K⁺) channels, which were found in the same membrane patches as the i-K⁺, an accurate analysis of P _o and τ was not possible with the SM. The μ value was 1.0±0.1 (SM), 0.9±0.1 (HMM) pA. P _o was 16.6±4.6%, the open τ value was 11.1±2.8 ms, and the closed τ value was 34.9±8.5 ms. The HMM allows the analysis of single-channel currents, P _o, and mean τ values when different or more than one ion channel(s) are colocalized in one membrane patch. Where analysis with the SM was possible results did not significantly differ from those obtained with the HMM. Thus for this kind of analysis the method of setting a 50% threshold appears justified.