ANALYZING ION CHANNELS WITH HIDDEN MARKOV-MODELS

Ion channel current amplitudes (mu) and open probabilities (P-o) have been analysed so far by defining a 50% threshold to distinguish betwee n open and closed states of the channels. With this standard method (S M) it is very difficult or even impossible to analyse channels of diff erent size in one membrane patch correctly. A stochastical model, name d the hidden Markov model (HMM), separates between observation noise a nd the stochastic process of opening and closing of ion channels. The HMM allows the independent analysis of mu, P-o, and mean dwell times ( tau) of different channels in one membrane patch, without defining thr eshold levels. Using this method errors in the analysis are not summar ized like in the SM because all different analysing procedures (e.g. f iltering, setting of threshold, fitting processes) are done in one ste p. Two different K+ channels in excised basolateral membranes of the c ortical collecting duct of rat (CCD) were analysed by the SM and the H MM. The mu 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% (HM M). The mean tau 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 me mbrane patches as the i-K+, an accurate analysis of P-o and tau was no t possible with the SM. The mu value was 1.0 +/- 0.1 (SM), 0.9 +/- 0.1 (HMM) pA. P-o was 16.6 +/- 3.6%, the open tau value was 11.1 +/- 2.8 ms, and the closed tau value was 34.9 +/- 8.5 ms. The HMM allows the a nalysis of single-channel currents, P-o, and mean tau values when diff erent or more than one ion channel(s) are colocalized in one membrane patch. Where analysis with the SM was possible results did not signifi cantly differ from those obtained with the HMM. Thus for this kind of analysis the method of setting a 50% threshold appears justified.