title: Hurst analysis applied to the study of single calcium-activated potassium channel kinetics.
abstract: The gating of ion channels has been modeled by assuming that the transitions between open and closed states is a memoryless process. Nevertheless, analysis of records of unitary current events suggests that the kinetic process presents short-term memory, i.e. the open- and closed-dwell times are short-term correlated. Here the rescaled range analysis (R/S Hurst analysis) is used as a method to test long-term correlation, in single calcium-activated potassium channels present in Leydig cells. The Hurst coefficients, calculated for four different voltages (V) are: 0.634+/-0.022 (n=3) for V=+20 mV; 0.635+/-0.012 (n=4) for V=+40 mV; 0.606+/-0.020 (n=4) for V=+60 mV and 0.608+/-0.026 (n=4) for V=+80 mV. This indicates that open- and closed-dwell times are long-term correlated and do not change with the voltage applied to the patch at a 5% significance level (F=2.2402;p=0.140715). Randomly shuffling the experimental data removes the correlation in all voltages. When the Hurst method was applied to the results from a simulated three-state Markovian model, it could not account for the long-term correlation found in the experimental data. In this case, H has the following values: 0. 5498+/-0.018 (n=100) for V=+20 mV; 0.5557+/-0.0202 (n=100) for V=+40 mV; 0.5565+/-0.0246 (n=100) for V=60 mV and 0.5595+/-0.0247 (n=100) for V=+80 mV. Even a four-state Markovian model was not adequate to correctly simulate the long-term memory found experimentally, with H values significantly different from those found for the experimental data, in the same voltage range (F=15.0355;p=0.00001). In conclusion, this paper shows that: (1) the open- and closed-dwell times of the single calcium-activated potassium channel of Leydig cells are long-term correlated; (2) three- and four-state Markovian models, which describe very well the dwell time distributions, are not adequate to describe the long-term correlation found between the open and closed states of this ion channel.
authors.affiliation: Department of Physiology-Faculty of Medicine of Ribeirão Preto, 14049-900, Brazil.
authors.forename: W A
authors.initials: WA
authors.lastname: Varanda
authors.forename: L S
authors.initials: LS
authors.lastname: Liebovitch
authors.forename: J N
authors.initials: JN
authors.lastname: Figueiroa
authors.forename: R A
authors.initials: RA
authors.lastname: Nogueira
mesh_terms: D000818:Animals; D002118:Calcium / Q000378:metabolism*; D002462:Cell Membrane / Q000378:metabolism; D003198:Computer Simulation; D015640:Ion Channel Gating / Q000502:physiology*; D007985:Leydig Cells / Q000378:metabolism; D008297:Male; D008390:Markov Chains; D015233:Models, Statistical; D015221:Potassium Channels / Q000502:physiology*
chemical_list: D015221:Potassium Channels; D002118:Calcium