Hurst Analysis Applied to the Study of Single Calcium-activated Potassium Channel Kinetics

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) forV =+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) forV =+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.