Long-term correlation in single calcium-activated potassium channel kinetics

Ion channels are protein molecules found in biological membranes, which can assume distinct open and closed conformational states, a phenomenon called ion channel kinetics. The transitions from one state to another are dependent on the potential energy barrier that separates them and can be controlled by the electrical field, ions and/or drugs. Both Markovian and fractal models have been used for modeling the ion channel kinetics. Ion single channel records are characterized by successive openings and closings, which are correlated in time. Here the rescaled range analysis (R/S Hurst analysis) is used to test for the occurrence of long-term correlation in the kinetics of a calcium-activated potassium channel of Leydig cells. A Hurst coefficient H=0.640±0.064 (n=5) was found for the single calcium-activated potassium channel clamped at −80mV and exposed to a free Ca2+ concentration equal to 10nM. This numerical value indicates the presence of long-term correlation (memory) in this kinetic process. However, when the R/S analysis was applied to ion channel data simulated using Markovian and fractal models, it could not account for the long-term correlation previously found in the experimental data. In summary, in this work we show that: (i) opening and closing dwell times for the single calcium-activated potassium channel of Leydig cells present long-term correlation and (ii) Markovian and fractal models, which describe well the dwell time distributions, are not adequate to describe the memory found in the kinetics of this channel.