Non-Markovian Gating of Ca2+-Activated K+ Channels in Cultured Kidney Cells Vero. Rescaled Range Analysis

Using the patch-voltage clamp technique and the rescaled range method, activity of single large conductance Ca²⁺-activated K⁺ channels (K_Ca channels) was studied. For the sequences of alternating open and shut time intervals, the dependence R/S vs. N in the double logarithmic coordinates presented a curve with two slopes, H₁ =0.60 ± 0.04, and H₂ = 0.88 ± 0.21, where H₁ and H₂ characterized the Hurst exponents for shot and long time ranges, respectively. Similar results were obtained for reduced data sets consisting of only open or only shut intervals. Randomization of the experimental data resulted in a single slope, H, of 0.52 ± 0.02. Simulations were performed with eight-state Markovian model without memory. The calculated Hurst exponent presented in average 0.54 ± 0.02. The results suggest that the activity of single Ca²⁺-activated K⁺ channel exhibits two regimes, with slight positive correlation at short time ranges (H₁ =0.6), and strong positive correlation at long time ranges (H₂ = 0.88); therefore the channel gating as a whole is not a steady-state Markovian process.