[Fractal properies of gating in potential-dependent K+-channels in Lymnaea stagnalis neurons]. / Fraktal'nye svoistva vorotnogo mekhanizma potentsialozavisimykh K+ - kanalov v neironakh Lymnaea stagnalis.

Sets of the channel open times, [tau(o)], and closed times, [tau(c)], and the full set of the channel open and closed times, [tau(o), tau(c)], in the activity of single voltage-dependent K+-channels in mollusc L. stagnalis neurons were analyzed using the rescaled range analysis (Hurst method), fast Fourier and wavelet transforms. It was found that the Hurst dependence for each time series could be approximated by a polygonal line with at least two slopes: H1 and H2 (Hurst exponents). The averaged values of H1 and H2 for the sets [tau(o), tau(c)] were equal to 0.61 +/- 0.03 and 0.83 +/- 0.11, respectively; for the [tau(o)] sets H1 = 0.66 +/- 0.03 and H2 = 0.95 +/- 0.10; for the [tau(c)] sets, H1 = 0.62 +/- 0.05 and H2 = 0.85 +/- 0.10. In some cases, a third slope appeared on the Hurst dependences. It was very variable and ranged between 0.5 and 1. The Hurst exponents H1, H2, and H3 characterized short, intermediate, and long time ranges, respectively. The ranges greatly varied from experiment to experiment. The data obtained show that the channel openings and closings (gating process) represent a persistent process correlated in time. The randomization of the time sets resulted in a single slope, H, of 0.52 +/- 0.02 characteristic of random processes. The results were confirmed by the fast Fourier and wavelet transforms. In addition, possible voltage dependences of Hurst exponents and their correlation with tau(o) and tau(c) were investigated. As a whole, single channel activity may be characterized as a multifractal process with a slight voltage dependence of the Hurst exponents.

[Study of fractal properties of single ionic channel gating mechanism by the fast Fourier transform]. / Issledovanie fraktal'nykh svoistv "vorotnogo" mekhanizma odinochnykh ionnykh kanalov metodom bystrogo Fur'e-preobrazovaniia.

Sets of the channel open times (tau o), closed times (tau c) and the full set of the channel open and closed times (tau o, tau c) in the activity of single Ca(2+)-activated K+ channels in cultured kidney cells Vero were analyzed using the fast Fourier transform. It was found that in the low-frequency range (about 0.01-10 Hz), power density can be described by the equation S(f) approximately f-alpha (as a rule, 0 < alpha < 1), and this part of the Fourier spectrum usually consists of narrow peaks at almost multiple frequencies. It was shown that the upper frequency boundary of this spectrum is determined by the kinetic parameters tau o [symbol: see text] tau c. The data obtained show that ion channel gating is a fractal process (correlated in time) and can be regarded as a random signal modulated by some periodical functions (sinuses). The data obtained by the Fourier method are in agreement with the earlier results obtained using the rescaled-range analysis.

Dose-dependent potentiation and inhibition of single Ca2+-activated K+ channels by flufenamic acid.

Using the patch-clamp technique in an inside-out configuration, we studied the action of an antiinflammatory drug, flufenamic acid (FFA), on single large-conductance Ca2+-activated K+ channels in cultured Vero kidney cells. Depending on its concentration, FFA caused either potentiation or inhibition of K(Ca) channel activity of the same channel. Within the concentration ranges of about 5 to 10 microM and of 50 to 500 microM, FFA increased the channel activity; and within the intermediate range of about 10 to 50 microM, FFA inhibited the channels. The effects were only partially reversible. The activating phases were accompanied by an increase in the channel open time and decreases in the channel closed time and slope factor of the Ca2+ concentration-response curve. An apparent dissociation constant of Ca2+ interaction with the channel changed slightly. Possible mechanisms of the FFA effects are discussed.

Refined equation for description of the influence of intracellular Mg2+ on the activity of single Ca2+-activated K+ channels in Vero kidney cells.

A refined empirical equation relating the mean value of the logarithm of the apparent dissociation constant (K0.5) to intracellular Mg2+ concentration is given. The equation is derived based on a more precise adjustment of analytical expressions to experimental data.

Non-markovian gating of ca(2+)-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 Ca(2+)-activated K(+) channels (K(Ca) channels) was studied. For the sequences of alternating open and shut time intervals, the dependence R/S vs. N(τ) in the double logarithmic coordinates presented a curve with two slopes, H(1) =0.60 ± 0.04, and H(2) = 0.88 ± 0.21, where H(1) and H(2) 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 Ca(2+)-activated K(+) channel exhibits two regimes, with slight positive correlation at short time ranges (H(1) =0.6), and strong positive correlation at long time ranges (H(2) = 0.88); therefore the channel gating as a whole is not a steady-state Markovian process.