Time correlation in ion channel gating. Rescaled range analysis

Using patch-voltage clamp technique, activity of single Ca2+-activated K+-c hannels from cultured kidney cells Vero was registered. The sequences of al ternating open and shut time intervals was studied by the rescaled range an alysis (Hurst method, RIS analysis). For the sequences, the dependence R/S v.s. N-tau presented a curve with two slopes, H-1 = 0.60 +/- 0.04, and H-2 = 0.88 +/- 0.20, where H-1 and H-2 characterized the Hurst exponents for sh ot and long time ranges, respectively. The linear regression on all plot po ints gives the averaged Hurst exponent, H = 0.67 +/- 0.06. Similar results were obtained for reduced data sets consisting of only open or only shut in tervals. Randomization of the experimental data resulted in a single slope, H, of 0.52 +/- 0.02. The data presented show that the channel openings and closings are not random, Markovian but correlated in time process (process with "memory"). Moreover, the events of single channel activity are slight ly correlated on short time intervals (H = 0.6) and greatly correlated on l arge time intervals (H = 0.88). Behaviour of the Hurst coefficient with tim e series length, its changing with time and connection with kinetic paramet ers of channel actitity was studied. It was established, that there are sli ghtly and strongly correlated areas in the events single channel gating. Si mulations were performed with eight-state Markovian model of Ca2+-activated K+-channel (3 - open states, 5 - closed states). The calculated Hurst expo nent presented in average 0.54 +/- 0.02. The results suggest that the well- known kinetic models of single channel activity does not reflect correlatio n in activity of real ion channels.