Calcium does not change memory in single calcium-activated potassium channel kinetics

Abstract

The gating of ion channels has been modeled by assuming that the transition 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. We have previously proposed the rescaled range analysis or R/S Hurst analysis as an efficient method to test for the existence of long-term correlation (memory) in single ion channel. In this paper, we investigate the effect of calcium on the memory of the single calcium-activated potassium channel present in Leydig cells. The Hurst coefficient (H; a parameter that predicts memory) was calculated for four different calcium concentrations and presented the following values: 0.634 ± 0.017 (n=8) for 10 $^{-6}$ M; 0.647 ± 0.001 (n=9) for 10 $^{-7}$ M; 0.614 ± 0.001 (n=6) for 10 $^{-8}$ M and 0.618 ± 0.001 (n=4) for 10 $^{-9}$ M. These values of H indicate that open- and closed-dwell times are long-term correlated and that this memory does not change in the presence of different calcium concentrations at a 5% significance level. When the R/S Analysis was applied to the results obtained from simulations of a markovian model (eleven states), it could not account for the long-term correlation found in the experimental data.