Nonlinear kinetics, fractals and chaos: applications to potassium single channel

The kinetics of ion channels have been widely modeled as a Markov process. In these models it is assumed that the channel protein has a small number of discrete conformational states and kinetic rate constants connecting these states are constant. In this paper, voltage-dependent K⁺ channel current is recorded using cell-attached patch-clamp technique in rat dorsal root ganglion neurons. Due to various sources of noise, such as, seal leakage, electronic noise in the equipment, and shot noise in the channel. Firstly wavelet packet (WP) analysis is applied denoise, the error analysis shown that max error is 10.658fA, the result shown patch-clamp signals exist partially noise eliminated. Secondly Spectral analysis of ion channel current is studied, the result make known that spectrum is not flat spectrum, the data set from wavelet reconstruction shows considerable variability with a broad 1/f-like spectrum. Thirdly the phase space plot of x(t+Δ t) versus x(t) is different for the random and the deterministic process, thus phase space analysis can be used to analyze time series to determine if it was generated by a random or a deterministics mechanism, the result is indicated that the gating kinetics of k⁺ channel in rat dorsal root ganglion neurons with nonlinear dynamics properties. Absolute values of C_a,b coefficients for different scales look similar, while resemblance index also resembles itself at difference scales. Thus, the voltage dependence of the gating of this ion channel exhibits nonlinear dynamics properties.