Fractal analysis of a voltage-dependent potassium channel from cultured mouse hippocampal neurons

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 the kinetic rate constants connecting these states are constant. In the alternative fractal model the spontaneous fluctuations of the channel protein at many different time scales are represented by a kinetic rate constant k = At1-D, where A is the kinetic setpoint and D the fractal dimension. Single-channel currents were recorded at 146 mM external K+ from an inwardly rectifying, 120 pS, K+ selective, voltage-sensitive channel in cultured mouse hippocampal neurons. The kinetics of these channels were found to be statistically self-similar at different time scales as predicted by the fractal model. The fractal dimensions were approximately 2 for the closed times and approximately 1 for the open times and did not depend on voltage. For both the open and closed times the logarithm of the kinetic setpoint was found to be proportional to the applied voltage, which indicates that the gating of this channel involves the net inward movement of approximately one negative charge when this channel opens. Thus, the open and closed times and the voltage dependence of the gating of this channel are well described by the fractal model.