Structural and dynamic interpretation of the fractal scalings of the open and closed time distributions from single channel recordings

The open and closed time histograms of ion channels can be described by scaling functions that relate how the probability to change states at one time scale is related to that probability at other time scales. In some channels these scaling functions have ε fractal form. We show how these scaling functions can be understood in terms of the structure or the dynamics of the ion channel protein. In the structural interpretation, the scaling functions determine the distribution of activation energy barriers between conformational substates. In the dynamic interpretation, the scaling functions determine the time dependence of the activation energy barriers.