Fractal models are inadequate for the kinetics of four different ion channels

The gating kinetics of single ion channels have been well described by models which assume that channels exist in a number of discrete kinetic states, with the rate constants for transitions among the states remaining constant in time. In contrast to such discrete Markov models, it has recently been considered whether gating might arise from transitions among a continuum of states, with the effective rate constants for leaving the collections of states given by a fractal scaling equation (Liebovitch, L.S., J. Fischbarg, J.P. Koniarek, I. Todorova, and M. Wang. 1987. Biochim. Biophys. Acta. 896:173–180; Liebovitch, L.S., and J.M. Sullivan. 1987. Biophys. J. 52:979–988). The present study compares discrete Markov with fractal continuum models to determine which best describes the gating kinetics of four different ion channels: GABA-activated Cl channels, ACh-activated end-plate channels, large conductance Ca-activated K (BK) channels, and fast Cl channels. Discrete Markov models always gave excellent descriptions of the distributions of open and shut times for all four channels. Fractal continuum models typically gave very poor descriptions of the shut times for all four channels, and also of the open times from end-plate and BK channels. The descriptions of the open times from GABA-activated and fast Cl channels by the fractal and Markov models were usually not significantly different. If the same model accounts for gating motions in proteins for both the open and shut states, then the Markov model ranked above the fractal model in 35 of 36 data sets of combined open and shut intervals, with the Markov model being tens to thousands of orders of magnitude more probable. We suggest that the examined fractal continuum model is unlikely to serve as a general mechanism for the gating of these four ion channels.