Beng 260 - Neurodynamics Final Report

The project aims to explore two fractal models (by Lowen and Liebovitch) of ion channel kinetics, and how this affects spike train patterns. The project also intends to extend the Liebovitch model and explore how fractal dimension affects potassium ion channel conductance profiles, and the behavior and rate of action potentials. 1 I n t r o d u c t i o n Fractal patterns have been used to model many different aspects of our natural world, from coastlines, to mountains, to neuromorphology, all of which deal with fractal behavior as applied to geometry. Fractal behavior can also be imparted to dynamical systems, particularly neural spike train patterns. Experimental evidence has indicated that neurons along the auditory pathway, demonstrate a fractal firing pattern, where the term fractal is used to signify that the fluctuations of spiking rate appear self similar over various integration time periods, as shown in Figure 1 [9]. Figure 1: a) A fractal fluctuation rate. Fluctuations don’t change in amplitude, even as the rate is taken over longer time periods. b) Non-fractal fluctuation rate. Fluctuations decline in amplitude and smooth out as the firing rate is taken over longer time periods. In considering possible biophysical origins of this fractal behavior of auditory nerve spiking trains, one possibility that has been suggested relates to fractal kinetics of neuronal ion channels.