Firing Pattern Of Neuron Affect By The Memory Of Ion Channels

Voltage-dependent ion channels mediate action potentials in excitable membranes, play an important role in signal generation and propagation in neurons. In different neurons and different parts of neurons, voltage-dependent ion channels are distributed heterogeneously to facilitate specific functions. In my dissertation, we investigated the effects of fractal gating of ion channels on neuronal behaviors.In chapter one, the structure of neurons, and the type and characteristics of ion channels were introduced. The patch clamp recording technique, which is a common measuring method of electrical properties of neurons, was also introduced.In chapter two, deterministic HH equation and stochastic HH equations were introduced. The classical model of voltage-gated ion channels assumes that the ion channels switch between a small number of conformational states with kinetic rate constants that depend only on the present state of the specific channel. In this Markov process, the physical state of the ion channel at one certain time does not depend on its physical state at the earlier time.In chapter three, the effects of fractal gating of ion channels on neuronal behaviors by Liebovitch method were introduced. The assumption of the classical model introduced in chapter two may not be consistent with the physical chemistry of the dynamics of the conformational changes in ion channel proteins. The ion channel protein consisting of thousands of amino acids is separated by only small energy barriers. The change in protein conformation occurs over the time scales from picosecond to minutes. Thus, a channel would be expected to have a continuum of many conformational states rather than a few discrete states, and significant dynamic processes with memory were exhibited. The Liebovitch method was employed to deal with the fractal gating of ion channels. This method takes the form of the classical neuronal model, Hodgkin-Huxley(HH), but makes use of fractal method to impart memory into ion channels. We find that the memory effect decreases the threshold voltage, and the average interspike interval, but increases the power spectrum and the average spiking rate.In chapter four, the method simulating directly the fractal gating of ion channels was introduced. The method is neither markov method nor fractal method, but the combination of the two methods. Our research results show that fractal gating of potassium channel subunits switching from closed state to open state has important effects on neuronal behaviors, increases excitability, rest potential and spiking frequency of the neuronal membrane, and decreases threshold voltage and threshold injected current of the neuronal membrane. So fractal gating of potassium channel subunits switching from closed state to open state can improve the sensitivity of the neuronal membrane, and enlarge the encoded strength of neural information.In chapter five, we make a summary of our work and some prospects for future work in this field.