The Effect Of Temperature On The Stochosticity In Ion Channels On Finite Size Of Neuron Membrane

Firstly, We introduce the development of neural biology in the field of theoretical biophysics. Then, we give some basic information about the neuron model we studied which given by Hodgkin and Huxley. It is including the structure of neurons, the distribution of ions concentration in or out of the neuron membrane, the electrochemical gradient of ions, the equilibrium potential, the resting potential and action potential of neuron, the ion theory of the transmembrane potential and the Hodgkin-Huxley(HH) equation.After we present the concepts of "coherence resonance" and "stochastic resonance" , to further study the HH neuron model, we introduce some properties of the HH equation, for example, the threshold of neuron's exciting, the responses of neuron toward different stimulations. Because of the noisy surrounding, the neuron system may exhibit stochastic resonance or coherence resonance with or without the help of external periodic signal. Under finite size of neuronal membrane, the transmembrane potential will fluctuate due to the random changes of conformational state of ion channels embedded in the membrane. We give two methods to describe the stochastic neuron system: Markov and Langevin, and there exist an optimal membrane area correspond to the most excitable system.Based on the HH neuron model, we investigate the effects of patch temperature on the spontaneous action potentials for finite size of membrane patch. The temperature of the membrane patch is a very important control parameter, it operates through affect the switching rate of ion channels, but little attention has been paid on the effects of variation in temperature. We simulate the evo-lution of the neuron system by numerical method, and get the following results. With the patch temperature increasing, it is found that (1) the mean open rates of sodium and potassium channels of the HH neuron are decreased, and the mean duration of spikes of membrane potential is also decreased, which are qualitatively consistent with previous experimental results of single ion channel. (2) Under moderate patch size, the mean interspike interval of membrane potential first decreases, reaches a minimum, and then increases with the increasing of patch temperature. (3) By defining a measure parameter B, we show that there is a maximal region for the measure B in the patch temperature and patch size parameter plane where the coherence resonance phenomena are very remarkable, and the characteristic time of the output also confirm our result.