A comparative study on the fox and lu equations versus the colored stochastic hodgkin - Huxley equations

ABSTRACT: In recent years, it has been argued and experimentally shown that ion channel noise in neurons can cause fundamental effects on the neuron’s dynamical behavior. Most profoundly, ion channel noise was seen to be able to cause spontaneous firing and stochastic resonance. It was recently found by Güler (2011) that a non-trivially persistent cross correlation regarding position among the trans-membrane voltage fluctuations, and the element of open channel fluctuations is attributed to gate multiplicity. This non-trivial phenomenon was found to play an essential role in the elevation of excitability and spontaneous firing in the small size cell. Furthermore, the phenomenon was found to significantly enhance the spike coherence. More recently, the effect of the above cross correlation persistency was modeled by the same author Güler (2013), through inserting some colored noise terms inside the conductance's in the stochastic Hodgkin Huxley equation. In this thesis, the broadly used stochastic of Hodgkin-Huxley equation, proposed by Fox and Lu, and the colored stochastic Hodgkin-Huxley equation, proposed by Güler recently, will be investigated in a comparative manner. The performance analysis of the two models will be performed with respect to the microscopic Markovain channel simulations. The statistic will be obtained using different membrane size and different input current values. Our investigation reveals that the performance of the Güler model is more effective than the Fox and Lu equations and gives better agreement with the microscopic simulation results. Keywords: Channel Gate, Ion Channel, Small Size Membrane, Channel Noise, Stochastic Hodgkin-Huxley Equations. …………………………………………………………………………………………………………………………