An Investigation of the Coefficient of Variation Using the Colored Stochastic Hodgkin-Huxley Equations

ABSTRACT: In recent years, it has been argued and experimentally shown that ion channel noise in neurons can have profound 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 takes place between the transmembrane voltage fluctuations and the component of open channel fluctuations attributed to the gate multiplicity. This non-trivial phenomenon was found to play a major augmentative role for the elevation of excitability and spontaneous firing in the small size cell. In addition, the same phenomenon was found to significantly enhance the spike coherence. More recently, Fox and Lu’s stochastic Hodgkin-Huxley equations were extended by incorporating colored noise terms into the conductances therein, to obtain formalism capable of capturing the addressed cross correlations (Güler, 2013). In this thesis, statistics of the coefficient of variation, obtained from the colored stochastic Hodgkin-Huxley equations, was studied. Our investigation reveals that the colored noise term enhances the agreement with the microscopic simulation results. Keywords: Colored Noise, Channel Noise, Stochastic Ion Channel, Small Size Membrane, Stochastic Hodgkin-Huxley Equations. …………………………………………………………………………………………………………………………