An Investigation into the Colored Stochastic Hodgkin-Huxley Equations Under Noisy Input Currents

In recent years, it has been argued and shown experimentally that ion channel noise in neurons can have profound influence 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 correlation takes place between the transmembrane voltage fluctuations and the element of open channel fluctuations attributed to the gate multiplicity. This non-trivial phenomenon was found to be playacting an essential important role for the elevation of excitability and spontaneous firing in the small size cell. In addition, the same phenomenon was found to be enhancing thе spike coherence significantly. More recently, thе effects of thе above cross correlation persistency was modeled; by thе same author M. Güler (2013), through inserting some colored noise terms inside the conductances in the stochastic Hodgkin- Huxley equations. In this thesis, the colored stochastic Hodgkin-Huxley equations were studied when the input current to the neuron is noisy. The spiking rates and the spike coherence were examined. In particular, the role played by the presence of the colored noise terms in the conductances was focused on in the examination. Our investigation reveals that the presence of the colored noise terms enhances the agreement with the microscopic simulation results not only in the case of the noise-free input currents but also in the case of the noisy currents. Keywords: ion channel, channel noise, colored noise, channel gate, small size membrane, stochastic Hodgkin-Huxley