A Comparative Study on ‘The Colored Stochastic HH Equations’ and ‘The Minimal Diffusion Formulation’

The voltage-gated ion-channels within the membranes facilitate the excitability of neurons. These channels accommodate a multiple number of gates individually. The number of open channels fluctuates with profound effects on the transmembrane voltage activity in small-size excitable membrane patches. Two recent models that can capture the collective dynamics of ion channels in excitable membranes are: 1.) The colored stochastic Hodgkin-Huxley equations [1] 2.) The minimal diffusion formulation of Markov chain ensembles [2] In this thesis, a comparative study on these two models was performed by numerical simulations. The statistics of the mean inter-spike interval (ISI), coefficient of variation and spike latency were used in the investigation. The obtained results are useful for better understanding of the efficiency of these models. Computation times of the models were also investigated. Our study shows that the Minimal Diffusion model generally yields more accurate results than the already satisfactory Colored Noise model. To determine the accuracy of the models, the model results are assessed with reference to the corresponding Microscopic Simulation (Monte Carlo) model results. Our simulations confirm that the Minimal Diffusion model requires less computation time than the Colored Noise model. Our findings indicate that the Minimal Diffusion model should be preferred to the Colored Noise model. Keywords: Ion channel, Channel noise, Colored noise, Stochastic Hodgkin-Huxley, Markov Chain, Minimal diffusion formulation