A Study on the Ion Channel Dynamics Using the Minimal Diffusion Formulation Variants 2v1n and 1v1n

The excitability of cells will be facilitated by voltage gated ion channels. Although, these channels are accommodating individually by a multiple number of gates. The effects of ion channel fluctuations on the transmembrane voltage activity are profound of small-size membranes patches. Recently, a model that captures the collective dynamics of Markov chain ensembles was proposed by Güler, M. (2015) [Physical Review E, 91(6), 062116] under the name "Minimal diffusion formulation of Markov chain ensembles". Additionally, two simpler variants of it. Called 2v1n and 1v1n formulations, were introduced by the same author [Physical Review E, 93(2), 022123]. By applying the minimal diffusion formulation to the gating dynamics which is in ion channel clusters and it was seen that the formulation accurately describes the excitability of neurons. On the other hand, the 2v1n and 1v1n formulations’ performance for the ion channel clusters are not examined. In this thesis, a study on the neural dynamics is performed using the 2v1n and 1v1n formulation. The study examined the accuracy of the formulation by numerical simulation. In doing so, the exact microscopic dynamic simulations of the ion channel cluster were taken as the reference point.