An Investigation into the Dissipative Stochastic Mechanics Based Neuron Model under input Current Pulses

Abstract

ABSTRACT: It has been recently 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. A physical approach for the description of neuronal dynamics under the influence of ion channel noise has been proposed through the use of dissipative stochastic mechanics by Güler in a series of papers (Güler, 2006, 2007, 2008). He consequently introduced a computational neuron model incorporating channel noise for a special membrane that gives the Rose-Hindmarsh model of the neuron in the deterministic limit. The most distinctive feature of the dissipative stochastic mechanics based model is the presence of so-called the renormalization terms therein. More recently, the model was generalized to the Hodgkin-Huxley type of membranes (Güler, 2011, 2013). In this thesis, the dissipative stochastic mechanics based neuron model was studied when the input current to the neuron is an input pulse. Statistics of firing efficiency, latency, and jitter were examined for various stimulus pulses. In particular, the role played by the presence of the renormalization terms was focused on in the examination. Keywords: Ion Channel Noise, Stochastic Ion Channels, Neuronal Dynamic, Rose-Hindmarsh Model. …………………………………………………………………………………………………………………………

ÖZ: Gerek deneysel, gerekse kuramsal ve benzeşim çalışmaları iyon kanal gürültüsünün nöron dinamiği üzerinde hayati etki yapabildiği kanıtlanmıştır. Bu kapsamda, kendi kendine ateşleme ve stokastik rezonans en önemli bulgulardır. İyon kanal gürültüsü altındaki nöron dinamiği, fiziksel bir yaklaşım olan disipatif stokastik mekanik kullanarak çalışılmış ve modellenmiştir (Güler, 2006, 2007, 2008). Sonsuz zar büyüklüğü limitinde Rose-Hindmarsh modeline dönüşen bu disipatif stokastik mekaniğe dayalı modelin en önemli özelliği renormalizasyon terimleri içermesidir. Model, daha sonra, Hodgkin-Huxley tipi zarlara uyarlanmıştır (Güler, 2011, 2013). Bu tezde, Rose-Hindmarsh tipi zarlarda iyon kanal gürültüsü için geliştirilmiş olan yukarıdaki model, basamaklı girdi akımları kullanılarak çalışılmıştır. Ateşleme etkinliği, gecikme ve jitter istatistikleri elde edilmiş ve renormalizasyon terimlerinin rolü incelenmiştir. Anahtar Kelimeler: İyon kanal gürültüsü, Stokastik iyon kanalları, Nöronal Dinamik, Rose-Hindmarsh Modeli.