Sinirileticilerin Etkisinin Matematiksel Modellenmesi: Ortaboy Dikensi Hücrelere Dopaminin Etkisi

Elibol, Rahmi
Süreli Yayın başlığı
Süreli Yayın ISSN
Cilt Başlığı
Fen Bilimleri Enstitüsü
Institute of Science and Technology
Sinir ileticiler, sinir hücrelerinin bağlantı noktaları olan sinaptik boşluklarda, sinirsel aktivitenin aktarılmasını sağlarlar. Striatumda, dopamin sinir ileticisinin etkili olduğu bilinmektedir. Dopamin miktarındaki değişimlerin striatumdaki MSN hücrelerinin davranışını nasıl etkilediği ve bu etki ile de öğrenme ve nöro dejeneratif hastalıkların modellenmesi, özellikle Parkinson hastalığı ve beyin pili uygulamaları (Deep Brain Stimulation) ile ilgili çalı ̧malar son yıllarda önem kazanmı ̧tır. Bu amaçla elde edilen MSN modeline, dopaminin etkisinin konulması için iki farklı yaklaşım ele alınmıştır. Bir dinamik sistemin, denklemlerinde bulunan bir parametrenin değişmesi ile durum portresinin topolojik olarak farklıla ̧masına dallanma, bu analizlerin elde edilmesine ise dallanma analizi denilmektedir.Dallanma analizleri için çeşitli bilgisayar yazılımları literatürde bulunmaktadır ve doğrusal olmayan dinamik sistemlerin incelenmesinde kolaylık sağlamaktadır. Dopaminin modellenmesi için ele alınan her iki yaklaşımda dopamin miktarına bağlı olarak MSN modelinin dallanma analizleri dinamik sistem açısından incelenmiştir. Elde edilen tüm sonuçlar yorumlanarak, sonuç bölümünde paylaşılmıştır.
It has been a great interest for humankind to understand how the brain works since antique. The unfortunate accident of Phines Gage opened a new era in the investigation of brain. Since then with work carried out and especially with the advent of imaging techniques, neuroscientist begin to grasp that the substructures of the brain are responsible for different processes but still effect each other and work together to accomplish tasks. Now, the electrophysiology of neurons and group of neurons along with the roles of substructures are known. How we can accomplish cognitive processes as action selection, decision making and furthermore realizing different tasks at the same time like reading and while driving bicycle through activation of neurons. It is mostly popular recently to investigate this phenomenon with mathematical models of neurons and group of neurons and especially find the relation between neuron activity and occurrence of the cognitive tasks. Many studies have been conducted to understand cognitive processes in recent years. According to the results of these studies, the brain consists of specialized sub-regions. Each subregion communicates with other subregions in order to fulfill certain functions. For example, for cognitive processes as decision-making, action selection Basal Ganglia nuclei have connections with prefrontal cortex and thalamus. Main input part of Basal Ganglia is Striatum and it plays an important role in the fulfillment of these functions. The biophysically realistic computational models of basal ganglia circuits have been proposed to provide insight to studies on deep brain stimulation. The role of these circuits in cognitive processes as decision making, reward related learning is well-known and there are biologically plausible models for these processes, too. Though computationally plausible models help our understanding of what is going on during these processes, they are not sufficient to explain the effect of neural structures completely. A biophysically realistic model of striatum will be proposed. In the proposed model, the conductance based neuron models are modified considering the properties of neural substrate. From the point of view of computational science, the behavior of subregions are modeled first. Then using these models the emergence of cognitive processes were studied. There are two types of nerve cells as the basic structure of the striatum. The first and the most available are the Medium Spiny neurons. Inhibitory neurons are the other kind of nerve cells in the striatum. Medium Spiny neurons approximately compose 80-95% of striatum. Medium Spiny neurons show bursting behaviour. Interneuron cells show fast spike behaviour. The striatal Medium Spiny neurons (MSN) play key role in the formation of the antagonistic functions of direct and indirect pathways. Medium Spiny Neurons (MSN) of striatum and the effect of neurotransmitter Dopamine (DA) on them, as it is widely accepted that Basal Ganglia (BG) circuits have an important role in cognitive tasks. This thesis focus on modeling the effect of DA on MSN with nonlinear dynamical system approach and try to explain the role of DA on the activation of MSN by considering DA as a bifurcation parameter and investigating the change in the dynamic behavior of MSN. Hodgkin Huxley model is the most meaningful of neuron models, but HH model is not sufficient to demonstrate all neurons behaviour. Therefore, ion channels were added to HH model. There are three ion channels in HH model: leak, potassium and sodium current. The model is expressed by fourth-order nonlinear equations. Noninactivity sodium current, fast or slow inactivity potassium current, T-type Ca current, L-type calcium current and afterhyperpolarization current were investigated in this thesis. Each current effect and dynamics were obtained by MATLAB. In the second chapter of this thesis focused on the state-space behavior of the conductance-based computational model of MSNs which is constituted with nonlinear dynamical systems’ approach. The typical behavior of the striatal MSNs is bursting activity as claimed and these neurons play a role in synaptic plasticity. Since the conventional Hodgkin-Huxley neuron model is not suitable for modelling the striatal MSNs, L-type Ca2+ (high threshold calcium), Kv1.2-containing K + , Calcium activated Calcium and Calcium activated Potassium (afterhyperpolarization) ion channels are also considered in connection with the role of dopamine receptors in MSNs. The bursting activity of the proposed MSNs minimal model is explained via the qualitative theory of fast-slow dynamical systems. The proposed model, the generation of bursting pattern depends on two different current mechanisms. Slow current system (sodium) is responsible for the bifurcation branch between equilibrium point and the limit cycles (Andronov-Hopf Bifurcation) by effecting the fast current system (afterhyperpolarization). At the same time, fast current system has a role in spiking activity of the bursting patterns (saddle-node of periodic orbits). The Subhopf/Fold Cycle type bursting activity of the proposed model is an example of Ca2+ gated inactivation of an inward current and it depends on fold limit cycle bifurcation. So, Medium Spiny Neuron model has six order. Slow and fast sub-systems carry out the bursting behavior of the model, so implementation of them were needed. Fast sub-system is sodium current, slow sub-system is AHP current. Medium Spiny Neuron model behavior were investigated with the XPPAUT program. Medium Spiny Neuron model were obtained to be biologically meaningful model. The proposed model is capable of explaining how dopamine release modulates the functions of striatum. In the third part of the thesis, modeling the effect of the neurotransmitter was studied. Some computational models aim to understand deep brain stimulation experiments. A conductance-based computational network model of the STN and GPe in the indirect pathway of the BG is developed in literature. Models feature spike producing currents of potassium and sodium, as well as low threshold calcium (Ca) current and a Ca-induced afterhyperpolarization potassium current. This model demonstrates the role of inhibition in the indirect action selection pathway. The results of multi-site stimulation of subthalamic nucleus in relation with the thalamocortical relay circuit is presented in literature. This model consists of a synaptically connected, conductance based model neurons of the BG and generates activity patterns of rhythmic bursts. Guthrie and colleagues developed a network model of the striatal direct DA pathway for action selection. This network can sequentially learn a task which is dependent on the BG. By manipulating the phasic and tonic levels of DA, the model can demonstrate the symptoms of Parkinson’s disease in humans. In the literature there are two different approaches to investigate the effect of dopamine. In both approaches integrate and fire model is considered. In the first approach calcium and potassium currents is multiplied with a dopamine factor in order to simulate the effect of dopamine. The second approach provides as additional currents of sodium, calcium and potassium. In this thesis the proposed model of Medium Spiny Neuron was considered and the effect of dopamine was investigated. Both approaches were cosidered and the bifurcation analysis was carried out with XPPAUT program. The geometry of the phase portraits, imported from significant bifurcation points, allow us to understand the ability of the proposed model. Thus, the whole architecture of the proposed model is shown to be captured by bifurcation analysis. It was shown that Medium Spiny Neuron behavior is changing with the change of the dopamine level.
Tez (Yüksek Lisans) -- İstanbul Teknik Üniversitesi, Fen Bilimleri Enstitüsü, 2013
Thesis (M.Sc.) -- İstanbul Technical University, Institute of Science and Technology, 2013
Anahtar kelimeler
Matematiksel Model, Dopamin, Ortaboy Dikensi Hücre, Hesaplamalı Sinirbilim, Mathematical model, Dopamine, Medium Spiny Neuron, Computational Nuroscience