Sinirileticilerin etkisinin matematiksel modellenmesi: Orta boy dikensi hücrelere dopaminin etkisi
Modelling the effect of neurotransmitters: Effect of dopamine on medium spiny neurons
Yazar: RAHMİ ELİBOL
Danışman: DOÇ. DR. NESLİHAN SERAP ŞENGÖR
İstanbul Teknik Üniversitesi / Fen Bilimleri Enstitüsü
Derece: Yüksek Lisans, 2013
Konu: Elektrik ve Elektronik Mühendisliği = Electrical and Electronics Engineering
Dizin: Elektronik = Electronics

Özet:
Hesaplamalı sinirbilim alanında yapılan bu çalışmada Striatum modellenmesi üzerine odaklanılmıştır. Striatum, eylem seçimi, karar verme ve öğrenme gibi bilişsel süreçlerde ve motor hareketlerin yapılmasında etkin rol oynamaktadır. Literatürde Striatumun matematiksel modeli elde edilerek, bilişsel süreçlerin ve Parkinson, Huntington gibi hastalıkların modellenmesi amacıyla kullanılmaktadır.
Striatumu modellemek için, striatumda en çok bulunan ortaboy dikensi hücre (MSN) ele alındı. Ortaboy dikensi hücrenin patlama davranışı yaptığı bilinmektedir. Modeli elde ederken biyolojik olarak anlamlı bir sinir hücresi modeli olan Hodgkin Huxley modeli (HH) ele alınmıştır. HH modeli, hücre duvarında bulunan iyon kanallarının açılıp kapanması ile, sinir hücresinin hücre duvarı geriliminin nasıl değiştiğini doğrusal olmayan dördüncü mertebeden bir dinamik sistem ile modeller. Bu modelde sodyum ve potasyum iyon kanalları iletkenlik tabanlı olarak modellenmi ?tir. HH modeli sinir hücrelerinin tüm davranışlarını gösteremese de, farklı davranışları elde edebilmek için üzerine iyon kanalları eklenebilir olması nedeniyle kullanışlı bir modeldir. HH modeline eklenebilecek sodyum, potasyum ve kalsiyum iyon kanalı modelleri ele alınarak, sinir hücresinin hangi farklı davranışları sergilediği gösterilmiştir. Bu tezde sinir hücresinin davranışının modellenmesinin yanısıra bu davranışı biyolojik olarak anlamlı bir model ile elde etmek amaçlanmıştır. Bu nedenle HH modeline kalsiyum ve potasyum iyon kanalları eklenmiştir. Böylece biyolojik olarak anlamlı, patlama davranışını gösteren bir MSN modeli elde edilmiştir.
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.

Abstract:
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.