Computational Dissection of the Basal Ganglia

Computational Dissection of the Basal Ganglia
Computational Dissection of the Basal Ganglia
functions and dynamics in health and disease
MIKAEL LINDAHL
Doctoral Thesis in Computational Biology
KTH Royal Institute of Technology
Akademisk avhandling som med tillstånd av Kungliga Tekniska högskolan framlägges till offentlig granskning av
teknologie doktorsexamen onsdagen den 4e Maj 2016 kl 13.00 i F3, Lindstedtsvägen 26, Kungliga Tekniska högskolan,
Stockholm
ISSN-1653-5723
TRITA-CSC-A-2016:07
ISRN-KTH/CSC/A—16/7-SE
ISBN 978-91-7595-925-2
1
Abstract
The basal ganglia (BG), a group of nuclei in the forebrain of all vertebrates, are important for
behavioral selection. BG receive contextual input from most cortical areas as well as from parts
of the thalamus, and provide output to brain systems that are involved in the generation of
behavior, i.e. the thalamus and the brain stem. Many neurological disorders such as Parkinson’s
disease and Huntington’s disease, and several neuropsychiatric disorders, are related to BG.
Studying BG enhances the understanding as to how behaviors are learned and modified. These
insights can be used to improve treatments for several BG disorders, and to develop braininspired algorithms for solving special information-processing tasks.
In this thesis modeling and simulations have been used to investigate function and dynamics of
BG. In the first project a model was developed to explore a new hypothesis about how conflicts
between competing actions are resolved in BG. It was proposed that a subsystem named the
arbitration system, composed of the subthalamic nucleus (STN), pedunculopontine nucleus
(PPN), the brain stem, central medial nucleus of thalamus (CM), globus pallidus interna (GPi)
and globus pallidus externa (GPe), resolve basic conflicts between alternative motor programs.
On top of the arbitration system there is a second subsystem named the extension systems,
which involves the direct and indirect pathway of the striatum. This system can modify the
output of the arbitration system to bias action selection towards outcomes dependent on
contextual information.
In the second project a model framework was developed in two steps, with the aim to gain a
deeper understanding of how synapse dynamics, connectivity and neural excitability in the BG
relate to function and dynamics in health and disease. First a spiking model of STN, GPe and
substantia nigra pars reticulata (SNr), with emulated inputs from striatal medium spiny
neurons (MSNs) and the cortex, was built and used to study how synaptic short-term plasticity
affected action selection signaling in the direct-, hyperdirect- and indirect pathways. It was
found that the functional consequences of facilitatory synapses onto SNr neurons are
substantial, and only a few presynaptic MSNs can suppress postsynaptic SNr neurons. The
model also predicted that STN signaling in SNr is mainly effective in a transient manner. The
model was later extended with a striatal network, containing MSNs and fast spiking
interneurons (FSNs), and modified to represent GPe with two types of neurons: type I, which
projects downstream in BG, and type A, which have a back-projection to striatum. Furthermore,
dopamine depletion dependent modification of connectivity and neuron excitability were added
to the model. Using this extended BG model, it was found that FSNs and GPe type A neurons
controlled excitability of striatal neurons during low cortical drive, whereas MSN collaterals
have a greater impact at higher cortical drive. The indirect pathway increased the dynamical
range over which two possible action commands were competing, while removing intrastriatal
inhibition deteriorated action selection capabilities. Dopamine-depletion induced effects on
spike synchronization and oscillations in the BG were also investigated here.
For the final project, an abstract spiking BG model which included a hypothesized control of the
reward signaling dopamine system was developed. This model incorporated dopaminedependent synaptic plasticity, and used a plasticity rule based on probabilistic inference called
Bayesian Confidence Propagation Neural Network (BCPNN). In this paradigm synaptic
connections were controlled by gathering statistics about neural input and output activity.
Synaptic weights were inferred using Bayes’ rule to estimate the confidence of future
observations from the input. The model exhibits successful performance, measured as a moving
average of correct selected actions, in a multiple-choice learning task with a changeable reward
schedule. Furthermore, the model predicts a decreased performance upon dopamine lesioning,
and suggests that removing the indirect pathway may disrupt learning in profound ways.
2
Svensk sammanfattning
Basala ganglierna (BG) är en grupp nervcellskärnor i storhjärnan hos ryggradsdjur som är
viktiga för beteendeselektion. BG får information från de flesta delarna av hjärnbarken samt
från talamus, och genererar i sin tur en utsignal till delar av talamus och hjärnstam som är
involverade i initiering av beteenden. Många neurologiska sjukdomar, såsom Parkinsons
sjukdom, Huntingtons sjukdom och flera neuropsykiatriska tillstånd, är relaterade till BG.
Genom att studera BG kan man uppnå en djupare förståelse för hur beteenden lärs in och
modifieras. Dessa insikter kan användas till att både förbättra behandlingar av BG-relaterade
sjukdomar samt för att utveckla hjärninspirerade beräkningsalgoritmer.
I denna avhandling har modeller och simuleringar använts för att undersöka olika aspekter av
BG. I det första delprojektet byggdes en modell för att testa en ny hypotes som handlar om hur
selektion görs i BG då man har konkurrerande beteenden att välja mellan. Ett delsystem,
”arbitration system”, som består av subthalamiska kärnan (STN), pedunculopontina kärnan
(PPN), hjärnstammen, centrala mediala kärnan i talamus (CM), globus pallidus interna (GPi)
and globus pallidus externa (GPe), kan göra enkla val mellan olika motorprogram. Ovanpå detta
”arbitration system”, finns ytterligare ett system som kallas ”extension system”, som involverar
den direkta och indirekta vägen från striatum. Detta system kan modifiera resultatet från
”arbitration system” utifrån kontextuell information från hjärnbarken.
I det andra delprojektet utvecklades en modell i två steg med syftet att skapa en djupare
förståelse för hur synapsdynamik, nervcellskopplingar och neural retbarhet i BG relaterar till
funktion och dynamik. Först utvecklades en spikande delmodell som bestod av STN, GPe och
substantia nigra pars reticulata (SNr), som i sin tur aktiverades med emulerat input från
striatala medium spiny neurons (MSNs) och från hjärnbarken. Modellen användes för att
studera hur beteendeselektion påverkas av synaptisk korttidsplasticitet i den s.k. direkta,
indirekta eller hyperdirekta vägen genom BG. Det visade sig att de funktionella konsekvenserna
av faciliterande synapser i SNr var stor, och endast ett fåtal presynaptiska MSN behövs för att
hämma postsynaptiska SNr neuroner. Modellen förutspådde också att STNs signalering i SNr
endast är effektiv för ett transient input. Modellen utvidgades sedan med ett striatalt nätverk,
innehållande MSN och ’fast spiking interneurons’ (FSN), och GPe var nu uppdelad i två typer av
neuroner; typ I, som signalerar nedströms i BG och typ A som kopplar tillbaka till striatum.
Vidare introducerades dopaminberoende synapskopplingar och neuroner i modellen. Med den
utvidgade BG-modellen såg vi att FSN och GPe typ A neuroner kontrollerade aktiviteten hos
MSN vid svagt input från hjärnbarken, medan MSN-kollateralerna hade större inflytande vid
starkt input från hjärnbarken. Den indirekta vägen genom BG var viktig för att utvidga
intervallet mellan den lägsta och högsta spikfrekvens i hjärnbarkens neuroner som striatala
celler kunde läsa av, medan detta intervall minskade när inhibitionen i striatum försvagades
eller togs bort. Effekten av att ta bort dopamin i systemet undersöktes också med avseende på
spiksynkronisering och nätverksoscillationer.
I det sista delprojektet byggdes en abstrakt, spikande modell av BG som användes för att testa
en hypotes om hur dopamin kan användas för inlärning av nya beteenden. Denna modell
inkorporerade dopaminberoende synapsplasticitet och använde sig av en plasticitetsregel som
bygger på probabilistisk inferens kallad Bayesian Confidence Propagation Neural Network
(BCPNN). I detta paradigm kontrolleras styrkan av de synaptiska kopplingarna av statistik från
pre- och postsynaptisk aktivitet. Vikter tas fram genom att använda Bayes regel för att ta
estimera kommande observationer av pre- och postsynaptisk aktiviteter. Modellen kan
framgångsrikt lära sig en flervalsuppgift med föränderligt belöningsschema. Vidare visar
modellen hur prestandan går ner vid lesion av dopamin neuronerna eller då man tar bort den
s.k. indirekta vägen genom BG.
3
Acknowledgement
My PhD were supported by EU SELECT AND ACT project, Vetenskapsrådet and SerC.
Stockholm brain institute have granted me generous mobility support for attending several
summer and winder schools as well as conferences.
I want to thank my supervisor professor Jeanette Hellgren Kotaleski for here support,
encouragement and inspiration and my co-supervisor professor Örjan Ekeberg for insightful
discussions. Both have made my PhD journey very pleasant.
I am grateful to have work with professor Anders Lansner who I have enjoyed many interesting
discussions with during lunch break. I am glad to have met Arvind Kumar and thrived from our
talks about scientific and general stuff.
Pawel, who I shared the master thesis room with for 6 months in the beginning and Marcus
have meant a lot to me as friends and as supporting colleagues. I am also very happy to have met
Stina and Martin through SBI. My fellow CB friends, who not yet mentioned, Phil, Iman, Pierre,
Bernhard, Pradeep, Simon, Mikael, Peter, Anu, Jan, Ekatarina, Dinesh, Jovana, Christina,
Daniel, Erik, Tony, Ramon, Ylva, Florian, Olivia and Alex. I cherish all the moments we have
shared.
Thank you Erik Aurell for your policy as a department head to give new PhD students a free
course in improvisational theater. That lead me into a fantastic new world where I have met a lot
of great friends and fellow improvisers, who I have shared a many unforgettable moments with
on and off stage.
I further want to acknowledge all my current colleagues and friends at Greencargo and Loredge.
Thank you for making my present so enjoyable. Also, thank you Jonatan for letting me take time
of and finish my PhD. Forever grateful.
Thank you Magnus and Kristina for helping me with the defense festivities, you both have a
special place in my heart.
My friends outside work have meant the world to me and you all have helped me through my
PhD with laughter and inspiration. Throughout my PhD, my family have been there for me in
good and bad times. I especially want to thank my father for his inspiring energy, my mother for
her emotional support and my sister for being such a funny, talented and caring person. I love
you all.
Finally, I thank you Sanne for your love, for your enthralling humor and for all the beautiful
moments we have shared. I am yours with all my heart.
4
Contents
1
2
Introduction
1.1
Why study basal ganglia? ................................................................................................... 7
1.2
What is a model? ................................................................................................................ 7
1.3
Why use computational models? ....................................................................................... 7
1.4
Scope of the thesis .............................................................................................................. 7
1.4.1
Project I (paper 1) ....................................................................................................... 7
1.4.2
Project II (paper 2 and 3) .......................................................................................... 8
1.4.3
Project III (paper 4) ................................................................................................... 8
1.5
List of papers included in this thesis ................................................................................. 8
1.6
Contribution to papers ....................................................................................................... 9
Biological background
2.1
10
The basal ganglia .............................................................................................................. 10
2.1.1
Input .......................................................................................................................... 10
2.1.2
Striatum .................................................................................................................... 10
2.1.3
Subthalamic nucleus ................................................................................................. 11
2.1.4
Globus pallidus .......................................................................................................... 11
2.1.5
Substantia nigra ........................................................................................................ 11
2.1.6
Pedunculopontine nucleus ....................................................................................... 11
2.2
3
7
Synaptic dynamics ............................................................................................................. 11
2.2.1
Short-term plasticity ................................................................................................. 11
2.2.2
Long-term plasticity ..................................................................................................12
2.2.3
Synaptic pruning .......................................................................................................12
2.2.4
Synaptogenesis ..........................................................................................................12
2.3
Dopamine...........................................................................................................................12
2.4
Action selection .................................................................................................................12
2.5
The direct, indirect and hyperdirect pathways ................................................................13
2.6
Reinforcement learning ....................................................................................................13
Models and methods
14
3.1
Computational neuroscience ........................................................................................... 14
3.2
Model components ........................................................................................................... 14
3.2.1
Hodgkin-Huxley model ........................................................................................... 14
3.2.2
Integrate and fire model ...........................................................................................15
3.2.3
Adaptive exponential integrate and fire model .......................................................15
3.2.4
Izhikevich simple model ...........................................................................................15
3.2.5
Conductance based synapses .................................................................................. 16
3.2.6
Tsodyks model.......................................................................................................... 16
3.2.7
Bayesian Confidence Propagation Neural Network ................................................ 17
3.3
Parameter estimation ....................................................................................................... 18
3.3.1
Short-term plasticity ................................................................................................ 18
3.3.2
GPe neuron ............................................................................................................... 19
3.3.3
SNr neuron ............................................................................................................... 20
5
3.3.4
3.4
4
STN neuron ...............................................................................................................21
Computational models of the basal ganglia .....................................................................21
3.4.1
Houk and Beiser 1998 ...............................................................................................21
3.4.2
Bar-Gad, Havazelet-Heimer, Goldberg, Ruppin and Bergman 2000 ................... 22
3.4.3
Terman, Rubin, Yew and Wilson 2002 ................................................................... 22
3.4.4
Frank 2006 ............................................................................................................... 22
3.4.5
Lo and Wang 2006 ................................................................................................... 22
3.4.6
Humphries, Stewart, Gurney 2006 ......................................................................... 22
3.4.7
Humphries, Wood and Gurney 2009 ..................................................................... 22
3.4.8
Ponzi and Wickens 2010 .......................................................................................... 22
3.4.9
Steward, Bekolay and Eliasmith 2012 .................................................................... 23
3.4.10
Nevado-Holgado, Mallet and Magill 2014 .............................................................. 23
3.4.11
Bahuguna, Aertsen and Kumar 2015 ...................................................................... 23
Results and Discussion
4.1
24
The arbitration and extension system hypothesis of basal ganglia ............................... 24
4.1.1
The arbitration system can select the most salient response ................................. 24
4.1.2
The extension system can store conjunction and disjunction patterns ................ 26
4.1.3
The extension system can store negation ............................................................... 26
4.2
Lessons learned through detailed spiking models of the basal ganglia ........................ 26
4.2.1
Filtering effect of synaptic short-term facilitation in MSN-SNr synapses ........... 26
4.2.2
Filtering effect of depressive STN-SNr synapses in the hyperdirect pathway...... 27
4.2.3
The control of MSN excitability through MSN collaterals, FSN and GPe ............ 28
4.2.4
Dopamine dependent changes enhancing oscillations and synchrony ................ 29
4.2.5
Does basal ganglia support action selection? ..........................................................31
4.2.6
Synaptic and neural perturbations improving dynamics and function ................ 32
4.3
Learning action selection in basal ganglia ...................................................................... 33
4.3.1
Action selection can be learned through Bayesian inference in basal ganglia ..... 33
4.3.2
Synaptic homeostasis with Bayesian inference ...................................................... 37
4.3.3
Relative importance in learning for MSN D1 and MSN D2 pathways .................. 37
4.3.4
Consequences of dopamine lesioning on learning ................................................. 37
4.3.5
RPE pathway affect learning rate ............................................................................ 38
5
Conclusions and further investigations
39
6
References
41
6
Introduction
1.1
Why study basal ganglia?
The basal ganglia (BG) are present in all vertebrates ranging from primates, with complex
behavior repertoires, down to the primitive lamprey thought to reflect the vertebrate system in
early ancestors. The conservative evolution of the vertebrate BG implicates that they serve a
function important to all vertebrates. BG are believed to be involved in important cognitive
functions such as reward-based learning, exploratory behavior, goal-oriented behavior, motor
initiation, working memory and action selection. BG receive input from a large portion of the
cortex and thalamus, and project to motor centers in the thalamus and brainstem effectively
influencing behavior. In addition, BG can control cortical processing, e.g. short term memory or
motor preparation, through loops back to prefrontal cortical and supplementary motor areas via
thalamus. Indeed BG are heavily involved in motor, associative and limbic information (Mink,
1996) and play a major role in some disorders such as Parkinson’s disease (PD), Huntington’s
disease (HD), Schizophrenia, Dystonia and Hemiballismus. Thus, by studying BG a better
understating of how behaviors are stored, utilized, formed and modified in all vertebrates can be
gained, potentially resulting in the discovery of novel treatments for severe debilitating
neurological diseases
1.2
What is a model?
Modelling is a crucial tool in many scientific disciplines including neuroscience. As the
complexity of a system grows, there is a need to integrate data and knowledge, and also to make
simplifications and build example systems from which a deeper understanding of aspects of the
complex system under study can be obtained. A model representation can have vast variations,
some consisting of a single equation, some requiring page after page of equations and computer
code, and some with only a descriptive presentation of a hypothetical system. Models are
important tools to test hypotheses or theories. Thus, a model can have many different shapes
but with a common goal; to reduce or make sense of the complexity of the system studied and
help us develop hypotheses and theories that deepen our knowledge of how the system works.
1.3
Why use computational models?
Computational models are used within the computational neuroscience field to help uncover
principles behind the development, organization, information-processing and functional
capacity of a neural system, on multiple levels of biological description and abstraction. A
computational model can be used in order to get a better comprehension of brain mechanism on
an explanatory level, developping information-processing algorithms where traditional
approaches have not produced satisfactory results or to generate ideas of new treatments for
neurological disorders.
1.4
Scope of the thesis
This thesis is based on three modeling projects (four papers). In the first project, a model with
focus on functionality was used to evaluate a new hypothesis about the organization of BG. The
second project, and the main body of the work, focused on broadening our understanding of
how different components of the BG network, such as synaptic dynamics, connectivity patterns,
neuron types and dopamine levels, affect function and network dynamics. In the third project, a
spiking network model with a novel biological plasticity rule was used to study how connectivity
patterns in BG can be learned.
1.4.1
Project I (paper 1)
In this project we took a fresh and brave look at the most recent findings on BG organization
and came up with a novel hypothesis on how different subsystems in BG come together to
produce action selection. The two-pathway model, with the direct- and indirect pathways, have
dominated BG research over the last 20 years. Although this model captures many important
aspects of BG information processing, there is room for improvement since many aspects of BG
organization have not yet been incorporated into a functional framework. Here, an idea was
developed that the arbitration system, composed of subthalamic nucleus (STN), globus pallidus
interna (GPi), globus pallidus externa (GPe), pendunculupontine nucleus (PPN) and central
7
medial (CM) nucleus of the thalamus, constitutes a winner-take-all network in which the
strongest input from the brainstem or thalamus is selected in the output nuclei, here GPi, and
that the extension system is made up of the direct and indirect pathway from striatum which in
turn can utilized cortical contextual information to modify the output from the arbitration
system.
1.4.2
Project II (paper 2 and 3)
The ambition here was to build a detailed spiking model that could push the boundary for our
understanding of how different parts of BG physiology contribute to dynamics and function in
healthy and pathological brain states. It was an ambitious goal and the project had to be divided
into two subprojects. The first part of the project (paper 2) focused on developing a model of
GPe), STN and substantia nigra pars reticulata (SNr). Great effort was made to make sure the
model complied with latest BG findings. In the second part (paper 3), the model was extended
with the striatum, GPe type A and I neurons, and also dopamine modulation effects were
included.
In the first part of the project, action selection in BG was explored with a focus on the role of
dynamic synapses originating in striatum GPe and STN. Transient strengthening or weakening
of synapses through short-term plasticity on a time scale of hundreds of milliseconds can
significantly affect functional signaling between neural groups in the brain. This short-term
plasticity is a common feature in several parts of BG, but still, prior to this project, models had
yet not incorporated it. Her, we could show how SNr cells become particularly responsive to a
burst in striatal cells due to facilitation in striato-nigral connections and depression in pallidonigral connections. Furthermore, the standard model suggests that the indirect pathway
controls SNr activity with striatal cells disinhibiting the STN via GPe. Our model rather
indicates that SNr activity is controlled more directly by the GPe projections to SNr. This is
partly because GPe cells strongly inhibits SNr cells, but also due to depressing STN to SNr
synapses.
In the second part of the project we broadened the scope to investigate not only action selection
but also oscillatory dynamics in both healthy and pathological brain states. The extended model
predicts that local inhibition in striatum and the indirect pathway are important for BG to
function properly over a larger range of cortical drive. The changes of AMPA efficacy in corticostriatal synapses, the reduction of connectivity between MSNs and the decreased excitability of
GPe neurons were found to be the main contributors to the facilitation of oscillations seen in
PD. Finally, we found multiple changes of synaptic efficacy and neural excitability which could
restore action selection ability and at the same time reduce the oscillations. Identification of
such targets could potentially generate new ideas for treatment of Parkinson’s disease.
1.4.3
Project III (paper 4)
In this project we started to explore how action selection can be learned in BG. The brain
enables animals to behaviourally adapt in order to survive in a complex and dynamic
environment, but how reward-oriented behaviours are achieved by its underlying neural
circuitry is an open computational question. We addressed this concern by developing a spiking
model of BG utilizing a novel probabilistic synaptic model that learns to dis-inhibit the action
leading to a reward despite ongoing changes in the reward schedule. The paper demonstrates
how a learning rule based on probabilistic inference in a spiking neural network model can be
used for long-term synaptic plasticity by the successful performance of the model in a multiplechoice learning task with a changeable reward schedule. Furthermore, it shows how the severity
of dopamine depletion correlates with decrease in model performance and that removing the
indirect pathway is far more debilitating than removing the direct pathway, although removing
the direct pathway still results in a significant performance drop.
1.5
List of papers included in this thesis
Paper 1: Kamali Sarvestani I, Lindahl M, Hellgren-Kotaleski J, Ekeberg Ö (2011) The
arbitration-extension hypothesis: a hierarchical interpretation of the functional organization of
the Basal Ganglia. Front Syst Neurosci 5:13.
Paper 2: Lindahl M, Kamali Sarvestani I, Ekeberg O, Kotaleski JH (2013) Signal enhancement
in the output stage of the basal ganglia by synaptic short-term plasticity in the direct, indirect,
and hyperdirect pathways. Front Comput Neurosci 7:76.
8
Paper 3: Lindahl M, Kotaleski JH. Untangling basal ganglia network dynamics and function –
role of dopamine depletion and inhibition investigated in a spiking network model (Manuscript
in preparation)
Paper 4: Berthet P, Lindahl M, Tully P, Hellgren-Kotaleski J, Lansner A. Functional Relevance
of Different Basal Ganglia Pathways Investigated in a Spiking Model with Reward Dependent
Plasticity. (In revision Frontiers in neural circuits)
1.6
Contribution to papers
Paper 1: Conception and design of research, interpreted results of simulations, drafted
manuscript, edited and revised manuscript, approved final version of manuscript.
Paper 2 and 3: Conception and design of research, performed simulations, analyzed data,
interpreted results of simulations, prepared figures, drafted manuscript, edited and revised
manuscript, approved final version of manuscript.
Paper 4: Conception and design of research, implemented the BCPNN model that works with
dopamine volume transmission in NEST, interpreted results of simulations, drafted manuscript,
edited and revised manuscript, approved final version of manuscript.
9
2 Biological background
2.1
The basal ganglia
BG consist of several nuclei in the brain of vertebrates and are situated in the forebrain. Nuclei
included are striatum consisting of the caudate, putamen and nucleus accumbens, subthalamic
nucleus (STN), globus pallidus pars externa (GPe), globus pallidus pars interna (GPi),
substantia nigra pars reticulata (SNr) and substantia nigra pars compacta (SNc), but also other
nuclei such as the pedunculupontine nucleus (PPN) have been suggested to be part of BG. Below
follows a more detailed description of each BG nucleus and the connectivity (also see Figure 1).
Figure 1 | Schematic pictures of BG nuclei location and connectivity. (A) Illustration of BG location in the brain, (B)
Illustration of BG connectivity
2.1.1
Input
The striatum receives excitatory input form the cortex, thalamus and amygdala but also
inhibitory input from GPe. The excitatory input is topographically organized, but any given
region of striatum receives overlapping input from multiple, and often related cortical areas.
The input is thought to provide BG with motor planning information to execute its role in motor
control (Reiner, 2010). Cortical input to STN is more restricted and mainly originates from
motor areas in cortex such as the primary and supplementary motor areas (M1 and SMA) as well
as frontal eye field and supplementary frontal eye field (FEF and SFEF) (Parent and Hazrati
1995). A major thalamic input to BG is the central medial nucleus (CM) and the parafascicular
nucleus (PF) of the thalamus (Smith et al., 2010) that projects to both striatum and STN. The
CM and PF nuclei get inputs from nuclei liable for preliminary transformation of sensory cues
into motor commands.
In addition to the motor command inputs from CM and PF, shared with the STN, striatum also
receives incoming connections from the sensory and the associative thalamus with visual,
auditory, and somatosensory association information.
2.1.2
Striatum
The striatum is the main input stage of BG and comprises the caudate nucleus, putamen and
nucleus accumbens. The striatum contains one principal projection neuron, the mediumspiny
neuron (MSN) (Bishop et al., 1982) which makes up around 95% of the neural population
(Kemp and Powell, 1971). The remaining striatal neurons are interneurons (Bishop et al., 1982)
that preferably project inside striatum. Despite being relatively few they constitute a variety of
morphological and neurochemically defined types. Included in these are the large aspiny
neurons with acetylcholine as a synaptic transmitter and the fast spiking neurons (FSN) with
GABA as a synaptic transmitter (Kawaguchi, 1993).
10
2.1.2.1 The direct and indirect pathways
The striatal projection neurons, MSNs, are currently seen as originating from two separate but
intermingled neuronal populations. The MSNs with dopamine receptor D1 targets GPi or SNr
whereas the MSNs with dopamine receptor D2 projects to the GPe. These projections have been
referred to as the direct and indirect pathways (Wichmann and DeLong, 1996). The direct
pathway is thought to arise from GABAergic neurons that co-express substance P and/or
dynorphin and the indirect pathway is believed to originate from GABAergic striatal neurons
that co-express encephalin.
2.1.2.2 Matrix and striosomes/patch
The striatum can also be divided along another axis: the striosomes (called patch in rat) and the
surrounding extrastriosomal matrix, which are known to have different chemical markers and
also have partly different connections (Gerfen et al., 1987; Graybiel, 1990; Gerfen, 1992). The
function of this compartmentalization is still poorly known, but experiments in rats and
monkeys have suggested differential relations of these two compartments with the SN. The
matrix is believed to get inputs from sensory and motor cortical areas and to project to the SNr,
whereas striosomes are thought to receive inputs from limbic cortical areas and to project to
SNc and SNr (Gerfen, 1985; Gerfen et al., 1987; Lévesque and Parent, 2005; Fujiyama et al.,
2015).
2.1.3
Subthalamic nucleus
The STN is the primary excitatory input nucleus of BG, and it consists of medium sized
glutamatergic projection neurons (Kita and Kitai, 1987). The STN receives input from cortex and
thalamus and projects to GPe, GPi, SNr and PPN.
2.1.4
Globus pallidus
The globus pallidus (GP) contains the medium sized GABAergic projections neurons and can be
subdivided into two parts GPe and GPi. GPe sits in the center of BG like a spider in a web,
whereas GPi is part of BG output (Smith et al., 1998). GPe receives excitatory input from STN,
and thalamus and inhibitory input from striatum, and sends inhibitory projections to striatum,
STN, neighboring GPe and SNr (Smith et al., 1998; Bolam et al., 2000). The internal segment
receives excitatory input from STN and inhibitory input from GPe (Smith et al., 1998) and sends
inhibitory projects to PPN, CM, some motor nuclei of ventral thalamus and several brain stem
nuclei.
2.1.5
Substantia nigra
The substantia nigra (SN) consists of two main cell types, SNc that use dopamine, and the SNr
that use GABA as neurotransmitter (Nakanishi et al., 1997). The SN receives a majority of
GABAergic input, 70%, mainly from striatum, GP and collaterals (Rinvik and Grofová, 1970).
The SNc projects sends mainly dopaminergic projections to the striatum in BG, but also to other
partslike GP SN and STN (Tepper, 2010). The SNr similar to GPi also projects to PPN, CM,
some motor nuclei of ventral thalamus and several brain stem nuclei.
2.1.6
Pedunculopontine nucleus
PPN, has traditionally not been thought of as part of BG, although it has been suggested (MenaSegovia et al., 2004). PPN receives glutamatergic projections from STN, GABAergic input from
GPi and SNr and sends mixed cholinergic/glutamatergic projections to STN (Bevan and Bolam,
1995; Sadikot and Rymar, 2009). PPN is included in BG model in the first project where a
hypothesis about BG organizations in action selection is developed.
2.2
Synaptic dynamics
2.2.1
Short-term plasticity
Short-term plasticity refers to facilitation or depression of synaptic efficacy from pre-synaptic
spiking lasting on the timescale of hundreds to thousands of milliseconds. Synapses showing
short-term plasticity are common throughout the whole brain (Creager et al., 1980; McCormick,
1989; Douglas and Martin, 1991; Nathan and Lambert, 1991; Tsodyks and Markram, 1997;
Varela et al., 1997; Dittman et al., 2000; Hanson and Jaeger, 2002; Sims et al., 2008; Connelly
et al., 2010). Such synapses are critical components contributing to the computational function
of neural networks (Abbott and Regehr, 2004). These synapses can dynamically enhance either
11
low frequency input or high frequency input (Fortune and Rose, 2001; Abbott and Regehr,
2004) or detect a transient increase or decrease of presynaptic input (Abbott et al., 1997;
Lisman, 1997; Markram et al., 1998; Puccini et al., 2007). Short-term plasticity is also
prominent in BG (Hanson and Jaeger, 2002; Sims et al., 2008; Connelly et al., 2010; Gittis et
al., 2010; Planert et al., 2010).
2.2.2
Long-term plasticity
Long-term plasticity is viewed as the corresponding neural mechanism for experience based
alteration of neural circuits. Synapses can increase in strength through long-term potentiation
(LTP) or decrease in strength through long-term depression (LTD). LTP and LTD are believed to
be the most important processes that enable learning and memory in the nervous system (Cooke
and Bliss, 2006).
Spike time dependent plasticity is a type of long-term plasticity where modulation of synaptic
efficacy occurs on the basis of precise pre- and postsynaptic activation times and as other LTP or
LTD forms lasts from hours up to years. With respect to BG such plasticity is prominent in the
synapses between cortex and medium spiny neurons in the striatum but not understood in great
detail (Reynolds and Wickens, 2000, 2002; Surmeier et al., 2007; Berretta et al., 2008; Pawlak
and Kerr, 2008; Shen et al., 2008; Fino and Venance, 2011; Paille et al., 2013).
2.2.3
Synaptic pruning
Synaptic pruning is a phenomenon in the mammalian brain where synapses are removed during
the period between from early childhood until the onset of puberty. It is a process that is
considered to reflect learning and is affected by the environment (Craik and Bialystok, 2006).
2.2.4
Synaptogenesis
Synaptogenesis is the growth of synaptic connections between neurons in the nervous system. It
is an ongoing process during the whole lifespan of a person, although particularly active during
initial brain development (Huttenlocher and Dabholkar, 1997). It is a process that is especially
important during the critical period since some connections formed during the critical period
cannot be form later in life (Comery et al., 1997).
Both formation of new synapses and removal of existing ones are seen throughout life, and
together with LTP and LTD these processes are likely all important for learning, memory and/or
adaptation in the brain.
2.3
Dopamine
Dopamine has been shown to be important both as a reward signal (Schultz, 1997) and as
modulator of neural excitability and synaptic efficacy (Cepeda et al., 1993; Shen and Johnson,
2000; Bracci et al., 2002; Hernández-Echeagaray et al., 2004; Hernández et al., 2006;
Baufreton and Bevan, 2008; Taverna et al., 2008; Zhou et al., 2009; Humphries et al., 2009a;
Chan et al., 2011; Chuhma et al., 2011; Gittis et al., 2011; Miguelez et al., 2012). Many
neurological disorders stem from a disruption in the dopaminergic system. It projects heavily to
striatum but also to other parts of BG. In PDthe dopaminergic neurons die which leads to a
deficiency of dopamine in BG. This has major consequences for the spike dynamics in BG with
increases in oscillations and spike synchronization.
2.4
Action selection
BG have for a long time been suggested to be involved in action selection (DeLong, 1990; Mink,
1996; Redgrave et al., 1999). The cortex/thalamus-BG-brain stem pathway is, besides the more
direct pathway from cortex to the brain stem, in a perfect position to modify motor program
execution in the brain stem based on contextual input from the cortex and thalamus. Recently
Kravitz et al. (2010) showed that activation of medium spiny neurons with dopamine receptor
D1 promotes actions and activation of medium spiny neurons while dopamine receptor D2
inhibits actions. This strongly supports the hypothesis that BG are involved in action selection.
12
2.5
The direct, indirect and hyperdirect pathways
In the BG system, three major pathways have been identified: the direct, the indirect and the
hyperdirect pathways, respectively which converge on GPi and SNr (Nambu, 2008). The direct
pathway is made up by the MSNs with dopamine receptor D1 projecting directly onto GPi and
SNr. The indirect pathway consists of the MSNs with dopamine D2 receptor projecting to GPe
and then via STN or directly influence GPi and SNr. The hyperdirect pathway is considered a
fast pathway where STN excites GPi and SNr. The direct pathway seems to be important for
promoting actions, whereas the indirect pathway seems to inhibit actions, and, finally, the
hyperdirect pathway works as a transient stop signal giving striatum and GP enough time to
resolve a high level of conflict in action selection (Frank, 2006; Kravitz et al., 2010).
2.6
Reinforcement learning
In engineering literature three main types of learning paradigms are commonly referred to:
supervised learning, reinforcement learning and unsupervised learning. In supervised learning a
model is built to predict an output given an input. This is done by supplying an algorithm with
example input data where the output is known. In unsupervised learning we try to find a hidden
structure in unlabeled data. Thus, there is no a priori knowledge of what output to expect. In
reinforcement learning an input is given, in response to which, during training, a reinforcement
signal is generated to indicate whether a good decision or a bad decision was made by the
model. During a training period parameters in the model are adjusted such that the model in the
end ‘knows’ exactly what the correct choices given any input are.
The striatum receives massive inputs from dopamine neurons. The dopamine signal has been
shown by Schultz et al. (1997) to behave like a reinforcement signal that can shift from
predicting a primary reward to a conditioning stimuli. The behavior of the dopamine neurons
resemble the reward prediction error in the temporal difference learning algorithm used in
reinforcement learning. In fact, it seems as if BG could be the biological substrate in the brain
for reinforcement learning, while cortex rather seems to be suited for unsupervised learning and
cerebellum seems to be involved in supervised learning (Doya, 1999).
13
3 Models and methods
3.1
Computational neuroscience
Computational neuroscience is one of the approaches to advance progress in the neuroscience
field, in addition to disciplines such as psychology, physiology, and medicine. The field of
computational neuroscience emerged from the realization that interdisciplinary studies are
necessary in order to deepen our understanding of how the nervous system works.
The nervous system has multiple levels of spatial organization ranging from molecules to the
nervous system as a whole. Neurons specialize in signal processing mainly through electrical
impulses called action potentials. Single neuron models can be utilized to study how ion
channels and biochemical signaling affect and modify the dynamics of neurons. Insights from
such studies may in turn be used to search for putative drug compounds able to restore normal
function of malfunctioning neurons.
Basic computational neural network models are used to study the information processing of
multiple connected neurons and their signaling through electrical impulses. Such models have
the potential to enhance the understanding of general computational principles of networks
with different organizations, such as random-, feed forward-, competitive and point attractor
networks.
System level network models are used to study specific parts of the brain where the
computational model can be developed based on the known or hypothesized anatomical
organization of the region. System level models are beneficial to address questions about what
computation a specific part of the brain can perform, and also can help us to identify important
mechanisms that are responsible for network dynamics seen in neurological diseases as well as
in the healthy system.
In addition, there are models that have abstracted away the neuron as a computational unit, and
instead use an equation to represent a population of neurons or describe the computation of a
particular area of the brain as one function. Such models are generally called top down models
since they are theory driven, as compared to bottom up models that are driven more by
biological constrains. In reality most models have borrowed features from both the top-down
and bottom-up approaches. Together, all these models are important for mapping out the bigger
picture of how the nervous system is functionally and structurally organized. Top down models
can be used to precede modeling studies with more detailed biologically constrained models that
thus are used to verify or reject hypotheses generated by more abstract models.
3.2
Model components
In this thesis, systems level network models are used, where the neuron is a basic computational
unit connected through chemical synapses. Examples of neuron- and synaptic models suitable
for such an abstraction level are given below.
3.2.1
Hodgkin-Huxley model
The Hodgkin-Huxley model came about through pioneering work by Hodgkin and Huxley
(1952) working on the axon of the giant squid. It was determined that the axon had three major
currents: voltage-gated persistent 𝐾 + current (𝐼𝐾 = 𝑔𝐾 𝑛4 (𝑉 − 𝐸𝑘 )) with four activation gates (the
term 𝑛4 in the equation below), voltage gated transient 𝑁𝑎 + current (𝐼𝑁𝑎 = 𝑔𝑁𝑎 𝑚3 ℎ(𝑉 − 𝐸𝑁𝑎 ))
with three activation gates and one inactivation gate (the term 𝑚3 ℎ in the equation below) and a
Ohmic leak current (𝐼𝐿 = 𝑔𝐿 (𝑉 − 𝐸𝐿 )) carried mostly by 𝐶𝑙 − ions. The equations Hodgkin-Huxley
come up with to describe the voltage dynamics on the giant squid is given by the equation below
where the 𝑉 is the voltage, 𝑛 is the activation variable for 𝐾 + , 𝑚 is the activation variable for 𝑁𝑎+
and ℎ the inactivation variable for 𝑁𝑎 + .
𝐶
𝑑𝑉
= 𝐼 − 𝑔𝐾 𝑛4 (𝑉 − 𝐸𝑘 ) − 𝑔𝑁𝑎 𝑚3 ℎ(𝑉 − 𝐸𝑁𝑎 ) − 𝑔𝐿 (𝑉 − 𝐸𝐿 )
𝑑𝑡
14
𝑑𝑛
= 𝛼𝑛 (𝑉)(1 − 𝑛) − 𝛽𝑛 (𝑉)𝑛
𝑑𝑡
𝑑𝑚
= 𝛼𝑚 (𝑉)(1 − 𝑚) − 𝛽𝑚 (𝑉)𝑚
𝑑𝑡
𝑑ℎ
= 𝛼ℎ (𝑉)(1 − ℎ) − 𝛽ℎ (𝑉)ℎ
𝑑𝑡
(1)
Here 𝛼𝑖 and 𝛽𝑖 are voltage dependent (but not time) rate constants for the 𝑖-th ion channel, 𝐼 is a
current source and 𝑔𝐾 , 𝑔𝑁𝑎 and 𝑔𝐿 are respectively the conductance for ion channels K, Na and
leakage. Most of the currents activated in the neuron can be represented in the manner above,
and if the 3-D morphology of the neuron is taken into account and one wants to represent active
membrane properties throughout the dendrites, this model approach can result in thousands of
equations for one neuron. A general challenge accompanying this approach is to find reasonable
parameters for all the ionic currents modelled.
3.2.2
Integrate and fire model
The leaky integrate and fire model (Tuckwell, 1988), represents a neuron as an unit having a
leakage current and several voltage-gated currents that are inactivated at rest. Subthreshold
behavior is given by the linear differential equation where 𝑉 is the membrane voltage:
𝐶
𝑑𝑉
= −𝑔𝐿 (𝑉 − 𝐸𝐿 ) + 𝐼
𝑑𝑡
𝑖𝑓 𝑉 > 𝑡 𝑓 𝑡ℎ𝑒𝑛 𝑉 = 𝑉𝑟
(2)
Here 𝐶 is the capacitance, 𝑔𝐿 is the leak conductance, 𝐸𝐿 is the resting potential and 𝐼 is a
current source. When the membrane potential 𝑉 reaches 𝑡 𝑓 it is reset to 𝑉𝑟 . Often one wants to
represent that neurons show spike adaptation or behave in characteristic ways when they start
to spike, etc. Below some of these ways are summarized.
3.2.3
Adaptive exponential integrate and fire model
The adaptive exponential integrate and fire model, also called AdEx, was introduced by Brette
and Gerstner (2005) and is a hybrid spiking neural model with two variables which uses an
exponential function to generate the upstroke of the action potential. It is a hybrid spiking
model since it combines a smooth spike generation with sharp spike reset. Unlike HodgkinHuxley conductance based models, a hybrid model has only a few parameters derived from
bifurcation theory. These models however lack the same degree of connection to physiology as
parameters used in Hodgkin-Huxley formalism.
The following equations control the dynamics of the exponential integrate and fire model with
adaptation, where 𝑉 is the membrane potential and 𝑤 is the contribution of the neurons slow
currents:
𝐶
𝑑𝑉
𝑉 − 𝑉𝑇
= −𝑔𝐿 (𝑉 − 𝐸𝐿 ) + 𝑔𝐿 𝛥 𝑇 𝑒𝑥𝑝 (
)−𝑤+𝐼
𝑑𝑡
𝛥𝑇
𝑑𝑡
𝜏𝑤
= 𝑎(𝑉 − 𝐸𝐿 ) − 𝑤
𝑑𝑡
𝑖𝑓 𝑉 > 𝑡 𝑓 𝑡ℎ𝑒𝑛 𝑉 = 𝑉𝑟 𝑎𝑛𝑑 𝑤 = 𝑤 + 𝑏
(3)
Here 𝐶 is the capacitance, 𝑔𝐿 is the leak conductance, 𝐸𝐿 and 𝑉𝑇 are the resting and threshold
potentials, Δ 𝑇 is the slope factor, 𝐼 is a current source, 𝜏𝑤 is the recovery current time constant
and 𝑎 is the voltage dependence of the recovery current above. When the membrane potential 𝑉
reaches 𝑡 𝑓 it is reset to 𝑉𝑟 and then the recovery current 𝑤 is increased with 𝑏.
3.2.4
Izhikevich simple model
The Izhikevich simple model (Izhikevich, 2003) is a two variable hybrid model which uses a
quadratic function for generating the upstroke of an action potential. It is similar to the AdEx
model in that is can capture the dynamics of neurons with few parameters.
15
The following equations control the dynamics of the quadratic integrate and fire model with
adaptation, where 𝑉 is the membrane potential and 𝑢 is the contribution of the neuron’s slow
currents:
𝐶
𝑑𝑉
= 𝑘(𝑉 − 𝑣𝑟 )(𝑉 − 𝑣𝑡ℎ ) − 𝑢 + 𝐼
𝑑𝑡
𝑢̇ = 𝑎(𝑏(𝑉 − 𝑣𝑟 ) − 𝑢)
𝑖𝑓 𝑉 > 𝑣𝑝𝑒𝑎𝑘 𝑡ℎ𝑒𝑛 𝑣 = 𝑐 𝑎𝑛𝑑 𝑢 = 𝑢 + 𝑑
(4)
Here 𝐶 is the capacitance, 𝑣𝑟 and 𝑣𝑡 are the resting and threshold potentials, 𝐼 is a current
source, 𝑎 is the recovery current time constant, 𝑏 is the voltage dependence of the recovery
current and 𝑘 is a parameter determining the steady-state current voltage (I-V) relation. When
the membrane potential 𝑉 reaches 𝑣𝑝𝑒𝑎𝑘 it is reset to 𝑐 and then the recovery current 𝑢 is
updated with 𝑑.
3.2.5
Conductance based synapses
A simple but realistic way to model the synapse dynamics is to use a conductance based synapse
model. The model is given by the equation below where 𝑔 is the conductance.
𝑔̇ =
𝑔
𝜏𝑔𝑎𝑏𝑎
+ 𝑔𝑜 ∗ 𝛿(𝑡 − 𝑡𝑠𝑝𝑖𝑘𝑒 )
(5)
When a pre-synaptic spike arrives, the conductance 𝑔 is updated with 𝑔0 and then, in between
the spikes, the conductance decays towards zero with time constant 𝜏𝑔𝑎𝑏𝑎 . The postsynaptic
current is given by 𝐼 = 𝑔 ∗ (𝐸𝑟𝑒𝑣 − 𝑉).
3.2.6
Tsodyks model
Synaptic short-term plasticity can be captured with the Tsodyks-Markram model (Tsodyks et al.,
1998). with the common FD formalism (Equations 6 and 7) (Abbott et al., 1997; Dittman et al.,
2000; Abbott and Regehr, 2004; Puccini et al., 2007). The FD formalism dictates that the
synaptic weight is changed by the product of facilitating (F) and depressing (D) components.
This characterization display quantitatively good similarity to experimentally measured synapse
dynamics (Tsodyks and Markram, 1997; Markram et al., 1998; Planert et al., 2010; Klaus et al.,
2011). The model formalism assumes a fixed pool of synaptic assets in active (𝑦), inactive (𝑧) and
recovered (𝑥) states. At rest 𝑦 and 𝑧 are 0 and 𝑥 is 1. Depression arise because some of the assets
remain for a while in the inactive state before going into the recovered state with a rate set by
the recovery time constant 𝜏𝑟𝑒𝑐 . The facilitation is modeled by 𝑢 which is a variable that is stepwise increased at each spike with the product of the utilization factor 𝑈 and 1 − 𝑢 (U is between
0 and 1) and decays exponentially towards 0 with time constant 𝜏𝑓𝑎𝑐 in between spikes
(Equation 6). The assets in the active state 𝑦 are increased with the product of the variables 𝑥
and 𝑢 (enabling depression and facilitation respectively) and are then rapidly inactivated by
decaying towards zero with time constant 𝜏𝑠𝑦𝑛 (Equation 7). The postsynaptic conductance is
proportional to the fraction of assets in the active state and is determined by 𝑔 = 𝑔0 ∗ 𝑦 with the
post-synaptic current 𝐼𝑠𝑦𝑛 = 𝑔 ∗ (𝐸𝑟𝑒𝑣 − 𝑉).
𝑑𝑢
𝑢
=−
+ 𝑈 ∗ (1 − 𝑢) ∗ 𝛿(𝑡 − 𝑡𝑠𝑝𝑖𝑘𝑒 )
𝑑𝑡
𝜏𝑓𝑎𝑐
𝑑𝑥
𝑧
=
− 𝑢 ∗ 𝑥 ∗ 𝛿(𝑡 − 𝑡𝑠𝑝𝑖𝑘𝑒 )
𝑑𝑡 𝜏𝑟𝑒𝑐
𝑑𝑦
𝑦
=−
+ 𝑢 ∗ 𝑥 ∗ 𝛿(𝑡 − 𝑡𝑠𝑝𝑖𝑘𝑒 )
𝑑𝑡
𝜏𝑠𝑦𝑛
𝑑𝑧
𝑦
𝑧
=
−
𝑑𝑡 𝜏𝑠𝑦𝑛 𝜏𝑟𝑒𝑐
16
(6)
(7)
3.2.7
Bayesian Confidence Propagation Neural Network
The Bayesian Confidence Propagation Neural Network (BCPNN) is a learning framework that
describes the relative activation levels of connected units together with their level of coactivation to probabilities that can be couple with Bayes rule (Lansner and Ekeberg, 1989;
Lansner and Holst, 1996). The assumptions made in the derivation of this rule are functionally
consistent with canonical microcircuits of the cerebral cortex (Johansson and Lansner, 2007)
and BG (Berthet et al., 2012). The framework can be approximated by spiking neurons and their
inter-synaptic connections (Tully et al., 2014), in which Hebbian learning arise both at the
synaptic level in the form of long-term potentiation and at the neural level in the form of longterm potentiation of intrinsic excitability.
The default, abstract representation of this network can learn randomly changing attractor
states (Sandberg et al., 2002). But the spiking implementation flexibly allows for a vast set of
dynamics within recurrent networks of integrate-and-fire neurons. Since probabilities can be
approximated by three sets of cascading memory traces at separate time scales (Figure 2),
different operating regimes can be reached by introducing relative differences between the time
constants of these memory traces. For example, asymmetric fast-acting synaptic traces can allow
the network to produce sequences of attractor states, and eligibility traces can enable the
network to perform spike-based delayed reward learning. Altogether, the framework allows a
principled methodology for modeling, and thus understanding, the interaction of different
plasticity mechanisms in large-scale networks of spiking neurons
Figure 2 | Trace-based synaptic learning. (A) A pair of neurons fire randomly and elicit changes in the pre- (red) and
postsynaptic (blue) primary Z traces of a BCPNN synapse connecting them. Sometimes by chance (pre before post*,
synchronous+, post before pre#), the neurons fire coincidentally and the degree of overlap of their Z traces (inset, light
blue), is propagated to the mutual eligibility trace Eij. (B) A reward (pink rectangle) is delivered as external supervision.
resulting in E trace modification (gray line, τe = 100 ms and black line, τe= 1000 ms). (C) Behavior of color
corresponding Pij traces and weights (inset) depends on whether or not the reward arrived in time.
The pre- Si and postsynaptic Sj spike trains are defined by summed Dirac delta pulses with
𝑗
𝑖
respective spike times 𝑡𝑠𝑝
and 𝑡𝑠𝑝 :
𝑗
𝑖
𝑆𝑖 (𝑡) = ∑ 𝛿(𝑡 − 𝑡𝑠𝑝
)
𝑆𝑗 (𝑡) = ∑ 𝛿(𝑡 − 𝑡𝑠𝑝 )
𝑠𝑝
(8)
𝑠𝑝
Traces with the fastest dynamics, Zi and Zj, are exponentially smoothed spike trains:
𝜏𝑍𝑖
𝑑𝑍𝑖
𝑑𝑡
=
𝑆𝑖
𝑓max ∆𝑡
− 𝑍𝑖 + 𝜀
𝜏𝑍𝑗
𝑑𝑍𝑗
𝑑𝑡
17
=
𝑆𝑗
𝑓max ∆𝑡
− 𝑍𝑗 + 𝜀
(9)
which lowpass filters pre- and postsynaptic activity with time constants 𝜏𝑍𝑖 and 𝜏𝑍𝑗 , like what
would be expected from rapid Ca2+ influx via NMDA channels or voltage-gated Ca2+ channels. It
is assumed that each neuron could fire maximally at 𝑓𝑚𝑎𝑥 Hz and minimally at 𝜀𝑓𝑚𝑎𝑥 Hz, which
serve as absolute certainty and doubt concerning the suggestive context of the input. In that
range, firing levels correspond to the approximated probability. Each spike event had a duration
of ∆𝑡 ms.
These Z traces are then passed on to the E eligibility traces:
𝜏𝑒
𝑑𝐸𝑖
= 𝑍𝑖 − 𝐸𝑖
𝑑𝑡
𝜏𝑒
𝑑𝐸𝑗
= 𝑍𝑗 − 𝐸𝑗
𝑑𝑡
𝜏𝑒
𝑑𝐸𝑖𝑗
= 𝑍𝑖 𝑍𝑗 − 𝐸𝑖𝑗
𝑑𝑡
(10)
where, in order to track the coincident activity from the Z traces, a separate equation is
introduced. τe is the time constant for these traces which are assumed to represent intracellular
Ca2+-dependent processes (Fukunaga et al., 1993). The E traces are then used in the calculation
of the P traces, whose longer time courses could correspond to processes like gene expression or
protein synthesis. These values correspond to the final probability estimates based on smoothed
activity levels:
𝜏𝑝
𝑑𝑃𝑖
𝑑𝑡
= 𝜅(𝐸𝑖 − 𝑃𝑖 ) 𝜏𝑝
𝑑𝑃𝑗
𝑑𝑡
= 𝜅(𝐸𝑗 − 𝑃𝑗 ) 𝜏𝑒
𝑑𝑃𝑖𝑗
𝑑𝑡
= 𝜅(𝐸𝑖𝑗 − 𝑃𝑖𝑗 )
(11)
where κ is the reward prediction error (RPE) value and τp the time constant of these P traces.
3.3
Parameter estimation
Many parameters for the neuron and synaptic models were retrieved from already published
studies in this work, however in some cases where no previous model existed we estimated
parameters ourselves. The models were previously derived in Lindahl et al. (2013), here follows
a summary of what was presented in the article plus additional information about the method
behind the estimation of model parameters.
To estimate the parameters to the AdEx model, different approaches were used depending on
the type of data on neuron dynamics that could be obtained. It is not a trivial task to estimate
the relatively few parameters in adaptive exponential integrate and fire model. Brette and
Gerstner (2005) describe how the parameters for a pyramidal cell can be estimated from specific
type of recordings. Similar techniques were used when applicable. Otherwise the parameters
were hand tuned such that whether the behavior of the neuron was in accordance with
recordings of current-voltage curves, current-frequency curves and miscellaneous stimulation
protocols. The following equations were used to approximate EL , VT and ΔT for GPe, SNr and
STN neuron model.
𝐶∗
𝑑𝑉
𝑉 − 𝑉𝑇
= −𝑔𝐿 (𝑉 − 𝐸𝐿 ) + 𝑔𝐿 𝛥 𝑇 𝑒𝑥𝑝 (
)−𝑤+𝐼 = 0
𝑑𝑡
𝛥𝑇
𝑑𝑡
𝜏𝑤
= 𝑎(𝑉 − 𝐸𝐿 ) − 𝑤 = 0
𝑑𝑡
⇒
𝑑𝑉
𝑉 − 𝑉𝑇
= −𝑔𝐿 (𝑉 − 𝐸𝐿 ) + 𝑔𝐿 𝛥 𝑇 𝑒𝑥𝑝 (
) − 𝑎(𝑉 − 𝐸𝐿 )
𝑑𝑡
𝛥𝑇
𝑑2𝑉
𝑉 − 𝑉𝑇
= −𝑔𝐿 + 𝑔𝐿 𝑒𝑥𝑝 (
)−𝑎
2
𝑑𝑡
𝛥𝑇
3.3.1
(12)
(13)
Short-term plasticity
The parameters for the Tsodyks synapse model were estimated in Matlab using a least square
method minimizing the squared error between experimental and model current pair pulse data.
18
To find the solution the fminsearch method in Matlab which implements the Nelder-Mead
Simplex method (Lagarias et al., 1998) was employed. For facilitating and depressing synapses
in SNr a data set collected from Connelly et al. (2010) was used. These data show the relative
synaptic current increase/decrease over 10 successive spikes at 10, 50, and 100 Hz as well as the
relative size of a recovery post synaptic current after 5 pulses at 100 Hz and measured after 60,
160, 560, 3000, and 9000 ms. For the facilitating MSN synapse in GPe a dataset from Sims et
al. (2008) with the relative synaptic current increase over 10 successive spikes at 20 and 50 Hz
was used. Figure 3A shows an example of the fit of the depressing GPe to SNr synapse, with 𝑈 =
0.191, 𝑡𝑟𝑒𝑐 = 0.196 ms and 𝑡𝑓𝑎𝑐 = 0 ms and Figure 3B show an example of the fit of facilitating
MSN to SNr synapse where 𝑈 = 0.02, 𝑡𝑟𝑒𝑐 = 551 ms and 𝑡𝑓𝑎𝑐 = 621 ms.
3.3.2
GPe neuron
The hyperpolarization triggered spike of the GPe neuron was estimated with a subthreshold
adaptation at 2.5 nS and a time constant 𝜏𝑤 at 20 ms. Steady-state current voltage relation was
captured with 𝑔𝐿 a 1.0 nS and a capacitance 𝐶 at 40 pF. Note that with these parameters a GPe
neuron exhibits subthreshold oscillations close to rheobase current (the minimal current
necessary to elicit a spike) (Touboul and Brette, 2008). To mimic the frequency acceleration and
the spike frequency adaptation of the, summed recovery current contribution, 𝑏, at spike reset
was set to 70 pA. With the spike voltage reset, 𝑉𝑟 , at −60 mV and spike cut off, 𝑉𝑝𝑒𝑎𝑘 , at 15 mV
the after hyperpolarization and spike amplitude were in accordance with literature. 𝐸𝐿 , 𝑉𝑇 and
Δ 𝑇 were estimated on membrane potential of spike initiation, threshold membrane potential
and acceleration of membrane potential at spike generation. Experiments indicate that the GPe
neuron goes from silent to spiking at around −53 mV and have a spike threshold at −43 mV,
defined as when the acceleration of the membrane potential reaches 50% of its max, estimated
to 1270 mV/ms2. Both the spike initiation and threshold membrane potential were given in
Bugaysen et al. (2010), whereas the acceleration had to be estimated, This was done by fitting a
sigmoid (Figure 3A) to the up stroke of an action potential (Bugaysen et al. 2010). With
equation 12 and 13 the following equation system was set up and then solved for 𝐸𝐿 , 𝑉𝑇 and Δ 𝑇 .
𝑑𝑉
(−53) = 0
𝑑𝑡
2
𝑑 𝑉
(−53) = 0
𝑑𝑡 2
𝑑2𝑉
(−43) = 1270
𝑑𝑡 2
(14)
In Figure 3A we show the acceleration nullcline of the solution 𝐸𝐿 = −55.1 (V), 𝑉𝑇 = −54.7 (V)
and Δ 𝑇 = 1.7 (ms).
19
Figure 3 | Parameter estimation of synapse and neuron models. (A) Blue, green and red dots in left panel show relative
synaptic current decrease over 10 successive spikes at 10, 50, and 100 Hz for GPe to SNr. The blue, green and red
solid lines in left panel show the model fit. The black dots in the middle panel shows the relative size of a recovery spike
after 5 pulses at 100 Hz and measured after 60, 160, 560, 3000, and 9000. The solid black line in the middle plot shows
the model fit. In the right panel the steady state amplitude for the synapse model over a range of post-synaptic spike
frequencies are shown. (B) Same as figure (A) but for facilitating synapses between MSN and SNr. (C) In the first panel
the diamond marker shows the data point V=-43, d2V/dt=1270 and dot marker shows the data point V=-43, d2V/dt=0 for
the GPe neuron. The solid line shows the fit of the adaptive integrate and fire model to these data points. The middle
diamond shows the fit of a sigmoidal curve to the upstroke of an action potential of the GPe neuron, where the dots
show experimental data and the solid line the model fit. In the right panel we show the data point where the speed of the
upstroke are 50 percent of the max speed of the sigmodal fit of the action potential. (D) The diamond shows the point
V=-52, dV/dt=10.2 and the dot shows the point V=-54, dv/dt=0 for the SNr neuron, and the solid line is the fit of the first
voltage derivative of the adaptive integrate and fire model to this data. (E) The diamond shows the point V=-52,
d2V/dt=0 and the dot shows the point V=-35, d2v/dt=50 for the STN neuron, and the solid line is the fit of the second
voltage derivative of the adaptive integrate and fire model to this data.
3.3.3
SNr neuron
The subthreshold adaptation 𝑎, time constant 𝑡𝑤 , capacitance 𝐶, summed current contribution 𝑏
at spike reset of the SNr neuron was set to 80 pF and 200 pA such that spike frequency
acceleration and spike frequency adaptation were in accordance with experiments. Spike voltage
reset 𝑉𝑟 and spike cut-off 𝑉𝑝𝑒𝑎𝑘 were set to capture the after-hyperpolarization and spike
amplitude of recorded neurons. Then to estimate resting and threshold potentials and slope
20
factor, 𝐸𝐿 , 𝑉𝑇 and Δ 𝑇 we used experimental data on SNr neuron that goes from silent to spiking
at approximately −54 mV and have spike threshold at −52 mV, defined as when the rate of rise
is 10.2 mV/ms (Richards et al., 1997; Atherton and Bevan, 2005; Chuhma et al., 2011). The
following equation system set up and then solve for EL , VT and ΔT .
𝑑𝑉
(−52) = 10.2
𝑑𝑡
𝑑𝑉
(−54) = 0
𝑑𝑡
𝑑2𝑉
(−54) = 0
𝑑𝑡 2
(15)
In Figure 3A the nullcline of the solution 𝐸𝐿 = −55.8 (V), 𝑉𝑇 = −55.2 (V) and Δ 𝑇 = 1.8 (ms) is
shown.
3.3.4
STN neuron
The subthreshold adaptation of the STN model was set at 0.3 nS below −70 mV with 𝜏𝑤 at 333
ms, such that 333𝑤̇ = 0.3(𝑉 + 70) − 𝑤 to account for the hyperpolarization activated inward
current that is behind the rebound bursts and was set to 0 nS above −70 mV, such that 333𝑤̇ =
−𝑤, to get minimal spike frequency adaptation. The STN neuron's steady-state current-voltage
relation was estimated by setting 𝑔𝐿 to 10.0 nS in accordance with experiments. To capture
delayed afterhypolarization caused by increased current injection as well as the spike frequency
acceleration the capacitance, 𝐶, the summed recovery current contribution, 𝑏, at spike reset and
the spike voltage reset, 𝑉𝑟 , was respectively set to 60 pF, 0.05 pA, and −70 mV. The
hyperpolarization-induced bursts were estimated by resetting V following a spike to 𝑉𝑟 +
max(𝑤 × −10,10) if 𝑤 < 0 and else to 𝑉𝑟 . A similar modification to the spike reset point has been
done by Izhikevich (2003). With the spike cut off, 𝑉𝑝𝑒𝑎𝑘 , at 15 mV we got a spike amplitude in
accordance with literature. To estimate 𝐸𝐿 , 𝑉𝑇 and Δ 𝑇 we again used equation 12 and
13. Experiments show that STN are silent at a membrane potential at −64 mV and a have a
spike threshold at −35 mV, within the acceleration of membrane potential at 50 mV/ms2 (Kass
and Mintz, 2006; Farries et al., 2010). Thus we got the following equation system and solve for
𝐸𝐿 , 𝑉𝑇 and Δ 𝑇 .
𝑑𝑉
(−64) = 0
𝑑𝑡
2
𝑑 𝑉
(−64) = 0
𝑑𝑡 2
𝑑2𝑉
(−35) = 50
𝑑𝑡 2
(16)
In Figure 3A the nullcline of the solution 𝐸𝐿 = −80.2 (V), 𝑉𝑇 = −64.0 (V) and Δ 𝑇 = 16.2 (ms) is
shown.
3.4
Computational models of the basal ganglia
Below a brief summary of selected BG related models are done. The model presented have been
chosen two show the broad spectrum of questions that system levels models of BG have
addressed and intended to put the models presented in this thesis in relation to previous work.
3.4.1
Houk and Beiser 1998
A model of a macroscopic module of prefrontal cortex-BG-thalamus-prefrontal cortex and
several similar microscopic modules within the macroscopic module was built (Houk and
Beiser, 1998). A single membrane-bound compartment with passive leakage was use to model
neurons. A sigmoidal activation function was used to convert membrane potential into
normalized spike count between 0-1. The model tested the hypothesis that BG are important for
serial order behavior in prefrontal cortex. It was shown that the activity sequences could be
represented in bi-stable cortical-thalamic loops which could be activated by MSNs. It was shown
21
that the model, when instantiated with randomly distributed corticostriatal weights, could
produce different patterns of prefrontal activity in response to different target sequences. Such
patterns were a clear spatially distributed encoding of the sequence in prefrontal cortex.
3.4.2
Bar-Gad, Havazelet-Heimer, Goldberg, Ruppin and Bergman 2000
A three-layer feedforward network with linear activation functions and lateral connectivity of
BG were built to test if BG could perform reinforcement driven dimensionality reduction (BarGad et al., 2000). The model had a cortical input layer, a striatal intermediate layer and a
pallidal output layer. The model shows how cortical salient information can be extracted by
means of dimensionality reduction, that used by prefrontal cortex through thalamus.
3.4.3
Terman, Rubin, Yew and Wilson 2002
A spiking neural network model of STN and GPe were used to investigate how the connectivity
strength between STN and GPe and within GPe effected activity patterns in STN and GPe
(Terman et al., 2002). It is shown how the network can sustain three types of firing, clustering,
propagated waves and regular firing dependent on the connectivity strength between STN and
GPe and within GPe. The model predicts that the STN-GPe network is capable of both correlated
rhythmic activity and irregular self-sustained firing that can block the rhythmic activity. It is
suggested that altered connectivity in STN-GPe network through dopamine depletions could be
responsible for the oscillations seen in PD.
3.4.4
Frank 2006
A rate model of BG is presented that includes all major BG nuclei, including STN. The model is
used to show that STN can prevent premature action selection when modulating the time of
response execution. It is also shows how oscillations emerge when dopamine is removed and
how lesioning STN have a beneficial effect by decreasing oscillations.
3.4.5
Lo and Wang 2006
A spiking model of cortex, superior colliculus and BG was built and used to se if the neural
substrate of the threshold passing seen in monkey experiments reaction time task could be
found (Lo and Wang, 2006). Here BG are represented by caudate nucleus and SNr. The model
shows that cortico-striatal synapses as opposed to cortico-colicular synapses can be used to
optimally tune the threshold passing of cortical neurons in a time reaction task.
3.4.6
Humphries, Stewart, Gurney 2006
A detailed spiking model of BG is built including all major features of BG known at that time
and verified by experimental data on nuclei firing rates and oscillation dynamics in dopamine
depleted state (Humphries et al., 2006). It is shown how BG can perform action selection and
action switching based on input salience. The model further predicts that action selection
deteriorates during low and high dopamine. The model also confirms results that were
previously obtained in a rate model of BG (Gurney et al., 2001).
3.4.7
Humphries, Wood and Gurney 2009
A large (~80000 neurons) network model of striatum including dopamine modulated MSNs
and FSNs are used to study striatal computations (Humphries et al., 2009b). The model predicts
that groups of synchronized cell assemblies on multiple time scale spontaneously can form. The
number of cell assemblies are shown to depend on the dopamine concentration. Counter
intuitively, the model also predicted that FSN neurons connected with both chemical synapses
and electrical gap junctions increase the firing rate of MSNs.
3.4.8
Ponzi and Wickens 2010
A spiking network model with sparse asymmetric randomly connected MSN neurons was built
by Ponzi and Wickens (2010). It was shown how episodic sequential firing of cell assemblies
emerged from the model. Members of the same assembly showed correlation on relevant
timescales of hundreds of milliseconds whereas members of different assemblies showed strong
negative correlation. It is speculated that such cell assemblies could be important for
information processing in the striatum.
22
3.4.9
Steward, Bekolay and Eliasmith 2012
A spiking model of BG, with a spike based learning rule and dopamine as a reward signal is built
and tested against experimental data (Stewart et al., 2012). A good match in terms of behavioral
learning and spike patterns in ventral striatum is obtained. The model is built on the model of
Gurney et al.( 2001). The model successfully learns the utilities of multiple actions, and how to
choose actions in different states. For dopamine signal a local signal for each action is used
instead of a global signal, which is not the current consensus of how dopamine is considered to
be released in striatum, i.e. on a global level. But as they argue, it might be that since
experiments have shown a variation of dopamine levels at different sites in striatum this could
reflect a localization of dopamine release.
3.4.10 Nevado-Holgado, Mallet and Magill 2014
Several candidate rate models of GPe type I, GPe type A and STN were matched against
experimental data (Nevado-Holgado et al., 2014). The best candidate model predicted that the
input and output to GPe type I differed significantly from GPe type A, counting striatal, STN and
thalamic connections. It was also predicted that the two types of GPe neurons where to have
different physiological properties reflected in their respective separate firing rates.
3.4.11 Bahuguna, Aertsen and Kumar 2015
Two striatal models, one rate based and one with spiking units, including MSNs and FSNs
accounting, were built (Bahuguna et al., 2015). The models accounted for recent experimental
finding showing that the recurrent as well as feedforward connectivity markedly differs. The rate
model predicts that the asymmetric connectivity of the two types of MSNs turn striatum into a
threshold device, which is later confirmed in the spiking model. MSN D2 neurons make stronger
inhibition on MSN D1 than for the opposite relation. It is show that MSN D1 neurons firing rate
for low cortical input surpass MSN D2 in firing rate, driven by the same cortical drive, but at
higher rates MSN D2 firing is higher than MSN D1. It is described how the decision threshold
crossing can be shifted by FSNs, dopamine level and pallidal back projections from GPe type A
neurons.
23
4 Results and Discussion
My different research projects concern action selection and network dynamics in BG. In section
4.1 the hypothesis on action selection created in project I is presented, and how it was tested
with a model. In section 4.2 selected results from the detailed model developed in project II is
presented. Finally, in section 4.3 results from the spiking neuron model with reinforcing
learning of project III is shown.
4.1
The arbitration and extension system hypothesis of basal ganglia
In the first project we developed a hypothesis of the functional organization of BG. It was
hypothesized that BG could be divided into two different subsystem, the arbitration system and
the extension system. The arbitration system was postulated to account for solving competition
between different action based on salience in a winner-take-all manner, whereas the extension
system extends the arbitration system and adds the possibility to learn logical expressions such
as conjunction, disjunction and negation. Below are selected results presented from project I,
for more details se paper 1.
Figure 4 | BG projections and connections to other CNS regions (excitatory and inhibitory projections are shown by
arrows and stars respectively). Decisions are made by several mechanisms organized hierarchically. (Modified from
Kamali Sarvestani et al. (2011))
4.1.1
The arbitration system can select the most salient response
The winner take all network in the arbitration system (Kamali Sarvestani et al., 2011) consisting
of PPN, brain stem, CM, GPe and STN (Figure 4) can successfully be used to escape an aversive
stimuli and to target the strongest stimuli. In a simulation with an artificial point-like animal
without BG each of the stimuli triggered a motor response, thus the model ends up activating
multiple direction neurons at once (Figure 5A). Instead in Figure 5B the winner-take-all
property of the arbitration system is demonstrated, the animal successfully suppresses all but
one of the responses at a time, resulting in an effective escape followed by a precise targeting.
24
The activities in all nuclei of the arbitration system show domination of a single action at any
given time and a proper soft switch between actions when the relative strength of the second
response takes over.
25
Figure 5 | Activity of the BG nuclei during decision making and corresponding decisions. The subplots to the left display
the activity of the nuclei indexed. The horizontal axes represent time (in seconds) whereas the vertical axes show 128
different neurons each corresponding to a certain directions of movement, i.e., the competing actions. The neuronal
activity is color coded in brightness of each neuron in a given point in time. (A) An animal without the BG will average
the mixed responses it receives. Such an animal is deprived of effective escape and precise targeting behaviors. (B) An
animal with arbitration system is capable of selecting one action and suppress all of its competitors hence enhancing the
escape and targeting behaviors. (C) An animal with MSN D1 connections to the GPe and the GPi can enforce learned
responses and suppress the otherwise strongest action in certain states. (D) An animal with MSN D2 collaterals can
suppress the learned responses in certain states. (Modified from Kamali Sarvestani et al. (2011))
4.1.2
The extension system can store conjunction and disjunction patterns
The capability of the extension system involving striatum direct and indirect pathways (Figure
4) of storing conjunction and disjunction patterns in an action unit is shown in Figure 5C. The
animal is assumed to have learned that either the combination of landmarks a and b or the
combination of landmarks e and f (interchangeable with landmark a and b in Figure 5C) will
transform the red stimulus (originally aversive) into an appetitive one. Lack of a proper
combination of landmark stimuli (a and b together or e and f together) fails to push the
membrane potential of the MSNs to the vicinity of threshold. However, a proper combination of
landmarks available activates either of the MSN D1 in the action unit responsible for approach
behavior. Activation of MSN D1 inhibits the GPe neurons representing the escape response
hence suppressing the innate tendency of the animal to escape from the aversive stimulus. The
same striatal neurons also inhibit GPi neurons representing approach response thus lifting
inhibition from corresponding PPN. The PPN neurons fire by the virtue of their intrinsic
spontaneous activity, enforcing the learned approach response. The same GPi neurons
disinhibit the CM neurons which in turn activates corresponding STN.
4.1.3
The extension system can store negation
The capability of MSN D1-MSN D2 inhibitory collaterals in negating a certain situation (Boolean
NOT) is shown in (Figure 5C). Landmarks c and d the combination of which is assumed to
restore the original nature of the red stimulus (as an aversive stimulus) are added in this
demonstration (still keeping landmark a and b). Since the learned action caused by stimulation
of the MSN D1 in previous demonstration is to be suppressed here, the MSN D2 stimulated by
components c and d of the state sends input not only to GPe but also to the MSN D1 hence
inhibiting them and removing the influence of the extension system on the GPi. It is worth
noting that although there is enough contextual support to activate both MSNs, since MSN D2 is
more excitable than the MSN D1, it fires more easily and wins the mutual competition.
4.2
Lessons learned through detailed spiking models of the basal
ganglia
In the above systems level model both simplified neurons and synapses have been used. In the
project relating to paper 2 and 3 we study BG dynamics and function using more detailed model
which were built in two steps. In the first step STN, GPe and SNr were included. It was studied
how signaling through the direct-, indirect- and hyperdirect pathways affect the output stage of
the BG and how this is controlled by synapses exhibiting short-term dynamics. Then in the
second step, the model is extended with striatum, including MSN and FSN as well as dividing
GPe into the two distinct population GPe type I and GPe type A. Dopamine modulation is also
included. With the second version of the model a more comprehensive coverage of BG was
accomplished. It enabled us to study how connectivity, neuron excitability and dopamine affect
function and dynamics in normal and dopamine depleted state. Below are selected results
presented from project II, for more details se paper 2 and 3.
4.2.1
Filtering effect of synaptic short-term facilitation in MSN-SNr synapses
Input arriving at high frequency rates is strengthen by facilitating synapses whereas low
frequency input is filter out. An experiment was set up where a group of emulated MSN D1 were
stimulated for five hundred milliseconds and then the firing rate in SNr where measured over
time (Figure 6A-C). This were done for three models, one with facilitating synapses and two
with static synapses (the minimum or maximum conductance of the facilitating synapse) as
references. Several simulation experiments were run where the frequency of the bursts and the
size of the bursting MSN population were varied. It was seen that stimulation of only a few
percent of pre-synaptic direct pathway MSNs results in powerful inhibition of SNr during
26
steady-state (Figure 6D) and that action signaling becomes more resource demanding for lower
MSN D1 spike frequencies requiring stimulation of significantly more pre-synaptic MSNs
(Figure 6E). Thus facilitating MSN D1 synapses in SNr indeed empower high frequency input
and filter out low frequency input.
Figure 6 | Short-term facilitation in MSN-SNr synapses have a profound filtering effect at different biologically realistic
spike frequencies. (A) Raster plot of the emulated activity of 15,000 pre-synaptic MSNs with 4% of the neurons bursting
(red) at 20 Hz for 500 ms and the rest of the population (blue) firing at 0.1Hz. (B) Firing frequency of pre-synaptic MSNs
shown in (A) averaged over the whole population (blue), and over the bursting inputs (red) (triangular kernel window 100
ms used). (C) The resulting inhibitory response in SNr over time. The 𝑓𝑎𝑐 𝑀𝑆𝑁𝐷1 synapses (magenta) need time to be
𝑀𝑆𝑁
𝑀𝑆𝑁
fully activated, delaying the threshold crossing for 200 ms here. With the 𝑟𝑒𝑓𝑖𝑛𝑖𝑡 𝐷1 (blue) and 𝑟𝑒𝑓𝑚𝑎𝑥 𝐷1 (green) synapses
the inhibitory effect appears immediately (triangular kernel window 100 ms). The standard deviation of population
activity between simulations is shown as shaded areas around the mean (solid or dotted lines). (D) The number of MSN
D1 bursting with a certain frequency (7–48Hz) which are needed for action selection, defined as decreasing SNr firing
under a certain threshold. If facilitated synapses are used (magenta), only a few MSNs are needed when bursting in the
𝑀𝑆𝑁
𝑀𝑆𝑁
interval 17–48Hz, and with performance closer to 𝑟𝑒𝑓𝑚𝑎𝑥 𝐷1 (green) synapses than to 𝑟𝑒𝑓𝑖𝑛𝑖𝑡 𝐷1 (blue) synapses during
the last 100 ms of the 500 ms burst. (E) Steady-state firing rate in post-synaptic SNr cells when all pre-synaptic MSN D1
successively increase their firing. Facilitating synapses (magenta) allow background activity to increase up to 1.2Hz
before suppressing SNr to action signal threshold. (Modified from Lindahl et al. (2013))
4.2.2
Filtering effect of depressive STN-SNr synapses in the hyperdirect pathway
Postulate that both the GPe and STN synaptic weights in SNr were fixed, then one would predict
that they counteracted each other, e.g., they might even cancel each other out where increased
stimulation of STN only leads to very small rate change in SNr (Figure 7A, blue dotted line). But
since GPe synapses in SNr are depressing (Connelly et al., 2010), the synaptic input from STN
would come to control the response in SNr where increased firing of STN cells causes increased
firing of SNr cells (Figure 7A, blue solid) because the inhibitory signal through the depressing
GPe-SNr synapses would saturate (Tsodyks and Markram, 1996) while the excitatory input from
27
STN would continue to increase with frequency. However, data from experiments in rat and
monkey contradict such results, and instead implicate that increased firing rate in STN do not
lead to increased firing rate in SNr/GPi (Maurice et al., 2003; Kita et al., 2005; Moran et al.,
2011). These results are well explained by published (Moran et al., 2011) and unpublished
observations (Rosenbaum et al., 2012) and by model simulations (Figure 7A, solid green) where
STN is hypothesized to connect to SNr with depressing synapses.
MSN D2 neurons have a significant effect on SNr activity with and without depressing STN to
SNr synapses (Figure 7B) whereas stimulation of STN for five hundred milliseconds shows
minor effect on SNr for the first hundred milliseconds, two-three hundred milliseconds and for
the last hundred milliseconds Figure 7C. Only for a very short synchronous activation of STN
(Figure 7D) a significant increase of SNr rate is seen. The time course of responses in SNr due to
such stimulation are supported by experiments in rat and monkey where a triphasic response is
triggered by a brief pulse directly in STN or in cortex (Maurice et al., 2003; Kita et al., 2005;
Jaeger and Kita, 2011). The inhibitory response in SNr following the short STN stimulation can
be quenched by removing STN to GPe connections (Figure 7E) which is in accordance with
experiments showing how application of Gabazine in GPi (homolog to SNr) in monkeys
quenches the inhibitory and late excitatory response in GPi succeeding cortical activation in vivo
(Tachibana et al., 2008). As foreseen, STN will indirectly inhibit SNr via GPe for a longer
duration when the connections between STN and SNr instead are removed (Figure 7F).
Figure 7 | Steady-state and temporal effects succeeding activation of the indirect and hyperdirect pathway. (A) Effects
𝐺𝑃𝑒
on SNr frequency when increasing the total STN population activity for 𝑑𝑒𝑝𝐺𝑃𝑒 (solid) and 𝑟𝑒𝑓30
𝐻𝑧 (dotted) GPe to SNr
synapses, and with static (blue) and depressing (green) STN-SNr synapses. (B) Effects on SNr frequency when
𝐺𝑃𝑒
increasing MSN D2 population activity for 𝑑𝑒𝑝𝐺𝑃𝑒 (solid) and 𝑟𝑒𝑓30
𝐻𝑧 (dotted) synapses. (C) SNr activity in response to a
500ms burst in STN during the first 100 ms (blue), between 250 and 350 ms (green) and during the last 100 ms (red)
using depressing (solid) and static (dotted) STN synapses in SNr. (D) Rate in SNr (blue), GPe (green) and STN (red)
after a brief (3 ms) high frequency excitatory pulse into STN. (E) Same as (D) but with STN to GPe lesioned. (F) Same
as (D) but with STN to SNr lesioned. (Modified from Lindahl et al. (2013))
4.2.3
The control of MSN excitability through MSN collaterals, FSN and GPe
In version two of the model, the GPe type A neurons were included. Thus the three main
contributors of GABAerigic inhibition in striatum, MSN collaterals, FSN and GPe, could now be
accounted for. Given the model, a simple question was asked; how are the excitability of striatal
MSNs controlled by the three sources of inhibition. It was found that inhibition from FSNs and
GPe were more important in controlling MSNs firing rate at low cortical drive, whereas
collaterals from neighboring MSNs were more important at higher cortical drive (Figure 8A).
28
Activated MSNs that are not connected by collaterals have significantly higher firing rate than
connected MSNs. In the arbitration and extension hypothesis the collaterals in MSN are
assumed to be strong enough to have an effect on surrounding MSNs firing rate, but
physiological evidence suggest that the connections are weak (Tunstall et al., 2002; Taverna et
al., 2004; Tepper et al., 2004). To test if weak connections between MSNs (between 0.15-0.45
nS) still can be important for action selection we simulated two scenarios. We planted in a
striatal network with 3000 neurons a number of non-connected groups of MSN neurons (Figure
8B-C). In the first scenario we randomly activated neurons from the pool of MSNs neurons, and
in the second scenario we specifically activated only non-connected MSNs. It is clear that nonconnected MSNs spikes higher than if connected (Figure 8D first panel) and that this holds over
a range of different percentage of activated MSNs (Figure 8D second panel). Weak collateral
MSN connectivity may thus be able to restrict the firing rate of neighboring MSNs and work as a
mechanism in increasing the contrast in action selection.
Figure 8 | Control of MSN neurons firing rate by striatal inhibition: (A) How firing of MSN D1 and MSN D2 neurons are
differentially influenced by inhibition form FSN, GPe and MSN collaterals. Left top panel shows the firing rate of MSN D1
neurons where cortical input is increased with a factor 1 to 1.5, when keeping all inhibition (dark blue), only using MSNMSN inhibition (light blue), only using FSN-MSN inhibition (cyan), only using FSN-MSN static synapse inhibition
(yellow), only GPe TA-MSN (orange) and without any inhibition (dark red). Right top panel shows the relative addition to
the inhibition with increased cortical input for MSN-MSN inhibition (light blue), FSN-MSN inhibition (cyan), FSN-MSN
static synapse inhibition (yellow) and GPe TA-MSN (orange). Left and right bottom panels shows the same as left and
right top panel respectively except it is for MSN D2. (B) Illustration of the role of lateral inhibition when a subpopulation,
10%, of MSNs are activated. Left top panel shows the result when randomly selected MSN D1 neurons are activated
and right top panel shows the result when only non-connected MSN D1 neurons are activated. Left and right bottom
panels show the same as left and right top panels for MSN D2. (C) Connection diagram for MSNs where a blue dot
indicated connection between MSNs. It is illustrating how groups of MSN are not connected. (D) Left top panel shows
the firing rate of the 10 percent of MSN D1 neurons activated with a 500 ms long input burst for the case when randomly
connected MSNs (blue) and specifically non-connected MSNs (red) are targeted. Right top panel shows the mean
difference between the firing rate of the two differently selected populations of MSN D1 neurons when varying the
activated MSN population size between 2-20 percent. Left and right bottom panels shows the same thing as left and
right top panels but for MSN D2.
4.2.4
Dopamine dependent changes enhancing oscillations and synchrony
Dopamine depletion leads to multiple changes in synaptic strength and neural excitability
(Figure 9A), all potentially contributing to the emergence of synchrony and oscillations in
29
dopamine depleted rats. We found that dopamine induced changes to neural excitability and
synaptic coupling have a diverse effect on synchrony and oscillations, with some nuclei showing
increase and others a decrease in synchrony and oscillations for a single dopamine parameter.
For each of the perturbations induced by dopamine depletion we run simulations where the
control state parameter value was restored one at a time, and then compared the simulation
result with the full lesioned simulation (Figure 9B-C).








Restoring the dopamine-depletion induced increase in coupling within GPe leads to a
decrease in synchrony for GPe TA neurons and to a smaller degree for MSN D2, but
there is also an increase in GPe TI. The effect on oscillations is predicted to be
negligible.
There is a decrease in synchrony and oscillations in STN when restoring the increased
synaptic strength in the STN to GPe synapse, however there is an increase in synchrony
in MSN D2 and TA, and to a lesser extent in MSN D1 and FSN.
Restoring the dopamine-depletion induced strenghtening of MSN D2 to GPe synapses
results in a decrease of synchronization in GPe TI and SNr neurons and a increase is
seen in MSN D2, and GPe TA, and to a lesser extent in MSN D1 and FSN. The effect on
oscillations seems to be negligible in MSN D2, GPe TA, GPe TI, SNr and STN and
resulting in a small increase in oscillations in MSN D1 and FSN.
Restoring the dopamine-depletion induced increase in the coupling between FSN and
MSN D2 leads to a decease in synchrony in MSN D2, FSN, GPe TA and GPe TI. The
effect on oscillations for FSN-MSN D2 synaptic dopamine parameter is predicted to be
negligible.
It can be seen that increased synaptic coupling between CTX and MSN D2 strongly
affect syncrony and/or oscillations in BG with a decrease seen in MSN D2, GPe TA, GPe
TI and SNr, and an increase seen in MSN D1, FSN and STN.
Restoring the dopamine induced decrease in the coupling between MSNs decrease
synchrony in MSN D1, MSN D2, GPe TA, GPe TI and SNr whereas it increase
synchrony in FSN and STN. The affect on oscilations is neglectible except for MSN D1
and to a small degree for FSN.
Restoring the dopamine depletion induced decrease in excitability in GPe neurons have
almost exclusively a dampening effect on synchrony (MSN D1, MSN D2, FSN, GPe TA,
GPe TI and SNr) and oscillations (MSN D1 and FSN) and only minor increase in
synchrony of STN.
Restoring the dopamine depletion induced increase in CTX to STN synapse has a
dampening effect on synchrony (GPe TA, GPe TI, SNr, STN) and oscillations (STN).
Figure 9 | Local network dynamics and the role of dopamine dependent perturbations: (A) Illustration of dopamine
depletion effect on neurons and connections in the network model. (B) Synchrony and oscillations in control and
lesioned network components. Upper panel shows amount of synchrony in MSN D1, MSN D2, FSN, GPe TA, GPe TI,
SNr and STN during control (black bars) and following lesion (white bars). Lower panel shows the same but for
oscillations instead of synchrony. (C) The upper panel shows the relative change in synchrony in MSN D1, MSN D2,
FSN, GPe TA, GPe TI, SNr and STN (y axis) compared to the lesioned network when restoring the parameter on the x
30
axis to the value it had in the control network (no dopamine depletion). Lower panels show the same but for oscillations
instead of synchrony.
4.2.5
Does basal ganglia support action selection?
BG are generally thought to be important in action selection. Kravitz et al. (2010) showed that
D1 receptor activation promotes actions and D2 receptor activation inhibits actions. To test
action selection with the model two competing actions (action 1 and action 2) were inserted into
the network, and then activated over a range of cortical input and with the output rate in SNr
measured. Selection of action 1 is defined as when the firing rate in SNr for action 2 is below 50
percent normal activity whereas action 1 is above. The opposite holds for selection of action 2.
Dual selection occurs when the SNr firing rate for both actions are below 50 percent of SNr base
rate whereas no selections occurs if SNr firing rate is above base rate for both actions. It was
found that the indirect pathway is important for improving the dynamical range of the inputoutput, given that cortical input should result in action selection (compare Figure 10A top
panels). Action selection was also robust when varying the action pools between 15-100 percent
(Figure 10B).
31
Figure 10 | Action selection performance of BG network: (A) Top left panel shows the action selection with only the
direct pathway activated with respectively cortical input from 1 x base level to 3x base level for action 1 and 2. Top right
panel shows the action selection when both direct and indirect pathways are activated (similar action inputs as in top left
panel). Middle left panel shows the action selection when both direct pathways are activated and MSN collaterals have
been removed (similar inputs as in top left panel). Middle right panel shows the result when both direct and indirect
pathways are activated and FSN-MSN inhibition has been removed (similar action inputs as in top left panel). Bottom
left panel shows the outcome when both direct and indirect pathways are activated and GPe TA-MSN inhibition has
been removed (action similar inputs as in top left panel). Bottom right panel shows the action selection when both direct
and indirect pathways are activated and in addition the hyperdirect pathway is co-activated through a burst in STN
(similar action inputs as in top left panel). For all six plots 20 percent of the MSN action pool was activated (one MSN
action pool equaled half of the simulated MSNs) (B) Action selection performance when scaling the size of the activated
MSN pool. First row shows the action selection with only direct pathway activated, same as top left figure in A, but
varying the relative size of the MSN pool between 10-100 percent. Second row shows the same as the first row, but for
the scenario when both direct and indirect pathways are activated. Third to fifth rows show the result for the scenario
when both direct and indirect pathways are activated (as in row 2) but when MSN collaterals are removed, FSN-MSN
inhibition is removed or GPe TA-MSN inhibition is removed. Sixth row show scaling effect when the hyperdirect pathway
is activated during action selection.
Action selection deteriorates when MSN collaterals and/or feed-forward striatal inhibition are
removed, whereas GPe inhibition to striatum has little effect. It was found that when removing
the inhibition on MSNs from either collaterals or the FSNs, the action selection performance
deteriorated with dual selection for high cortical input combinations (Figure 10A middle
panels). The model thus predicts that both MSN collaterals and FSNs are important for action
selection in BG.
STN, through the cortical hyperdirect pathway, is proposed to act as a stop signal (Frank, 2006),
giving striatum and GPe enough time to resolve high conflict in action selection. Experiments
suggest that STN is involved in the cancellation of already initiated motor responses (Eagle and
Robbins, 2003; Eagle et al., 2008). Input to STN as a strong hundered milisecond pulse was
injected in parallel with activation of the striatal action pools (Figure 10A bottom right panel).
The model predicted that action selection at low cortical input could be stopped in line with the
claim that STN is responsible for stop signaling in BG.
4.2.6
Synaptic and neural perturbations improving dynamics and function
Decreasing or increasing the synaptic efficacy in around half of the modeled connections can
lead to a decrease in synchrony and/or oscillations, and in 6 of them also improve action
selection ability (Figure 11). Thus all connections that have an effect on reducing synchrony
and/or oscillations could serve as potential treatment methods for PD. Especially interesting are
the six manipulations that also improves action selection (see Figure 11C)
By silencing and/or increasing the activity of specific BG nuclei, an improvement in action
selection is achieved (Figure 11B-C). Lesioning GPe and STN both decrease the synchrony and
oscillations in several nuclei in the network, especially lesioning STN proves more effective.
Both predictions are in accordance with experiments. Lesion therapies targeting GPe, GPi and
STN have successfully been used to elevate PDsymptoms (Okun and Vitek, 2004). The model
predicts that synchrony and oscillations in GPe and SNr are decreased when lesioning GPe, and
additionally also in STN when lesioning STN (Figure 8B). Thus it seems STN lesions are more
effective than GPe lesions. Interestingly STN have been the more common target in lesion
treatments of PD(Okun and Vitek, 2004). It can also be seen that increases in the activity in GPe
type I and STN leads to decrease in synchrony and oscillations, which is in line with that deep
brain stimulation has proven to be an effective method for relieving symptoms in Parkinson’s
disease.
Both decreasing and increasing MSN D2 activity counteracts synchrony and oscillations in GPe
and SNr. Loss of dopamine leads to increased activity in MSN D2 neurons. Decreasing MSN D2
activity (Figure 11A) proves to be an effective measure to annihilate synchrony and oscillations
in GPe and SNr. Interestingly, increasing their activity also is effective (Figure 11A). When
increasing MSN D2 activity, GPe becomes suppressed thus resulting in the same output as a GPe
lesion.
32
Figure 11 | Restoring network dynamics and function after dopamine lesion: ((A) Change in synchrony and oscillation in
MSN D1, MSN D2, FSN, GPe TA, GPe TI, SNr and STN relative to the lesioned network model when
silencing/increasing each connection. (B) Change in synchrony and oscillation in MSN D1, MSN D2, FSN, GPe TA, GPe
TI, SNr and STN relative to lesioned network model when inhibiting/exciting each nucleus separately. A current were
injected over a range of values from negative to positive in each nucleus as indicated on the x axes. Each nucleus was
silent at the most hyperpolarizing current thus mimicking a lesion of the nucleus. (C) Action selection performance for a
number of manipulations either to neuron excitability or to synaptic efficacy.
4.3
Learning action selection in basal ganglia
Finally, in project III a very interesting but difficult topic in BG were studied, that is how actions
are learned. Below are selected results presented, for more details se paper 4.
4.3.1
Action selection can be learned through Bayesian inference in basal ganglia
It was found that a spiking model (Figure 12) with a learning rule utilizing Bayesian inference
could learn the correct reward mapping in simulations consisting of 15 blocks of 40 trials
(Figure 13) The average success was well above chance level (1/3) and approached the maximum
value 1 at the end of each block Figure 14C. Thus the model had successful performance in a
multiple-choice learning task with a transiently changing reward schedule. It can be seen in the
Figure 14A upper panel that the D1 weight of the previously rewarded action stay high for a
couple of trial after a reward mapping shift followed by a rapid decline when D2 started to
suppress it and pre and post correlation are lost. It can be seen in Figure 14A lower panel how
the weights in the D2 population that can suppress the previous rewarded action, grow very
rapidly in the beginning of the new block. Thus the model predicted that the synaptic weight
change comes first in the D2 when learning a new reward mapping, results that are in line with
(Groman et al., 2011).
33
Figure 12 | Schematic representation of the model with relevant biological substrate. In striatum, two actions A and B
are here used as an example. The population “AD1” thus corresponds to the population of MSNs in the D1 pathway
coding for action A. Striosomes and matrisomes are segregated for visual guidance, but they were intermingled in the
model, with striosomes often referred to as “islands” in the matrix. Thalamus and brainstem were not explicitly
implemented in the model but are shown above for completeness.
34
Figure 13 | Raster plot of the model consisting of 3 states and 3 actions, illustrated over 30 seconds of activity during a
change in the reward mapping. In (A), a single trial is detailed. In (A) and (B) the states (blue), D1 (green), D2 (red) and
GPi/SNr (purple) populations, grouped by representation coding, are shown. The indices of the states and actions begin
from the top. For example, neurons with an ID between 160-220 represent the D1 and D2 populations coding for action
1. In (C) both the raster plot and a histogram of the dopaminergic neurons spiking activity are displayed. The width of
the bins is 10 ms. A trial lasts for 1500 ms and starts with the onset of a new state. The simultaneous higher phasic
firing rates in the D1 and D2 populations correspond to the population coding for the selected action receiving inputs
form the efference copy. The vertical orange dashed line signals a change in the reward mapping.
35
Figure 14 | Evolution of weights in the D1, D2 and RP pathways, as well as the performance over a simulation of 15
blocks with 40 trials each. In (A), the three colored lines represent the average weight of the three action coding
populations in D1 and D2 from state 1. (B) represents the color coded average weights from the nine state-action
pairing striosomal sub-population to the dopaminergic population. (C) displays the moving average success ratio of the
model over the simulation. Vertical dashed grey lines denote the start of a new block. In (A) and (B), the black line is the
total average of the plotted weights. Color-coded shaded areas represent standard deviations.
36
4.3.2
Synaptic homeostasis with Bayesian inference
During phasic dopamine changes, synaptic modification occurred not only between the active
pre- and postsynaptic populations, but also at synapses where either only the pre- or
postsynaptic population were active. The relative changes in magnitude taking place between
inactive units were very small. Furthermore, changes in the weights were of opposite signs for
the connections between co-active neurons and connections where only one was active. These
features led to some degree of homeostasis of the average weight (Figure 14B).
4.3.3
Relative importance in learning for MSN D1 and MSN D2 pathways
Lesioning the MSN D2 have a more profound negative effect on success rate than lesioning MSN
D1. Two simulations were run either with MSN D2 weights set to zeros or MSN D1 weights. In
Figure 15 it is shown that the success ratio at the end of a learning block when lesioning MSN D1
is significantly higher than when lesioning MSN D2. The selection pattern revealed that the
system with MSN D2 lesioned got stuck constantly selecting the same action: the one that was
initially associated with the reward before lesioning the MSN D2 connections. Thus in one block
the performance was good, around 70 percent, whereas in the two other blocks the system got
stuck always choosing the wrong actions with performance close to 0 percent. MSN D2 is
needed to suppress the previously selected action such that pre and post correlations are lost. It
is only D2 that can learn from negative reward thus there is no change in D1 weights for two out
of three blocks. Without the D2 pathway the RPE could not become positive for the remaining
actions in subsequent block.
It has been reported that Parkinson’s patients exhibit better learning from negative than from
positive outcomes. The model predict that the MSN D2 pathway have a more beneficial effect on
selection because it can preserve plasticity despite low dopamine levels. This is in line with other
authors who argues that D2 pathway is more valuable since it is impacted by negative RPE
(Frank et al., 2004; Cox et al., 2015). Thus our model supports observations indicating that
dopaminergic medication in mild Parkinson’s patients impaired reversal learning when
reversals were signaled by unexpected punishment (Swainson et al., 2000),
4.3.4
Consequences of dopamine lesioning on learning
Deletion of dopamine neurons had a more severe effect on model performance, with degrading
performance depending on the lesion size. Following deletion, performance immediately
deteriorated for all conditions with 70 percent success rate at 16 percent lesioned, 50 percent
success rate at 33 percent lesioned and below 40 percent success rate at 66 percent lesions
Figure 15A-B. Thus the model predicts that dopamine depletion severely deteriorates action
selection learning.
37
Figure 15 | Box plot of the mean success ratio and standard deviation of the examined conditions. In (A), the first 20
trials of each block were used whereas in (B), the analysis was carried out on the last 20 trials. Data from the last 7
blocks of the PD conditions were used. All differences are significant (p<.0001) unless stated otherwise (ns = nonsignificant). The horizontal dotted line represents chance level. For all conditions except PD33, PD66, noD2 and no
Efference, differences within conditions between the first and last 20 trials are significantPD16, PD33 and PD66 display
the results of the 7 blocks following the deletion of respectively 16%, 33% and 66% of the dopaminergic neurons.
4.3.5
RPE pathway affect learning rate
Recall how D2 weights grow very rapidly for the previously rewarded actions right after change
of reward schedule in intact model (Figure 14). We wondered if the RPE pathway somehow
could be responsible for the growth speed. A simulation without the RPE pathways, now with a
model that only depended on primary reward, were run. It can be seen in Figure 15A, showing
the performance after 20 trials (out of 40) how the performance is well below intact model,
while during the following 20 trial the performance improve and become as good as the intact
model. Thus, the model predict that the RPE pathway is important for learning rate. Both the
RPE and the primary reward inhibits dopamine neurons for the previously rewarded action
right after reward schedule shift (since a reward is expected but a punishment is received)
producing a stronger dopamine dip than with only primary reward, thus affecting D2 plasticity
change more rapidly. Faster growth of D2 weight leads to faster suppression of D1 neurons of
previous chosen action so that the weights of the correct D1 population can grow.
38
5 Conclusions and further investigations
In this thesis I have explored BG function and dynamics, with different types of computational
spiking neural network system level models. Three different projects were carried out and here
are the main lessons learned from them:
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

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
BG can be divided into an arbitration system, acting as a conflict resolver in a winnertake-all network, and an extension system which can modify the selection of the
arbitration system by logical operations: conjunction, disjunction and negations.
Multiple synapses in BG exhibit short-term plasticity, which significantly affects
signaling in the direct-, indirect- and hyper-direct pathways. Short-term plastcity
enables both the direct and indirect pathway to become sensitive to bursting
presynaptic MSN neurons
MSNs in striatum are controlled by three main sources of inhibition; neighboring
MSNs, FSNs and GPe type A. Simulations predict that FSN and GPe type A are
relatively more important at low cortical input drive whereas MSN collaterals are more
important at higher cortical drive.
Simulations predict that a) the dopamine-depletion induced increases in connectivity
between cortex and MSN D2; b) the decrease in connectivity in MSN-MSN; and c) the
decrease in excitability in GPe neurons, are the main contributors to the enhancement
of BG oscillations and synchrony.
The direct pathway enhances the dynamical range over which BG can perform selection
between cortical commands, and removing either MSN collaterals or FSN to MSN
inhibition reduce the dynamical range.
Simulations show that Bayesian inference together with synaptic plasticity in D1- and
D2-MSNs can successfully lead to learning to select the correct actions. Here
corticostriatal synapses onto D1 MSNs are only updated following increased dopamine,
and synapses onto D2 MSNs are only updated for decreased dopamine signals.
The indirect pathway seems to be more important than the direct pathway, since action
selection performance without the indirect pathway is worse than without the direct
pathway, something which is also partly supported by literature.
It is important to further understand how changes to dopamine levels affect the dynamics in BG.
In the present thesis, I have only investigated how dopamine depletion affect the dynamics in
BG but it would be equally important to study what happens following dopamine elevation and
compare the effect to repeated injections of the dopamine stimulant amphetamine (Wang and
Rebec, 1993; Waszczak et al., 2001; Gulley et al., 2004) or injection into striatum of nonselective
dopamine agonists (Waszczak et al., 2002).
The system level model presented in project II can be further extended to include, CM, PPN and
brainstem to further challenge our hypothesis about the arbitration and extension system in a
quantitatively more detailed model. It could also be used to study how the dynamics in BG
during dopamine depletion are affected by a loop through CM back to striatum. This pathway
has yet to be included in a detailed spiking model of BG. It would be interesting to study the
dynamics of a detailed model where cortical and thalamic inputs are separated. Would thalamic
input increase or decrease correlations in BG?
Another line of inquiry would be to connect the more detailed BG model in project II with
dopamine dependent synaptic plasticity as in project III. Thus, to include more nuclei and
pathways and test weather learning of action selection can be done in a more detailed model.
There is also a need to further develop the model of the reward prediction system when more
experimental data becomes available.
The hypothesis that BG function as an action selection device has been strengthened by the
work in this thesis. It has expanded the concepts of how BG organization enables action
selection and has contributed to a deeper understanding of how BG physiology and structure
relate to action selection capabilities and influence network dynamics, and has furthermore
proposed hypotheses of how learning of new actions in BG is realized. Still, much remain to be
done, the knowledge of basal ganglia physiology and organization is constantly pushed by new
experiments and future models to test the action selection hypothesis need to take into account
new data. Much focus in BG research has been on models which have no learning, thus there is a
39
need to build additional models that test how actions can be learned in a biologically realistic
manner.
40
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