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Modeling astrocyte-neural interactions in CMOS neuromorphic circuits

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Modeling astrocyte-neural interactions in CMOS neuromorphic circuits

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Content Modeling Astrocyte-Neural Interactions in
CMOS Neuromorphic Circuits
Yilda Irizarry-Valle
Department of Electrical Engineering
University of Southern California
A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulllment of the
Requirements for the Degree
Doctor of Philosophy
(ELECTRICAL ENGINEERING)
August 2016
Abstract
Neuromorphic engineering is a relatively new eld that nds its strength in its
multidisciplinary approach. It brings together disciplines such as neuroscience, biology,
and many other areas of engineering. The eld gains its motivation from the curiosity
of discovering what makes the brain outperforms any known system, particularly in
terms of power, robustness, and sensory computations.
Our research uses electronics technology, such as CMOS to emulate biological be-
haviors inspired by brain computations. Although, similar experimentation could, in
principle, be done through software programming, circuit simulation is one step closer
to the physical properties of integrated circuit technology. This sets the basis to further
evaluate and explore the limitations of embedding biological computations.
This thesis presents an initial framework from the neuromorphic engineering per-
spective on the computations involved in communication processes between astrocytes
and neurons. It aims to contribute and provide guidance to the early stage develop-
ment of hardware systems for testing and evaluation on the computational power of
astrocyte-neuronal interactions in health and cognition. The main focus of our work is
on understanding the in
uence of astrocytes on neuronal activity, and the translation of
biological computations into circuits, using the characteristics of MOSFET transistors.
Our designs are rst-order bio-inspired/bio-mimetic circuits. We look at astrocytes
as peers of neurons moving away from the neuro-centric view. We design circuits that
represent biological functions of astrocytes, neurons, and the interaction between them.
Astrocytes are the majority of the subtype of glial cells and contribute to learning,
memory and cognition. Astrocytes cause changes at the synaptic level and promote
neuronal health by the modulation of neuronal activity and by phagocytic clearance.
While the scientic community has given much attention to neurons, astrocytes have
been overlooked and it is not until few decades ago that signicant progress has been
made on unraveling astrocytes as computational units on high level brain cognitive
processing.
Among our research achievements include the design and simulation of astrocytic
functions for the modulation of synaptic information as well as neuronal functions for
the dynamics of synaptic activity. To our knowledge, our group is the rst to have
ii
electronically captured an astrocytic microdomain circuit, i.e. compartments able to
sense neuronal activity and feed back a response to neurons.
Through our circuits we test a variety of biological processes, such as the uptake
of glutamate by astrocytes and show how astrocytes are key in the maintenance of a
healthy neuronal environment. We have captured the primary steps in this process
along with the communication between an astrocyte and a group of neurons showing
how neurons may undergo a toxic regime and how astrocytes could potentially balance
the neuronal environment.
Our most recent work explores the ability of astrocytes to in
uence phase syn-
chronization on neurons by the slow inward currents (SICs) mechanism. We have
successfully shown, in a small group of neurons, how phase synchronization could be
caused through astrocytic triggering activation of NMDA receptors.
We have designed and captured the dynamics of a depressing synapse and the
changes induced to the synapse according to changes in presynaptic rate of spikes.
We have captured the Weber-Fechner relationship and shown synaptic adaptability by
sudden changes in the spike rate. In the long-term future, we envision as part of a
larger and collaborative eort to introduce synaptic adaptability to the interactions
of neurons and astrocytes for further testing and evaluation of hypothesis on astro-
neuronal processing.
iii
Dedication
This thesis is dedicated to those who have contributed to my professional and/or
personal growth throughout these years. I am elated that I have had many people
caring about me without whom none of this would be possible. I would like to thank
them all and I will surely strive to pay them forward. Thank you all.
iv
Acknowledgment
During these years at University of Southern California (USC), I have met great
people whose guidance and support helped me with achieving my academic goal. I am
specially thankful to my advisor, Prof. Parker, for giving me the opportunity to join
her group, leading me through my academic path, and providing me with constructive
feedback. Prof. Parker, thank you for having me so close to yourself during all these
years and giving me the opportunity to learn your teaching and research methods.
I am very thankful for the opportunity to be part of a highly diverse and inclusive
group open to dialogue and exploration. I take with me so many lessons. I deeply
appreciate all you have done for me throughout these years. Prof. Slaughter, I will be
forever thankful for the amenable conversations that have greatly shaped my leadership
skills. Thank you for having the doors of your oce open for me since my rst week at
USC, and providing me with guidance and motivation throughout these years. Prof.
Pinkston, Prof. Beerel, and Prof. Grcywacz, thank you for always being supportive
with my academic needs and caring about my progress in the PhD program. Thank
you Prof. McCain because whenever I knocked your door to seek for assistance you
always said \yes" to me.
Thank you to all PhD's and Master's students from all over the world who shared
their knowledge and experience with me. I have learned in so many ways from all of you.
USC allowed me to pursue and complete one of my very important life goals. It provided
the nancial support and exposed me to a wide range of career opportunities. I am
deeply thankful to USC for such a great opportunity. Moreover, the education I gained
at USC was denitely an enriching experience. My professional and interpersonal skills
have been greatly shaped at USC through the everyday interactions with professors,
students and sta. USC made a very versatile and skillful person out of me throughout
these years, and prepared me in so many ways for my forthcoming career goals. Thank
you all.
v
Contents
List of Figures ix
1 Introduction 1
1.1 Problem Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Overview of Astrocytes as a Computational Unit . . . . . . . . . . . . . 2
1.3 Research Contribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.4 Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.5 Related Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.6 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2 Background and Related Work 11
2.1 Neuroscience Background . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.1.1 Communication in the Tripartite Synapse . . . . . . . . . . . . . 11
2.1.2 Astrocytes: Glutamate Uptake and the Maintenance of a Balance
Extracellular Environment . . . . . . . . . . . . . . . . . . . . . . 12
2.1.2.1 Astrocyte Glutamate Uptake . . . . . . . . . . . . . . . 13
2.1.3 Astrocytes activate neuronal NMDAR for synchronization . . . . 13
2.1.3.1 Biology of the NMDAR channel . . . . . . . . . . . . . 13
2.1.3.2 Astrocyte's role on the activation of NMDAR channel . 14
2.1.4 A mathematical model for astrocyte SICs . . . . . . . . . . . . . 15
2.1.4.1 Astrocytes' role in binding information . . . . . . . . . 16
2.2 Ongoing Research on Astrocytes . . . . . . . . . . . . . . . . . . . . . . 17
2.2.1 Astrocytes Contribute to a Wide Range of Biological Processes . 17
2.2.2 Ca
2+
Waves: A coding Mechanism in Astrocytes . . . . . . . . . 19
2.2.3 Patterns of Astrocytic Ca
2+
Waves . . . . . . . . . . . . . . . . . 20
vi
CONTENTS
2.2.4 Ca
2+
Waves Intercellular Propagation in Astrocytes . . . . . . . 21
2.2.5 Mathematical Models for Astrocytes . . . . . . . . . . . . . . . . 22
2.2.6 Astrocyte-Astrocyte Networks and their implications in Integra-
tion of Synaptic Information . . . . . . . . . . . . . . . . . . . . 24
2.3 Background in Neuromorphic Engineering . . . . . . . . . . . . . . . . . 25
3 Neuro-Astrocyte Interactions: A CMOS Neuromorphic Approach 28
3.0.1 The Synapse and Astrocyte Mechanisms . . . . . . . . . . . . . . 29
3.1 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
4 Astrocytes on Neuronal Phase Synchrony in CMOS 38
4.0.1 Contribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
4.1 Circuit implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
4.1.1 The excitatory synapse circuit . . . . . . . . . . . . . . . . . . . 40
4.1.2 Neuron block diagram and ring rule . . . . . . . . . . . . . . . . 41
4.1.3 Extrasynaptic NMDA Block and the activation of SICs . . . . . 43
4.1.4 A system view of the Network used for Simulation Experiments . 45
4.1.5 Extrasynaptic NMDAR channel circuit for SIC generation . . . . 46
4.1.6 The astrocytic microdomain circuit . . . . . . . . . . . . . . . . . 51
4.2 Simulation results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
4.2.1 Network conguration for our simulation experiments . . . . . . 53
4.2.2 Simulation results for Network 1 and Network 2 . . . . . . . . . 54
4.2.3 Microdomain interactions increase Ca
2+
levels . . . . . . . . . . 57
4.2.4 Eect of variations of SIC time constant . . . . . . . . . . . . . . 58
4.2.5 Contribution of synchronization to neuron excitability . . . . . . 60
4.2.5.1 Description of the simulation test . . . . . . . . . . . . 60
4.2.5.2 Simulation results: contribution of synchronization to
neuron excitability . . . . . . . . . . . . . . . . . . . . . 61
4.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
5 An Adaptable CMOS Depressing Synapse with Detection of Changes
in Input Spike Rate 65
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
5.2 Contribution and Related Work . . . . . . . . . . . . . . . . . . . . . . . 67
vii
CONTENTS
5.3 Implementation of the Depressing Synapse . . . . . . . . . . . . . . . . . 68
5.4 Approximation of the Weber-Fechner relation . . . . . . . . . . . . . . . 71
5.5 Simulation Results of the Depressing Synapse . . . . . . . . . . . . . . . 72
6 Conclusion and Future Work 74
References 77
viii
List of Figures
1.1 An astrocyte forming tripartite synapses with a group of neurons (g-
ure taken from (1)). The astrocyte is represented by many long thin
branches. Neurons are surrounding the astrocyte. . . . . . . . . . . . . . 3
1.2 Compartments of an Astrocyte. Presynaptic neurons are represented
by black-thin lines and postsynaptic neurons are represented by orange-
thick lines. At the intersection between both neurons the synapse is
formed. Compartments C1{C3 are represented by the blue-dashed box. 3
1.3 Tripartite synapse (gure taken from (2)). The release of transmitters
from the presynaptic terminal diuses and binds receptors in the astro-
cyte, i.e. metabotropic glutamate receptors (mGluRs) channels, -amino-
3-hydroxy-5-methyl-4-isoxazole propionic acid receptors (AMPARs) chan-
nels. Activation of mGluRs channel triggers production of IP3 in the as-
trocyte and initiates a calcium-induced, calcium-released process through
the interplay of IP3Rs channels and SERCA-pumps causing the release
of calcium from the endoplasmic reticulum (ER) and inducing regener-
ative calcium waves. Such waves initiate the events for the release of
transmitters in the astrocyte by the activation of receptors located at
the outer membrane. This induces the synapse to undergo changes by
astrocytic modulatory eects. . . . . . . . . . . . . . . . . . . . . . . . 4
2.1 a) A tripartite synapse, where an astrocytic process stimulates subunits
of the NMDAR channel (Figure taken from (3)). b) A
ow diagram
describing the main steps in the activation by the astrocyte of the ex-
trasynaptic NMDAR channels. . . . . . . . . . . . . . . . . . . . . . . . 15
ix
LIST OF FIGURES
3.1 The synapse with the astrocytic mechanisms. Dashed boxes separate dif-
ferent stages of the circuit. Stage (2) and Stage (4) represent the pre- and
postsynaptic sides of a synapse. Stage (6) is the inactivation mechanism
that controls the presynaptic input by means of Stage (1). Stage(3) and
Stage (5) correspond to the astrocytic mechanisms. Stage (3) represents
the astrocytic uptake mechanism, while Stage (5) is the microdomain
mechanism that injects gliotransmitters into the Synaptic cleft. The
adder (4) is used to incorporate the gliotransmitter contribution into
the cleft. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.2 The astrocytic microdomain mechanism (5). . . . . . . . . . . . . . . . . 31
3.3 Neural network illustrating astrocyte connections. The gure shows a
schematic of the network we simulated. The astrocyte in
uences the
behaviors of synapses S1{S4 through its glutamate uptake mechanism
and the injection of gliotransmitters into the cleft. . . . . . . . . . . . . 33
3.4 The total EPSP and the ring of action potentials for NeuronsN
4
{N
6
in
the absence of an astrocyte. The top panel shows N
4
, the middle panel
N
5
, and the bottom panel N
6
. . . . . . . . . . . . . . . . . . . . . . . . . 34
3.5 In Fig. 3.5(a) the top panel shows the cleft signals for synapsesS
1
,S
4
and
S
5
. The middle panel shows the AstroCa
2+
control signals for synapses
S
1
{S
3
, while the bottom panel shows the gliotransmitter release from
the astrocytic microdomain. The synaptic cleft of S
4
is controlled by
the astrocytic glutamate uptake mechanism. Since synapse S
5
lacks
an astrocytic uptake, the Synaptic cleft node rises above the S
4
level.
Synapse S
5
is eventually disconnected from the presynaptic side after a
delay. In Fig. 3.5(b), neuron N
4
begins ring due to the contribution of
astrocytic gliotransmitters, even though it has only two normal synapses.
Neuron N
5
continues ring by the virtue of the astrocytic glutamate
uptake mechanism. Neuron N
6
is not able to maintain regular ring
because the astrocytic glutamate uptake mechanism is not present on
synapse S
5
, so it is eventually disabled. . . . . . . . . . . . . . . . . . . 37
x
LIST OF FIGURES
4.1 The BioRC synapse circuit. The presynaptic side is activated when an
action potential (AP) is received. The cleft node emulates the release of
transmitters from the presynaptic side. Stage (1) behaves like a low pass
lter, where a high rate of input spikes increases the cleft node voltage
accordingly. In Stage (2), an EPSP is produced when the cleft voltage
is suciently strong. The red arrow shows the extrasynaptic side used
to emulate the NMDAR channel contribution. . . . . . . . . . . . . . . . 41
4.2 A system view of the neuron components. . . . . . . . . . . . . . . . . . 42
4.3 The concept of phase synchronization. . . . . . . . . . . . . . . . . . . . 43
4.4 A system view: the extrasynaptic NMDAR channel for the induction of
SICs connected to the synapse and astrocyte. . . . . . . . . . . . . . . . 44
4.5 A system view diagram showing the main circuit blocks used for the
neurons and astrocyte. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4.6 The circuit of extrasynaptic NMDAR in (a), consists of sections (4), (5),
and (6) with a compact control circuit shown in (b). . . . . . . . . . . . 47
4.7 Two astrocytic microdomains (M1, M2) connected by pass transistors
allowing interaction between synapses in group 1 and group 2. The nodes
Ci
MX
represent the astrocytic compartments. The voltages V
b
andV
ref
are bias voltages to control the resistive paths of the transistors. . . . . 52
4.8 Two small neural networks interacting with astrocyte microdomains M1
and M2. The green (dashed) arrows represent the release of neurotrans-
mitters (NTs) from synaptic clefts to the astrocyte microdomain. The
blue (solid) arrows labeled SICs illustrate glutamate binding the extrasy-
naptic receptors to produce SICs on nearby synapses. . . . . . . . . . . 53
4.9 The top panels in (a) and (b) show the Total EPSPs for neurons N3{
N4 and N7{N8. The middle panels show the action potentials (APs)
of each neuron. The bottom panels show a zoom-in of the APs for two
dierent regions. This simulation was conducted for V
bias
= 700mV ,
V
ref
=1:8V and V
b
= 1V . Other circuit parameters can be obtained
from the author. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
xi
LIST OF FIGURES
4.10 Calcium wave signals. The top panel shows the calcium waves due to
the activity on Network 2. The bottom panel shows the calcium waves
when both astrocytic microdomains interact with each other and so are
in
uenced by the activity of both networks. . . . . . . . . . . . . . . . 57
4.11 Changes in the active time of the synchronization window versus changes
of V
bias
measured on Network 2. . . . . . . . . . . . . . . . . . . . . . . 59
4.12 Synchronization window for action potentials of postsynaptic neurons
N7 (red-solid) and N8 (black-dashed) of Network 2 versus variations of
V
bias
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
4.13 A cartoon diagram that shows the eect of synchronization on neuron
N9 in Network 2 according to the arrival phase of spikes from neuron N7
and N8. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
4.14 Simulation showing the eect of synchronization on neuron N9 in net-
work 2. The top panel shows the cleft signals for synapses S13 and S15
(S14 and S16 behave the same as S13 and S15, respectively). The middle
panel shows the Total EPSP of N9. The bottom panel shows the ring
of N9 when N7 and N8 are synchronized in phase. Note the scale of
EPSPs and APs in the traces shown. . . . . . . . . . . . . . . . . . . . . 61
4.15 A zoom into the results obtained in Fig. 4.14 for (a) the region where,
in the absence of a SIC event, the ring of spikes out of synchrony does
not elicit action potentials and (b) the region where, in the presence of
SIC event, the ring of spikes in phase synchrony elicits action potentials. 62
5.1 Biological data of a depressing synapse taken from (6). (a) Lowering
the extracellular Ca
2+
concentration decreases the initial EPSP without
having an eect on the average membrane voltage and the steady state
amplitude, (b) Average postsynaptic membrane under presynaptic spike
stimulation for 200 dierent Poisson spike trains, (c) Recorded EPSPs
for dierent spike rates. . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
xii
LIST OF FIGURES
5.2 Adaptable depressing synapse circuit following an approximation of the
Weber-Fechner relation during a change in spike rate. The discrete-
component equivalent circuit sketch illustrates the function of Stage (1).
The circuit details (parameter settings and simulation materials) will be
found in an appendix in the thesis. . . . . . . . . . . . . . . . . . . . . . 69
5.3 An illustration of the Weber-Fechner approximation. A comparison be-
tween the nonlinear sawtooth signal (solid red) based on our approach,
and a linear approach (dashed blue). . . . . . . . . . . . . . . . . . . . . 72
5.4 EPSP response for V
Ca
2+ from .7 to 1.8 V. . . . . . . . . . . . . . . . . . 72
5.5 Response of the depressing synapse circuit under changes of input spike
rates. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
xiii
1
Introduction
1.1 Problem Motivation
Two decades ago the discover of a new form of bidirectional communication between
astrocytes, a subtype of glial cells, and neurons turned attention to astrocytes. Recent
evidence has shed light on biological mechanisms through which astrocytes receive, inte-
grate and transmit information to establish astro-neuronal and astro-astrocyte commu-
nication. Astrocytes participate in the modulation of sleep homeostasis, the formation
of synapses, and control of synaptic strength. It is due to their role in many higher
level functions in the brain that astrocytes are now being considered computational
units that work together with neurons in major brain communication processes.
This thesis is motivated by the possible contributions of astrocytes through their
morphology, biophysical properties, and location in the brain that are attuned to the
interests in applied neuromorphic engineering. We explore, through CMOS circuit de-
signs, the functions and computational capability of astrocytes at the sub-cellular level
with emphasis on the modulation of neuronal activity from the astrocyte perspective.
The circuits to be discussed in the next chapters capture important dynamics of astro-
cytes and their interaction with neurons. This is done through the design of rst-order
custom CMOS circuits with bio-inspired/biomimetic features.
The next sections will discuss the basis of astrocytes as potential computational
units, the research accomplishments, and the methodology behind the circuits. We
also provide with an outline of the next Chapters.
1
1.2 Overview of Astrocytes as a Computational Unit
1.2 Overview of Astrocytes as a Computational Unit
In the process of reverse engineering astrocytic computations it is necessary to clearly
draw the distinctions between astrocyte cells and neurons. Astrocytes are chemically
excitable cells with a very slow response in the form of analog graded potentials, and
they do not re action potentials. They have shown ability to encode synaptic informa-
tion through intracellular calcium waves by complex nonlinear processes that involve a
wide variety of chemicals and the activation of many dierent receptors. Yet, although
they are slow compared to neurons, they do contribute to neuronal processing and have
in
uence over the message transmitted across group of neurons.
A single astrocyte is estimated to be able to contact about 100,000 synapses through
their long thin processes. This endows the astrocyte with the ability to potentially
coordinate a massive amount of neuronal information between a spatial distributed
group of neurons. See Fig. 1.1 for a cartoon representation of an astrocyte.
A single astrocytic process could be visualized as many compartments, i.e. mi-
crodomains. Each of these compartments behaves as a complete subsystem with huge
computational power, able to sense activity from their local group of neurons and to
communicate with spatially compartments. The activity sensed by each microdomain
induces changes in amplitude, frequency and speed of propagation in their intracellular
calcium waves. The propagation of these waves across the microdomain conveys infor-
mation between spatially distant and independent group of neurons. See Fig. 1.2 for a
cartoon representation of a microdomain.
When neurons and astrocytes nd each other a tripartite synapse is formed. The
tripartite synapse is the main computational unit, consisting of three terminals, the
presynaptic, postsynaptic neuron and the astrocytic process. Since all terminals are
able to release/uptake transmitters, they all can have in
uence on each other. Astro-
cytes are known to exert modulatory properties on receptors located at the extrasynap-
tic side, while neurons, through the spillover of transmitters out of the synapse, could
reach and modulate receptors in the outer membrane of the astrocyte. See Fig. 1.3
for a cartoon representation of a tripartite synapse, and the basis of the interaction
between an astrocyte's process and a synapse.
2
1.2 Overview of Astrocytes as a Computational Unit
Figure 1.1: An astrocyte forming tripartite synapses with a group of neurons (gure
taken from (1)). The astrocyte is represented by many long thin branches. Neurons are
surrounding the astrocyte.
Figure 1.2: Compartments of an Astrocyte. Presynaptic neurons are represented by
black-thin lines and postsynaptic neurons are represented by orange-thick lines. At the
intersection between both neurons the synapse is formed. Compartments C1{C3 are rep-
resented by the blue-dashed box.
3
1.3 Research Contribution
Figure 1.3: Tripartite synapse (gure taken from (2)). The release of transmitters from
the presynaptic terminal diuses and binds receptors in the astrocyte, i.e. metabotropic
glutamate receptors (mGluRs) channels, -amino-3-hydroxy-5-methyl-4-isoxazole propionic
acid receptors (AMPARs) channels. Activation of mGluRs channel triggers production of
IP3 in the astrocyte and initiates a calcium-induced, calcium-released process through the
interplay of IP3Rs channels and SERCA-pumps causing the release of calcium from the
endoplasmic reticulum (ER) and inducing regenerative calcium waves. Such waves initiate
the events for the release of transmitters in the astrocyte by the activation of receptors
located at the outer membrane. This induces the synapse to undergo changes by astrocytic
modulatory eects.
1.3 Research Contribution
This thesis focuses on neuro-glia interactions and represents a contribution to funda-
mental research. We intend to bring an innovative view and diverge from the neuro-
centric approach, to consider glial cells as peers of neurons.
Our design approach incorporates hybrid CMOS biomimetic/bio-inspired circuits
that capture rst{order communication between astrocytes and neurons. Through sim-
ulation of circuits we perform experiments for the evaluation of current hypotheses on
possible roles of astrocyte cells on neuronal synchrony. The circuits are characterized
by ne-grained details of biology, e.g., \single astrocytes are capable of inducing slow
inward currents with a high degree of correlation into extrasynaptic NMDAR channels
of adjacent dendrites, causing synchronized events in adjacent neurons." We have initi-
ated eorts to capture synchronous activity in neurons induced by astrocytes. Synchro-
4
1.3 Research Contribution
nization is a fundamental process in cognition and it could be involved in the binding
of information that travels through dierent pathways; hence studying how astrocytes
may modulate neuronal activity and adapt synaptic delays is of major importance for
the understanding of neuronal integration of information.
On a higher level view, we have investigated the biological processes involved in
excitotoxicity. Excitotoxicity is caused by overstimulation and activation of neuronal
receptors due to an excessive release of transmitters and it can be detrimental for neu-
rons, causing cell damage. Biological mechanisms of astrocytes, i.e., the uptake and reg-
ulation of transmitters, contribute with supportive roles to the maintenance of a proper
environment and prevention of cell damage. There are many cognitive processes that
become vulnerable in the absence or malfunction of astrocytes, e.g., sensorimotor activ-
ities. Our circuits present an initial framework through the design of rst{order CMOS
hybrid biomimetic/bio-inspired circuits to further advance research for neuroscience
experimentation. This framework is aimed to contribute to neuroscience investigations
by the design of hardware tools that serve as platforms for testing of neurodegenerative
diseases.
In another line of research, we have designed a very detailed biomimetic circuit that
captures the computational processing of a depressing synapse and its adaptation ac-
cording to changes of spike rates. Depressing synapses respond to novelty and discard
redundant information. Their temporal information is characterized by their sensitivity
to changes in spike rates which causes a considerable increment in the excitatory post-
synaptic potential. Such response follows the Weber-Fechner relation which we have
captured in our circuit. Depressing synapses are particularly tuned to recognize irreg-
ularities in the pattern of ring of spikes and seek novelty while discarding redundant
activity. The behavior of depressing synapses may represent an energy saving process
by maintaining neural silence unless surprising events occur. Building the modules
for a depressing synapse circuit is a rst step toward studying interactions between
astrocytes and neurons with depressing synapses to investigate energy expenditures in
processing of astro-neuronal information.
5
1.4 Approach
1.4 Approach
Our central goal in the BioRC research (7) is to demonstrate electronic circuits that
mimic the intelligence, learning and memory capabilities of the brain through the use of
analog electronic circuits forming neuromorphic systems of networked neurons. While
fabrication of custom analog integrated circuits is a desired long-term goal of the BioRC
project, knowledge gained with circuit simulations of these intricate neural-glial inter-
actions is an important step, and provides validation that our understanding of the
biological mechanisms simulated is accurate. Implementation of the model in ultimate
biomedical hardware is possible, the current goal is to demonstrate the mechanism pro-
posed via simulation. This goal is commensurate with the central goal of the BioRC
project to reverse engineer the human brain.
We use an analog approach to build novel custom circuits that exploits the resis-
tive and capacitive properties of transistors rather than using standard analog blocks.
Analog circuits oer several advantages and share a similar physical environment to
that experienced by the nervous system, e.g., they are susceptible to noise and highly
unreliable, for which careful design skills are required. They allow for emulation of
biophysical characteristics with fewer numbers of transistors than their digital circuit
counterparts, and oer higher{speed performance at lower energy cost. Specically,
our approach generally follows the original approach of Carver Mead (8, 9, 10), taking
advantage of the similarity of transistors and the elementary functions found in the
brain.
We use nMOS and pMOS transistors as our main computational circuit elements
and focus on their resistance and capacitance to represent the time constants of biolog-
ical computations. Voltages and currents are used to represent the chemical elements
involved in the computations. Each input to a transistor is used to represent a bio-
logical event. Our circuit designs are at accelerated time, of several order faster than
real-time biology. The focus of our work is on fundamental research and as such we
are concerned with nding ways to represent biological processes using circuits and at
this point we are not evaluating the power or speed constraints in our circuits in this
thesis.
One of the main challenges we face in our designs is nding the trade-o on the level
of biological details to be incorporated in our circuits for an accurate representation
6
1.4 Approach
while keeping our circuits as simple as possible. This is a daunting task and an ill-posed
problem. To explain this brie
y we could think of modules of computations to be used
over and over in a network, e.g., the synapse, unnecessary details drastically increase
the overall circuit overhead. This downgrades computational performance by limiting
the number of functions embedded on a chip. To minimize circuit overhead, we take the
approach of customizing our designs with focus on the biological functions rather than
on the mathematical models. This implies that we design our own circuit topologies
rather than using standard blocks such as analog ampliers, OTAs, etc. We capture in
our circuits rst-order interactions and as such we aim to describe biological principles
of computations while minimizing circuit complexity/overhead. We focus on exploiting
the properties of transistors and using their resistive and capacitive intrinsic functions
so that biological time constants can be modeled without the need for discrete elements
which often times take a large portion of the silicon area.
Interconnectivity between blocks is important as they will be used as part of a
large system where a variety of congurations will be tested. Therefore, we provide
this capability and guarantee that circuit modules can be connected in a plug and play
fashion. Our circuits are designed to be robust and stable over a wide range of inputs.
Montecarlo simulations are used for parameter variations.
We have a library of circuits with main circuit components such as synapses, den-
drites, and axon hillocks among others. This thesis has introduced new modules of
computations to emulate astrocyte functions and communication with neuronal cells.
Tunability of specic features allow us to test dierent biological functions in neuronal
networks.
There are many control inputs in the neuromorphic circuits that we produce; in
actual implementations those control inputs would be common to many neurons or
would be generated internally on chip, based on the state of the circuit as execution
progressed. Here, we show them as inputs into the circuit to illustrate the level of
control the designer and user have over the behavior of each circuit. In an integrated
neural circuit, such inputs would be produced by additional circuits found on the nal
chip modeling biological mechanisms.
The use of control knobs (voltages on transistor gates) to modulate transistor behav-
ior allows a broad range of neural behaviors with a simple, single-transistor mechanism.
For example, one way of controlling an input signal, let us say the Reuptake input, is
7
1.5 Related Work
by assigning a DC bias voltage that could be common to many synapses to control the
reuptake process of neurotransmitters in a static manner. Another way could be to
control the synapses in a dynamic manner where the input Reuptake could be used to
sense the level of neurotransmitters released in the cleft through a feedback mechanism.
Additional modeling may be required to capture the biomimetic aspects of a dynamic
mechanism.
A hypothetical example could be as follows. Considering that an increase in the
Reuptake input voltage would cause a faster discharge in the cleft node and thus a
faster EPSP decay. Assuming the spike rate arriving at the presynaptic side increases,
an increase in the neurotransmitter release is observed by the change in the average
voltage in the cleft node; this in turn may be sensed by feedback circuitry causing an
increase in the voltage at the Reuptake node which thus decreases the discharging time
constant in the node, thus emulating a faster reuptake of neurotransmitters. This
would have impact on the temporal dynamics of the EPSP node in our circuit as the
EPSP node is dependent on the cleft node.
The proposed circuits are a high design, containing parasitic capacitances along with
transistor channel and interconnection resistances. We utilize such nonlinearities to
avoid using discrete elements such as resistors and capacitors. While our small example
circuits are quite fast, the performance will be slowed signicantly when the massive fan
and fan proportional to biological neurons are implemented, due to capacitive loading
and interconnect resistance. Thus the relative timing dierences between our electronics
and the biological waveforms will be signicantly reduced.
1.5 Related Work
Previous research done in our group, as part of the BioRC Biomimetic Real-time Cor-
tex project (7), includes synapse circuits (11, 12) with focus on emulating biological
features such as the neurotransmitter release, neurotransmitter concentration, neuro-
transmitter reuptake, spike-timing dependent plasticity and transmitter-receptor inter-
action. An increasing interest in astrocytic-neuronal communication has paralleled our
development of neuromorphic circuits incorporating astrocytes. Recent progress on the
study of astrocytes and their interaction with neurons has led us to incorporate new
bio-inspired designs to emulate some important functions of astrocytes that play a role
8
1.6 Outline
in neuronal modulation of synaptic information. To our knowledge, our group is the
rst to have emulated an astrocytic microdomain circuit electronically, with astrocytic
compartments able to sense information from the neuronal environment and to feed
back to neurons (5). We have also emulated the astrocytic glutamate uptake circuit
(described in Chapter 2) (13), an important mechanism for maintaining a healthy neu-
ronal environment for preventing a cognitive decline by the loss of synapses that could
lead to neurodegenerative diseases, e.g. Alzheimer (14). In this mechanism, astrocytes
behave as the key players in the prevention of neurotoxicity by the regularization of
otherwise excessive release of neurotransmitters.
1.6 Outline
In Chapter 2 we present a detailed discussion about astrocytes and their interaction
with neurons. We discuss the physiology and response of astrocytes when subjected
to synaptic activity. We explain in detail the process of astrocyte encoding synaptic
information using calcium signaling. We provide the necessary research background
on the area of neuromorphic engineering that is related to our work. The chapter
also discusses the biological computations we captured in the circuits that are to be
discussed in the next chapters. Such computations include the mechanisms involved
in glutamate uptake by astrocytes as well as in the activation of NMDA channels that
leads to local neuronal synchrony.
In Chapter 3 we present a circuit design of a group of neurons interacting with an
astrocyte to test the role of the uptake of glutamate by astrocytes in the prevention of
neuronal toxicity. Transmitters at the cleft can induce neuronal death if not properly
cleared from the extracellular environment. Neurons do not have an advance mechanism
that allow them to uptake these transmitters. In contrast, astrocytes are particularly
ecient in the uptake of glutamate. Through a network of neurons interacting with
an astrocyte we show how a neuron may undergo a toxic regime in the absence of an
astrocyte. We also show how the presence of the astrocyte promotes neuronal survival
by the uptake of the excess of transmitters. Our group of neurons interacting with an
astrocyte shows the ecacy of the astrcoyte in the uptake of glutamate and maintenance
of neuronal survival using rst-order circuit designs.
9
1.6 Outline
In Chapter 4 we design and simulate circuits to show the role of astrocytes in the
synchronization of neurons. We use a small network of neurons that interact with
the astrocytic microdomains to show how the release of transmitters from a group of
neurons induces slow inward currents in another group of neurons. These currents
are induced with a high degree of synchronicity causing neuronal phase synchrony.
Astrocytes activate NMDA channels located at the extrasynaptic side. They activate
adjacent synapses and induce synchronicity in nearby neurons. We show this process
in detail through our circuit simulations. We also show how neuronal phase synchrony
leads to neuronal excitability.
In Chapter 5 we present a circuit that captures the adaptability of a synapse. Our
circuit demonstrates short-term synaptic depression and also captures an important
behavior, the Weber-Fechner relationship. We show that a synapse subjected to a
change in spike rates at high and low frequency have similar contribution in terms of
the updated synaptic strength. Our circuit is designed such that we can capture time
between spikes. By detecting the time between spikes we can detect when changes in
spike rates occur. Finally, in Chapter 6 we present our conclusion and future work.
10
2
Background and Related Work
2.1 Neuroscience Background
This chapter provides an overview of the neuroscience background and related research
on astrcoytes. In the following sections we summarize the details of the physiological
characteristics of astrocytes as well as their communication with neurons. We cover
the biological process for the uptake of glutamate by astrocytes. We also cover the
role of astrocytes in the integration of neuronal information and possible consequences
on the synchronization of neuronal activity. This information is used in the design of
the CMOS neuromorphic circuits we present in the next chapters. Also this chapter
presents a survey on additional mechanisms of communication between astrocytes and
neurons as well as a description of the neuromorphic area.
2.1.1 Communication in the Tripartite Synapse
The role of glial cells, in particular astrocytes, in neuronal communication has been a
subject of debate during recent decades. Unlike neurons, astrocytes are not electrically
excitable cells, i.e. their excitability is not based on the generation of action potentials.
Instead, they posses a chemical and mechanical form of excitability that is manifested
in their intracellular Ca
2+
waves. Astrcoytes have a high resting potential, a high
conductance, and a low intracellular concentration of glutamate. Each astrocyte has
hundred of long thin processes that contact thousands of neuronal synapses, and can
span over a hundred neurons. Astrocytes form \tripartite synapses"(15), i.e. at the
11
2.1 Neuroscience Background
synaptic level the pre- and post-synaptic elements are enwrapped by an astrocytic
element.
In tripartite synapses, conventional synapse communication between pre- and post-
synaptic sides is modulated by the astrocyte. There are a variety of mechanisms which
have been discovered in recent years for the signaling of astrocytes to other cells in the
brain. These discoveries highlight the complexity of interactions between astrocytes
with dierent cells, including other atrocytes, neurons and subtypes of glial cells such
as oligodendrocytes, and M uller cells. A special focus of study in recent years has
been on the communication between astrocytes and neurons at the tripartite synapse.
While it still remains to be elucidated to what extent astrocytes may in
uence the
ow
of information in the brain, there is substantial evidence that shows astrocytes are not
silent in this process (16, 17). As an active element in the communication between
neurons, astrocytes are endowed with the ability to also modulate synapses by the up-
take/release of transmitters, so called gliotransmitters, in
uencing synaptic transmis-
sion (18, 19, 20, 21). There is a wide variety of receptors by which astrocytes sense activ-
ity at tripartite synapses, such as purinergic receptors, AMPA receptors (AMPARs),
metabotropic glutamate receptors (mGluRs), GABA receptors (GABARs), nicotinic
acetylcholine receptors (nAChRs), and muscarinic receptors (mAChRs), among others
(40,41). By means of these receptors, astrocytes uptake neurotransmitters such as glu-
tamate, D-serine, GABA, and ATP and then, according to astrocytic calcium levels,
may also release transmitters back to neurons.
Calcium waves in the intracellular space of the astrocyte represent the encoding
mechanism that carries the information regarding the communication to be established
with the surrounding synapses. It is now well established that the properties of intra-
cellular calcium can be modulated by neurotransmitters released from nearby neurons.
Subsections 2.1.3-2.1.5 are dedicated to the discussion of astrocytic calcium waves and
their ability to encode and modulate synaptic information.
2.1.2 Astrocytes: Glutamate Uptake and the Maintenance of a Bal-
ance Extracellular Environment
The following information is relevant for the design of the CMOS neuromorphic circuit
discussed in Chapter 3.
12
2.1 Neuroscience Background
2.1.2.1 Astrocyte Glutamate Uptake
It is well known that astrocytes are particularly ecient in the uptake of glutamate
due to their excitatory amino acids such as EAAT1 and EAAT2 (22). They are in-
deed, by far, more ecient than neurons. Although neurons have their own uptake
mechanism, their transporters face the opposition of a higher electrochemical gradi-
ent and constant variations in the membrane potential (23),(22),(24). The astrocyte's
ecacy in the uptake of glutamate contributes to maintain the balance in the extra-
cellular space and prevent excitotoxicity and possible pathological conditions. In the
absence of astrocytes, an uncontrollable amount of glutamate in the extracellular space
would lead to the saturation of synapses and the eventual loss of synaptic connections
(25, 26). Undoubtedly, the uptake mechanism of astrocytes represents an important
synapse regulator.
Astrocyte uptake of glutamate limits the calcium entry into neurons through NM-
DAR channels, and contributes to support a healthy neuronal environment by the
prevention of neurodegenerative diseases. Without an uptake mechanism, such as the
astrocyte uptake, and under an excessive release of glutamate into the extracellular
space, neurons become vulnerable to the in
ux of calcium ions by the overstimulation
of neuronal NMDAR channels. An imbalance of calcium in the cell is highly undesir-
able and associated with neuronal death by toxicity (27). Without the astrocyte uptake
mechanism presynaptic neurons would disconnect their synapses from the postsynaptic
neurons when a large amount of neurotransmitters is released into the synaptic cleft
(25).
2.1.3 Astrocytes activate neuronal NMDAR for synchronization
The following information is relevant for the design of the CMOS neuromorphic circuit
discussed in Chapter 4.
2.1.3.1 Biology of the NMDAR channel
N-methyl-D-aspartate receptor (NMDAR) channels can be seen as coincidence detec-
tors, an important function demonstrated about 30 years ago (28) that has a key role
in long-term potentiation (LTP) and long-term depression (LTD), as well as in other
13
2.1 Neuroscience Background
cognitive functions through which they exhibit their Hebbian nature of synaptic plas-
ticity (29). The receptor is composed of three main subunits: GluN1, GluN2, and
GluN3. For the complete activation of the NMDAR, each subunit needs to be bound
by transmitters. Glutamate transmitters bind the GluN2 subunit, while either glycine
or D-serine binds GluN1 and GluN3 subunits.
Synaptic plasticity is dened by the ability of neurons to sense information from
presynaptic and postsynaptic sides of the synapse. NMDAR channels are able to sense
activity from both sides through a series of cascade events. Initially, the NMDAR
channel at the postsynaptic membrane is unable to open, even when glutamate release
from the presynaptic side binds the receptor, due to its inherent magnesium block that
opposes the in
ux of sodium andCa
2+
ions into the cell. The magnesium block can be
expelled away from the NMDAR if there is enough depolarization at the postsynaptic
membrane. This depolarization can be done through AMPAR (-amino-3-hydroxy-5-
methyl-4-isoxazolepropionic) channels. AMPAR is able to open upon sensing a consid-
erable level of glutamate. Activation of AMPAR allows sodium ions to rush into the
postsynaptic cell, causing temporal summation of EPSPs to depolarize the membrane,
so that the magnesium block is removed from the NMDAR by a process known as
electrostatic repulsion. The coincidence{detection nature of the NMDAR is the result
of two simultaneous events, the presynaptic release of transmitters binding the receptor
and the postsynaptic depolarization by EPSPs.
2.1.3.2 Astrocyte's role on the activation of NMDAR channel
Studies have shown that astrocytic release of glutamate, binding extrasynaptic NMDAR
located at the postsynaptic membrane, leads to the induction of excitatory currents with
slow kinetics and large amplitudes, capable of inducing synchronized neuronal activity
(30). These currents are known as slow inward currents (SICs).
The relevance of astrocytic induction of SICs lies in the role they could potentially
play in the coordination of neuronal activity. Two aspects of SICs appear to be im-
portant for the induction of synchronized activity: 1) SICs activate NMDAR with a
high degree of correlation on synapses of adjacent neurons, and 2) their amplitudes are
overwhelmingly larger than typical excitatory postsynaptic currents (EPSCs); the ratio
is one to ve, with SICs about ve times larger than EPSCs on average. Their slow de-
cay time constants allow for a time window through which synchronization of neuronal
14
2.1 Neuroscience Background
(a) The synapse stimulated by the astrocytic
process (3).

High neuronal
activity triggers
release of
neuroTs
neuroTs
bind the
astrocyte receptors
NMDAR activation
in adjacent
neurons induce
SICs with a high
degree
of correlation
Astrocyte in turn
releases glioTs
that binds on
Neuronal
extrasynaptic
NMDARs

(b) Steps in the activation by astrocytic re-
lease of transmitters of the neuronal NMDAR
channels.
Figure 2.1: a) A tripartite synapse, where an astrocytic process stimulates subunits of
the NMDAR channel (Figure taken from (3)). b) A
ow diagram describing the main steps
in the activation by the astrocyte of the extrasynaptic NMDAR channels.
activity remains active. The SIC decay is signicantly slower compared to EPSCs, i.e.
about 60 times slower than EPSCs (30). The activation of an NMDAR extrasynaptic
receptor by the astrocyte is summarized by the steps in Fig. 2.1(b). The release of
glutamate transmitters from surrounding neurons, sensed by the astrocyte, induces in-
tracellular calcium waves in the astrocytic microdomain. These calcium waves in turn
stimulate the release of transmitters back to the synapse, and such transmitters bind
and activate extrasynaptic NMDAR channels, causing the induction of SIC events at
the postsynaptic side of the synapse. Fellin presents comprehensive biological detail on
this mechanism (30).
2.1.4 A mathematical model for astrocyte SICs
In an eort to reveal the dynamics and eect of slow inward currents on neuronal
synchrony, Wade (31) formulates a mathematical model that describes the astrocyte-
neural interactions for the induction of slow inward currents. Unlike other mechanisms
of astrocytes, such as calcium waves, there is no current biophysical model that details
the steps in the generation ofslow inward currents. In an eort to capture the empirical
relationship between neurotransmitter release from the synapse, calcium oscillations,
15
2.1 Neuroscience Background
andSIC generation, Wade has combined biophysical models of neuron (Leaky Integrat-
and-Fire model), synapse (Tsodyks's model (32)), astrocyte calcium waves (Li-Rinzel
and the Nadkarni and Jung model (33, 34, 35)) along with an empirical model of
SICs. Wade presents an early empirical model of slow inward currents that captures
important aspects of the process.
Calcium oscillations are generated by the Li-Rinzel biophysical model, as it is a
versatile model with amplitude modulation (AM), frequency modulation (FM) and a
mixed AM-FM, allowing the encoding of the levels of IP3. IP3 allows for the sensing of
synaptic activity. Slowinwardcurrents in Wade's model are triggered when coincidental
events occur. These events include a presynaptic stimulus that arrives within a 100 ms
time window along with calcium oscillations crossing from below a dened calcium
threshold. Empirical observations show that glutamate released by astrocytes only
binds NMDA receptors, however, activation of NMDA receptors requires a coincidental
independent stimulus that allows the opening of AMPAR channels. As there is no
clear evidence on how AMPA receptors are activated, Wade assumes that a presynaptic
stimulus is the independent depolarizing signal that serves for the activation of AMPA
channels. The total current applied to the postsynaptic side is a function of the synaptic
weight, the presynaptic release of transmitters as well as the astrocyte-driven SICs.
Wade's model allows for tuning of the SIC amplitude and time constant to match
the kinetics of experimentally observed SICs. Wade takes SICs activity a step beyond
to show how astrocytes play a role in LTP/LTD. Wade's model shows how dynamic
coordination in the brain is in
uenced by the bidirectional communication between
neurons and astrocytes. A detailed description of the model can be found in (31).
2.1.4.1 Astrocytes' role in binding information
The implication of the role of astrocytes in the coordination of massive neuronal activity
is undergoing research that could dramatically impact our understanding of cognitive
functions (36), as well as neurodegenerative diseases such as epilepsy (37). A very im-
portant consideration is that a single astrocyte in rodents is capable of reaching between
20,000 and 100,000 synapses, while in humans a protoplasmic astrocyte can contact be-
tween 270,000 and two million synapses (38). More important is that astrocytes in the
brain are not usually working as single units; they form an astrocytic syncytium, i.e.
network of astrocytes connected by gap junctions, while a single astrocyte has about
16
2.2 Ongoing Research on Astrocytes
235 gap junctions (39). Astrocytes rely on neurons to access sensory information. The
binding of information refers to the process where independent features of an object
are encoded in the brain through dierent neuronal paths with dierent axonal delays
(40). It remains unknown how these paths are combined and this is known as the
binding problem (41). The Astrocentric hypothesis proposed by Robertson (42) consid-
ers the astrocyte as the missing link in the binding of information, where independent
information is consolidated. The basis for this hypothesis is the ability of astrocytes to
integrate neuronal information. Binding of information is important for conscious pro-
cessing, where synchrony of activity is considered to be a fundamental process. Pereira
Jr. conjectured that astrocytic calcium waves carry the content of perceptual conscious
processes (43). He proposed a model of brain mental functions that combines the role
of large-scale calcium waves in a network of astroglial cells with signals that modulate
neuronal networks (36). In his model, large-scale calcium waves are produced through
neuronal synchronized events (43). These neuronal synchronized events can be poten-
tially activated by astrocytes through the induction of SICs into extrasynaptic NMDA
receptors as observed in experiments (30).
2.2 Ongoing Research on Astrocytes
2.2.1 Astrocytes Contribute to a Wide Range of Biological Processes
Recent publications have shown that astrocytes, like neurons, integrate, process in-
formation, and discriminate between synapses (15, 44). The ability of astrocytes to
discriminate synaptic information was experimentally shown by Araque et. al. (45).
The experiment shows that glutamatergic axons from the Alveus area of the hippocam-
pus do not elicit calcium waves in astrocytes; however astrocytes respond to cholinergic
axons from the Alveus and to glutamatergic axons from the Schafer collateral areas.
In another study, Perea and Araque (46) experimentally demonstrated the ability of
astrocytes to integrate synaptic information by the simultaneous stimulation of both
pathways. The authors reasoned that if astrocytes have the ability to integrate synaptic
information, then it should elicit a non-linear calcium wave when both pathways are
stimulated simultaneously. In agreement with this reasoning, the authors have shown
experimentally synaptic integration by the non-linear response of astrocytic calcium
17
2.2 Ongoing Research on Astrocytes
waves. In the hippocampus area, astrocytes selectively discriminate between gluta-
matergic synapses from dierent pathways, and appear to distinguish pathways with
same type of neurotransmitters.
In another role, astrocytes control neuronal inhibition in the barrel cortex of rats
by means of GABAA and GABAB receptors (47). Two of the principal GABA trans-
porters (GATs) are known to exist preferentially in astrcoytes. In the thalamus, as-
trocytes act as a gatekeeper controlling the spillover of GABA transmitters to other
extrasynaptic sides and thus, preventing the formation of seizures (48).
Astrocytes also play a role in tonic inhibition, a form of feedback which is important
in the balance between inhibition and excitation, by complex feedback that consists in
the uptake of glutamate from a network of neurons and the release of GABA back to
the network (49). The Glu/GABA exchange is a mechanism important in a network
with high activity and it is thought to play a fundamental role in preventing epilep-
tic seizures due to its negative feedback nature. Heja (49) proposed a hypothetical
model in which GABA is released from astrocytes gradually according to the uptake
of glutamate based on his current experimental work. The release of GABA is Ca
2+
independent and occurs via transporter reversals of the subtype GAT-2 and GAT-3.
In this mechanism Na
2+
plays an important role since the GAT-2 and GAT-3 driving
forces are believed to depend on the dierence of Na
2+
between the intracellular and
extracellular spaces. Following the generation of action potentials from the presynap-
tic neuron, Glu is released and transported along with Na
2+
from the extracellular
space into the astrocyte's intracellular space by means of the glutamate transporters
EAAT1/2. This causes putrescine to synthezise GABA, which is released back into
the extracellular space, binding extrasynaptic receptors in the postsynaptic membrane
(49). Another experimental study shows that the anion channel Best1 (bestrophine-1)
appears to be involved in astrocytic GABA release. Best-1 can be activated by means
of elevated intracellular Ca
2+
in the astrocyte (50).
Studies have also shown that stimulation at one synapse leads to inhibition at a
nonoverlapping synapse by the release of ATP from astrocytes (51, 52). ATP transmit-
ters released from astrocytes through metabotropic P2Y receptors have been found to
induce long term depression (LTD) in neighboring hippocampal neurons (52). Heterosy-
naptic depression, a form of LTD, where the ecacy of neighboring inactive synapses is
decreased by active synapses, can be mediated by the release of ATP or by the release
18
2.2 Ongoing Research on Astrocytes
of glutamate from astrocytes. In the former case, ATP is released by astrocytes upon
glutamate stimulation from neurons (51); while in the latter case, GABA released from
neurons triggers glutamate release from astrocytes modulating mGluR channels (53).
Heterosynaptic depression is a form of intersynaptic communication in which astrocytes
appear to have a signicant role. Moreover, about 75% of astrocytes' gap junctions are
autologous (intradomain) which means that they can represent the main path for this
form of intersynaptic communication (53).
Another form of inhibition by astrocytes is the production of slow outward currents
(SOCs) at the extrasynaptic GABA receptors (54). SOCs have shown to have, like slow
inward currents (SICs), slow rise and decay times with a high amplitude. They were
shown to inhibit neurons in the olfactory bulb synchronously (54). They may also be
involved in the production of tonic inhibition in the thalamus (54, 55) and thus in the
prevention of seizure generation.
2.2.2 Ca
2+
Waves: A coding Mechanism in Astrocytes
The encoding of information in astrocytes occurs via calcium waves that are formed
in the cell by the activation of dierent mechanisms, enabling them to propagate over
long distances. Intracellular calcium dynamics is primarily considered to be modulated
by an IP3 (inositol trisphosphate)-dependent calcium-induced calcium-release (CICR)
mechanism. The activation of this mechanism is caused by the stimulation of neuro-
transmitters released from synapses enwrapped by the astrocyte. These neurotransmit-
ters bind and activate receptors located in the extracellular membrane of the astrocyte
to cause the hydrolization of the membrane lipid phosphatidylinositol 4,5-bisphosphate
by canonical phospholipase C (PLC). This generates diacylglycerol(DAG) and IP3 (56).
The IP3 production acts on IP3R channels located in the the endoplasmic reticulum
(ER). Enough production of IP3 causes the activation of IP3R channels. Calcium is
released from the ER into the intracellular membrane (cytosol) in the form of sparks or
successive pus through the IP3R channels. The cell is endowed with SERCA-pumps
that uptake back calcium into the ER. The interplay between these channels causes the
calcium wave production and propagation.
IP3 receptors close when the astrocytic extracellular stimulation from the released
neurotransmitter decreases and thus the binding of transmitters into the receptors at
the astrocytic outer cell membrane is reduced, causing a reduction in the formation
19
2.2 Ongoing Research on Astrocytes
of inositol triphosphate in the cytosol. The high concentration of calcium is then
reversed by the autocatalitic action ofCa
2+
release which along with the SERCA (sarco-
endoplasmic reticulum Ca
2+
-ATPase) pumps cause the inactivation of IP3R channels.
SERCA-pumps are activated by the increase of calcium in the cytosol. Their role is to
pump back the excess of intracellular calcium into the endoplasmic reticulum so that
calcium in the intracellular space goes back to its natural concentration. The activation
of SERCA-pumps causes the inactivation of IP3R channels. The repetition of these
events by the constant release of neurotransmitters can lead to calcium oscillations.
As the calcium wave propagates, it is self-amplied by the release of calcium from the
nearby IP3 receptors located on dierent sides of the endoplasmic reticulum.
It should be highlighted that the transmitter ATP (adenosine triphosphate) is the
main source of energy for the astrocyte cell which is produced by the mithocondria.
Without ATP, SERCA-pumps would not be activated, which could lead to eventual
cell death (57, 58). It is important to mention that the calcium concentration in the
endoplasmic reticulum is about 10-15 times higher in calcium than in the intracellular
space and proteins are about 1,000 times more likely to bind calcium in the intracellular
space rather than in the ER (58).
2.2.3 Patterns of Astrocytic Ca
2+
Waves
Experiments have shown that the activation of dierent types of metabotropic gluta-
mate receptors (mGluR1, mGluR5) induce dierent patterns of intracellular calcium
waves (39). Biphasic elevations of calcium (initial peak followed by a sustained plateau)
are caused by activation of mGluR1 and typically have little in
uence in the astrocytic
release of transmitters. Ca
2+
oscillations are induced by mGluR5 and can vary in
frequency and amplitude over time, triggering the release of transmitters (39). These
are the two most recognize patterns of calcium signaling.
Experiments have shown that biphasic elevations of calcium in astrocytes only evoke
a single release of glutamate having little eect on neuronal activity. Calcium oscilla-
tions in the astrocyte appear to be more in
uential by the pulsatile release of glutamate;
and have been viewed as a possible representation of synaptic activity by encoding in-
formation through frequency variations (39, 59, 60). In other words, activity induced
by astrocytes appear to have dierent levels. The lowest level induces no release of
transmitters from astrocytes due to the lack or small activity in the neuronal release of
20
2.2 Ongoing Research on Astrocytes
glutamate. A medium level is observed with a substantial increase of glutamate, caus-
ing the astrocyte to release successive pus of glutamate. Under excessive stimulation,
astrocytes have shown to release only a single event of glutamate. This case is usually
seen in pathological diseases, such as epilepsy.
Studies have shown that the amplitude and frequency of calcium waves in astrocytes
may be controlled by dierent biological processes. Nitric oxide (NO), for example,
could be implied in the frequency variations of oscillations with little in
uence on the
amplitude and pattern of the calcium wave. Experiments have shown that the increase
in the frequency of oscillations is inactivated by inhibition of NO even when mGLUR
channels remain active.
2.2.4 Ca
2+
Waves Intercellular Propagation in Astrocytes
Astrocytes have the ability to process a wide range of synaptic information through
their syncitium, i.e., network of astrocytes connected by gap junctions. There are
suggestions based on a study made in the optic nerve indicating that the strengths of
the connections in the syncitium are dynamically regulated by neuronal activity (61).
Astrocytes in vivo express connexin CX43 localized at gap junctions between processes
near the somata, dendritic, and synaptic glomeruli (61). When astrocytes are working
together in a network, they in
uence each other through intercellular calcium waves or
possibly by adenosine triphosphate (ATP) released into the extracellular space.
Intercellular calcium waves can propagate through nonlinear gap junctions. Gap
junctions are the channel by which two non-physically connected cells are able to in-
terchange molecules and proteins. Between two astrocytes there can be up to 235
connections by gap junctions (39). There are two main vias through which the prop-
agation of intercellular calcium waves occur. Once is by the diusion of IP3 molecule
from one astrocytic cell to another astrocytic cell through gap junctions (62). This
causes activation of IP3 channels in the cytosol of the cell and thus inducing calcium
release through the IP3R channels. A second mechanism found is by the diusion of
ATP in the extracellular space binding plasma receptors and causing the regulation of
IP3 production in nearby cells. These two mechanisms are not necessarily mutually
exclusive.
It is noteworthy to mention that gap junctions are shared between astrocyte-
astrocyte cells as well as astrocyte-oligodendrocyte-cells (63). Oligodendrocyte cells
21
2.2 Ongoing Research on Astrocytes
are a subtype of glial cells, known for their role in axon myelination. This represents
another complex form of communication by which astrocytes may be able to in
uence
neuronal responses in an indirect manner.
2.2.5 Mathematical Models for Astrocytes
Mathematical models have been developed to study the modulation of amplitude,
frequency, or both in astrocytic calcium waves and its correlation with neuronal ac-
tivity. In astrocytes, the intensity of stimulation, i.e. the amount of neurotransmitters
that bind astrocytic receptors, is known to establish the level of interaction between as-
trocytes and neurons. Astrocytes can communicate with a few neurons sending a local
message if calcium waves do not have the strength to propagate to other microdomains
or eventually through the entire cell. Global communication may occur only under
high levels of neuronal activity. Such type of communication would allow all neurons
spanned by the astrocyte to be contacted. Moreover, calcium waves may propagate
to other astrocyte cells in a syncitium (network of astrocytes) allowing them to reach
neurons far away and thus establishing an indirect form of communication between
neuronal paths that otherwise were not able to contact each other.
In the last decade mathematical models have been focused on 1) the description of
the mechanisms that leads to the generation of calcium waves in astrocytes, 2) the use of
these models to incorporate neuro-astrocyte interactions, particularly the capability of
astrocytes to facilitate neuronal ring, and 3) the gap junction communication between
astrocytes.
The Li-Rinzel (33) model has been a pioneer work in the description of the IP3
mechanism for the induction of intracellular calcium waves. De Pitta (57) extended
the Li-Rinzel model (33) to account for more complex signaling that includesCa
2+
reg-
ulation by the IP3-dependent Calcium-induced Calcium-released mechanism, as well as
IP3 dynamics resulting from PLC-mediated synthesis and degradation by IP3 3-kinase
(3K) and inositol polyphosphate (IP) 5-phosphatase (5P) (57). In his study, DePitta
shows that long distance propagation of regenerative waves is closely related to the in-
tracellular encoding of calcium. Frequency modulation encoding of calcium oscillations
with pulsating dynamics induces regenerative waves that travel a long distance through
nonlinear gap junctions, while amplitude modulation encoding produce calcium waves
that are constrained within a specic domain. De Pitta suggests that nonlinear gap
22
2.2 Ongoing Research on Astrocytes
junctions in the case of weak coupling could explain the oscillation dynamics observed
during intercelullar calcium wave propagation in astrocyte networks (64).
The gatekeeper model (65) introduces the ability of astrocytes to reduce the cal-
cium
ux by means of presynaptic mGluR channels using the Li-Rinzel model (33) for
the calcium dynamics. In the gatekeeper model, a phenomenological variable has been
used to account for the amount of nite glutamate in the astrocyte. Astrocytes release
glutamate that binds presynaptic terminals, activating mGluR channels, causing the
decrease of calcium in
ux into the presynaptic neuron, and reducing the probability of
evoked transmitter release. The gatekeeper model shows that the amplitude of exci-
tatory and inhibitory postsynaptic currents is decreased due to the astrocytic control
over the calcium in
ux into the presynaptic neuron mediated by glutamate.
Nadkarni (34, 35) model is the rst to incorporate the astrocyte's capability to
modulate a synapse using the Li-Rinzel model for the calcium dynamics. Amiri (66)
constructed a minimal neuronal network of two Moris-Leccar neuron models. The work
includes dynamics between astrocytes and neurons which follows Nadkarni's model (34).
Amiri provides a theoretical analysis establishing that a healthy astrocyte increases the
threshold value of synchronization and thus has the potential to induce desynchroniza-
tion in neurons.
Digarbo (67) developed a biophysical model for the calcium dynamics that describes
experimental results (68). The model is able to show the ATP-evoked biphasic calcium
response in the astrocyte. This response is described by the transient part, evoked by
the release of calcium from the endoplasmic reticulum, and the sustained part that is
dependent on the in
ux of extracellular calcium mediated by P2X purinoreceptors (69).
Digarbo also developed a biophysical model for a minimal network consisting of
a single astrocyte, pyramidal neuron, and an interneuron (70). The model shows the
modulation properties of astrocytes on both the pyramidal neuron and interneuron by
the release of glutamate. Following experimental results, DiGarbo shows the role of
astrocytic released ATP in the modulation of the ability of the interneuron to re.
DiGarbo's results also shows that the increase in intracellular calcium leads to a de-
crease in the calcium oscillations, which is in agreement with experimental data (71, 72,
73). DiGarbo shows that the reduction of calcium in
ux from the ER to the cytoplasm
does not result in calcium oscillations, which is also in agreement with experimental
data (74). Moreover, it was also shown that the increase of intracellular calcium leads
23
2.2 Ongoing Research on Astrocytes
to a decrease in the period of the calcium oscillations, in agreement with experimental
results (71).
A main dierence found in Digarbo's results compared with the experiments in (71,
75, 76) is that, while in these experiments the inhibition of SERCA-pumps leads to
a decrease in the frequency and amplitude of the calcium oscillations, the Digarbo
model (70) shows an increase in the frequency of calcium oscillations, while the ampli-
tude of the oscillations is in agreement with the previous studies.
2.2.6 Astrocyte-Astrocyte Networks and their implications in Inte-
gration of Synaptic Information
Glial cells have been proposed as suitable cells for the implementation of information
routing mechanisms (77). The routing of information requires mechanisms that allow
astrocytes to modify the strength of a group of synapses which do not necessarily
share the same presynaptic and postynaptic neuron. Some type of interneurons in
the cortex (78) only target the axon hillock and are able to deactivate communication
between thousands of synapses connected to the neuron by merely inhibiting the neuron
through the axon hillock. Some types of neurons in the cortex preferably target the
dendritic tree near the soma of their postynaptic neuron which allows them to modulate
homogeneously a wide number of synapses of the same dendritic tree. However, for
information routing, selectivity is required. We need to control the synaptic ecacy
of a subset of synapses even if they belong to the same dendritic tree. This requires
a mechanism which does not modulate synapses in an homogeneous manner. Moller
proposed the astrocyte to play a role in attentional mechanisms, due to the astrocyte's
capability to autonomously modulate synapses at dierent microdomains (77).
Pereira Jr. (36) oers theoretical insights for the behavior of a single astrocyte
interacting with a group of neurons with aims to explain possible contributions to
astrocytes in the conscious binding process. An astrocyte surrounded by a group of
neurons is dened as a \local hub", while astrocytic networks interacting with group of
neurons is described as a \master hub". In a \master hub", \local hubs" can interact
with each other by means of propagating their calcium waves through gap junctions to
combine synaptic information from dierent \local hubs". The \master hub" can be
viewed as a global workspace that integrates information from many local neurons to a
brain-wide network (36). Two mechanisms for the contribution to the formation of the
24
2.3 Background in Neuromorphic Engineering
intercellular calcium wave were dened, the \domino eect" and the \carousel eect".
The \domino eect" is based on previous experimental ndings that calcium waves
elicit non-linear saltatory behavior; it states that the waves in astrocytes syncitium
may propagate like an eect of domino pieces that falls one after another, where in
a small group of these dominos the last piece may fall almost simultaneously as the
rst piece. For conscious binding, this process is very important, since the binding
of information should happen quickly. The \domino eect" may represent the ATP
signaling between astrocyte cells.
The \carousel eect" is used to describe the possible role of synchronized neurons
in the generation of intercellular calcium waves. In this putative description, neurons
that are synchronized coordinate calcium waves in dierent microdomains in astrocytic
syncitiums. Each calcium wave in a dierent microdomain would be analogous to a
horse in the carousel, while the movement of the carousel will be orchestrated by the
synchronized neurons. The astrocytes feedback to the synchronized neurons, strength-
ening or weakening the neurons. Pererira Jr. has also dened a theoretical calcium
wave model of the perception action cycle (79).
2.3 Background in Neuromorphic Engineering
The human brain is strikingly energy ecient and outperforms Von Neumann computer
architectures on sensory computations. Computers struggle at performing operations
that seem eortless to the brain; object recognition, motor functions, and sound local-
ization are only few examples.
Some key challenges of hardware cognitive systems that inspire us to look at the
brain for new ideas include: 1) Power consumption: the brain consumes only 10Watts
of energy while performing 10
16
operation per seconds. A computer with same number
of operations would require about a million times more energy. 2) Robustness: massive
numbers of connections in the brain gives room for a highly ecient fault tolerant sys-
tem not even conceived by current computers. 3) Sensory computations: it takes only
100 ms for the brain to recognize a face and only 10 synaptic steps for the processing
of information from the retina to the temporal lobe. This is a highly challenging task
to current computers that lack the computational power of parallelism widely used in
the brain.
25
2.3 Background in Neuromorphic Engineering
Neuromorphic systems exploit brain computational methods using electronic cir-
cuits with the goal to demonstrate brain capabilities that today's digital computers,
based on von Neumann architecture, are either unable to solve or, if theoretically
plausible, would exhibit a long execution time with a dramatic impact on energy and
hardware costs. Large-scale networks, for example, may require massive computations
and could take days to be simulated on current computer systems (80, 81). Neuro-
morphic engineering is also valuable for hardware that communicates with the real
world, i.e., biological systems, sensory data, or prosthetic devices where size and power
consumption are crucial (10, 82, 83, 84).
A wide number of dedicated architectures for emulating large{scale neural networks
have been proposed; some of them have been designed to run at accelerated time with
the goal of speeding up simulations using available processors on integrated circuits for
parallel computations. However, small-grain parallelism is a paradigm largely seen in
the brain and not in the von Neumann architecture used in modern processors. Other
hardware designs have exhibited the biophysical characteristics of brain-like computa-
tions (81), i.e., depending on the application they run either at accelerated or real{time.
One of the most important trade-os in the design of neuromorphic hardware as
a tool for neuroscience is to determine what level of biophysical details would be ad-
equate to provide sucient correlation with brain computations without reducing the
complexity of the neurons in a neural network on a chip to a level that yields less accu-
rate results than desired. In the literature, we nd silicon neurons with a very detailed
level of biological properties occupying a large silicon area (85), and thus using these
models would only allow for simpler neural networks; we also nd simplied neuron
circuits whose correspondence with biology is highly abstracted, allowing for a very
large{scale neural network but lacking a realistic system that could mimic complex
brain dynamics (86).
Corporate research eort is seen by \proof of concepts" of cognitive chips such as
TrueNorth and Zeroth by IBM and Qualcomm, respectively. Government agencies such
as NIH, NSF, and DARPA are some of the sources of funding for projects to advance
neuromorphic research. To mention one, the SyNAPSE project, funded by DARPA,
forms a coalition between IBM, HP labs, and HRL labs and performs research at
dierent levels. In the academic sphere, there are a growing number of laboratories
focusing on cognitive neuromorphic research. Research in academia nurture widely
26
2.3 Background in Neuromorphic Engineering
diverse goals; some researchers contribute to new biologically inspired technologies for
engineering applications, while others pursue a scientic research to discover ecient
mechanisms of the brain that allow for higher computational performance.
Recent advances in neuromorphic engineering have focused mainly on neural mecha-
nisms such as spike timing dependent plasticity (STDP) (87, 88), synaptic rewiring (89,
90) and neural spiking (91, 92). There has been a focus on emulating biological neural
networks based on these mechanisms to demonstrate learning.
An increasing interest in astrocytic-neuronal communication has paralleled our
development of neuromorphic circuits incorporating astrocytes. Our designs include
synapse circuits (11, 12) with focus on emulating biological features such as neuro-
transmitter release, neurotransmitter concentration, neurotransmitter reuptake, and
transmitter-receptor interaction. Recent progress on the study of astrocytes and their
interaction with neurons have led us to incorporate new designs that include glutamate
uptake, the generation of synchronize slow inward currents through NMDA receptors,
as well as the astrocytic microdomain circuit. To the best of our knowledge, the BioRC
group lead by Prof. Parker at University of Southern California has provided with one
of the rst contributions to the area with the detection of neural activity and emulation
of the glutamate release by astrocytes upon calcium excitability (5). Signicant eort
has been made recently to implement digitally through FPGAs the interaction between
neurons and astrocytes (93). This is in contrast with our analog approach of designing
custom circuits that capture the biological process in the interaction of neurons and
astrocytes.
The design of biomimetic circuits to be used in large scale networks is a major
challenge due to the massive interconnections in the brain. The existence of synaptic
divergence (fan out in engineering terms) and convergence (fan in), causes signicant
delays in electronic circuits. Thereafter, our small example circuits work at nanosecond
(CMOS) speed. These circuits, when incorporated into large networks with thousands
of synapses per neuron, will slow down signicantly due to wiring interconnection ca-
pacitances (94). The compartmentalized construction of our neuromorphic circuits and
the ability to control neural parameters directly by means of specic control voltages
allow us to insert additional mechanisms without extensive circuit redesign.
27
3
Neuro-Astrocyte Interactions: A
CMOS Neuromorphic Approach
Our goal for the experiment described in this chapter is to create neuromorphic circuits
incorporating the in
uence of astrocytes on synapses as part of the BioRC Biomimetic
Real-time Cortex project (7). The aim is to demonstrate some gross rst-order inter-
cellular behavior of the astro-neuronal communication, focusing on synapse modulation
and regulation by an astrocyte. Specically, we propose CMOS circuits to emulate the
astrocytic uptake of glutamate, an important mechanism in astrocytes that contributes
to the healthy balance of transmitters in the extracellular space. We model synapses
undergoing toxicity in the absence of the astrocyte uptake mechanism. Inspired by the
biological processes involved in neuronal toxicity, we show the inactivation of presy-
naptic neurons by the excessive release of transmitters sensed at the synapse. We refer
to this process as \synaptic inactivation". We show the in
uence of both mechanisms
on the ring of a small network of neurons interacting with an astrocyte. We also in-
corporate the release of transmitters by the astrocytic microdomain into this network
according to the activity in neighbor synapses, and show the communication between
neurons via an astrocyte.
We have designed and simulated a small network of neurons spanned by an astrocyte
that captures the in
uence of astrocytic mechanisms on neuronal ring. The presynap-
tic neurons are excited with regular spike trains. The ring of post-synaptic neurons
depends on the total excitatory postsynaptic potential (EPSP) that may vary according
to the in
uence of astrocyte mechanisms and the number of synapse connections.
28
The interplay between the \astrocytic uptake" and the \synaptic inactivation"
mechanisms is controlled by two dierent thresholds. The astrocyte uptake mecha-
nism process has been captured through a pathway controlled by a transistor that
limits the voltage (neurotransmitter concentration) at the synaptic cleft node. The up-
take mechanism is only active when the synaptic cleft voltage rises above the threshold
of the astrocytic uptake stage. The synaptic inactivation process has been designed
through a feedback stage that monitors the cleft voltage, so that pre- and postsynaptic
circuits are disable when the synaptic cleft voltage (neurotransmitter concentration)
rises above the threshold of the inactivation stage. The feedback stage is only activated
when no astrocytic uptake mechanism is present and the voltage at the cleft node rises
beyond the stage threshold. In the presence of the astrocytic uptake, the mechanism
would be activated earlier as it has a lower stage threshold, maintaining the synapse
stability. In the circuit described in this chapter, it is the astrocyte uptake mechanism
that prevents the synapse from toxicity, and limits the cleft voltage below the threshold
of the inactivation stage that emulates the condition when synapses are disabled due
to toxicity.
3.0.1 The Synapse and Astrocyte Mechanisms
The excitatory synapse along with the astrocytic and the synapse inactivation mech-
anisms are shown in Fig. 3.1. Stages (2) and (4) show the pre- and post-synaptic
sections separated by the synaptic cleft. The circuit for the astrocytic uptake mecha-
nism is shown in Stage (3). The circuit in Stage (5) captures the communication process
that involves the release of transmitters by the astrocyte according to calcium activity
in the astrocyte. This activity is in
uenced by transmitter released from synapses in
the network. The circuit for the synapse inactivation mechanism is shown in Stage (6).
This stage feds back the synaptic cleft activity into the presynaptic neuron by means
of Stage (1).
The synapse circuit consists of two main parts: neurotransmitter (presynaptic) and
receptor (postsynaptic) sections. The Presynaptic Input normally receives a regular
train of spikes from the Input Spikes terminal. On the presynaptic side, the input
pull-up transistors charge the Synaptic cleft node during the spike time. The input
NT Conc. modulates the concentration of neurotransmitters. Within the time duration
that no arrival of spikes occur the Synaptic cleft node is discharged through the input
29
Reuptake
NT_Conc.
(2)
Spread
Receptor
(4)
+
AstroCa
2+
Astro_glut_control
Synapatic_cleft
(3)
Presynaptic_Input
EPSP
Astro_glut_release
(5)
Delay Delay
Input_Spikes
(1)
Reset
Q
Q D
ck
(6)
Figure 3.1: The synapse with the astrocytic mechanisms. Dashed boxes separate dierent
stages of the circuit. Stage (2) and Stage (4) represent the pre- and postsynaptic sides of
a synapse. Stage (6) is the inactivation mechanism that controls the presynaptic input
by means of Stage (1). Stage(3) and Stage (5) correspond to the astrocytic mechanisms.
Stage (3) represents the astrocytic uptake mechanism, while Stage (5) is the microdomain
mechanism that injects gliotransmitters into the Synaptic cleft. The adder (4) is used to
incorporate the gliotransmitter contribution into the cleft.
pull down transistors. This mimics the drop of neurotransmitters in the synaptic cleft
by the reuptake process which can be tuned by the input Reuptake. The charge in
the Synaptic cleft node mimics the concentration of neurotransmitters in the cleft over
time. The Synaptic cleft signal is characterized by a relatively fast rise time and a slow
fall time constant.
The presynaptic section is a modied version of the BioRC excitatory synapse circuit
(5). We have removed a pMOS transistor in the pull-up part that self-limited the cleft
voltage (cleft neurotransmitter concentration) to increase the dynamic range in the
Synaptic cleft node. This further modication allows us to show the interaction betwee
the astrocyte and neurons through the interplay of the astrocyte uptake mechanism and
the synapse. The nMOS transistor in Stage (2) with source and drain tied toVdd is used
to increment the capacitance at the Synaptic cleft node and maintain existing circuit
timing The adder (4) was introduced into the cleft section in a previous publication (5)
to account for the contribution of transmitters released from the astrocyte by Stage (5).
The output of the postsynaptic stage is the excitatory postsynaptic potential (EPSP),
which is roughly proportional to the neurotransmitter concentration in the synaptic
30
cleft, modulated by receptor availability on the synaptic ion channels. The gliotrans-
mitters released from Stage (5) adds to the neurotransmitters in the Synaptic cleft to
facilitate the ring of postsynaptic neurons. These gliotransmitters are released from
one of the compartments of the astrocytic microdomain (a distributed resistive net-
work), when the other compartments of the microdomain have been excited by neuro-
transmitters released from other synapses, as shown in Fig. 3.2. In this process neighbor
synapses mediated by the propagation of Ca
2+
through the microdomain in
uence each
other. The AstroCa
2+
is the control signal that causes the synaptic cleft to increase
by a voltage, Astro glut release. This models the amount of glutamate gliotransmitter
that is injected into the cleft by the astrocyte.
Figure 3.2 shows several compartments of an astrocyte circuit. It is a distributed
resistive (pass transistor) network that takes inputs from the voltages representing
synaptic cleft neurotransmitter concentrations of dierent synapse circuits. The neu-
rotransmitter voltage from each synapse is fed into a non-inverting delay circuit whose
output voltage representing released neurotransmitters is summed with delayed neuro-
transmitter voltages from other synapses. This delay captures the time taken by the
astrocyte to take up neurotransmitters and generate Ca
2+
. The rise in potential at
the resistive network (AstroCa
2+
) models the increase and spread of calcium across
Delay Delay Delay Delay Delay
Synaptic_cleft1 Synaptic_cleft2 Synaptic_cleft3 Synaptic_cleft4 Synaptic_cleft5
+ + + + + + + + + +
V
bias
V
bias
V
bias
V
bias
V
bias
AstroCa
2+
1 AstroCa
2+
2 AstroCa
2+
3 AstroCa
2+
4 AstroCa
2+
5
+ + + + + + + + + +
Figure 3.2: The astrocytic microdomain mechanism (5).
31
the astrocyte. The outputs of the astrocyte compartments control transistors in each
synapse such that the synapse adds an oset voltage Astro glut release to the synaptic
neurotransmitter concentration voltage to emulate the increase in neurotransmitters
in the synapse due to the astrocytic release of glutamate caused by the increase of
intracellular calcium in the astrocyte.
The neurotransmitter concentration in the cleft is also in
uenced by the astrocytic
glutamate uptake mechanism in Stage (3). The nMOS transistor connected as a diode
represents the astrocyte uptake of neurotransmitters. In biological neurons, the as-
trocytic uptake mechanism exert control over the transmitters in the cleft. This is to
support the balance in the neuronal environment and prevent death of cells by excess
of transmitters in the synapse. To model this behavior, an upper limit is set by the
Astro glut control voltage. The mechanism is activated when the cleft node rises above
V
th
+ Astro glut control voltage, where V
th
is the threshold of the transistor. In the
absence of the astrocytic uptake, a large enough rise in the cleft voltage triggers the ac-
tivation of the circuit in Stage (6). We have set the threshold of Stage (6) to be greater
than the threshold of Stage (3), thus giving priority to the astrocytic mechanism when
available at the synapse.
Stage (6) consists of a negative level-sensitive latch component, where the input ck
is controlled by an inverting stage. The outputs (Q, Q) determine the synapse state
by means of selecting the input to the presynaptic stage in Stage (1). An excess of
voltage in the cleft node above the threshold of Stage (6) causes the inverting stage
to set ck to 0.0 V through the pull down transistor, so that the output Q becomes
V
dd
. This forces 0.0V into the presynaptic input, resulting in the synapse inactivation.
The transistors connected to the input of the nMOS transistor in the inverting stage in
Stage (6) provide a two-fold operation. They increase the activation threshold and also
allow us to delay the process of inactivation by increasing the delay in the path, using
the intrinsic capacitances of the transistors. An asynchronous reset signal (Reset) is
also available to reestablish the synapse function.
The latch component consists of one pMOS pass transistor that allows transferring
the input V
dd
when ck is low, and a transmission gate that controls a feedback loop
that saves the data into the latch when ck is high. The feedback loop consists of a
NAND gate to introduce the reset signal, and an inverter.
32
3.1 Simulation Results
3.1 Simulation Results
The network shown in Fig. 3.3 illustrates the conguration we used for this experiment.
In a network of silicon neurons an astrocyte spans several synapses to create the neuro-
astrocyte interactions. In our experiment, synapses S1{S4 are modulated by the two
astrocytic mechanisms, i.e. glutamate uptake and the astrocytic microdomain (dashed
cyan arrows). The presynaptic neurons N
1
{N
3
re regular train of spikes at the same
N
1
N
4
N
2
N
5
N
6
Astrocyte
AP
AP
AP
S
1
S
2
S
3
S
4
S
5
S
6
N
3
S
6
S
7
Figure 3.3: Neural network illustrating astrocyte connections. The gure shows a
schematic of the network we simulated. The astrocyte in
uences the behaviors of synapses
S1{S4 through its glutamate uptake mechanism and the injection of gliotransmitters into
the cleft.
rate. The ring of spikes by postsynaptic neurons N
4
{N
6
is determined by the EPSP
contributions of their respective synapses. We set the ring threshold so that these
neurons re when there is enough dendritic potential (about equal to the sum of the
EPSPs of the three synapses). To show the in
uence of the astrocytic mechanisms
on the ring of neurons, we run simulations of the circuit network for two dierent
conditions: rst in the absence of astrocytic mechanisms, and second in the presence
of astrocytic mechanisms.
The NT Conc. voltage in synapses S
1
{S
3
, S
6
and S
7
is set to 900 mV , while S
4
and S
5
are set to 2.0 V . For the ease of description let us refer to these two type of
synapses as \normal" and \strong". Notice that the contribution of one strong synapse
to the total EPSP of a neuron is more than that of two normal synapses, so that a
neuron with a strong synapse needs only the help of one additional normal synapse to
33
3.1 Simulation Results
generate action potentials. Nevertheless, the strong synapse cannot keep contributing
to the total EPSP due to the triggering of its inactivation mechanism. Conversely,
when the astrocytic uptake mechanism is available, the cleft voltage is bounded by the
astrocytic uptake threshold that inhibits the inactivation mechanism and thus keeps
the synapse enabled.
The simulation in Fig. 3.4 shows the action potential of postsynaptic neurons along
with their respective total EPSPs in the network without astrocytic mechanisms. Neu-
ronN
4
is connected only to two normal synapsesS
1
andS
2
, so it does not have sucient
EPSP to re. While neuron N
5
has the same number of synaptic connections to S
3
and S
4
, it is able to re due to the fact that S
4
is a strong synapse and so provides
Figure 3.4: The total EPSP and the ring of action potentials for Neurons N
4
{N
6
in the
absence of an astrocyte. The top panel shows N
4
, the middle panel N
5
, and the bottom
panel N
6
.
34
3.1 Simulation Results
N
5
with enough EPSP to start ring. However, as shown in the middle panel, the
total EPSP:N
5
decays over time, so that after some spikes the neuron stops ring.
This happens due to the triggering of the inactivation stage in synapse S
4
. Notice that
this mechanism is triggered after a delay giving an opportunity for the synapse to stay
connected by reducing the amount of neurotransmitters.
Neuron N
6
has three synapse connections, where S
5
has a similar condition to S
4
and thus it cannot continue contributing to EPPS.N6. This eventually leaves the neuron
with only two normal synapsesS
6
andS
7
that are not enough to reN
6
. Nevertheless,
N
6
res one action potential more than N
5
. This is because the total EPSP:N
6
is
initially larger than that of N
5
, and so after triggering the inactivation mechanism the
decaying process starts from a higher EPSP voltage.
In steady state, withS
4
andS
5
deactivated, the totalEPSP:N
6
is larger than that of
N
5
, but as the same as that ofN
4
. This corresponds to the contribution ofS
6
andS
7
to
N
6
which is the same contribution asS
1
andS
2
toN
4
, whileN
5
receives a contribution
from only S
3
. Notice that in the absence of an astrocytic uptake mechanism, synapses
S
4
andS
5
are inactivated due to the toxic increase of neurotransmitters in their clefts.
For this experiment we have set the Astro glut control voltage in Stage (3) to 200
mV , so that the astrocytic uptake activation level for this experiment is 850 mV . The
Astro glut release voltage in Stage (5) is set to 200 mV , while the Reuptake, Spread,
and Receptor voltages are set to 470 mV , 500 mV , and 800 mV respectively. The
circuit simulations were conducted using TSMC 18 CMOS technology in SPECTRE
using a power supply of 1.8 V .
The results for the network interacting with the astrocytic mechanisms is illustrated
in Fig. 3.5. These results show that the astrocytic circuits in
uence the ring of neurons
N
4
{N
6
by the modulation of synapses S
1
{S
4
. Notice that without the help of an
astrocyte, neuron N
4
cannot re as illustrated in the previous simulation of Fig. 3.4.
Now, in Fig. 3.5(b), neuron N
4
starts ring after a time delay, that is when suf-
cient gliotransmitters are added into the synapses. The sum of gliotransmitters to
the cleft voltage strengthens the synapses S
1
and S
2
, raising the EPSP:N
4
above
the ring threshold. These contributing signals are illustrated by Cleft:Glio:S
1
and
Cleft:Glio:S
2
in the bottom panel of Fig. 3.5(a), respectively. The cleft voltage of S
1
is shown bycleft:S
1
signal in the top panel, where the normal synapses (S
1
{S
3
,S
6
and
S
7
) have similar cleft signals.
35
3.1 Simulation Results
The AstroCa
2+
control signals are shown in the middle panel of Fig. 3.5(a), which
are the control of transistors in Stage (5) of synapsesS
1
{S
3
. The major contribution of
gliotransmitters from the microdomain is for synapse S
3
as the AstroCa
2+
3 compart-
ment is under the direct in
uence of synapseS
4
which releases more neurotransmitters
than other synapses within the astrocytic microdomain.
In Fig. 3.5(b), the middle panel shows that neuron N
5
continues ring a regular
train of spikes. This is in contrast with the case of Fig. 3.4, where neuron N
5
stops
ring after some time since synapse S
4
is inactivated without the intervention of the
astrocyte. Now, synapse S
4
is controlled by the astrocytic uptake mechanism that
prevents the inactivation process by limiting the cleft voltage of S
4
to 850mV , i.e. the
threshold of the uptake mechanism in Stage (3). Thus the glutamate uptake plays a
fundamental role in the ring of neuron N5.
We also show the cleft signal of synapse S
5
, Cleft.S5, in Fig. 3.5(a). This signal
illustrates the time taken for the synapse to disconnect from the postsynaptic neuron
N
6
. As we previously mentioned, this synapse has an excess of neurotransmitters and
does not have an astrocytic uptake mechanism to regulate its behavior. As shown in
Fig. 3.5(b), after some presynaptic action potentials the synapse will be inactivated
and thus N
6
cannot continue ring.
36
3.1 Simulation Results
(a) Cleft signals and relevant signals for the astrocytic microdomain.
(b) The total EPSP and the ring of action potential of NeuronsN4{N6.
Figure 3.5: In Fig. 3.5(a) the top panel shows the cleft signals for synapsesS
1
,S
4
andS
5
.
The middle panel shows the AstroCa
2+
control signals for synapsesS
1
{S
3
, while the bottom
panel shows the gliotransmitter release from the astrocytic microdomain. The synaptic
cleft of S
4
is controlled by the astrocytic glutamate uptake mechanism. Since synapse S
5
lacks an astrocytic uptake, the Synaptic cleft node rises above the S
4
level. Synapse S
5
is
eventually disconnected from the presynaptic side after a delay. In Fig. 3.5(b), neuron N
4
begins ring due to the contribution of astrocytic gliotransmitters, even though it has only
two normal synapses. NeuronN
5
continues ring by the virtue of the astrocytic glutamate
uptake mechanism. NeuronN
6
is not able to maintain regular ring because the astrocytic
glutamate uptake mechanism is not present on synapse S
5
, so it is eventually disabled.
37
4
Astrocytes on Neuronal Phase
Synchrony in CMOS
This chapter presents hybrid bio-inspired/biomimetic CMOS neuromorphic circuit de-
signs and simulations as part of an initial eort that aims to capture the role of astro-
cytes in phase synchronization of neuronal activity. We present some gross rst{order
circuit designs and capture the main steps involved in the process of an astrocyte in-
ducing synchronization in a small group of neurons. Biological experimental results
have shown that a single astrocyte is capable of inducing simultaneous activation of
neuronal N-methyl-D-aspartate receptors (NMDAR) channels located at the extrasy-
naptic side. The activation of these channels elicits simultaneous slow inward currents
(SICs) on adjacent neurons. The amplitude of SICs is several orders of magnitude
larger compared to synaptic currents. A single SIC event drastically enhances the exci-
tatory postsynaptic potential (EPSP). Because the astrocyte induces SICs with a high
degree of synchronicity, adjacent neurons experience a sudden rise in their membrane
potential, ring synchronously in phase. Phase synchrony holds for a duration of time
proportional to the time constant of the SIC decay. This decay is about sixty times
slower compared to typical synaptic currents. Once the SIC decay has completed, the
neurons go back to their natural phase dierence, inducing desynchronization of their
ring of spikes. The amplitude of SICs is several orders of magnitude larger compared
to synaptic currents. A single SIC event drastically increases the excitatory postsy-
naptic potential (EPSP). Because the astrocyte induces SICs with a high degree of
synchronicity, adjacent neurons experience a sudden rise in their membrane potential,
38
ring synchronously in phase. Phase synchrony holds for a duration of time propor-
tional to the time constant of the SIC decay. This decay is about sixty times slower
compared to typical synaptic currents. Once the SIC decay has completed, the neurons
go back to their natural phase dierence, inducing desynchronization of their ring of
spikes.
We emulate, to a rst order, the ability of slow inward currents (SICs) evoked
by the astrocyte, acting on extrasynaptic NMDAR channels of adjacent neurons, as a
mechanism for phase synchronization. We describe important aspects of the process of
communication between astrocytes and neurons in Sections 1.2 and 2.1, and would like
to refer the reader to these sections for a detailed description of astrocytes.
In this chapter we demonstrate, via simulations, our proposed model for the syn-
chronization of adjacent neurons through astrocyte modulatory activity on extrasynap-
tic NMDAR channels. Simulations of the circuits are performed to demonstrate the
ecacy of the circuits in synchronous ring.
In order to test the SIC mechanism, we perform simulations on circuits to emulate
the indirect communication between two isolated small neuronal networks that are able
to interact with each other, inducing SICs on adjacent synapses on each network by
means of the activity in the astrocytic microdomains. This activity is controlled by
intracellular calcium waves evoked by neuronal stimulation. Astrocytic microdomains
are portions of astrocyte processes (arms) that interact with adjacent neurons. Each
microdomain consists of compartments, where each compartment is able to sense the
modulatory eects of adjacent synapses. The compartments are designed using tran-
sistors as resistive and capacitive components forming a ladder network. We have used
pass transistors for the interaction between microdomains.
4.0.1 Contribution
The main contribution of this chapter is the design of hybrid bio-inspired/biomimetic
neuromorphic circuits that demonstrates some gross rst-order intercellular signaling
between astrocytes and neurons. The simulation experiments conducted in this work
contribute to the analysis of current hypotheses on the role of astrocytes in neuronal
synchronization.
We capture the induction of slow inward currents (SICs) by astrocytes through the
activation of extrasynaptic NMDAR channels located at the postsynaptic membrane
39
4.1 Circuit implementation
of neighboring neurons. Induction of SICs into adjacent dendrites with a high degree
of temporal correlation is a biological event that has been observed in experiments
(30, 31, 95), and is particularly important because of its possible implications in binding
of information in cognitive processes (see Subsection 2.1.4.1) . In Section 2.1.3 we
discuss the biological details of the activation of neuronal NMDAR by astrocytes and
current hypotheses that link astrocytes to cognitive processes.
4.1 Circuit implementation
The section describes each component used in our circuit demonstrating astrocyte-
neuron signaling. We begin by describing the synapse circuit and the rule of ring
in our neuron followed by a discussion of the extrasynaptic NMDAR circuit to be
incorporated into the synapse circuit. We also discuss the astrocytic microdomain
circuit and how the synapse and astrocytic microdomain blocks interact with each
other. The circuits are run at accelerated time. Note that our proposed circuits in
this section represent simulation models that may need more circuit components to
complete the system before being implemented as fabricated chips.
4.1.1 The excitatory synapse circuit
The tripartite synapse circuit used in this simulation test is shown in Fig. 4.1. Stages (1)
and (2) show the pre- and post-synaptic sections separated by the synaptic cleft. The
cleft voltage represents the neurotransmitter concentration in the synaptic cleft. The
low-pass ltering characteristic of Stage (1) provides the cleft node with information
about the average input spike rate. The pull-up transistors allow the cleft to be charged
with a fast rise-time constant during the spike duration. The steady amplitude can be
tuned by the input NT Conc. (neurotransmitter concentration). The pull-down tran-
sistors allow the cleft to be discharged in the absence of a spike or some time after
a spike has occurred. This mimics the drop of neurotransmitters in the cleft by the
reuptake process which can be tuned by the input Reuptake. Stage (2) generates the
EPSP voltage. The red arrow shows the extrasynaptic side used to emulate the NM-
DAR channel contribution. Stage (3) is a mechanism previously published by our group
showing the ability of modulating the neuron excitability by the diused gliotransmit-
40
4.1 Circuit implementation
Reuptake
NT_Conc.
Presynaptic Side
Spread
Receptor
Postsynaptic Side
+
cleft
EPSP
Delay Delay
APs
Extrasynaptic
Side
(3)
AstroCa
2+
Astro_glut_release
Synapse Circuit
(1) (2)
Figure 4.1: The BioRC synapse circuit. The presynaptic side is activated when an action
potential (AP) is received. The cleft node emulates the release of transmitters from the
presynaptic side. Stage (1) behaves like a low pass lter, where a high rate of input spikes
increases the cleft node voltage accordingly. In Stage (2), an EPSP is produced when the
cleft voltage is suciently strong. The red arrow shows the extrasynaptic side used to
emulate the NMDAR channel contribution.
ters added into the cleft and it is considered o/out of the loop for the simulations
described here (5).
For the purpose of this work, since our interest is to show the in
uence of astro-
cytic evoked SICs on extrasynaptic receptors that leads to phase synchronization on
postsynaptic neurons, we assumed no diusion of gliotransmitters into the cleft; as in
biological neurons, glutamate from an astrocyte mainly binds extrasynaptic receptors
of postsynaptic neurons (95). The extrasynaptic in
uence is shown by a red arrow on
the top right-hand side that comes from the extrasynaptic NMDAR circuit (see Fig. 4.4
and transistor X10 in Fig. 4.6). The release of transmitters mimicked by the cleft volt-
age is of an excitatory type and for the purpose of the discussion, by neurotransmitters,
we mean glutamate transmitters. However, based on the application, a dierent inter-
pretation may be given in the case of using a dierent type of excitatory transmitter.
The synapse circuit is a rst-order approximation and does not incorporate detailed
receptor circuitry for the dierent types of transmitters as such receptor circuits would
depend on the mechanisms being modeled.
4.1.2 Neuron block diagram and ring rule
In Fig. 4.2, we show a diagram of the dierent blocks of the neuron circuit, excluding
astrocytic interaction. Each of these blocks has been previously designed by the BioRC
group (7). The inputs AP
1
, AP
2
, ..., AP
n
are action potentials or spikes that arrive at
41
4.1 Circuit implementation
Axon
Hillock
Dendritic
Arbor
Synapse
Synapse
Synapse
AP1
AP2
APn
APout
EPSP
EPSP
EPSP
Total EPSP
Synapse
Figure 4.2: A system view of the neuron components.
the presynaptic terminal of each synapse (the typical shape of an AP is shown in the
simulation results in Section 4.2). The Synapse block corresponds to the circuit shown
in Fig. 4.1. The output of each synapse generates an EPSP voltage. The EPSP of the
dierent synapses is then added at theDendritic arbor block to produce theTotal EPSP
voltage that is input to the axon{hillock block. We show a simplied arbor here. Hsu
has implemented complex arbors (96). When the Total EPSP voltage crosses the axon
hillock threshold voltage from below, the neuron elicits an action potential (AP
out
).
A train of spikes at AP
out
is generated when the Total EPSP crosses the threshold
from below in successive occasions. If presynaptic spikes (AP
1
, AP
2
, ..., AP
n
) are in
phase, such output train of spikes would follow the input phase. When the arrival of
presynaptic spikes is out of phase, then the neuron may enter an unreliable condition,
since the amplitude of the Total EPSP would not necessarily be enough to cross the
axon hillock threshold to cause the ring of spikes. When the phase dierence between
input spikes is small enough to provide enough Total EPSP for the neuron to re, a
phase shift may occur atAP
out
. Our neuron in the simulation test we perform is set to
re when the Total EPSP is equivalent to the sum of the EPSP voltages corresponding
to three synapses that are in phase. Our group has also designed neurons that re
based on the rate of change of the membrane potential, so that the threshold varies
inversely with the rate of change (96).
Two neurons with the same ring rate are considered synchronized if their APs
happen within 10% of phase dierence. Considering 360 degrees of phase angle for
each cycle starting with the rising edge of AP, we consider two series of APs phase
synchronized if their phase misalignment is less than 36 degrees, i.e., maximum 10%
42
4.1 Circuit implementation
360 degree = Firing period
Synchronized bound ≤ 36 deg ≤ 10% of firing period
Synchronized Firing
Phase misalignment
Non-synchronized Firing
Phase misalignment
Figure 4.3: The concept of phase synchronization.
misalignment (see Fig. 4.3).
4.1.3 Extrasynaptic NMDA Block and the activation of SICs
Slow inward currents are initiated upon activation of NMDAR channels. The block
diagram depicted in Fig. 4.4 shows the connections between the synapse, the Extrasy-
naptic NMDA Block, and the astrocyte. The focus of the following description is on
the Extrasynaptic NMDA Block (green-shaded box). This block has two outputs that
in coordination enable the neuron to have a sudden raise of amplitude in the neu-
ron Total EPSP. The Total EPSP is a signal that represents the summation of each
EPSP contributed by individual synapses, that is, the output of the dendritic arbor
summation.
The Extrasynaptic NMDA Block receives inputs from the presynaptic neuron and
the astrocyte. These inputs are the presynaptic spikes (AP1) and the calcium signal
from the astrocytic microdomain (Astrocyte glioTs (Astro Ca2+)). The calcium signal
is currently representing the release of gliotransmitters. When these two signals are
active, that is, the presynaptic neuron res spikes (AP1) and the astrocyte elicits a
calcium signal beyond a threshold, the rst stage in the diagram of the NMDA block
becomes active. This models the opening of the NMDA channel and the output of the
rst stage is a pulse of short time duration. In the following paragraphs, let us provide
the details of the generation and the changes in the neuron, in the assumption the
channel is open, and SIC activity occurs, that is, the SIC and Control Circuit stages
become active.
43
4.1 Circuit implementation
We focus on the two outputs of the Extrasynaptic NMDA Block. The output that
connects to theTotalEPSP node only serves as a reset signal so that the neuron updates
its state according to the contribution of the SIC event. This output connection is
enabled by two pathways that are controlled by switches SW1 and SW2. The dynamic
activities of these switches will coordinate the time duration at which the neuron senses
the SIC event. Switch SW1 is enabled for a short time duration, thus sending the
Total EPSP voltage to 0.0 V. Switch SW1 is disconnected after the duration of the
pulse, which enables the voltage at the Total EPSP to receive the incoming activity of
synapses from the dendritic arbor. The same pulse that enables and disables SW1 also
forms the SIC event to be generated at the Extrasynaptic side (red arrow). The pulse is
characterized by a fast rise and fall time constant, while the output of the SIC stage has
a fast rise time but very slow decay to approximate the biological response. The second
pathway in the control circuit is enabled when switch SW2 closes, and becomes active
for a short time duration. Switch SW2 is activated when the SIC event has vanished,
NMDAR
(AMPAR; Mg
2+
BR Section)
Extrasynaptic
Side
Astrocyte glioTs
(Astro_Ca2+)

SIC Stage
(shaping)
Axon
Hillock
Dendritic
Arbor
Synapse Synapse
AP3 AP2
APout
EPSP EPSP
EPSP
Astrocyte
Microdomain
Presynaptic
Side
Postsynaptic
Side
AP1
Extrasynaptic NMDA Block
S1
(Cleft)
Total_EPSP

Delay
Control
Circuit
SW1
SW2
Synapse
Figure 4.4: A system view: the extrasynaptic NMDAR channel for the induction of SICs
connected to the synapse and astrocyte.
44
4.1 Circuit implementation
that is, the voltage signal has decreased below 50% of its amplitude. Activation of
SW2 sends the Total EPSP voltage to 0:0 V . Once SW2 becomes inactive, that is,
the SIC event reaches its minimum voltage, the neuron output (AP
out
) continues its
normal operation; in the absence of a SIC event, receiving and integrating incoming
information from its synapses.
The input block represents the NMDAR activation section which includes the mag-
nesium block removal (Mg
2+
BR). The SIC stage is used for shaping the decay time
constant of the SIC signal. While these blocks perform biomimetic functions, the Con-
trol circuit is a bio-inspired circuit used as a reset mechanism that acts at the beginning
and at the end of SIC event, sensing the SIC activity and in the absence of a SIC event
resetting the neuron to its natural ring phase of action potentials; its role will be dis-
cussed in detail in Subsection 4.1.5. This reset mechanism is not biomimetic, and more
modeling of the astrocyte physiology will be required to balance the SICs in the neurons
so they are indeed synchronized in a biomimetic manner. This biological mechanism is
under active investigation; however enough is understood to mimic biology more closely
in the future when we generate astrocytic calcium waves in our circuits.
4.1.4 A system view of the Network used for Simulation Experiments
Our simulation experiments are based on astrocyte compartments and neurons con-
nected in a small network, with up to nine neurons and two astrocytic microdomains.
We show a simplied system view in Fig. 4.5 of the circuit conguration we simulate. It
combines the blocks in Fig. 4.4 and Fig. 4.2 along with the astrocytic microdomains in
Fig. 4.7. We have connected the Extrasynaptic NMDAR block to only one postsynap-
tic neuron on each network. This block senses activity from the incoming presynaptic
spikes and the astrocytic microdomain. The astrocytic microdomains individually sense
information from their respective neurons and can interact with each other.
TheExtrasynaptic NMDAR block is activated according to the strength of the signal
(Astrocyte glioTs) and in the presence of presynaptic stimulation. The activation of
the block induces a signal (red arrow) into the postsynaptic side that emulates the
SIC event. Because of the interaction of the two microdomains, SICs will be induced
simultaneously in both networks of neurons causing the neurons to be synchronized as
they both cross the activation threshold simultaneously, which leads to the generation
of action potentials (AP
out
). The signal that is output from the Extrasynaptic NMDAR
45
4.1 Circuit implementation
Axon
Hillock
Dendritic
Arbor
AP1_N1
AP2_N1
APout_N1
EPSPs
Total_EPSP_N1
Presynaptic
Side
Postsynaptic
Side
Presynaptic
Side
Postsynaptic
Side
Extrasynaptic
NMDA
Astrocyte
Microdomain_1
Astrocyte
glioTs_M1

Extrasynaptic_side
S1 S2
Total_EPSP_N2
Extrasynaptic
NMDA
Astrocyte
Microdomain_2
Astrocyte
glioTs_M2

Extrasynaptic_side
S4 S3
Axon
Hillock
Dendritic
Arbor
AP3_N2
AP4_N2
APout_N2
EPSPs
Presynaptic
Side
Postsynaptic
Side
Presynaptic
Side
Postsynaptic
Side
Fig.4.7
Figure 4.5: A system view diagram showing the main circuit blocks used for the neurons
and astrocyte.
block into the output of the Dendritic arbor is used to reset the Total EPSP as it was
already above the axon hillock threshold, and the neuron was spiking. This reset is the
role of the control circuit block shown in Fig. 4.4. It is part of our current research
to remove this control circuit from our nal implementation, and replace it with a
biomimetic redesign of the neurons so that they become sensitive not only to the Total
EPSP crossing the threshold but also to the amplitude of the total EPSP itself as
otherwise it would not be possible to account for the contribution of SICs.
4.1.5 Extrasynaptic NMDAR channel circuit for SIC generation
This subsection presents and discusses the NMDAR channel circuit used for extrasy-
naptic SIC generation in the neuron. Figure 4.6 shows the extrasynaptic NMDAR
channel (a) along with a control circuit (b) designed for the phase synchrony of adja-
cent neurons upon initiation of a SIC event. The bottom diagram corresponds to the
Extrasynaptic NMDA Block already discussed. Dashed lines are used to identify the
circuit structure for each block. The extrasynaptic NMDAR in Fig. 4.6(a) is divided
46
4.1 Circuit implementation
into three main sections: the NMDA activation in subcircuit (4), the Magnesium block
removal in subcircuit (5), and the Induced SIC in subcircuit (6). Subcircuits (4) and
(5) are modied versions of previously published circuits to include the role of SICs
(11).
The role of each subcircuit will now be discussed. Subcircuit (4) roughly plays the
role of AMPAR channels. The input section is activated to remove the magnesium
block when coincidence detection occurs between the arrival of presynaptic spikes and
the transmitters released by the astrocyte. We use the input Presynaptic Spikes for
the activation of the AMPAR channel. The AMPAR channel is usually needed to
remove the magnesium NMDAR block. As there is no clear evidence what triggers
the AMPAR activation, we follow the assumption that presynaptic spike stimulation is
used as the coincidental stimulus that triggers the receptor activation (31). The basis

SIC
cntrl

AstroCa
2+
Mg
2+
Delay
Vbias

Extrasynaptic
Receptor
(ERC) SIC
Presynaptic
Spikes
NMDA Activation
Section
Extrasynaptic
Side

C D
D
C
Vref
Total EPSP
E
LPF

Receptor
Deactivation

Magnesium Block
Removal Section
Induced SIC
Section
ERC
LPF
E
Low Pass Filter (LPF)
SW1 SW2
NMDAR
(AMPAR; Mg
2+
BR Section)
Extrasynaptic
Side
Astrocyte glioTs
(Astro_Ca2+)

AP1
Extrasynaptic NMDA Block

Delay
Control
Circuit
SW1
SW2
SIC Stage
(shaping)
Total EPSP
X1
X2
X3 X4
X5
X6
X7
X8
X9
X10
X11 X12
X13
X14
X15
X16
(a) (b)
Figure 4.6: The circuit of extrasynaptic NMDAR in (a), consists of sections (4), (5), and
(6) with a compact control circuit shown in (b).
47
4.1 Circuit implementation
for this assumption is Wade's model of neural-astrocytic interaction (31).
The voltage ReceptorDeactivation in Subcircuit (4) can be used to control the
time duration at which the receptor remains active (11). It is a xed bias voltage
of 350 mV that controls the resistance of its transistor. Subcircuit (5) is designed
so that the removal of the magnesium block occurs only if there are three coincidental
inputs (Astro Ca
2+
, NMDA activation, andSIC cntrl) for the activation of transistors
X1, X2, and X5 simultaneously. This results in the production of a SIC event at
the extrasynaptic side (in X10). The activation of X1 is controlled by the calcium
level (AstroCa
2+
) generated at the astrocyte compartment. The AstroCa
2+
signal
represents the astrocyte's contribution that triggers the SIC event. The activation
of X2 depends on the AMPAR activation, that is when there is presynaptic spike
stimulation at subcircuit (4). Transistor X5 is controlled by the input SIC cntrl, a
global periodic single pulse that emulates the time activity of SIC events. The pulse
width of SIC cntrl signal determines the minimum time window over which the SIC
amplitude at the extrasynaptic receptor node (ERC) remains at its maximum voltage.
Astrocytes trigger SIC activity by a single glutamate release, correlated with cal-
cium oscillations (97). The control circuit presented here is bio-inspired, since it is not
purely autonomous. The mechanism disables the current EPSP to reinitiate EPSP at
the exact time that the EPSP is reinitiated at other neurons, inducing synchronous
ring. As future work, we plan to extend the astrocytic microdomain circuit (Fig. 2 in
(5)) to generate dierent forms of calcium oscillations (39). Thus, the SIC cntrl input is
an artice that will not be necessary once the calcium wave detection circuit is included
and will be eventually produced from the astrocytic calcium oscillations. Subcircuits
(4) and (5) are modied versions of previously published circuits in our group (11),
where here we incorporate the role of the astrocyte in the activation of NMDAR for
the production of SIC events.
The control circuit in Fig. 4.6(b) is designed to discharge the Total EPSP voltage
at the axon hillock circuit (98) through either transistors X11 or X12, supporting the
timing activity of the synchronization and desynchronization phases that happen at
the beginning and at the end of SIC event occurrence (see Fig. 4.2 for the Total
EPSP node connection to the neuron). We plan to replace the control circuit with a
more-biomimetic mechanism in the future.
48
4.1 Circuit implementation
Upon activation of the NMDA channel, when there is coincidental activity, a short
time pulse impinges node A at section (5) that activates transistor X11. During this
short activation of transistor X11, the Total EPSP node resets the ring activity of
action potentials. A SIC event is evoked at node ERC in section (6) to be further
processed by the postsynaptic stage of the synapse through the extrasynaptic side (red
arrow on the top right hand side in Fig. 4.1). The deactivation of X11 after the short
time pulse causes the neuron to initiate its ring again by the rise of the Total EPSP
which is in
uenced by the SIC contribution.
Phase synchronization happens since neurons with adjacent synapses receive SIC
events simultaneously, produced by their respective extrasynaptic receptors. Such
events are strong enough to drastically increase the Total EPSP of each neuron. Upon
removing the SIC event, neurons are desynchronized through transistor X12 which is
activated to reset the Total EPSP node and so stops the ring of the corresponding
neurons for a short time. Upon deactivation of X12, i.e. in the absence of SIC con-
tribution to the Total EPSP, the neurons return back to their initial conditions where
they re out of phase synchrony following the phase dierence of their presynaptic
neurons. We emphasize that phase synchrony happens only if the Total EPSP of both
neurons crosses the axon hillock threshold nearly simultaneously, i.e. when a SIC event
is produced on adjacent synapses.
In Fig.4.6(a), the SIC cntrl input contributes to the magnesium block removal by
pulling down node B when coincidental input activity occurs. In other words, the
current mirror in subcircuit (5) is properly biased if X1 and X2 are activated, thus en-
abling node A to rise when a single pulse SIC cntrl is applied. The voltageMg
2+
Delay
emulates the magnesium block removal delay, i.e. the time (at node B) that takes to
deactivate X8 in subcircuit (6) after the SIC cntrl arrival. In our simulation it is a bias
voltage of 450 mV . It contributes to increase the time width at which the ERC node
remains at its maximum voltage. When X8 is deactivated, the ERC node decays with
a slow time constant to 0.0 V, which emulates the SIC decay. This decay is controlled
by the resistance of X7 and the capacitance of X9 along with the diusion capacitances
in the node. The small waveform diagram in Fig.4.6(b) shows the ERC signal at the
input of X10.
When node A is activated, the Total EPSP discharges down to 0.0 V through X11
at the control circuit in Fig.4.6(b). Since node A sees a pulse of short duration, X11
49
4.1 Circuit implementation
is deactivated immediately after A returns to 0.0 V. That is when SICs are produced
simultaneously into adjacent synapses of postsynaptic neurons through X10, causing
the Total EPSP of each neuron to rise simultaneously, and thus synchronizing in phase
the postsynaptic neurons. Therfore, the Total EPSP amplitude is increased by the
increase of the EPSP for the synapse that receives the induced SIC event.
After the ERC node drops to about 50% of its voltage, the nodes C and D become
high and low, respectively. This activates the transmission gate (X15, X16), transfer-
ring the low pass lter (LPF) voltage to the gate of X12. Transistors X13 and X14
respectively provide the resistance and capacitance of the low pass lter. Notice from
the waveform diagram shown in Fig.4.6(b) that the LPF voltage activates X12 for a
short time. The activation of X12 indicates that the SIC event has passed and thus
neurons are no more synchronized in phase. The Total EPSP is discharged, so that
when X12 is deactivated the postsynaptic neurons return to the desynchronized state.
Transistor X12 is deactivated through the pull down path of the inverter connected
at node D. The choice to use the ERC node when it drops to 50% of its voltage to
desynchronize the neurons is not a biomimetic process and it is mainly inspired by the
biological events reported by experiments. A more biomimetic design would require
the desynchronization to wait until the signal ERC has reached its minimum voltage
to emulate the absence of the SIC event. Whether neurons are desynchronized in the
absence of a SIC event is not still clear based on biological experiments.
Once X12 is deactivated, the Total EPSP on each neuron is enabled to rise again.
The phase dierence between the neurons in the desyncronization state depends on the
time at which each neuron crosses the axon hillock threshold. The maximum phase
dierence is proportional to the phase dierence of the presynaptic spikes. When
neurons are not synchronized in phase, the Total EPSP is decreased, since it no longer
receives the contribution of SIC event.
The circuit shown in Fig. 4.6 has a total active power of 148 W. In the absence
of an input stimulus, the circuit has no active path between V
dd
and Gnd terminals.
This is only a rst estimation of the circuit and as the circuit evolves, a bio-realistic
model of calcium wave activity in the astrocyte should be designed and taken into
consideration for a more accurate measurement. The inputs Receptor Deactivation and
Mg
2+
Delay have bias voltages around the threshold of the transistor. Transistors X1
and X2 are enabled during the time their respective input signals are active. The
50
4.1 Circuit implementation
SIC cntrl signal should be provided by a circuit that emulates the crossing of the
astrocyte calcium wave threshold. A careful design should be done to capture calcium
waves along with an activation threshold that is aimed to determine the activity of
slow inward currents. Since SIC generation is expected to be active only under certain
conditions, which depends on the intensity of glutamate release according to activity of
calcium waves, we expect to have power savings. In the future an optimization analysis
that considers power expenditures will be performed after the design of a bio-realistic
model of astrocyte calcium wave activity is incorporated.
4.1.6 The astrocytic microdomain circuit
As previously mentioned, the activation of the NMDAR extrasynaptic receptor re-
quires sucient calcium-level excitation (AstroCa
2+
) at the astrocytic compartment
associated with the synapse. In Fig. 4.7 we show two astrocytic microdomain circuits
(orange boxes) able to interact with each other. Each microdomain consists of several
compartments and is a distributed resistive (pass transistor) network that takes inputs
from the voltages representing synaptic cleft neurotransmitter concentrations of dier-
ent synapse circuits. The cleft voltage from each synapse (see Fig.4.1) is fed into a
non-inverting delay circuit (D) whose output voltage representing released neurotrans-
mitters is summed with delayed cleft voltages from other synapses (5). This emulates
the time taken by the astrocyte to induce calcium waves at the astrocytic compart-
ments due to the accumulation of neurotransmitters. In the next section we show a
simulation test where M1 and M2 trigger SIC events on adjacent synapses according to
the neuronal activity sensed by M1. We also show how the production of SIC events by
the astrocytic calcium waves leads to phase synchronization on postsynaptic neurons.
The rise of potential at the Ci
MX
nodes in the resistive network emulates the
increase and spread of calcium across the astrocyte (5). In turn, these astrocytic outputs
are able to in
uence the activation of the NMDA extrasynaptic receptor circuit when
connected to the input AstroCa
2+
in Fig. 4.6.
A PMOS pass transistor between the outputs of each microdomain allows them to
interact with each other, so that neuronal activity from both group of synapses can use
the microdomains as a media to establish communication. For such communication
to occur, any or both microdomain 1 (M1) and microdomain 2 (M2) need to sense a
strong stimulation from the cleft nodes of their respective synapses.
51
4.1 Circuit implementation
V
b
V
b
V
b
V
b
V
b
C1
M1
C2
M1
C3
M1
C4
M1
C5
M1
V
b
V
b
V
b
V
b
V
b
C1
M2
C2
M2
C3
M2
C4
M2
C5
M2
V
ref
V
ref
V
ref
V
ref
V
ref
Synapses Group 1
+
D
+
D
+
D
+
D
+ +
D D
+
D
+
D
+
D
+
D
+ +
D D
Synapses Group 2
Microdomain_M1
Microdomain_M2
Figure 4.7: Two astrocytic microdomains (M1, M2) connected by pass transistors al-
lowing interaction between synapses in group 1 and group 2. The nodes Ci
MX
represent
the astrocytic compartments. The voltages V
b
and V
ref
are bias voltages to control the
resistive paths of the transistors.
By tuning the widths and the lengths of transistor gates we can exploit the transis-
tors' resistive and capacitive characteristics. Transistor size optimization to make our
circuits more robust, along with circuit performance measurements including power
consumption, are part of our future plans. Currently the sizes we have used in our
design are in the range of 400 nm to 4 m width and length. Transistors X9 and X14
behave as capacitances in Fig. 4.1.5, with sizes from 5 m up to 8 m.
The bias voltagesV
b
andV
ref
at the microdomain circuit in Fig. 4.7 were set to 1V
and -1.8V , respectively. These voltages have impact on the resistances of the transistors
they control and also limit the interaction between any two nodes in the microdomain.
The resistance between the microdomains controlled by transistors connected to V
ref
is small so that both microdomains can have enough in
uence on each other. The
nodes in the microdomains are in
uenced by their respective added synaptic clefts,
their neighbor synapses added at the adjacent nodes from their own microdomain or
the microdomains with which they interact.
52
4.2 Simulation results
4.2 Simulation results
4.2.1 Network conguration for our simulation experiments
Our simulation experiments illustrate the synchronization of unconnected neurons via
astrocytic involvement, and the result of the simulation on a down-stream neuron. The
network depicted in Fig. 4.8 illustrates the conguration we used for this simulation
test. It shows the neuro-astrocyte interactions of two small networks of silicon neurons,
where synapses S1{S6 of Network 1 are spanned by the astrocytic microdomain M1,
and synapses S7{S12 of Network 2 are spanned by M2. The astrocytic microdomains
sense neurotransmitters released from their corresponding networks and feed back glio-
transmitters, through the activity of calcium waves at each related compartment, to
the extrasynaptic NMDA circuits corresponding to the synapses S3, S4, S9, and S10.
Both microdomains are capable of interacting with each other, symbolized by the thick
blue bidirectional arrow.
In this simulation test we have set the frequency of spikes of the presynaptic neurons
in Network 2 lower than that in Network 1, so that we can show the capability of
Network 1 to support the induction of SIC events in Network 2 by means of increasing
the calcium waves in M2. In other words, M2 alone is not able to produce a substantial
increase in the amplitude of calcium waves as it does not receive sucient stimulation
from its synapses.
N1
M1 M2
NTs
NTs
SICs SICs
N3
N2 N4
N5 N7
N6 N8
N9
Network 1 Network 2
S1
S2
S3
S4
S5
S6
S7
S8
S9
S10
S11
S12
S13
S14
S15
S16
NTs
NTs
Figure 4.8: Two small neural networks interacting with astrocyte microdomains M1
and M2. The green (dashed) arrows represent the release of neurotransmitters (NTs) from
synaptic clefts to the astrocyte microdomain. The blue (solid) arrows labeled SICs illustrate
glutamate binding the extrasynaptic receptors to produce SICs on nearby synapses.
53
4.2 Simulation results
Presynaptic neurons N1 and N2 at Network 1 have a higher frequency of spikes
which increases the release of neurotransmitters at the synaptic clefts of S1{S6, sensed
by microdomain M1, strengthening calcium waves at the compartments of M1 by means
of increasing the amplitude at theCi
M1
nodes. In the microdomain M2, calcium waves
at compartments of M2, besides receiving the small in
uence from the weak release
of transmitters from synapses S7{S12 of Network 2, also see the contribution of the
calcium waves propagated from microdomain M1.
We have connected extrasynaptic NMDA circuits to each adjacent synapse S3{S4
and S9{S10 in Network 1 and Network 2, respectively. The induction of SIC events
into these synapses is controlled by compartments C3
Mx
andC4
Mx
of their respective
microdomain circuits. These compartment outputs act on the input AstroCa
2+
of
the extrasynaptic NMDA circuit, activating transistor X1 when the amplitude of the
calcium wave signal is large enough (see Fig. 4.6).
Calcium waves at nodes C3
M1
andC4
M1
are strong enough to soon propagate the
signal to the compartments C3
M2
and C4
M2
of microdomain M2 through the related
PMOS pass transistors (see Fig. 4.7). This causes the activation of the extrasynaptic
NMDAR circuits of S9 and S10 in Network 2, inducing synchronized SIC events. In
other words, each adjacent synapse (S3, S4, S9, and S10) receives SIC events triggered
by the calcium wave induced at its respective astrocytic compartment.
As the simulations will show in Subsection 4.2.2, the high degree of correlation of
SIC events at the adjacent synapses of dierent postsynaptic neurons causes phase
synchronization in the activity of neurons N3, N4, N7 and N8 on each network. We
connected neuron N9 to postsynaptic neurons of Network 2 to show the role of neuronal
excitability when postsynaptic neurons re in phase synchrony. The latter will be
discussed in Subsection 4.2.4.
4.2.2 Simulation results for Network 1 and Network 2
Results for the phase of the ring of postsynaptic neurons N3{N4 and N7{N8, corre-
sponding to Network 1 and Network 2 are shown in Fig. 4.9. We set the ring threshold
such that these neurons re in the presence of enough dendritic potential (about equal
to the sum of the EPSPs of three synapses). Postsynaptic neurons N3{N4 and N7{N8
can initially re since they each receive the contribution of the coincident EPSPs of
three synapses (see Fig. 4.8 and Fig. 4.9). This is shown in section (1) in Fig. 4.9.
54
4.2 Simulation results
The frequency of postsynaptic spikes is the same as that of the presynaptic neurons.
Thus, in the absence of a SIC event, the asynchronous phase dierences of action
Desynchronized Phase (3)
Synchronized
Phase (2)
EPSP increases due SIC contribtion
(1)
1.0
0.5
.75
.25
0
V(V) 2.0
1.0
1.5
0.5
0
V(V)
2.0
1.0
1.5
0.5
0
V(V)
2.0
1.0
1.5
0.5
0
V(V)
time (µs)
2.0 2.1 2.2 2.3 2.4
time (µs)
5.0 5.1 5.2 5.3 5.4
2.0 1.0 0 3.0 4.0 5.0 6.0 7.0
EPSP .N7 EPSP .N8
AP .N7
AP .N8 AP .N8
AP .N7
time (µs)
(a) Simulation results for N7 and N8 in network 2.
Desynchronized Phase (3)
Synchronized
Phase (2)
EPSP increases due SIC contribtion
(1)
EPSP .N3 EPSP .N4
AP .N3
AP .N4
AP .N3
AP .N4
time (µs)
2.1 2.2 2.3 2.4
time (µs)
5.0 5.1 5.2 5.3 5.4
1.0
0.5
.75
.25
0
V(V) 2.0
1.0
1.5
0.5
0
V(V)
1.0
1.5
0.5
0
V(V)
2.0
2.0 1.0 0 3.0 4.0 5.0 6.0 7.0
time (µs)
2.0
1.0
1.5
0.5
0
V(V)
2.0
(b) Simulation results for N3 and N4 in network 1.
Figure 4.9: The top panels in (a) and (b) show the Total EPSPs for neurons N3{N4 and
N7{N8. The middle panels show the action potentials (APs) of each neuron. The bottom
panels show a zoom-in of the APs for two dierent regions. This simulation was conducted
forV
bias
= 700mV ,V
ref
=1:8V andV
b
= 1V . Other circuit parameters can be obtained
from the author.
55
4.2 Simulation results
potentials on each pair of postsynaptic neurons, N3{N4 and N7{N8, are respectively
proportional to the phase dierence of their corresponding presynaptic neurons. The
circuit simulations were conducted in TSMC 180 nm technology using a power supply
of 1:8 V . The input frequencies were set at 8:3 MHz for Network 1 and the higher
frequency is 33:3 MHz for Network 2, respectively.
In order to synchronize the ring of neurons in the presence of a SIC event, the
NMDA block removal section of each adjacent synapse in both networks must be ac-
tivated via meeting the necessary conditions discussed in Subsection 4.1.5, leading to
the activation of X11 of each synapse (refer to Fig.4.6). Upon triggering X11, the Total
EPSP on each of the postsynaptic neurons, i.e. EPSP.N3, EPSP.N4, EPSP.N7 and
EPSP.N8, is initially discharged to 0:0V (at time 1.25s in Fig. 4.9; the end of section
(1) of the simulation trace). This causes N3{N4 and N7{N8 to stop ring in the time
interval corresponding to the pulse width at node A.
SICs are simultaneously produced (at 1.6s in Fig. 4.9; the beginning of simulation
trace section (2)) on the extrasynaptic side of synapses S3{S4 and S9{S10, i.e. when
the NMDA block removal is activated. The simultaneous raise of the SIC event allows
the neurons to cross their activation thresholds at the same time by the increase of
the Total EPSP, enabling N3{N4 and N7{N8 to begin ring synchronously with each
other. While the SIC event is active, neurons N3{N4 and N7{N8 remain synchronized
in phase. Note that the increase of the EPSP amplitude in the synchronized phase
(section (2) in Fig. 4.9) is due to the contribution of SIC amplitude (the top panels in
Fig. 4.9(a) and 4.9(b)).
Neurons N3{N4 and N7{N8 remain synchronized while the SIC amplitude is high
enough not to trigger X12 by the E path in Fig. 4.6. After theSIC event has passed, X12
is activated and the neurons arrive at a desynchronization phase. Thus, X12 in each of
these neurons simultaneously discharges the corresponding Total EPSPs to 0.0 V in a
short time (at 2.8 s in Fig. 4.9; the end of section (2)). Upon passing this time, i.e.
when X12 is deactivated, the Total EPSPs of N3{N4 and N7{N8 are charged to new
states in which the ring of neurons is desynchronized in phase (at 3.6s in Fig. 4.9; the
beginning of Section (3)). The phase dierence depends on the time at which the Total
EPSP of each neuron crosses its axon hillock threshold. In the desynchronized phase
(section (3) in Fig. 4.9), the Total EPSP receives only the contribution of synapses
connected to each postsynaptic neuron and lacks the SIC event, so the phase dierence
56
4.2 Simulation results
between postsynaptic neurons on each network is dominated by the phase dierence of
their corresponding presynaptic neurons.
4.2.3 Microdomain interactions increase Ca
2+
levels
The calcium wave signals at compartment nodes C3
M2
and C4
M2
are shown in Fig.
4.10. The top panel shows the results at these compartments when microdomain M2 is
not in
uenced by microdomain M1, i.e. M2 is disconnected from M1, while the bottom
panel shows the Ca
2+
waves when both microdomains (M1, M2) interact with each
other.
The peak value of the calcium signal at C3
M2
(black dashed) is smaller compared
with that of C4
M2
(red solid) in both cases. The dierence lies in the in
uence of the
synapses sensed by each compartment. The astrocytic compartment C4
M2
is directly
in
uenced by the release of transmitters from the synapses that belong to the same
presynaptic neuron, i.e. synapses S10 and S11 corresponding to N6. Presynaptic neuron
N6 induces its spiking phase to both synapses, and so the zero phase dierence between
S10 and S11 causes an increase in the peak value of C4
M2
. The compartment C3
M2
,
225
175
200
150
125
V(mV)
875
825
850
800
775
V(mV)
750
725
5.0 5.25 5.5 5.75
time (µs)
Ca^{2+}_C3
M2b

Ca^{2+}_C3
M2a

Ca^{2+}_C4
M2a

Ca^{2+}_C4
M2b

Figure 4.10: Calcium wave signals. The top panel shows the calcium waves due to the
activity on Network 2. The bottom panel shows the calcium waves when both astrocytic
microdomains interact with each other and so are in
uenced by the activity of both net-
works.
57
4.2 Simulation results
on the other hand, receives the direct in
uence from transmitters released by synapses
connected to dierent presynaptic neurons, i.e. synapses S9 and S10 corresponding to
N5 and N6, respectively (see Fig. 4.8). Presynaptic neurons elicit action potentials with
dierent phases, causing the cleft nodes at these synapses to be shifted away from each
other. Due to the phase shifting, when the cleft nodes of S9 and S10 are added at the
stage of the microdomain circuit (see Fig. 4.7), a shorter peak is produced compared
to that of C4
M2
.
Without the help of microdomain M1, the Ca
2+
waves at C3
M2
and C4
M2
would
not be suciently strong to trigger the induction of SIC events on Network 2. The peak
values of Ca
2+
waves at C3
M2
and C4
M2
signicantly increase due to the activation
of microdomain M1 through the release of neurotransmitters from the synapses on
Network 1 (the bottom panel Fig. 4.10). The strengths of the synapses of Network
1 is due to the higher input spiking frequency of their presynaptic neurons. Since
the compartments C3
M1
and C4
M1
interact with C3
M2
and C4
M2
, this strength is
transferred to M2 as well, increasing the peak value of calcium waves at compartment
nodes of M2.
4.2.4 Eect of variations of SIC time constant
In Fig. 4.11 we show the time window of synchronized activity as a function of V
bias
.
The input V
bias
controls the SIC time constant measured at node ERC (see Fig. 4.6).
This is shown in the upper waveform, where SIC events are shown for dierent values
of V
bias
.
The NMOS transistor in the SIC stage connected to V
bias
increases its resistance
with the decrease of V
bias
causing the RC time constant at node ERC to increase (see
Fig. 4.6). The increase in the SIC time constant by the decrease of V
bias
widens the
time window in which the synchronized action potentials from postsynaptic neurons
occur.
In Fig. 4.12 dierent spiking time windows of synchronized activity for dierent
values ofV
bias
are shown, whereV
bias
is the gate input to transistor X7 in Fig. 4.6. Note
the quality of synchronization at the rst spike of the window is dierent for dierent
values ofV
bias
. We conjecture the variations in the voltage of power supply/ground lines
and/or nonlinear eects of transistors cause this mismatch. This could be investigated
in future research.
58
4.2 Simulation results
0
100
200
300
400
500
600
700
800
0.8 1 1.2 1.4 1.6
Duration of synchronized
spikes (ns)
Vbias at the NMDA SIC circuit (mV)
SIC_event (V)
time (µs)
Vbias = 800 mV
Vbias = 900 mV
Vbias = 1.2 V
Vbias = 1.6 V
Vbias
1.6V
Vbias
800 mV
Figure 4.11: Changes in the active time of the synchronization window versus changes
of V
bias
measured on Network 2.
V
bias
= 900 mV
V
bias
= 800 mV
V
bias
= 700 mV
V
bias
= 600 mV
V
bias
= 1.6 V
V
bias
= 1.4 V
V
bias
= 1.2 V
V
bias
= 1.1 V
V
bias
= 1.0 V
V(V)
2.0
0
V(V) 2.0
0
V(V)
2.0
0
V(V) 2.0
0
V(V)
2.0
0
V(V) 2.0
0
V(V)
2.0
0
V(V) 2.0
0
V(V) 2.0
0
time (µs)
1.5 1.75 2.0 2.25 2.5 2.75 0.4 1.6 1.8 2.0 2.2
time (µs)
Figure 4.12: Synchronization window for action potentials of postsynaptic neurons N7
(red-solid) and N8 (black-dashed) of Network 2 versus variations of V
bias
.
59
4.2 Simulation results
4.2.5 Contribution of synchronization to neuron excitability
4.2.5.1 Description of the simulation test
In order to test the contribution of synchronization to neuron excitability, we have
connected neuron N9 to the postsynaptic neurons of Network 2, i.e. N7 and N8.
The diagram in Fig. 4.13 shows the synapses corresponding to each of these neurons.
Synapses S13 and S14 are connected to N7, while synapses S15 and S16 belong to
N8. The panels (black line boxes) show a sketch to illustrate the excitability of N9
by the Total EPSP (EPSP.N9) produced by the addition of EPSPs from N7 and N8
(EPSP.N9N7 and EPSP.N9N8).
On the top panel, N7 and N8 elicit action potentials out of phase synchrony, this
causes the added EPSP.N9 not to cross the axon hillock threshold and so does not induce
spikes at N9. On the bottom panel, action potentials from N7 and N8 arrive at the
same time, so the phase dierence is zero. This can be seen through the EPSP.N9N7
and EPSP.N9N8. A zero time{lag dierence generates a larger added amplitude in
EPSP.N9, contributing to the neuron excitability and making N9 re.
N7
N8
N9
Neuron
Threshold
+
EPSP .N9N7
EPSP .N9N8
EPSP .N9
EPSP .N9
Neuron
Threshold
+
EPSP .N9N7
EPSP .N9N8
EPSP .N9
EPSP .N9
EPSP out of
Phase decreases
neuron’s ability
to fire
EPSP in Phase
increases
neuron’s ability
to fire
S13
S14
S15
S16
Figure 4.13: A cartoon diagram that shows the eect of synchronization on neuron N9
in Network 2 according to the arrival phase of spikes from neuron N7 and N8.
60
4.2 Simulation results
4.2.5.2 Simulation results: contribution of synchronization to neuron ex-
citability
The simulation results in Fig. 4.14 show the ring activity of neuron N9 according to
the phase dierence of N7 and N8. The top panel shows the cleft signals for synapses
S13 and S15. Synaptic clefts for S14 and S16 are not shown in the waveform as they
are similar to those of S13 and S15, respectively.
The phase dierence at N7 and N8 can be observed through the phase shift of
Cleft.S13.N9 and Cleft.S14.N9. Phase synchrony between N7 and N8 causes the EPSP
produced by each synapse (S13{S16) to arrive in phase, thus increasing the excitability
of N9 by the increase of the Total EPSP (middle panel). A phase dierence between
action potentials of N7 and N8 causes the EPSP arriving from each pair of synapses
S13{S14 and S15{S16 to be out of phase, thus the added Total EPSP contributed by
these synapses is not big enough to trigger the ring of activity at neuron N9, causing
its inhibition.
Figure 4.15 shows a zoom-in of the regions of Fig. 4.14 that shows the excitability of
N9 for two dierent cases of phase dierence in N7 and N8. It is shown in Fig. 4.15(a)
that the Total EPSP (middle panel) arriving from synapses that are out of phase is too
600
400
200 V(mV)
0
600
400
200
V(mV)
2.0
1.0
V(V)
0
2.5 5.0 7.5 10.0
time (µs)
EPSP .N9
Cleft.S13.N9 Cleft.S15.N9
0
AP .N9
Figure 4.14: Simulation showing the eect of synchronization on neuron N9 in network
2. The top panel shows the cleft signals for synapses S13 and S15 (S14 and S16 behave the
same as S13 and S15, respectively). The middle panel shows the Total EPSP of N9. The
bottom panel shows the ring of N9 when N7 and N8 are synchronized in phase. Note the
scale of EPSPs and APs in the traces shown.
61
4.2 Simulation results
small to induce the ring of N9. In Fig. 4.15(b), however, the EPSPs corresponding to
each synapse arrive in phase and thus the Total EPSP increases, eliciting the ring of
spikes in N9.
EPSP .N9=sum_EPSPs( S13, S14, S15, S16)
AP .N9
EPSP .S13
EPSP .S15
125
75
V(mV)
25
700
300
500
100
V(mV)
2.0
1.0
V(mV)
0
5.85 5.9 5.95 6.0 6.05
time (µs)
(a) The top panel shows the EPSPs out of phase, where the EPSP corresponding to the pairs of
synapses S13{S14 and S15{S16 have similar EPSP. The addition of the EPSPs is shown in the
middle panel. The bottom panel shows no action potentials at N9 as the Total EPSP is small due
to the phase dierence between N7 and N8.
EPSP .N9=sum_EPSPs(S13, S14, S15, S16)
EPSPs for S13, S14, S15, S16 in phase
AP .N9
125
75
25
V(mV)
700
300
500
100
V(mV)
2.0
1.0
V(mV)
0
7.05 7.1 7.15 7.2 7.25
time (µs)
7.3 7.35
(b) The top panel shows the EPSPs in phase for the four synapses connected to N9, i.e. S13{
S14 and S15{S16 . The addition of the EPSPs is shown in the middle panel. The bottom
panel shows action potentials at N9 as the Total EPSP is large enough due to the in neuronal
activities of N7 and N8.
Figure 4.15: A zoom into the results obtained in Fig. 4.14 for (a) the region where,
in the absence of a SIC event, the ring of spikes out of synchrony does not elicit action
potentials and (b) the region where, in the presence of SIC event, the ring of spikes in
phase synchrony elicits action potentials.
62
4.3 Summary
4.3 Summary
We have developed a rst-order model that describes the activation of slow inward
currents in CMOS. Our circuit results and the steps involved in the process of generation
of slow inward currents are similar to Wade's mathematical model and capture the
phenomenon observed in biological experiments. Like in Wade's work, we have circuit
parameters for the sensing of calcium and injection of transmitters into the synapse
as well as for the kinetics of slow inward currents, such as the decay time constant.
These parameters are discussed in the circuit section. Our results are initial steps for
the emulation of slow inward currents and we have not considered a biophysical model
of calcium waves at this early stage. Calcium signaling is a signicant part of the
process of activation of astrocytic release of glutamate and induction of slow inward
currents for NMDA channel activation. Calcium waves in our circuit represent only
rst-order events and a more detailed comparison with a bio-physical mathematical
model, such as the Li-Rinzel model, would require the inclusion of additional biological
mechanisms, such as calcium-induced and calcium-released. Once the circuit model
for calcium waves is designed and incorporated to the NMDAR circuit, a correlation
analysis with biological data and biophysical models will be performed.
Through circuit simulation we have learned the missing parts for the design of
a bio-realistic model as well as the required trade-os between accuracy and circuit
overhead. We have also learned that slow inward currents elicited by an astrocyte may
represent a mechanism that can be implemented in hardware applications that pursue
the synchronization and neuronal adaptation of activity in pathways with dierent
delays. This hypothesis will be tested as a future work. Our fundamental goal has
been the representation of the activation of NMDA channels through the activity of slow
inward currents that is triggered by astrocytes. Improvement to our circuit models can
be performed as a future work by accurately dening the range of voltages and currents
that replicate the biological response. Such denitions would only be of value as we
move forward towards the goal of designing a system that covers the biological subtleties
of the calcium signaling events that trigger the activation of slow inward currents. The
inclusion of calcium waves is a future work in the design of our circuits. Biophysical
models of slow inward currents are not currently available. However, empirical results
have demonstrated the dependency of slow inward currents amplitude with calcium
63
4.3 Summary
waves activity (99). These results will be used as the basis for comparison of our
circuit model and the activation of slow inward currents according to calcium activity.
A more ambitious goal would be to show in a complex network of neurons how calcium
signaling in astrocytes and the activation of slow inward currents dynamic can bring
together uncorrelated distant neurons to re synchronously.
64
5
An Adaptable CMOS Depressing
Synapse with Detection of
Changes in Input Spike Rate
Sensory pathways in the brain attain large dynamic ranges and novelty detection
through adaptive mechanisms. Sensory adaptation is found in almost all cortical areas
of the brain and it is believed to be important in the process of encoding of infor-
mation. Synapses in the brain exhibit adaptation mechanisms such as enhancement
of inhibition and depression of the excitatory response. In this chapter, we present
a CMOS neuromorphic circuit that captures the dynamics of a short-term depressing
synapse for both transient and steady state, including synapse potentiation, synapse
adaptation, and synapse detection of changes of spike rates following the nonlinear
Weber-Fechner relationship. The Weber-Fechner relationship shows a very important
property of a short-term depressing synapse, that is, the ability to sense changes in
synaptic information at low and high frequency rates. In this way, novelty is captured
by the synapse. Our circuit captures the one over frequency law in the excitatory post-
synaptic potential (EPSP) amplitude
uctuation for the steady state. In the case of a
long term interval of inactivity, the circuit is able to detect a novel change caused by a
rate of spikes. The design comprises a small number of transistors, while capturing the
desired input-output relationship. The amplitude of both transient and steady state
EPSP are tunable. To our knowledge, our short-term depressing synapse circuit is the
rst to incorporate the dynamics of the Weber-Fechner relation.
65
5.1 Introduction
5.1 Introduction
Sensory neurons are endowed with the ability to adapt to the environment and perform
novelty detection. A neural mechanism of adaptation and novelty detection involves
synaptic depression. In such a synapse, strong presynaptic activity causes the reduction
of neurotransmitter release through the transient depletion of synaptic vesicles. This
synaptic mechanism leads to three types of nonlinear behavior: 1. a transient signal for
the EPSP indicating novelty in the input; 2. depression of the excitatory-postsynaptic-
potential (EPSP)
uctuations during the steady state; 3. a sublinear dependence of
the average steady-state EPSP amplitude on spiking rate. All three are implemented
in the circuit presented here.
The rst nonlinear eect consists of an abrupt change in the membrane voltage
(EPSP) with a sudden modulation of the input spiking frequency, resembling the
Weber-Fechner relation (100). This abrupt, transient EPSP depends on the extra-
cellular levels ofCa
2+
concentration (6). An increase inCa
2+
concentration leads to a
stronger synapse with a higher depression rate (Fig. 1a). The initial peak of the tran-
sient EPSP is roughly proportional to the fractional rather than the absolute change
a) b)
c)
Figure 5.1: Biological data of a depressing synapse taken from (6). (a) Lowering the
extracellular Ca
2+
concentration decreases the initial EPSP without having an eect on
the average membrane voltage and the steady state amplitude, (b) Average postsynaptic
membrane under presynaptic spike stimulation for 200 dierent Poisson spike trains, (c)
Recorded EPSPs for dierent spike rates.
66
5.2 Contribution and Related Work
of the input spike rate ((100), (6)). Thus, a change in the input spike rate from 15 Hz
to 30 Hz or from 50 Hz to 100 Hz results in a similar initial transient peak.
To illustrate the nonlinearity of the Weber-Fechner relation quantitatively, Fig. 1b
shows the postsynaptic membrane response of a cortical neuron. In the transitions from
low to high input spike rates we observe an abrupt change in the membrane voltage
followed by a transient response. The transition from 1 Hz to 10 Hz elicits a response
about 2.5 times larger than that from 10 Hz to 40 Hz. In the rst transition, the
fractional change is 10 (10 Hz/ 1 Hz), while in the second transition, the fractional
change is 4 (40 Hz/ 10 Hz). Thus, the Weber-Fechner relation predicts that the peak
amplitude of the rst transition will be about 2.5 times larger than the second one.
The second and third nonlinear eects occur at steady state. The amplitude of
EPSP
uctuations decreases with the increase of the input spike rate (Fig. 1b and
Fig. 1c). Moreover, an increase in the input spike rate results in a sublinear rise of
the average steady-state response until a maximum limiting frequency is reached (6).
In Fig. 1b the limiting frequency is 40 Hz, thus the average steady state response
undergoes a small change when the spiking rate goes from 10 Hz to 40 Hz.
All these nonlinear behaviors are important in many cortical computations. For
example, neural coding in cortical neurons is widely in
uenced by synaptic depression
(6), (100), (101). A depressing synapse provides a postsynaptic neuron with better
information about its aerent inputs. We already mentioned that synaptic depression
contributes to adaptation and novelty detection. Thus, short-term synaptic depression
has been proposed as a gain-control mechanism to allow the detection of small rate
changes [2]. Furthermore, depression helps balance synaptic inputs. Cortical neurons
receive information from about 10,000 synapses (102) with a wide range of presynaptic
input rates. The response of a neuron without depressing synapses is mainly the av-
erage of its presynaptic input spikes. As a consequence, aerents with low input rate
have little contribution to the neural response. In a neuron with depressing synapses,
aerents with low and high input rates contribute in a more-balanced manner.
5.2 Contribution and Related Work
Our main contribution is the design of rst-order circuit mechanisms involved in a
short-term depressing synapse, including the Weber-Fechner relation (100). To our
67
5.3 Implementation of the Depressing Synapse
knowledge this is the rst CMOS circuit design to emulate this important relation.
Our work is distinct from the literature (103, 104) in some aspects. In (103) and
(104), the CMOS circuit designs do not detect changes in the input spike rate. In (103),
the tuning seems to modify both the initial EPSP and the steady state amplitude for
a constant input spike rate, which is dierent from the synaptic depression behavior
discussed in Fig. 1. These circuits perform at the real biological time scale (ms),
compared with our circuit that provides a response in a much shorter time (ns) while
preserving the subtleties of biological neurons. The circuits in (103) and (104) use
discrete capacitors. Our circuit is a high frequency design, where parasitic capacitances
are unavoidable, but we utilize such nonlinearities to avoid using discrete elements.
In addition, our circuit is tunable and follows the biological behavior of the de-
pressing synapse with the Weber-Fechner relation shown in Fig. 1. This synapse circuit
requires only a single power supply of 1.8 V, compared with other VLSI neural imple-
mentations (105), like the integrate and ring neuron (106, 107), the FitzHugh-Nagumo
neuron (108), and others (109), (106), (110). Those circuits require about 20 transistors
per synapse to implement basic computations, while by the same number of transistors
we also include the ability of imitating the nonlinear processing of depressing synapses.
While there are many control inputs in the neuromorphic circuits that we produce,
in actual implementations those control inputs would be common to many neurons or
would be generated internally on chip, based on the state of the circuit as execution
progressed. We show them as inputs to the circuit to illustrate the level of control
the designer and user can have over the behaviors of each circuit. Versions of our
neuromorphic circuits have such inputs produced by additional circuits that would be
found on the nal chip.
5.3 Implementation of the Depressing Synapse
In Fig. 5.2, we introduce a depressing synapse circuit that consists of a pre- and a
post-synaptic side separated by the cleft. The charge in the synaptic cleft node capac-
itance mimics the concentration of neurotransmitters in the extracellular space. The
EPSP response on the postsynaptic side is roughly proportional to the neurotransmit-
ter concentration in the synaptic cleft. On the presynaptic side, the input is a regular
68
5.3 Implementation of the Depressing Synapse
Spikes
VCa2+
(1) (3)
(4) (5)
Ibias
Vbias
(2)
C
E
MX
F
Reuptake
NT_Conc.
Spread
Receptor
(7)
Synapatic_cleft
EPSP
Delay Delay
(6)
Vref
IF
IX
Figure 5.2: Adaptable depressing synapse circuit following an approximation of the
Weber-Fechner relation during a change in spike rate. The discrete-component equiva-
lent circuit sketch illustrates the function of Stage (1). The circuit details (parameter
settings and simulation materials) will be found in an appendix in the thesis.
train of spikes with dierent frequencies generated by the axon hillock circuit previ-
ously published by our group (98). Stages (1){(4) implement the synaptic computation
of change detection in the input spike rate. Stage (5) performs the transient decay of
the depressing synapse, while Stage (6) performs the averaging computation over the
presynaptic spike rate. At the synaptic cleft node, the output currents from Stage (5)
and (6) add, modifying the concentration of neurotransmitters. Notice that in the case
of a non-depressing synapse we only use Stage (6) on the presynaptic side.
Stage (1) generates a control impulse arriving immediately after a spike's falling
edge. The discrete-component conguration in Fig. 5.2 shows the role of each transistor.
The steady state voltage at node C equalsV
dd
V
th
, whereV
th
is the threshold voltage
of the transistor. Thus, in steady state condition, the inverter output is 0 V. During the
spike's rising edge transition the voltage at node C,V
C
, increases abruptly, being limited
by the PMOS transistor that emulates a clamping diode. Thus, the inverter output
remains 0 V. At the spike's falling edge V
C
decreases as much as the spike amplitude.
This forces the inverter output to V
dd
where it remains at the same voltage until the
discharging path of the high pass lter pulls V
C
back to its steady state voltage.
At the output of Stage (2) we produce a nonlinear sawtooth signal whose voltage
goes from .6 V up to a maximum of 1.05 V. This signal is shaped using a slow rise
69
5.3 Implementation of the Depressing Synapse
and a fast fall time constant. The NMOS transistor is activated by the control impulse
generated in Stage (1). This pulls down the sawtooth signal to its minimum voltage,
V
bias
. After falling the control impulse the sawtooth signal increases with a slow time
constant shaped through the pull up PMOS transistor and the equivalent capacitance
at the stage output. This equivalent capacitance consists of the gate capacitance of a
transistor with drain and source terminals grounded, as well as diusion capacitances
in the node. An illustration of the nonlinear sawtooth signal is depicted in Fig. 5.3.
Stage (3) processes the nonlinear sawtooth signal and outputs a voltageV
E
propor-
tional to the synapse silent time, i.e. the time duration between two successive spikes.
In other words, Stages (1), (2) and (3) allow the synapse to memorize the time length
by which the presynaptic input has been inactive. Stage (3) consists of an NMOS pass
transistor and a capacitive load, where the pass transistor is controlled by the presynap-
tic input. The capacitive load together with the diusion capacitances in the node hold
the encoded voltage until the next spike arrives. For a constant spike rate, V
E
remains
unchanged. In case of a change in the input spike rate,V
E
is updated to a new voltage.
The dierence between the new and the previous voltage is approximately proportional
to the fractional change in the input spike rate. The details of this proportionality are
explained in the next section.
In Stage (4), the voltage V
E
is amplied by a common source amplier with active
load. We have connected an NMOS transistor (M
X
) between the output and input of
the active load to improve the input dynamic range, where the source terminal of M
X
is connected to the output node F. An increase in the amplier input voltageV
E
results
in a decrease in the output current I
F
, thus the output voltageV
F
is decreased. When
M
X
is activated, a feedback current I
X
is driven from I
bias
. The current I
X
partly
compensates for the decrease of I
F
, thus increasing the output voltage V
F
.
While Stage (1){(4) implement the approximate Weber-Fechner relation, Stage (5)
implements the transient decay of the depressing synapse. This is conceptually made
through a high pass ltering operation capturing the sudden change in V
F
. The volt-
age V
Ca
2+ controls calcium uptake from the extracellular space which is mimicked by
V
ref
. Tuning the voltageV
Ca
2+ mainly contributes to modulate the peak amplitude of
transient EPSP; it has minimum eect on steady state characteristics, similar to the
biological results in Fig. 5.1a.
70
5.4 Approximation of the Weber-Fechner relation
Stage (6) is a modied version of the presynaptic circuit previously published by
our group (5). Due to its low-pass ltering characteristic, it provides the synaptic cleft
node with information about the average of the input spike rate. The pull-up transis-
tors allow the synaptic cleft node to be charged with a fast rise time constant during
the spike duration. The steady state amplitude can be tuned by the input NT Conc.
(neurotransmitter concentration). The pull-down transistors allow the synaptic-cleft
node to be discharged in the absence of a spike. This mimics the drop of neurotrans-
mitters in the synaptic cleft by the reuptake process which can be tuned by the input
Reuptake. Stage (7) is the postsynaptic stage that generates the EPSP voltage. For
the detailed explanation of stages (6) and (7), the interested reader is referred to (5).
5.4 Approximation of the Weber-Fechner relation
We have previously mentioned that depressing synapses elicit a transient EPSP mem-
brane voltage whose amplitude results from a fractional rather than an absolute change
in the input spike rate, similar to the Weber-Fechner relation (100), (111). A change in
the input spike rate from 10 Hz to 20 Hz has a similar initial transient peak amplitude
as a change from 50 Hz to 100 Hz. Thus, the fact that the change in spike rate occurs
at a high frequency is of little importance for the initial transient peak amplitude.
We approximate the Weber-Fechner relation through the nonlinear behavior of saw-
tooth signal, the solid red line in Fig. 5.3. As shown, changing input spike rate from
12.5 MHz to 25 MHz, from 25 MHz to 50 MHz, or from 50 MHz to 100 MHz al-
most result in the same change in voltage. This contrasts with the linear approach
(dashed blue), where the change in voltage is proportional to the absolute rather than
the fractional change. With the linear approach, synapses that respond to low spike
rates do not have the same contribution as those with high spiking rates. For exam-
ple, in the linear approach the voltage change for an input spike rate from 50 MHz to
100 MHz is twice of the change from 25 MHz to 50 MHz. Therefore, our approach
more appropriately implements the Weber-Fechner relation than a linear approach.
71
5.5 Simulation Results of the Depressing Synapse
0.85
0.9
0.95
1
1.05
1.1
100 MHz 50 MHz 25 MHz 12.5 MHz
900 mV
1000 mV
1100 mV
0 10 20 30 40 50 60 70 80 90 100
0.6
0.65
0.7
0.75
0.8
0.85
10 ns 20 ns 40 ns 80 ns
600 mV
700 mV
800 mV
Figure 5.3: An illustration of the Weber-Fechner approximation. A comparison between
the nonlinear sawtooth signal (solid red) based on our approach, and a linear approach
(dashed blue).
5.5 Simulation Results of the Depressing Synapse
In Fig. 5.4 and Fig. 5.5, we demonstrate the computational features of the depressing
synapse circuit. In Fig. 5.4, we show the detection of spikes by the synapse upon a long
Figure 5.4: EPSP response for V
Ca
2+ from .7 to 1.8 V.
72
5.5 Simulation Results of the Depressing Synapse
interval of inactivity.
In the absence of an incoming spike the synapse remains silent at its circuit resting
potential. When the synapse receives the rst spike, the EPSP increases with an abrupt
change. We also show that the initial amplitude is tunable byV
Ca
2+. Thus, a change of
V
Ca
2+ from .7 V to 1.8 V elicits an approximate change of 50 mV in the initial transient
peak. This provides us with a wide range of tunability in the initial transient peak with
respect to its maximum feasible value.
In Fig. 5.5, we demonstrate additional biomimetic features of the depressing synapse
circuit. First, while the average membrane potential increases with an increase in the
input spike rate, the steady state amplitude decreases. The latter mimics the 1=f law
in biological synapses. Second, the simulation shows the circuit response of the EPSP
under changes in the input spike rate. The rst transient peak shows an amplitude
x corresponding to a fractional change of 2 (16 MHz=8 MHz) in the input spike rate.
Since the fractional change for the second peak is 1.5 (24 MHz/16 MHz), the amplitude
y is approximately .75 (1:5=2) times the amplitude ofx. From 24 MHz to 40 MHz, the
fractional change is about 1.7, so the amplitude z is approximately 1.7/1.5 times the
amplitude of y and 1:7=2 times the amplitude x.
8 MHz 16 MHz 24 MHz 40 MHz
y
z
x
y
Figure 5.5: Response of the depressing synapse circuit under changes of input spike rates.
73
6
Conclusion and Future Work
This thesis comprises rst-order CMOS neuromorphic circuit designs and simulations
to test and evaluate the communication between neurons and astrocytes. Astrocytes
modulate synapses through the uptake of neurotransmitters and/or the release of glio-
transmitters. Our main focus in Chapter 3 has been the astrocytic uptake mechanism.
We have done an analysis of the mechanism in a small network of neurons interacting
with an astrocyte. This has been a rst step in the design of a circuit platform as
a \proof of concept" for the evaluation of neuronal survival upon activity of astro-
cytes. Our future plan is to include the biology of synaptic and extrasynaptic NMDAR
channels and evaluate the astrocyte role on the regulation of these channels. Extrasy-
naptic NMDAR channels have been viewed as the pathway through which excess of
calcium ions is uptake by neurons, causing neuronal death. We would like to capture
this process and perform a comparative analysis with experimental biological results.
In the long{term, we envision a robust model for these interactions that would have
to incorporate the dynamics of astrocytic intracellular calcium waves. These waves
are highly complex and capturing them in circuits represent a major challenge and a
pioneer contribution in the circuit modeling of astrocyte's dynamics.
In Chapter 4, we are, in essence, reverse engineering the role of astrocytes in syn-
chronization of neural ring. We have relied on experimental data from others (30, 31)
and have integrated the measurements into our neural-astrocyte synchronization model.
We have designed hybrid biomimetic/bio-inspired circuits that emulate current exper-
iments on the role of slow inward currents on the synchronous activity of adjacent
neurons. By circuit simulations, we have seen that our hypothesis on the changes of
74
the excitability of neurons is dependent on the arrival of slow inward current events
which greatly in
uences the amplitude of excitatory postsynaptic potentials. This work
suggests, for real biological circuits, the possible implications of phase synchronization
on the ring of neurons and the way the astrocytes interact with each other that could
potentially elicit synchronization at dierent locations in a group of unrelated neurons.
This is a rst step to demonstrate more complex interactions between neurons and
astrocytes.
In Chapter 5, we have designed a novel depressing synapse CMOS neuromorphic
circuit that mimics biological aspects of cortical neurons. Our circuit includes important
biological features such as the adaptation of a synapse under the change of input spike
rate, variations in the EPSP amplitude with changes ofCa
2+
, the detection of changes
upon a long interval of inactivity, and, last but not least, an approximation of the
Weber-Fechner relation in the presence of change in the spike rate.
Modeling the mechanisms for short-term synaptic depression in CMOS is only a
rst step to design and test in a circuit environment short-term astrocyte-mediated
depression. Experimental data have shown that when astrocytes are subjected to a
short synaptic burst, they reduce the probability of synaptic release at presynaptic
sides, causing synaptic depression. This has been also seen in heterosynaptic depres-
sion, through the depression of inactive synapses. Investigating the dynamics of the
communication between astrocytes and adaptable synapses would bring more insights
on the modulatory role of astrocytes, specically for the delay of synaptic information
across dierent pathways.
Although the role of glial cells in neural functioning is not completely understood,
our circuits aim to provide an experimental platform for researchers to investigate on
possible in
uences of glial cells on neuronal processes. While we have been able to
demonstrate the modulation of synapses by astrocytic mechanisms, and the excitation
of astrocytes by neurons, this is only a rst step in circuits.
In small networks of neurons interacting with an astrocyte, transistor variability
could be an issue that may lead to circuit mismatches. We plan to run Monte Carlo
simulations for testing the robustness of our circuit designs. We expect that the feed-
back loop formed by astrocytes should help reduce overall noise by weakening the
impact of uncertainties in the signals received from the neurons at a lower level of
computation.
75
We are currently exploring how sensory information that enters the brain through
dierent pathways and with dierent delays is combined so that an image of a con-
scious scene is produced. Such process of binding of information is believed to require
synchronous activity. Astrocytes are hypothesized to be able to induce such synchro-
nization due to their capability to reach and in
uence a wide number of neurons. We
aim to design circuits as a \proof of concept" that capture the role of astrocytes in the
regulation of these delays coming from dierent pathways. In order to achieve this, we
rst need to design circuits for the encoding of information in astrocytes through the
calcium waves and dene the necessary trade-os in the design of large{scale systems
imposed by current CMOS technologies. We believe that by capturing the biological
mechanisms where astrocytes adapt the delays in neuronal pathways, we can provide
with a circuit environment that can serve as a \proof of concept" for the testing and
evaluation of cognitive tasks.
No doubt much more work remains to be done in order to achieve our goals and
this work represents the very initial steps. A nal chip for cognitive tasks is envisioned
in which neurons sense and transmit information from sensory inputs and astrocytes
monitor activity to make decisions according to the biological events that are intrinsic
of themselves in the form of calcium waves.
76
References
[1] DS Antanitus. A Theory of Cortical Neuron-Astrocyte Interaction. Neurosci-
entist, 4:154{159, 1998. ix, 3
[2] Michael J. Berridge. Cell Signalling Biology. Portland Press limited, 2012. ix, 4
[3] Philip G. Haydon and Giorgio Carmignoto. Astrocyte Control of Synaptic
Transmission and Neurovascular Coupling. Physiol. Rev., 86(3):1009{1031, 2006.
ix, 15
[4] H. Chaoui. CMOS analogue adder. Electronics Letters, 31(3):180{181, 1995. x, 30
[5] Jonathan Joshi, Alice C. Parker, and Ko-Chung Tseng. An in-silico glial
microdomain to invoke excitability in cortical neural networks. In Circuits and
Systems (ISCAS), 2011 IEEE International Symposium on, pages 681 {684, may 2011.
x, 9, 27, 30, 31, 41, 48, 51, 71
[6] M. Tsodyks and H. Markram. The neural code between neocortical pyramidal
neurons depends on neurotransmitter release probability. Proceedings of the
National Academy of Sciences of the United States of America, 94(2):719{723, January
1997. xii, 66, 67
[7] Alice C. Parker. The BioRC Biomimetic Real-Time Cortex Project. University
of Southern California, http://ceng.usc.edu
~
parker/BioRC_research.html,2013. 6,
8, 28, 41
[8] C. Mead. Analog VLSI and Neural Systems. 1989. 6
[9] R. Douglas, M. Mahowald, and C. Mead. Neuromorphic Electronic Systems.
78, pages 1629{1636, 1990. 6
[10] R. Douglas, M. Mahowald, and C. Mead. Neuromorphic Analogue VLSI. 18,
pages 255{281, 1995. 6, 26
[11] Jonathan Joshi, Alice C. Parker, and Chih-Chieh C. Hsu. A carbon nanotube
cortical neuron with spike-timing-dependent plasticity. Conference proceedings:
77
REFERENCES
Annual International Conference of the IEEE Engineering in Medicine and Biology So-
ciety, EMBC, 2009:1651{1654, 2009. 8, 27, 47, 48
[12] J. Joshi, C.C Hsu, A.C Parker, and P. Deshmukh. A Carbon Nanotube
Cortical Neuron with Excitatory and Inhibitory Dendritic Computations. In
IEEE/NIH LIfe Science Systems and Applications Workshop, 2009. 8, 27
[13] Yilda Irizarry Valle, Jonathan Joshi, and Alice C. Parker. In A CMOS
Neuromorphic Approach to Emulate Neuro-Astrocyte Interactions, aug 2013. 9
[14] D. Allan Butterfield and C. Pocernich. The glutamatergic system and
Alzheimer's disease: therapeutic implications. CNS Drugs, 17(9):641{652, 2003.
9
[15] G. Perea, M. Navarrete, and A. Araque. Tripartite synapses: astrocytes
process and control synaptic information. Trends in Neurosciences, 32(8):421 {
431, 2009. 11, 17
[16] Philip G. Haydon. Glia: listening and talking to the synapse. Nature Rev.
Neuroscience, 2:185{93, 2001. 12
[17] R. Douglas Fields and Beth Stevens-Graham. New Insights into Neuron-Glia
Communication. Science, 298(5593):556{562, 2002. 12
[18] Michael M. Halassa and Philip G. Haydon. Integrated brain circuits: as-
trocytic networks modulate neuronal activity and behavior. Annual review of
physiology, 72:335{355, March 2010. 12
[19] George J Augustine. How does calcium trigger neurotransmitter release?
Current Opinion in Neurobiology, 11(3):320 { 326, 2001. 12
[20] Philip G. Haydon and Giorgio Carmignoto. Astrocyte Control of Synaptic
Transmission and Neurovascular Coupling. Physiol. Rev., 86(3):1009{1031, July
2006. 12
[21] Maria A. Di Castro, Julien Chuquet, Nicolas Liaudet, Khaleel Bhaukau-
rally, Mirko Santello, David Bouvier, Pascale Tiret, and Andrea
Volterra. Local Ca2+ detection and modulation of synaptic release by as-
trocytes. Nature Neuroscience, 14(10):1276{1284, September 2011. 12
[22] Y.H.Huang, S.R.Sinha, K.Tanaka, J.D.Rothstein, and D.E.Bergles. Astro-
cyte Glutamate Transporters Regulate Metabotropic Glutamate Receptor-
Mediated Excitation of Hippocampal Interneurons. The Journal of Neuroscience,
24(19):4551{4559, 2004. 13
78
REFERENCES
[23] Y.H. Huang and D.E. Bergles. Glutamate transporters bring competition to
the synapse. Current Opinion in Neurobiology, 14(3):346 { 352, 2004. 13
[24] D.E. Bergles and C.E. Jahr. Synaptic Activation of Glutamate Transporters
in Hippocampal Astrocytes. Neuron, 19(6):1297{1308, 1997. 13
[25] N.C.Danbolt. Glutamate uptake. Progress in Neurobiology, pages 1{105, 2001. 13
[26] T.H. Gillingwater and R.R. Ribchester. Compartmental neurodegeneration
and synaptic plasticity in the Wld
s
mutant mouse. The Journal of Physiology,
534(3):627{639, 2001. 13
[27] Jeffrey S. Diamond. Neuronal Glutamate Transporters Limit Activation of
NMDA Receptors by Neurotransmitter Spillover on CA1 Pyramidal Cells. J.
Neurosci., 21(21):8328{8338, November 2001. 13
[28] J. W. Johnson and P. Ascher. Glycine potentiates the NMDA response in
cultured mouse brain neurons. Nature, 325:529{531, 1987. 13
[29] Graham L. Collingridge, Arturas Volianskis, Neil Bannister, Grace
France, Lydia Hanna, Marion Mercier, Patrick Tidball, Guangyu Fang,
Mark W. Irvine, Blaise M. Costa, Daniel T. Monaghan, Zuner A. Bor-
tolotto, Elek Molnr, David Lodge, and David E. Jane. The NMDA receptor
as a target for cognitive enhancement. Neuropharmacology, 64(0):13 { 26, 2013. 14
[30] T Fellin, O Pascual, S Gobbo, T Pozzan, PG Haydon, and G Carmignoto.
Neuronal synchrony mediated by astrocytic glutamate through activation of
extrasynaptic NMDA receptors. Neuron, 43:729{743, 2004. 14, 15, 17, 40, 74
[31] John J. Wade, Liam J. McDaid, Jim Harkin, Vincenzo Crunelli, and
J. A. Scott Kelso. . PLoS ONE, 6(12):e29445, Dec. 2011. 15, 16, 40, 47, 48, 74
[32] Misha Tsodyks, Klaus Pawelzik, and Henry Markram. Neural Networks with
Dynamic Synapses. Neural Comput., 10(4):821{835, May 1998. 16
[33] J Rinzel and Y. Li. Equations for InsP3 receptor-mediated [Ca
2+
]
i
oscillations
derived from a detailed kinetic model: a Hodgkin-Huxley like formalism.
Theor. Biol., 166:461{473, 1994. 16, 22, 23
[34] S. Nadkarni and P. Jung. Dressed neurons: modeling neuralglia interactions.
Phys. Biol., 1(1-2):35 { 41, 2004. 16, 23
[35] S. Nadkarni and P. Jung. Modeling synaptic transmission of the tripartite
synapse. Phys. Biol., 4(1):1 { 9, 2007. 16, 23
79
REFERENCES
[36] A. Jr. Pereira. Astrocytes and human cognition: modeling information inte-
gration and modulation of neuronal activity. Prog.Neurobiol. 92, 405420., 92:405{
420, 2010. 16, 17, 24
[37] Schuichi Koizumi. Synchronization of Ca
2+
oscillations: involvement of ATP
release in astrocytes. FEBS Journal, 277(2):286{292, 2010. 16
[38] Nancy Ann Oberheim, Takahiro Takano, Xiaoning Han, Wei He, Jane H. C.
Lin, Fushun Wang, Qiwu Xu, Jeffrey D. Wyatt, Webster Pilcher, Jef-
frey G. Ojemann, Bruce R. Ransom, Steven A. Goldman, , and Maiken Ned-
ergaard. Uniquely Hominid Features of Adult Human Astrocytes. Journal of
Neuroscience, 29(10):3276{3287, 2009. 16
[39] G. Carmignoto. Reciprocal communication systems between astrocytes and
neurones. Progress Neurobiology, 62(6):561{581, 2000. 17, 20, 21, 48
[40] Eugene M. Izhikevich. Polychronization: computation with spikes. Neural
Computation, 18(2):245{282, February 2006. 17
[41] Anne Treisman. Solutions to the binding problem: progress through contro-
versy and convergence. Neuron, 24(1):105 { 125, 1999. 17
[42] J. Robertson. The Astrocentric Hypothesis: proposed role of astrocytes in
consciousness and memory formation. Journal of Physiology, pages 251{255. 17
[43] Alfredo Pereira Jr. and Fbio Augusto Furlan. On the role of synchrony for
neuronastrocyte interactions and perceptual conscious processing. J Biol Phys,
35:465480, 2009. 17
[44] Gertrudis Perea and Alfonso Araque. Synaptic information processing by
astrocytes. Journal of Physiology-Paris, 99(2-3):92 { 97, 2006. 17
[45] A. Araque, E. Martn, G. Perea, J. Arellano, and W. Buo. Synaptically-
released acetylcholine evokes Ca2+ elevetations in astrocytes in hippocampal
slides. The Journal of Neuroscience, 22:2443{2450, 2002. 17
[46] G. Perea and A. Araque. Properties of Synaptically Evoked Astrocyte Cal-
cium Signal Reveal Synaptic Information Processing by Astrocytes. The Jour-
nal of Neuroscience, 25(9):2192{2203, 2005. 17
[47] B. Benedetti, V. Matyash, and H. Kettenmann. Astrocytes control GABAer-
gic inhibition of neurons in the mouse barrel cortex. The Journal of Physiology,
589(5):1159{1172, 2011. 18
[48] M. P. Beenhakker and J. R. Huguenard. Astrocytes as gatekeepers of
GABAB receptor function. The Journal of Neuroscience, 30(45):15262{15276, 2010.
18
80
REFERENCES
[49] Laszlo Heja, Gabriella Nyitrai, Orsolya Kekesi, Arpad Dobolyi, Pal Szabo,
Richard Fiath, Istvan Ulbert, Borbala Pal-Szenthe, Miklos Palkovits, and
Julianna Kardos. Astrocytes convert network excitation to tonic inhibition
of neurons. BMC Biology, 10(1):26, 2012. 18
[50] S. Lee, B. E. Yoon, K. Berglund, S. J. Oh, H. Park, H. S. Shin, G. J. Au-
gustine, , and C. J. Lee. Channel-mediated tonic GABA release from glia.
Science, 330:790{796, 2010. 18
[51] J. Zhang, H. Wang, C. Ye, W. Ge, Y. Chen, C. Jiang, M. Poo, and S. Duan.
ATP Released by Astrocytes Mediates Glutamatergic Activity-Dependent
Heterosynaptic Suppression. Neuron, 40(5):971{982, 2003. 18, 19
[52] Chen J., Tan Z., Zeng L., Zhang X., He Y., Gao W., Wu X., Li Y., Bu B.,
Wang W., and Duan S. Heterosynaptic Long-Term Depression Mediated by
ATP Released from Astrocytes. Glia, 61(2):178{191, 2013. 18
[53] M. Andersson, F. Blomstrand, and E. Hanse. Astrocytes play a critical role in
transient heterosynaptic depresion in the hippocampal CA1 region. J. Physiol.,
585(3):843{852, 2007. 19
[54] AS. Kozlov, MC. Angulo, E. Audinat, and S. Charpak. Target cell-specic
modulation of neuronal activity by astrocytes. Proc Natl Acad Sci U S A,
103:10058{10063, 2006. 19
[55] C. Jimenez-Gonzalez, T. Pirttimaki, DW. Cope, and HR. Parri. Non-
neuronal, slow GABA signalling in the ventrobasal thalamus targets delta-
subunit-containing GABAA receptors. Eur J Neurosci., 33:1471{1482, 2011. 19
[56] C. Agulhon, M.Y. Sun, T. Murphy, T. Myers, K. Lauderdale, and T. Fiacco2.
Calcium Signaling and Gliotransmission in Normal vs. Reactive Astrocytes.
Front Pharmacol, 3(139):1{16, 2012. 19
[57] De Pitt M., Goldberg M., Volman V., Berry H, and Ben-Jacob E. Glutamate
regulation of calcium and IP3 oscillating and pulsating dynamics in astrocytes.
J Biol Phys, 35(4):383{411, 2009. 20, 22
[58] Andrew Koob. The Root of Thoughts. FT Press., 2009. 20
[59] Lucia Pasti, Andrea Volterra, Tullio Pozzan, and Giorgio Carmignoto.
Intracellular calcium oscillations in astrocytes: A highly plastic, bidirectional
form of communication between neurons and astrocytes in situ. J. Neurosci,
pages 7817{7830, 1997. 20
81
REFERENCES
[60] Micaela Zonta and Giorgio Carmignoto. Calcium oscillations encoding
neuron-to-astrocyte communication. Journal of Physiology-Paris, 96(34):193 { 198,
2002. 20
[61] J.I. Nagy and J.E. Rash. Connexins and gap junctions of astrocytes and
oligodendrocytes in the CNS. Brain Res Brain Res Rev., 32(1):29{44, 2000. 21
[62] Mati Goldberg, Maurizio De Pitt a, Vladislav Volman, Hugues Berry, and
Eshel Ben-Jacob. Nonlinear gap junctions enable long-distance propagation
of pulsating calcium waves in astrocyte networks. PLoS computational biology,
6(8), 2010. 21
[63] JI. Nagy and JE. Rash. Astrocyte and Oligodendrocyte Connexins of the
Glial Syncytium in Relation to Astrocyte Anatomical Domains and Spatial
Buering. Cell Commun Adhes., 10(4-6):401{406, 2007. 21
[64] AH Cornell-Bell, SM Finkbeiner, MS Cooper, and SJ Smith. Glutamate in-
duces calcium waves in cultured astrocytes: long-range glial signaling. Science,
247(4941):470{473, 1990. 23
[65] V. Volman, E. Ben-Jacob, and H. Levine. The astrocyte as a gatekeeper of
synaptic information transfer. Neural Comput., 19(2):303{326, 2007. 23
[66] Mahmood Amiri, Ghazal Montaseri, and Fariba Bahrami. On the role of
astrocytes in synchronization of two coupled neurons: a mathematical per-
spective. Biological Cybernetics, 105(2):153{166, 2011. 23
[67] Angelo Di Garbo, Michele Barbi, Santi Chillemi, Susanna Alloisio, and
Mario Nobile. Calcium signalling in astrocytes and modulation of neural
activity. Biosystems, 89(13):74 { 83, 2007. Selected Papers presented at the 6th Inter-
national Workshop on Neural Coding Neural Coding 2005 6th International Workshop
on Neural Coding. 23
[68] M. Nobile, I. Monaldi, S. Alloisio, C. Cugnoli, and S Ferroni. ATP-induced,
sustained calcium signalling in cultured rat cortical astrocytes: evidence for
a non-capacitative, P2X7-like-mediated calcium entry. FEBS Lett., 538(1-3):71
{ 76, 2003. 23
[69] S. Koizumi, K. Fujishita, and K. Inoue. Regulation of cell-to-cell communica-
tion mediated by astrocytic ATP in the CNS. Purinergic Signal., 1:211{217, 2005.
23
[70] Angelo Garbo. Dynamics of a minimal neural model consisting of an astro-
cyte, a neuron, and an interneuron. Journal of Biological Physics, 35(4):361{382,
2009. 23, 24
82
REFERENCES
[71] H.R. Parri and V. Crunelli. The role of Ca2+ in the generation of sponta-
neous astrocytic Ca
2+
oscillations. Neuroscience, 120:979{992, 2003. 23, 24
[72] J. Sneyd, K. Tsaneva-Atanasova, D.I. Yule, J.L. Thompson, and T.J. Shut-
tleworth. Control of calcium oscillations by membrane
uxes. Proc. Natl. Acad.
Sci. U. S. A., 101:1392{1396, 2004. 23
[73] M. Lavrentovich and S. Hemkin. A mathematical model of spontaneous cal-
cium (II) oscillations in astrocytes. J. Theor. Biol., 251:553{560, 2008. 23
[74] W. Nett, S.H. Oloff, and K.D. McCarthy. Hippocampal astrocytes in situ
exhibit calcium oscillations that occur independent of neuronal activity. J.
Neurophysiol., 87:528{537, 2002. 23
[75] F. Aguado, J.F. Espinosa-Parrilla, M.A. Carmona, and E. Soriano. Neu-
ronal activity regulates correlated network properties of spontaneous calcium
transients in astrocytes in situ. J. Neurosci., 22:9430{9444, 2002. 24
[76] A. Tashiro, J. Goldberg, and R. Yuste. Calcium oscillations in neocortical
astrocytes under epileptiform conditions. J. Neurobiol., 50:45{55, 2002. 24
[77] Caroline Mller, Jrg Lcke, Junmei Zhu, Pedro M. Faustmann, and Christoph
von der Malsburg. Glial cells for information routing? Cognitive Systems
Research, 8(1):28 { 35, 2007. 24
[78] Gilad Silberberg, Sten Grillner, Fiona E.N. LeBeau, Reinoud Maex, and
Henry Markram. Synaptic pathways in neural microcircuits. Trends in Neuro-
sciences, 28(10):541 { 551, 2005. 24
[79] A. Jr. Pereira. The calcium wave model of the perception-action cycle: evi-
dence from semantic relevance in memory experiments. Frontiers in Psychology,
4:1{4, 2013. 25
[80] J. Schemmel, K. Meier, and E. Mueller. A new VLSI model of neural mi-
crocircuits including spike time dependent plasticity. In Neural Networks, 2004.
Proceedings. 2004 IEEE International Joint Conference on, 3, pages 1711{1716 vol.3,
July 2004. 26
[81] Jayawan H. Wijekoon and Piotr Dudek. VLSI circuits implementing compu-
tational models of neocortical circuits. Journal of neuroscience methods, February
2012. 26
[82] E. Chicca, F. Stefanini, C. Bartolozzi, and G. Senior Indiveri. Neuromorphic
Electronic Circuits for Building Autonomous Cognitive Systems. Proceedings
of the IEEE, 102(9):1364{1366, Sept 2014. 26
83
REFERENCES
[83] G Indiveri and TK. Horiuchi. A new VLSI model of neural microcircuits in-
cluding spike time dependent plasticity. InFrontiers in Neuromorphic Engineering.,
5, page 118, 2011. 26
[84] G. Indiveri, B. Linares-Barranco, T. Hamilton, A. van Schaik, R. Etienne-
Cummings, T. Delbruck, S-C. Liu, P. Dudek, P. Hfliger, S. Renaud, J. Schem-
mel, G. Cauwenberghs, J. Arthur, K. Hynna, F. Folowosele, S. SAGHI,
T. Serrano-Gotarredona, J. Wijekoon, Y. Wang, and K. Boahen. Neuro-
morphic silicon neuron circuits. Frontiers in Neuroscience, 5(73), 2011. 26
[85] Sylvain Saighi, Yannick Bornat, Jean Tomas, Gwendal Le Masson, and
Sylvie Renaud. A library of analog operators based on the Hodgkin-Huxley
Formalism for the design of tunable, real-time, silicon neurons. IEEE Transac-
tions on Biomedical Circuits and Systems, 5:3{19, 2011. 26
[86] R.J. Vogelstein, U. Mallik, J.T. Vogelstein, and G. Cauwenberghs. Dynam-
ically Recongurable Silicon Array of Spiking Neurons With Conductance-
Based Synapses. Neural Networks, IEEE Transactions on, 18(1):253{265, Jan 2007.
26
[87] John Arthur and Kwabena Boahen. Learning in Silicon: Timing is Every-
thing. In Y. Weiss, B. Sch olkopf, and J. Platt, editors, Advances in Neural
Information Processing Systems 18, pages 75{82. MIT Press, 2006. 27
[88] G. Indiveri. Neuromorphic Bistable VLSI Synapses with Spike-Timing-
Dependant-Plasticity. In Advances in Neural Information Processing Systems, pages
1091{1098, 2002. 27
[89] Sime Bamford, Alan F. Murray, and David J. Willshaw. Large Developing
Receptive Fields Using a Distributed and Locally Reprogrammable Address
Event Receiver. IEEE Transactions on Neural Networks, 21(2):286{304, February
2010. 27
[90] Brian Taba and Kwabena Boahen. Silicon growth cones map silicon retina. In
NIPS, 2005. 27
[91] G. Indiveri. A low-power adaptive integrate-and-re neuron circuit. In Circuits
and Systems, 2003. Proceedings of the 2003 International Symposium on, 4, pages IV{
820{IV{823 vol.4, 2003. 27
[92] E. Farquhar and P. Hasler. A bio-physically inspired silicon neuron. Circuits
and Systems I: Regular Papers, IEEE Transactions on, 52(3):477{488, 2005. 27
[93] Soheila Nazari, Karim Faez, Mahmood Amiri, and Ehsan Karami. A digital
implementation of neuronastrocyte interaction for neuromorphic applications.
Neural Networks, 66:79 { 90, 2015. 27
84
REFERENCES
[94] A. C. Parker, A. K. Friesz, and A. Pakdaman. Towards a Nanoscale Arti-
cial Cortex. In Proceedings of The 2006 International Conference on Computing in
Nanotechnology (CNAN'06), June 2006. 27
[95] Giorgio Carmignoto and Tommaso Fellin. Glutamate release from astrocytes
as a non-synaptic mechanism for neuronal synchronization in the hippocam-
pus. Journal of Physiology-Paris, 99(23):98 { 102, 2006. 40, 41
[96] Chih-Chieh Hsu and Alice C. Parker. Dynamic Spike Threshold and Non-
linear Dendritic Computation for Coincidence Detection in Neuromorphic
Circuits. International Conf. IEEE Engineering in Medicine and Biology Society, 2014.
42
[97] Lucia Pasti, Micaela Zonta, Tullio Pozzan, Stefano Vicini, and Giorgio
Carmignoto. Cytosolic Calcium Oscillations in Astrocytes May Regulate Ex-
ocytotic Release of Glutamate. J. Neurosci., 21(2):477{484, January 2001. 48
[98] J. Joshi, A.C Parker, and C.C Hsu. A Carbon Nanotube Spiking Cortical
Neuron with Tunable Refractory Period and Spiking Duration. In IEEE Latin
American Symposium on Circuits and Systems (LASCAS), 2010. 48, 69
[99] Vladimir Parpura and Philip G. Haydon. Physiological astrocytic calcium
levels stimulate glutamate release to modulate adjacent neurons. Proceedings
of the National Academy of Sciences of the United States of America, 97(15):8629{8634,
July 2000. 64
[100] L. F. Abbott, J. A. Varela, Kamal Sen, and S. B. Nelson. Synaptic depression
and cortical gain control. Science, 275(5297):221{224, January 1997. 66, 67, 71
[101] L. F. Abbott and S. B. Nelson. Synaptic plasticity: Taming the beast. Nature
neuroscience, 3 Suppl:1178{1183, November 2000. 67
[102] Gordon M. Shepherd. Introduction to Synaptic Circuits. Oxford University
Press, 2004. 67
[103] Shih-Chii Liu, Malte Boegershausen, and Pascal Suter. Circuit model of
short-term synaptic dynamics. In In Advances in Neural Information Processing
Systems. MIT Press, 2002. 68
[104] C. Rasche and R. Hahnloser. Silicon synaptic depression. Biological Cybernetics,
84(1):57{62, 2001. 68
[105] A.D. Tete, A.Y. Deshmukh, P. Bajaj, and A.G. Keskar. Design of cortical
neuron circuits with VLSI design approach. International Journal on Soft Com-
puting, 2(4), November 2011. 68
85
REFERENCES
[106] C. Bartolozzi and G. Indiveri. Synaptic dynamics in analog VLSI. Neural
Computation, 19(10):2581{2603, Oct 2007. 68
[107] J.H.B. Wijekoon and P. Dudek. Spiking and bursting ring patterns of a
compact VLSI cortical neuron circuit. In Neural Networks, 2007. IJCNN 2007.
International Joint Conference on, pages 1332 {1337, aug. 2007. 68
[108] J. Cosp, S. Binczak, J. Madrenas, and D. Fernandez. Implementation of
compact VLSI FitzHugh-Nagumo neurons. In Circuits and Systems, 2008. ISCAS
2008. IEEE International Symposium on, pages 2370 {2373, may 2008. 68
[109] Kazuki Nakada, Tetsuya Asai, and Hatsuo Hayashi. Analog VLSI imple-
mentation of resonate-and-re neuron. International Journal of Neural Systems,
16(06):445{456, 2006. 68
[110] G. Indiveri. A low-power adaptive integrate-and-re neuron circuit. In Circuits
and Systems, 2003. ISCAS '03. Proceedings of the 2003 International Symposium on, 4,
pages IV{820 { IV{823 vol.4, may 2003. 68
[111] Lucinda A. Grande and William J. Spain. Synaptic depression as a timing
device. Physiology (Bethesda, Md.), 20:201{210, June 2005. 71
86

Abstract (if available)

Abstract Neuromorphic engineering is a relatively new field that finds its strength in its multidisciplinary approach.It brings together disciplines such as neuroscience, biology, and many other areas of engineering. The field gains its motivation from the curiosity of discovering what makes the brain outperforms any known system, particularly in terms of power, robustness, and sensory computations. ❧ Our research uses electronics technology, such as CMOS to emulate biological behaviors inspired by brain computations. Although, similar experimentation could, in principle, be done through software programming, circuit simulation is one step closer to the physical properties of integrated circuit technology. This sets the basis to further evaluate and explore the limitations of embedding biological computations. ❧ This thesis presents an initial framework from the neuromorphic engineering perspective on the computations involved in communication processes between astrocytes and neurons. It aims to contribute and provide guidance to the early stage development of hardware systems for testing and evaluation on the computational power of astrocyte-neuronal interactions in health and cognition. The main focus of our work is on understanding the influence of astrocytes on neuronal activity, and the translation of biological computations into circuits, using the characteristics of MOSFET transistors. Our designs are first-order bio-inspired/bio-mimetic circuits. We look at astrocytes as peers of neurons moving away from the neuro-centric view. We design circuits that represent biological functions of astrocytes, neurons, and the interaction between them. ❧ Astrocytes are the majority of the subtype of glial cells and contribute to learning, memory and cognition. Astrocytes cause changes at the synaptic level and promote neuronal health by the modulation of neuronal activity and by phagocytic clearance. While the scientific community has given much attention to neurons, astrocytes have been overlooked and it is not until few decades ago that significant progress has been made on unraveling astrocytes as computational units on high level brain cognitive processing. ❧ Among our research achievements include the design and simulation of astrocytic functions for the modulation of synaptic information as well as neuronal functions for the dynamics of synaptic activity. To our knowledge, our group is the first to have electronically captured an astrocytic microdomain circuit, i.e. compartments able to sense neuronal activity and feed back a response to neurons. ❧ Through our circuits we test a variety of biological processes, such as the uptake of glutamate by astrocytes and show how astrocytes are key in the maintenance of a healthy neuronal environment. We have captured the primary steps in this process along with the communication between an astrocyte and a group of neurons showing how neurons may undergo a toxic regime and how astrocytes could potentially balance the neuronal environment. ❧ Our most recent work explores the ability of astrocytes to influence phase synchronization on neurons by the slow inward currents (SICs) mechanism. We have successfully shown, in a small group of neurons, how phase synchronization could be caused through astrocytic triggering activation of NMDA receptors. ❧ We have designed and captured the dynamics of a depressing synapse and the changes induced to the synapse according to changes in presynaptic rate of spikes. We have captured the Weber-Fechner relationship and shown synaptic adaptability by sudden changes in the spike rate. In the long-term future, we envision as part of a larger and collaborative effort to introduce synaptic adaptability to the interactions of neurons and astrocytes for further testing and evaluation of hypothesis on astro-neuronal processing.

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Asset Metadata

Creator Irizarry-Valle, Yilda (author)

Core Title Modeling astrocyte-neural interactions in CMOS neuromorphic circuits

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Electrical Engineering (VLSI Design)

Publication Date 06/17/2016

Defense Date 03/23/2016

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag astrocytes,bioinspired circuits,biomimetic circuits,cognition,glial cells,neuromorphic,NMDA receptors,OAI-PMH Harvest,synchrony

Format application/pdf (imt)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Parker, Alice C. (committee chair)

Creator Email yildair@gmail.com,yirizarr@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c40-252839

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