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Astrocyte-mediated plasticity and repair in CMOS neuromorphic circuits

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Astrocyte-mediated plasticity and repair in CMOS neuromorphic circuits

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Content Astrocyte-Mediated Plasticity and
Repair in CMOS Neuromorphic
Circuits
by
Rebecca Kim Lee
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 2018
Abstract
Electronic circuits inspired by astrocytes can be utilized as mechanisms of plasticity and
self-repair in neuromorphic hardware systems. Through their slow, integrative properties,
astrocytes can monitor neural activity and trigger plasticity processes that are important for
maintaining useful neural activity. Astrocytes also provide indirectly-connected neurons with
a widespread form of communication that is not present in neuron-only networks. In this
research, we explore biological phenomena related to astrocytes that have not been imple-
mented in other neuromorphic systems. We present CMOS circuit models for these mech-
anisms and demonstrate applications where they are benecial to plasticity, homeostasis,
fault tolerance, and development in hardware astromorphic systems.
i
Acknowledgements
Thank you to my family and friends who supported me. Thanks to my lab mates in the
BioRC group. A huge thank you to my advisor, Professor Alice Parker, for her guidance
and patience. Thank you for believing in me. Also thank you to my committee members,
Professor Peter Beerel and Professor Francisco Valero-Cuevas, for their suggestions and
advice.
ii
Contents
Glossary vi
List of Figures viii
1 Introduction 1
1.1 Problem Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Astrocytes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 Problem Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.4 Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.5 Outline of this Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2 Background and Related Work 7
2.1 Neuroscience Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.1.1 Neurons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.1.2 Astrocytes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.1.3 Retrograde Signaling . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.1.4 Homeostatic Plasticity . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2 Neuromorphic Engineering Background . . . . . . . . . . . . . . . . . . . . . 15
2.2.1 Large-Scale Neuromorphic Architectures . . . . . . . . . . . . . . . . 16
2.2.2 The BioRC Project: Neural Circuits . . . . . . . . . . . . . . . . . . 20
2.2.3 Hardware Models of Astrocytes . . . . . . . . . . . . . . . . . . . . . 23
iii
3 Retrograde Signaling in Astrocyte-Neuromorphic Circuits 26
3.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.1.1 Retrograde Signaling and Plasticity in Biological Astrocyte-Neuron
Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.1.2 Self-Repair in Astrocyte-Neuron Networks . . . . . . . . . . . . . . . 30
3.2 CMOS Circuit Models of Neurons and Astrocytes with Retrograde Signaling
Mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.2.1 The Retrograde Messenger (RGM) Generation Circuit . . . . . . . . 32
3.2.2 The Retrograde (RG) Excitatory Synapse Circuit . . . . . . . . . . . 35
3.2.3 The Astrocyte Circuit . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.3 Self-Repair by RGM-Mediated Synaptic Plasticity in an Astrocyte-Neuromorphic
Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
4 Astrocyte Mechanisms for Homeostatic Plasticity through Modulation of
Postsynaptic AMPA Receptors 47
4.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
4.1.1 Glutamate Receptors at Excitatory Synapses . . . . . . . . . . . . . . 48
4.1.2 Role of Astrocytes in Homeostatic Plasticity . . . . . . . . . . . . . . 50
4.2 Circuit Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
4.2.1 An Astrocyte Circuit that Integrates Neural Activity . . . . . . . . . 54
4.2.2 Astrocyte Circuit that Determines when Neural Activity Levels Are
In a Stable Range . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
4.2.3 Synapse with Short- and Long-Term Weight . . . . . . . . . . . . . . 58
4.3 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
4.3.1 Inactivity-Induced STP Modulates the Long-Term Weight . . . . . . 70
4.3.2 Sample Demonstration of Various Plasticity Mechanisms . . . . . . . 72
iv
5 Dendritic Morphology and Plasticity 78
5.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
5.2 Background: Dendrite-Specic Action Potential Shapes . . . . . . . . . . . . 79
5.3 A Neuron Circuit with Input-Specic Spiking . . . . . . . . . . . . . . . . . 82
5.3.1 Structure of a Neuron with Multiple Dendrites and HVA Ca
2+
Channels 82
5.3.2 Axon Hillock Circuit with Eects from Multiple Dendrites . . . . . . 83
5.3.3 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
5.4 Signaling Astrocyte-Mediated Repair in a Bio-Inspired Ocular Network . . . 89
5.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
6 Conclusion and Future Work 98
Bibliography 102
v
Glossary
2-AG 2-Arachidonoylglycerol
AMPA -amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid receptor
AMPAR AMPA receptor
AP Action potential
CB1R Cannabinoid type 1 receptor
CI-AMPAR Calcium impermeable AMPAR
CNS Central nervous system
CP-AMPAR Calcium permeable AMPAR
DSE Depolarization-induced suppression of excitation
EPSC Excitatory postsynaptic current
EPSP Excitatory postsynaptic potential
GT Gliotransmitter
HVA High-voltage-activated
LTD Long-term depression
LTP Long-term potentiation
vi
NMDA N-methyl-D-aspartate
NMDAR NMDA receptor
NT Neurotransmitter
PSP Postsynaptic potential
RG Retrograde
RGM Retrograde messenger
STP Short-term potentiation
e-SP Synaptic potentiation through an RGM-mediated pathway
mGluR Metabotropic glutamate receptor
vii
List of Figures
2.1 A simplied illustration of the tripartite synapse taken from [1]. An astrocyte
process envelopes the terminals of a synapse connecting two neurons. Neu-
rotransmitters (Nt) are released from the presynaptic terminal and travel to
the postsynaptic terminal. The astrocyte detects synaptic activity by taking
up neurotransmitters from the synaptic cleft and in response, its intracellu-
lar Ca
2+
level increases. The astrocyte releases gliotransmitters (Gt) in a
Ca
2+
-dependent manner, modulating neuronal activity. . . . . . . . . . . . . 10
2.2 Dierent types of Ca
2+
signaling in astrocytes. From [2]. Signaling is re-
stricted to microdomains when there is little synaptic activity. When the
intensity of activity is higher, signaling can propagate intracellularly through
the astrocyte. With even higher activity levels, Ca
2+
signals can spread in-
tercellularly to other astrocytes. . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.3 Homeostatic plasticity can prevent runaway excitation [3]. . . . . . . . . . . 14
2.4 A block diagram of the BioRC neuron circuit. Synapse, dendritic arbor, and
axon hillock components are connected to form a neuromorphic neuron circuit. 21
2.5 The BioRC excitatory synapse circuit. A presynaptic action potential (AP)
is converted into an excitatory postsynaptic potential (EPSP). [4] . . . . . . 22
2.6 One-Shot Circuit [4]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.7 The BioRC excitatory synapse circuit with astrocyte-neuron interactions. [5] 24
2.8 The BioRC astrocyte microdomain circuit. [5] . . . . . . . . . . . . . . . . . 25
viii
3.1 Activity in postsynaptic neuron 1 causes DSE at presynaptic axon terminal
1 and e-SP at presynaptic axon terminal 2. (1) Activity in neuron 1 causes
(2) 2-AG to be synthesized and relesed in postsynaptic dendrite 1. (3) 2-AG
activates CB1R's on homoneuronal presynaptic terminal 1. (4) This then in-
hibits glutamate release by presynaptic terminal 1, causing DSE. (5) 2-AG can
also activate CB1R's on an adjacent astrocyte. (6) This causes elevations in
intracellular Ca
2+
and (7) stimulates the release of glutamate. (8) Astrocytic
glutamate activates mGluR's on heteroneuronal presynaptic terminal 2. (9)
This potentiates glutamate release causing e-SP. . . . . . . . . . . . . . . . . 28
3.2 Results showing plasticity eects caused by endocannabinoids, from [6]. (a)
Relative probability of neurotransimtter release (Pr) after neural depolariza-
tion (ND) plotted against the distance between somas of the stimulating neu-
ron and recording neuron. (b) Schematic diagram of the stimulation setup
used in the experiment. Stimulation (ND) is applied to the green neuron and
synaptic responses are recorded at a homoneuronal (green) and heteroneu-
ronal (blue) synapse. (c) EPSC responses and average response before (basal)
and after (ND) stimulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.3 A block diagram of the Neuron
RG
circuit. . . . . . . . . . . . . . . . . . . . . 32
3.4 The RGM Generation Circuit. . . . . . . . . . . . . . . . . . . . . . . . . . . 33
ix
3.5 Sample outputs from the RGM Generation Circuit. (a) A postsynaptic action
potential (AP
post
) causes a transient increase in RGM. The rate of production
r
RGM
was varied from 0.45V to 0.55V and the RGM signals were plotted. The
decay constant,
RGM
, was 0.4V for the rst spike and 0.45V for the second
spike. (b) A train of AP
post
spikes (black curve) emitted from the postsynaptic
neuron can cause RGM (blue curve) to increase even more. Here, six AP
post
spike were red with a period of 10ns. (c) A train of AP
post
spikes red with
a period of 20ns can not cause increased RGM. In (b) and (c),
RGM
was set
to 0.45V and r
RGM
was 0.55V. . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.6 The Retrograde (RG) Excitatory Synapse Circuit. . . . . . . . . . . . . . . . 36
3.7 Sample results from the RG Depression Circuit block whenRG dep control =
0:4V and VSS =0:4V . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.8 Design methodology for the Astrocyte Circuit. Astrocytes are divided into mi-
crodomains that ensheathe groups of synapses. Microdomain
1
and Microdomain
2
ensheathe three synapses each in this example. Each synapses releases an
amount of retrograde messenger depending on its activity level. The RGM
i
signals from each synapse get sent to their associated microdomains. The
microdomain Ca
2+
concentration (Ca
microdomain,i
) is represented by the aver-
age of RGM signals (1). Ca
microdomain,i
signals from adjacent microdomains
can in
uence each other (2). Microdomains release glutamate (glu
astro
) in a
Ca
microdomain
-dependent manner. Glu
astro
is the same for all synapses in the
same microdomain. Synapses in Microdomain
1
receive glu
astro,1
, and synapses
in Microdomain
2
receive glu
2
. . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.9 Microdomain Ca
2+
Circuit. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.10 Astrocyte Microdomain Coupling Circuit. . . . . . . . . . . . . . . . . . . . 40
x
3.11 (a) The Astrocytic Glutamate Release Circuit. (b) Example output from the
circuit when f glu = 1V, r glu = 0.32V, and glu = 0.35V. The circuit output,
glu
astro
, starts to increase when Ca
microdomain
is over a threshold of 0.49V. . . 42
3.12 (a) The astrocyte-neuron network used to demonstrate self-repair. (b) Illus-
tration of the expected results during normal operation. (c) The network with
one synaptic fault at S
8
. (d) Illustration of the results when no self-repair is
used in the damaged network. (e) Illustration of the desired results when
self-repair is used in the damaged network. . . . . . . . . . . . . . . . . . . . 43
3.13 Circuit simulation results for network. (a) Results during normal operation.
(b) Results when RGM signaling is omitted and one synapse (S
8
is broken.
(c) Results when RGM signaling is included and S
8
is broken. (d) Neuro-
transmitter (NT) signals for the synapses when S
8
is broken. (e) Number of
input spikes required before self-repair occurs as a function of r
RGM
when S
8
is broken. (f) Results when two synapses (S
7
and S
8
) are broken. . . . . . . . 46
4.1 AMPARs can be permeable or impermeable to calcium [7]. . . . . . . . . . . 49
4.2 Basic plasticity mechanisms caused by NMDARs and AMPARs. Adopted
from [7]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
4.3 Astrocyte as a memory element [8]. . . . . . . . . . . . . . . . . . . . . . . . 52
4.4 AstroCa circuit. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
4.5 AstroCa Threshold circuit. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
4.6 Sample output of the AstroCa Threshold circuit. . . . . . . . . . . . . . . . . 57
4.7 Block diagram of the synapse. . . . . . . . . . . . . . . . . . . . . . . . . . . 60
4.8 Flowchart of astrocyte control over synaptic plasticity mechanisms. . . . . . 62
4.9 Flowchart for dierent synaptic plasticity mechanisms. (a) STP during low
activity. (b) LTP/LTD during stable activity. (c) LTD during high activity. . 63
4.10 The synapse circuit. Includes CP-AMPARs and CP-AMPARs. . . . . . . . . 64
4.11 CI-AMPAR circuit. Generates long-term weight of a synapse. . . . . . . . . 65
xi
4.12 4-Bit Digital Counter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
4.13 Flip-
op circuit used in the digital counter circuit. . . . . . . . . . . . . . . . 66
4.14 DAC circuit used in Figure 4.11. . . . . . . . . . . . . . . . . . . . . . . . . . 66
4.15 Short-term weight circuit. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
4.16 NMDAR circuit. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
4.17 Short-term potentiation of a synapse by CI-AMPARs. . . . . . . . . . . . . . 71
4.18 Experimental network with one synapse and astrocyte components. . . . . . 73
4.19 Astrocyte controls type of plasticity at a synapse. . . . . . . . . . . . . . . . 77
5.1 Events that occur during remapping of contralateral forelimb sensory maps
after stroke damage. From [9]. . . . . . . . . . . . . . . . . . . . . . . . . . . 80
5.2 Adopted from [10]. (a) Illustration of neural stimulation. (b) Spike waveforms
recorded from dierent neurons have shapes that depend on stimulus location. 81
5.3 Block diagram of a neuron with multiple dendrites and HVA Ca
2+
channels. 83
5.4 Axon hillock circuit with eects from 2 dendrites. . . . . . . . . . . . . . . . 84
5.5 Neuron with 2 dendrites. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
5.6 Simulation results for neuron with 2 dendrites. . . . . . . . . . . . . . . . . . 86
5.7 Zoom-in of AP OUT in Figure 5.6. . . . . . . . . . . . . . . . . . . . . . . . 87
5.8 Ocular network. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
5.9 Previous BioRC excitatory synapse with astrocyte in
uence. . . . . . . . . . 91
5.10 (a) Simulation results from ocular network demonstrating that network can
recover from loss of a neuron. Zoomed-in portions of the waveforms for
AP POST1 and AP POST2 are shown from 90-120μs (b) and 500-530μs (c).
AP POST1 is shown in the upper, blue trace, and AP POST2 is shown in the
lower, black trace. Durations of the repolarizing tail are also shown. . . . . . 95
5.11 Ocular network remapping after recovery from damage in N1. . . . . . . . . 96
5.12 Ocular network remaps back to its original conguration if N1 functionality
is restored. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
xii
Chapter 1
Introduction
1.1 Problem Motivation
Neuromorphic engineering describes the eld of design of very large-scale integration (VLSI)
electronic circuits that model biological architectures and mechanisms found in the central
nervous system of humans and other living beings. The most basic component in neuro-
morphic circuits is the neuron. Neurons are connected to form neural networks that perform
various tasks. Hardware circuits are created using semiconductor electronic components
such as transistors, resistors, and capacitors, and other devices such as memristors and those
based on nanomaterials. Neuromorphic engineers aim to emulate the biological behaviors
and spike-based computations that make the brain one of the most ecient and powerful
computational units. From an engineering standpoint, the goal is for neural networks to
implement functions found in the brain in order to solve computational problems that are
dicult for traditional computers based on von Neumann architecture. Neuromorphic hard-
ware is well-suited for applications including computer vision, object recognition, and speech
recognition tasks. While von Neumann computers process data sequentially, neural network
computations are performed in a parallel-fashion across many neurons and memory is dis-
tributed throughout the network. This parallelism could allow neuromorphic computers to
1
1.1. PROBLEM MOTIVATION
be quicker and more energy-ecient.
One particular advantage of neuromorphic hardware can be the plasticity of its connec-
tions. There are two main types of plasticity in neural systems: synaptic plasticity and
structural plasticity. In synaptic plasticity, synaptic weights between connected neurons
can increase or decrease depending on the level of neural activity. In structural plasticity,
new connections can be made or already-existing connections can be lost between neurons.
Plasticity allows a neuromorphic system to learn and adapt to changing environments by
reconguring its connectional structures in response to perceived inputs and outputs. Re-
congurability and the parallelism of neuromorphic networks could also allow such systems
to be fault-tolerant and self-repairable. When a neuron fails, it is possible for the network to
restructure itself so that it could work around the faulty neuron and still provide the correct
output. This kind of fault tolerance is not usually realizable in systems that operate sequen-
tially. When one component in a sequential system fails, the entire downstream output can
fail as well. Plasticity is also important in developing neural networks.
The goal of the Biomimetic Real-Time Cortex (BioRC) project group at USC is to
reverse engineer the human brain and to research the feasibility of building an articial
electronic cortex. It has been estimated that the human brain contains 85 billion neurons
[11]. Of these, 20 billion neurons have been estimated to constitute the cerebral cortex
alone [12]. Thus a large number of circuit components and connections will be required to
build a synthetic cortex. Due to reliability issues in semiconductor processing and the sheer
amount of required components, it is probable that some components will be faulty when
a cortical circuit is fabricated. In order to circumvent this issue, fault-tolerant strategies
could and probably should be implemented in neuromorphic chips. Fault-tolerant and self-
repairing neuromorphic systems are also benecial to applications that require high degrees of
reliability but are not easily maintained. Examples of these applications include autonomous
cars that drive on busy city streets, unmanned spacecrafts, surgical robots, and neural
prosthetics.
2
1.2. ASTROCYTES
1.2 Astrocytes
Most of the work in neuromorphic engineering focuses on neurons as the main computa-
tional unit with information being transmitted from a presynaptic neuron to a postsynaptic
neuron. Networks are built using only neurons and biological mechanisms related only to
neurons are included. Much of this work is on spiking neural networks [13, 14], plasticity
[15, 16], and synaptic rewiring [17, 18]. However, recent research in neuroscience suggests
that astrocytes, a type of glial cell, have a signicant role in neuronal interactions. Stud-
ies have shown that astrocytes modulate synaptic transmission and plasticity mechanisms
through the regulation of neurotransmitter and gliotransmitter concentrations [1, 19, 20].
By uptaking or releasing glutamate and other chemicals in the synaptic cleft, astrocytes can
ne-tune neuronal excitability and behavior. Astrocytes have been implicated in synaptic
plasticity, synaptogenesis [21], and homeostatic functions [22, 23]. Through Ca
2+
signaling,
astrocytes also provide a form of communication between neurons that are not directly con-
nected through synapses. Astrocytes allow the activity of a neuron to have far-reaching
eects on neurons that are not in its immediate vicinity. This type of global communication
is not realizable by neuron-only networks, where communication only occurs locally between
connected neurons.
1.3 Problem Statement
Plasticity and adaptability are important for neuromorphic networks that are to be deployed
in the real world. Including multiple plasticity mechanisms can enhance the robustness
and fault-tolerance of a system. We hypothesize that homeostatic mechanisms inspired
by biological astrocytes can be used to reorganize synaptic weights in electronic neuronal
networks, compensating for damage or changing inputs. We hypothesize that astrocyte
circuits can be used to control plasticity mechanisms when neural activity deviates from a
set point. By varying the weights in the network, signals can be routed around areas where
3
1.4. APPROACH
inputs are lost. Homeostatic plasticity mechanisms can also be useful for development and
tuning of neural networks where synaptic weights start at zero or low values. The goal of this
work is to demonstrate how astrocytic intervention can be advantageous to neuromorphic
networks.
1.4 Approach
Our circuits are designed using the approach taken by the BioRC group. First-order eects of
behaviors found in the biological brain are emulated using hardware circuit models. Instead
of using standard cells, custom analog and mixed-signal circuits are built and used as the
system components. We exploit transistor resistances and capacitances to obtain desired
output voltages and time constants. Circuit voltages and currents are used to model biolog-
ical voltages and chemical signals. Signal amplitudes do not exactly match those found in
biology and circuit time constants are several orders faster than biological time constants.
The circuits we present t with the BioRC group's plug-and-play methodology where system
components are built in a modular fashion and control knobs are used for easy tunability of
circuit parameters.
While recent trends have pushed towards the use of nanotechnology in neuromorphic
hardware, we choose to use CMOS as the underlying technology for our circuit designs. The
reason for this is that CMOS is a mature and reliable technology. CMOS processes are
already established and circuits can be readily fabricated.
In this thesis, circuits are built using 45nm and 180nm CMOS technology. Circuits are
simulated in HSPICE and Cadence softwares. Fabrication of designed circuits is a long-term
goal for the BioRC group.
4
1.5. OUTLINE OF THIS THESIS
1.5 Outline of this Thesis
In Chapter 2, we review relevant topics in biology and in neuromorphic hardware. We discuss
new forms of neurotransmission and plasticity found in neuroscience literature including
communication through astrocytes, retrograde signaling, and homeostatic plasticity. Circuits
presented in this thesis are inspired by these biological mechanisms and our goal is to emulate
their rst-order eects. We also review dierent neuromorphic hardware approaches. First
we discuss the characteristics of several large-scale neuromorphic architectures. Then we
review neuron and astrocyte circuit components previously designed in our group (BioRC).
Finally we discuss electronic models of astrocytes designed by other groups.
A hardware model of retrograde signaling in astrocyte-neuromorphic circuits is presented
in Chapter 3. It models a type of homeostasis mechanism where synaptic potentiation and
depression caused by retrograde messengers balance each other out. The circuits are used to
demonstrate a self-repairing neuromorphic hardware circuit inspired by [24]. Similar circuits
and results were presented in [25].
In Chapter 4, we present a circuit for astrocyte eects on homeostatic plasticity through
postsynaptic AMPA receptors. We discuss our theory for astrocytic in
uence based on
evidence neuroscience literature. We present a view of astrocytes as integrators of neural
activity over long time scales. By integrating over long periods of neural activity, astrocytes
can determine when spiking rates are out of a healthy range and initiate compensatory
plasticity processes. We present the astrocyte as a thresholding unit with multiple thresholds.
When neural activity is above a high threshold, astrocytes depress synapses to bring activity
levels down. This is useful in preventing over-excitation and saturation of synaptic weights
in neuronal networks. If activity is below a low threshold, astrocytes potentiate synapses to
bring activity levels up into a normal operating range. This could be implemented in the
initial development phase of neural networks when synaptic weights are too low to generate
useful signals. It could also be useful for repairing damage in neuronal networks.
In Chapter 5, we present a multi-dendrite neuron circuit with spiking signals that depend
5
1.5. OUTLINE OF THIS THESIS
on specic input activation. We assume that potentials generated in a dendritic branch can
activate high-voltage calcium channels on that branch. The spatial location of these channels
allow a neuron to output action potentials with dierent shapes. We suggest that dierent
spike shapes can be used to signal when plasticity mechanisms have occurred in a neural
network. This output specicity allows downstream neurons to determine how they should
respond. We demonstrate an example where a network of bio-inspired ocular neurons in
the visual cortex repairs damage through astrocyte-mediated eects. An astrocyte detects
damage and initiates repair, and subsequent neural signaling re
ects the repair.
The circuit designs and implementations presented in this thesis are summarized in Chap-
ter 6, and recommendations for future work are discussed.
6
Chapter 2
Background and Related Work
2.1 Neuroscience Background
This section provides a brief overview of the neuroscience behind neurons and astrocytes.
Details for specic biological mechanisms related to the circuit models presented in this
thesis are discussed in later chapters.
2.1.1 Neurons
Neurons are nerve cells that are thought to be the main computational unit in the central
nervous system. They can send, receive, and process electrical and chemical signals. Neurons
connect with other neurons through synapses. The basic structure of a neuron contains four
main components: the soma (or cell body), dendrites, axon, and axon terminals. Synapses
connect the axon terminals of presynaptic neurons to the dendrites of postsynaptic neurons.
In the simplest model, neurons receive synaptic inputs at their dendrites and send outputs
by means of their axon terminals. Active neurons emit neurotransmitters into the synapses
at their axon terminals. Neurotransmitters diuse across the synaptic clefts and bind to
receptors on postsynaptic dendrites. Activation of receptors opens ion channels on the
cell and generates a postsynaptic potential (PSP), a change in the postsynaptic neuron's
7
2.1. NEUROSCIENCE BACKGROUND
membrane potential at the activated site. The soma integrates PSPs received from its
dendrites. Once the soma potential goes over a threshold, voltage-gated ion channels open,
allowing a large in
ow of positively-charged ions. This is followed by an out
ow of positive
ions, resulting in a voltage spike called an action potential. The action potential travels down
the axon away from the soma towards the axon terminals. The arrival of action potentials
causes neurotransmitters to be released by the axon terminals that stimulate other connected
neurons.
The process above is how neural communication has been described in conventional
neuroscience. However, modern studies have uncovered other mechanisms that aect neuro-
transmission. The mechanisms relevant to this thesis include synaptic modulation by astro-
cytes, retrograde signaling, and dendritic computation.
2.1.2 Astrocytes
While conventional neuroscience regards astrocytes as passive components in the brain whose
role is to support neurons, recent studies suggest that they may actually be able to process
synaptic information and actively participate in neurotransmission. Astrocytes are a type of
glial cell that contiguously tile the entire central nervous system in a non-overlapping fashion.
Astrocyte processes enwrap synapses to form what is called the "tripartite synapse" [1, 26].
Here, communication occurs bi-directionally between neurons and astrocytes in addition
to the conventional communication between pre- and postsynaptic neurons. An illustration
showing the communication pathways at the tripartite synapse is shown in Figure 2.1. Astro-
cytes can detect synaptic activity through the uptake of neurotransmitters in the synaptic
cleft. They can also release molecules that modulate synaptic activity such as glutamate,
GABA, D-serine, and ATP. The released molecules are called gliotransmitters since their
functions are similar to neurotransmitters with the exception that they are released from
glial cells rather than neurons. Astrocytes have both passive and active eects on neuronal
networks. As a passive eect, astrocytic uptake of neurotransmitters regulates ion levels in
8
2.1. NEUROSCIENCE BACKGROUND
the synaptic cleft to maintain homeostasis [27]. Astrocytic release of gliotransmitters modu-
lates synaptic acitivity. For example, glutamate released by astrocytes can activate receptors
on presynaptic terminals, increasing the amount of neurotransmitter they can release.
Astrocytes release gliotransmitters in a Ca
2+
-dependent manner. Neural activity increases
Ca
2+
concentrations in astrocytes, initiating intracellular Ca
2+
waves. Ca
2+
elevations can
be triggered by the activation of receptors for neurotransmitters and dierent chemicals
such as glutamate, GABA, ATP, and 2-Arachidonoylglycerol (2-AG), a type of retrograde
messenger. Gliotransmitters are released from astrocytes in concentrations that depend on
the local Ca
2+
concentration and they can have varying eects on neural activity. The
probability of neurotransmitter release from synaptic vesicles can be modulated by activat-
ing presynaptic receptors for glutamate, GABA, and 2-AG. Glutamate can also synchro-
nize neural populations by generating slow inward currents through NMDA receptors [28].
Astrocytically-released D-serine can control the activation of NMDARs [29], aecting long
term potentiation mechanisms. Through these mechanisms, astrocytes play an important
role in neurotransmission and plasticity in the brain.
Astrocytes provide neurons with a form of long-range communication. Through Ca
2+
signaling in astrocytes, neurons that are not directly connected to each other through
synapses can in
uence each other. Ca
2+
signaling behavior depends on the intensity of
neural activity [2]. The types of Ca
2+
signaling are illustrated in Figure 2.2 and include mi-
crodomain, intracellular, and intercellular signaling. When activity is low, astrocytic stim-
ulation is low and Ca
2+
levels increase only slightly in spatially-localized regions adjacent
to active synapses. These regions are called microdomains. When neural activity is higher,
Ca
2+
in the microdomain is higher and it can start a wave of Ca
2+
through a regenerative
process called calcium-induced-calcium-release (CICR) [30]. During CICR, initial elevations
of intracellular Ca
2+
trigger the formation of inositol 1,4,5-trisphosphate (IP3). IP3 then
activates IP3 receptors (IP3R), inducing the release of Ca
2+
inside the astrocyte from the
endoplasmic reticulum. The released Ca
2+
can then form more IP3 which activates neigh-
9
2.1. NEUROSCIENCE BACKGROUND
Figure 2.1: A simplied illustration of the tripartite synapse taken from [1]. An astrocyte
process envelopes the terminals of a synapse connecting two neurons. Neurotransmitters
(Nt) are released from the presynaptic terminal and travel to the postsynaptic terminal. The
astrocyte detects synaptic activity by taking up neurotransmitters from the synaptic cleft
and in response, its intracellular Ca
2+
level increases. The astrocyte releases gliotransmitters
(Gt) in a Ca
2+
-dependent manner, modulating neuronal activity.
10
2.1. NEUROSCIENCE BACKGROUND
Figure 2.2: Dierent types of Ca
2+
signaling in astrocytes. From [2]. Signaling is restricted
to microdomains when there is little synaptic activity. When the intensity of activity is
higher, signaling can propagate intracellularly through the astrocyte. With even higher
activity levels, Ca
2+
signals can spread intercellularly to other astrocytes.
boring IP3Rs and releases more Ca
2+
from internal stores in a regenerative process. Through
CICR, oscillating Ca
2+
waves are produced that can spread out intracellularly to other parts
of the astrocyte. Gliotransmitters are then released at synapses outside of the initial mi-
crodomain due to the propagating calcium wave. This mechanism allows a neuron to aect
the activity of other neurons that are not in direct synaptic contact. Territories formed by
astrocytes have been found to be in contact with more than 100,000 synapses. Thus astro-
cytes provide neurons with a form of global, indirect communication. This is in contrast
with communication via synapses which is a type of local communication between neurons
that are in direct contact. Ca
2+
waves can also propagate intercellularly between astrocytes
through gap junctions, increasing the area of in
uence. This type of communication requires
even higher levels of neuronal activity.
Astrocytes communicate at time scales much slower than that of neurons. Astrocyte
calcium signaling has been found to operate on the order of 10s of seconds to minutes [31],
orders of magnitude greater than the typical millisecond duration of neural action potentials.
Due to delayed response times, it is improbable that astrocytes can exert immediate eects
11
2.1. NEUROSCIENCE BACKGROUND
on synaptic activity. However, slow and gradually-rising responses of astrocytes may make
them useful for dierent forms of communication such as homeostatic plasticity. Also, recent
evidence suggests that many astrocytes may actually exhibit rapid responses in addition to
slow responses [32]. It was found that astrocytes in the somatosensory cortex could respond
to external stimuli with brief Ca
2+
elevations within 1s of stimulus onset. Responses also
contained slow components with a mean latency of 14.4s. Although the fast astrocytic
response is still much slower than neuronal communication, these ndings suggest that the
role of astrocytes on neurocommunication should be reconsidered.
2.1.3 Retrograde Signaling
Traditionally, neurotransmission has been thought to be a unidirectional process with infor-
mation being communicated from the presynaptic neuron to the postsynaptic neuron. How-
ever retrograde messengers have been found that allow communication in the opposite direc-
tion, from postsynaptic to presynaptic neuron [33, 34]. Retrograde messengers are released
from postsynaptic neurons and travel in a "backwards" direction to activate presynaptic
receptors, ultimately in
uencing presynaptic neurotransmitter release. Signaling by retro-
grade messengers has been implicated in forms of synaptic plasticity and neuroprotection [6].
Neurotransmission eects of retrograde messengers have been found to be related to both
neurons and astrocytes [6, 8]. In regard to fault-tolerance, recent computational studies
have demonstrated that retrograde signaling could be used to initiate self-repair in neuron-
astrocyte networks [24, 35].
In light of these new ndings, it would be worthwhile to create neuromorphic systems
that include models for astrocytic mechanisms and retrograde signaling. These mechanisms
could give neuromorphic circuits extra functionalities that cannot be achieved by networks
formed using only neurons. In particular, it is benecial to the BioRC project to investigate
whether these mechanisms can be implemented to create fault-tolerant and self-repairing
neuromorphic circuits.
12
2.1. NEUROSCIENCE BACKGROUND
2.1.4 Homeostatic Plasticity
Homeostatic plasticity, or synaptic scaling, refers to plasticity mechanisms that potentiate
or depress all of a neuron's synapses in order to maintain stable ring rates. In contrast to
Hebbian plasticity, which selectively modulates weights based on the activity of individual
synapses, homeostatic plasticity induces global changes over multiple synapses.
In excitatory networks, homeostatic plasticity can be used to prevent runaway excitation
caused by Hebbian plasticity by globally depressing synapses once neural activity reaches
an activity set point. The eects are illustrated by the cartoon in Figure 2.3. Correlated
presynaptic and postsynaptic activity potentiates synapses by Hebbian mechanisms. In turn,
increased synapse strengths may generate more activity between correlated neurons, creating
a positive feedback loop (Figure 2.3(a)). Unconstrained potentiation can eventually lead to
a loss in synapse specicity of a neuron (Figure 2.3(b)). After one synapse experiences LTP,
the postsynaptic neuron is driven more strongly, making it easier for the neuron to re. This
could lead to LTP of other synapses that should not be potentiated. Figure 2.3(c) shows
what could happen if synaptic scaling is used. The left gure shows the original weight
conguration and desired ring rate of the output neuron. In the middle gure, the middle
synapse is potentiated by LTP, leading to an increase in output neural activity. In response
to increased activity, homeostatic plasticity mechanisms depress all synapses so that a stable
ring rate is maintained (right gure). The weight of the middle synapse is still larger than
the other synapses, preserving input specicity.
In biology, demonstrations of homeostatic plasticity have been found in the visual and
auditory systems [3, 36]. During early stages of postnatal development in the visual cortex,
synaptogenesis and the number of synaptic connections is high. It has been found that there
is an inverse relationship between mESPC frequency and amplitude. Furthermore, this type
of relationship does not exist when animals are raised in the dark. These ndings suggest
that when visual drive and mESPC frequency increase, synaptic strengths are decreased to
lower neural ring rates.
13
2.1. NEUROSCIENCE BACKGROUND
Figure 2.3: Homeostatic plasticity can prevent runaway excitation [3].
14
2.2. NEUROMORPHIC ENGINEERING BACKGROUND
Homeostatic plasticity can also be used to increase synaptic strengths when neural ac-
tivity is too low. It has been found that AMPA-silent synapses are transiently unsilenced
following periods of inactivity [37]. After minutes of inactivity, AMPARs move in to the
synapse membrane, eectively increasing the synaptic weight. It has also been demon-
strated that neurons in the postnatal visual cortex exhibit homeostatic behavior through
increased responses following inactivation of the optic nerve over a time period of 2 days
[38]. Interestingly, the eects were reversed after vision was restored.
Activity thresholds for homeostatic plasticity have been found to vary over developmental
stages. For example, layer 4 cortical neurons respond homeostatically during early develop-
ment [38]. At later stages of the visual system critical period, homeostatic responses in layer
4 neurons are turned o and moved into layers 2 and 3. In layers 2 and 3, the responses were
shown to persist into adulthood [39, 40]. It was hypothesized that homeostatic plasticity in
layer 4 neurons were switched o because homeostasis responses to sensory deprivation in
adults would amplify noise in layer 4 neurons, an undesirable eect. Layer 2 and 3 neurons,
on the other hand, receive many lateral and feedback connections from other areas in the
cortex. Switching on homeostatic plasticity in these neurons during adulthood could encour-
age remapping of cortical areas deprived of sensory drive. Areas that receive low levels of
sensory input activity could be taken over by areas with intact sensory drive, increasing the
signal processing eciency of intact regions.
2.2 Neuromorphic Engineering Background
Diverse approaches to building bio-inspired hardware neural circuits have been proposed
by dierent groups using analog, digital, and mixed mode designs. Silicon neurons have
been built using hybrid analog-digital hardware [41, 42], digital hardware [43], FPGAs [44],
and GPUs. Some architectures aim to capture only the most basic spiking properties of
neurons. Many of the neurons in these systems implement a simple integrate and re model,
15
2.2. NEUROMORPHIC ENGINEERING BACKGROUND
and they are used to build large-scale systems to solve complicated computational problems
such as computer vision [45, 46]. Others take a more biophysical approach based on Carver
Mead's work by utilizing the resistive and capacitive properties of silicon devices to model
ion channels and other complex behaviors in neurons [47]. Silicon models of the retina [48]
and cochlea [49] have been built.
Neuromorphic hardware is usually comprised of neural elements such as synapses, den-
dritic arbor, and soma cells or axon hillocks. Spikes (action potentials) input to synapses
are converted into postsynaptic potentials (PSPs). The amplitude of PSPs are controlled by
the weights of the synapses. PSPs are summed through the dendritic arbor and sent to the
axon hillock. When the total PSP received by the axon hillock is above the ring threshold,
the axon hillock emits an output spike.
2.2.1 Large-Scale Neuromorphic Architectures
Several architectures for large-scale neuromorphic hardware include implementations by
TrueNorth [50], NeuroGrid [42], and BrainScaleS (FACETS) [51]. Neurons built by TrueNorth
are based on custom fully digital hardware. Each core of the network consists of a neuron
circuit with a co-located memory (SRAM) that stores data from the neuron, a router to
receive and transmit spike events, a scheduler that buers received spike events to model
axonal delays, and an event-driven controller that controls operation of the core. Neuron
cores are arranged in a two-dimensional mesh network, and spike events are communicated
between cores through time-multiplexed interconnection wires. Information regarding ax-
onal delay and the destination of a spike are found in the memory of each core and encoded
into a packet. The packet is input into the interconnection mesh where it gets routed to its
target core. TrueNorth has built a chip with 1 million neurons in CMOS technology, and
they were able to demonstrate real-time object detection and classication using the chip
[50]. Each neuron was programmable and power consumption was found to be 20mW/cm
2
,
which is lower than conventional CPUs that usually consume 50-100W/cm
2
. While the
16
2.2. NEUROMORPHIC ENGINEERING BACKGROUND
neuron circuits and systems designed by TrueNorth are inspired by biology, they are not
biomimetic and lack many of the elaborate details of biological neurons such as ion channel
dynamics. Their network also required oine learning in order to train the network with
well-known algorithms, such as convolutional networks and support vector machines, that
could be used for object detection and classication. Once trained, the algorithms could
be run successfully on the network, but the algorithms could not be modied. This is in
contrast with the human brain, that can continuously learn and modify itself online. The
human brain does not lose its ability to learn new things once fully developed. The brain
has the remarkable ability of changing and adapting in response to dierent stimulations
and environments even in adulthood.
The FACETS project used custom analog hardware to design neuron circuits with the
ultimate goal of building neuromorphic models of neural tissue for neuroscience research [51].
They were able to build neurons that could have more than 10,000 input synapses using
CMOS application-specic integrated circuits. Systems were fabricated at wafer-scale, with
single wafers containing 4x10
7
synapses and up to 180,000 neurons. For their neuron, they
used the integrate-and-re model with several additions to allow dierent spiking patterns
such as spike frequency adaptation, phasic spiking, tonic spiking, and bursting. Synaptic
weights are represented by currents. The weight of an individual synapse is stored in a 4-bit
SRAM memory cell, and an analog signal controls the maximum conductance of a column
of synapses. The conductance is multiplied by the 4-bit weight to get the synapse's actual
weight. The synaptic weights are not completely analog and have a resolution of 6 to 8 bits,
limiting capabilities of this architecture. FACETS neurons exhibit forms of plasticity such
as short-term depression and facilitation, and STDP. Synaptic weights are changed using a
digital control circuit. Implementing neural networks on the scale of the human brain could
become expensive due to the number of digital control circuits that will be required. In
addition, FACETS requires specialized software in order to interface with the hardware, and
FPGAs are required for communication between multiple wafers.
17
2.2. NEUROMORPHIC ENGINEERING BACKGROUND
The Neurogrid project also uses custom analog hardware in their neuromorphic systems
[42]. Their systems use shared synapse and shared dendritic arbor architectures in order
minimize the number of transistors and connections in their circuits. The only element that
is not shared between neurons is the soma. Interconnections were made using a tree net-
work rather than a two-dimensional mesh network in order to maximize throughput since
signals would not need to be multiplexed. Each neuron has four synapses, and biological
properties of neurons were emulated by operating CMOS transistors in the subthreshold
regime. Properties include membrane capacitances, ion channel conductances, refractory
periods, spike-frequency adaptation, and ion channel gating. They fabricated a chip con-
sisting of 1 million neurons and 8 billion synapses. By conguring the system to implement
recurrent inhibition with 15 layers they demonstrated globally synchronous spiking activity
in the network, a behavior that is found in biological neurons. The system consumed 2.7W
during simulation. Although the system is easily implementable and energy ecient, it has
several limitations. Neurons found in the human brain may have thousands of synapses,
leading to rich and complex behaviors. Neurogrid neurons, on the other hand only have four
synapses each. This could limit the capabilities of the neural networks that are built from
these neurons. Neural connectivity and signal routing is controlled by event-driven digital
circuitry based on FPGAs and SRAMs. When scaled up to larger networks, the addition of
digital circuitry and memory could become expensive and take away from the eciency of
the analog portion of the design. Another limitation of Neurogrid is that it does not include
plasticity mechanisms which are important for learning and network adaptability.
While the architectures presented above are all excellent approaches to neuromorphic
hardware, they omit many important features that are found in biological neurons. Most
approaches use simplied neuron models, such as the integrate-and-re model, or they model
only the most prominently-studied attributes, such as ion channel conductances. Some
neuromorphic hardware designs even exclude plasticity mechanisms that are necessary for
learning and recongurability. These systems also leave out models for other important cells
18
2.2. NEUROMORPHIC ENGINEERING BACKGROUND
found in the brain, such as astrocytes. The reason for omitting detailed neural behavior is
that there is a tradeo between accurate biological models and device count. Creating real-
istic models that capture neural behavior entirely requires larger, more complicated circuitry
and connectivity. It is especially dicult to implement accurate models and vary parame-
ters in analog hardware due to the nonlinear characteristics of CMOS transistors. However,
emulations of other biological features could still be benecial to neuromorphic systems.
Although there is a tradeo in cost, detailed models could provide neuromorphic systems
with brain-like functionalities that are not realizable with simplistic models. Exploring other
less-studied neural mechanisms could help neuroscientists unshroud the mysteries surround-
ing the human brain and provide engineers with methods that could be used to bring the
eciency of neuromorphic hardware closer to that of the brain.
Furthermore, the above approaches omit mechanisms for fault tolerance and self-repair.
Some of these approaches mention that fault-tolerance is a behavior that will inherently
emerge from large networks due to the distributed processing power and parallel activity of
neural networks. However not much analysis can be found for the fault tolerance of neural
networks and it is still relatively unknown how networks will handle faults. In order for
networks to be fault-tolerant, they will need to be very large with many dense connections.
Even so, these mechanisms may not be foolproof. Other mechanisms for fault tolerance
use redundancy. The SpiNNaker system uses redundant neural components and redundant
circuits for control signal generation, system memory, and interconnections [52]. Other
methods such as triple modular redundancy (TMR) use multiple identical circuits to nd
the output of a neuron. The circuits perform the same process and their outputs are sent
throug a majority-voting circuit to nd a single best output [53]. These methods for fault
tolerance require extra circuitry that could become costly in large networks. Fault tolerance
and self-repair are important features that the human brain manages quite well without too
many redundant resources. For example, many patients survive and spontaneously start
recovery following brain damage from a stroke [54]. Plasticity mechanisms such as synaptic
19
2.2. NEUROMORPHIC ENGINEERING BACKGROUND
strengthening and activity-dependent rewiring allow the brain to recover functionality and
re-learn behaviors that may have been lost. In light of this, it would be benecial to study
how fault-tolerance is implemented in the human brain with the goal of nding a ecient
solution that could be utilized in neuromorphic systems.
2.2.2 The BioRC Project: Neural Circuits
The work is presented here is part of the BioRC Project at USC. The BioRC group designs
neuromorphic hardware and systems in silico using analog electronic circuits. Previous
work from our group include circuit designs of excitatory and inhibitory synapses, dendritic
arbor, and axon hillock. These circuit components are designed in a modular fashion and
can be connected together to form neuron circuit models. A block diagram of the BioRC
neuron is shown in Figure 2.4. Presynaptic action potentials (AP
pre
) are sent to synapses.
Excitatory synapses turn the input action potentials into positive excitatory postsynaptic
potentials (EPSP), and inhibitory synapses turn action potentials into negative inhibitory
postsynaptic potentials (IPSP). The dendritic arbor is a tree of analog adders that sums the
EPSPs and IPSPs to generate the total PSP. The axon hillock circuit generates an output
postsynaptic action potential (AP
post
) when the total PSP is greater than the ring threshold
(V
thr
).
The BioRC exciatory synapse circuit is shown in Figure 2.5. It focuses on emulation
of biological attributes including neurotransmitter release, neurotransmitter concentration
in the synaptic cleft, and neurotransmitter reuptake [55]. The synapse circuit converts an
input action potential (AP) at its presynaptic terminal into an excitatory postsynaptic po-
tential (EPSP). NTe represents the amount of excitatory neurotransmitters released from
the presynaptic terminal. ReU represents the reuptake mechanism that clears neurotrans-
mitters from the synaptic cleft. RR models the resting return of the synapse and controls
how fast the EPSP returns to resting potential. The voltage at Syn. Cleft represents the
actual amount of neurotransmitter in the synaptic cleft, and the potential ECh represents
20
2.2. NEUROMORPHIC ENGINEERING BACKGROUND
Figure 2.4: A block diagram of the BioRC neuron circuit. Synapse, dendritic arbor, and
axon hillock components are connected to form a neuromorphic neuron circuit.
the electromotive force. When an AP arrives at the presynaptic terminal, it increases the
voltage at Syn. Cleft through the pull-up path formed by transistors X3, X4, and X7. Syn.
Cleft is limited by transistor X7 and NTe. The neurotransmitters then get cleared from the
synaptic cleft by ReU and transistors X5 and X6. The output EPSP gets pulled up close
to ECh through transistor X8. Its amplitude is controlled by Syn. Cleft, and it returns to
resting potential (0V) at a rate controlled by RR. An STDP circuit based on activation of
NMDA receptors was also designed [56].
A one-shot circuit that is useful for generating voltage pulses with controlled duration
was shown in [4]. A high input discharges the capacitor to 0V, pulling up the output voltage.
VCNTL is a control voltage that modulates the resistance in a pull-up path connected to
the capacitor. The duration of the output pulse is controlled by VCNTL. Lower voltages
decrease the charging time and pulse width while higher voltages decrease the pulse duration.
21
2.2. NEUROMORPHIC ENGINEERING BACKGROUND
Figure 2.5: The BioRC excitatory synapse circuit. A presynaptic action potential (AP) is
converted into an excitatory postsynaptic potential (EPSP). [4]
Figure 2.6: One-Shot Circuit [4].
22
2.2. NEUROMORPHIC ENGINEERING BACKGROUND
2.2.3 Hardware Models of Astrocytes
To the best of our knowledge, the BioRC group has designed some of the rst hardware
circuit models of astrocytes. These circuits emulated the ability of astrocytes to detect
neural activity and release glutamate in response to calcium excitability [5]. Further designs
modeled and investigated interactions between neurons and astrocytes [57]. The ability
of astrocytes to generate slow inward currents in neurons through NMDA receptors, and
its in
uence on neural phase synchrony has also been modeled [58]. The BioRC astrocyte
circuits have all been designed in analog circuits.
The BioRC excitatory synapse with added circuitry modeling astrocyte-neuron interac-
tions is shown in Figure 2.7. It is a modication of the circuit in Figure 2.5 that emulates
how astrocytes increase excitability of synapses in a Ca
2+
-dependent manner. The voltage
AstroCa
2+
represents the concentration of Ca
2+
in an astrocyte microdomain adjacent to the
synapse. When it is high enough, it causes the voltage V
astro glut
to be added to the Synaptic
Cleft voltage through an analog voltage adder. This models the release of gliotransmitters by
the astrocyte and subsequent increase in neurotransmitters and excitability in the synaptic
cleft, increasing the amplitude of the output EPSP, Out(EPSP).
The BioRC astrocyte microdomain circuit is shown in Figure 2.8. It shows several com-
partments of an astrocyte. The microdomain is a resistive network whose resistivities are
controlled by the NMOS transistors and voltage Vbias. Inputs to the microdomain are
the Synaptic Cleft voltages from its connected synapses representing the amount of neuro-
transmitter in each synapse.
Other groups have since generated models of astrocyte behavior in hardware. Valenza et
al. used a bipolar junction transistor to model the nonlinear interactions between a single
neuron and a single astrocyte [59]. Ranjbar and Amiri demonstrated an analog astrocyte
circuit that can be used to change the spike frequency of connected neurons [60]. They also
demonstrated an astrocyte that synchronizes two adjacent neurons [61]. A digital hardware
model was presented by Nazari et al. [62]. Here, complex mathematical models of astro-
23
2.2. NEUROMORPHIC ENGINEERING BACKGROUND
cyte dynamics were implemented on an FPGA. Haghiri et al. also demonstrated FPGA
implementations of astrocyte dynamics including a multiplier-less design [63{65].
Figure 2.7: The BioRC excitatory synapse circuit with astrocyte-neuron interactions. [5]
24
2.2. NEUROMORPHIC ENGINEERING BACKGROUND
Figure 2.8: The BioRC astrocyte microdomain circuit. [5]
25
Chapter 3
Retrograde Signaling in
Astrocyte-Neuromorphic Circuits
In this chapter, a CMOS circuit model of retrograde signaling is presented. The circuits were
motivated by recent computational models that showed how retrograde signaling eects can
be used to initiate "self-repair" in astrocyte-neuron networks.
3.1 Background
3.1.1 Retrograde Signaling and Plasticity in Biological Astrocyte-
Neuron Networks
Following sucient neural activity, the postsynaptic dendrites of a neuron produce and re-
lease 2-arachidonylglycerol (2-AG), a retrograde messenger, back into its synaptic clefts [66].
2-AG is a lipid neurotransmitter that is a part of the body's endogenous endocannabinoid
system. Recent work in neuroscience has shown that the endocannabinoid system has impor-
tant neuromodulatory functions in the CNS with implications in learning, memory, anxiety,
and response to pathologies. Endocannabinoids are stored in the lipid membrane of neurons
and are rapidly released "on-demand" following membrane depolarization [67]. This mech-
26
3.1. BACKGROUND
anism is dierent from other synaptic exocytosis mechanisms where neurotransmitters are
stored in synaptic vesicles that must fuse with the cell membrane before secretion.
2-AG activates CB
1
and CB
2
cannabinoid receptors in the CNS. CB
1
receptors are readily
expressed in areas of the brain including the cortex, basal ganglia, and hippcampus. Sig-
nicant amounts of CB
1
receptors have been found in both glutamatergic neurons [68] and
GABAergic interneurons [69]. CB
1
receptors are prominently found at perisynaptic locations
on presynaptic axon terminals of neurons, and they have also been found on glial cells [70].
CB
2
receptor expression is much lower than that for CB
1
receptors. However they are found
neural and glial cells, and they seem to have roles following neural injury and pathological
conditions [71, 72].
Endocannabinoids are thought to be a type of retrograde messenger due to the locations
of CB
1
receptors (CB1R). Localization at presynaptic dendrite terminals allow CB1Rs to
respond rapidly to 2-AG that is released following postsynaptic activity. Activation of CB1Rs
can modulate the probability of neurotransmitter release from presynaptic terminals. This
forms a feedback loop where postsynaptic activity can control presynaptic plasticity.
Presynaptic modulation by 2-AG can have both depressing and potentiating eects.
These eects usually have rapid onset and are short-lived, leading to short-term forms of
plasticity. By binding directly to presynaptic cannabinoid type 1 receptors (CB1R), 2-AG
reduces presynaptic neurotransmitter release in glutamatergic neurons in a process called
depolarization-induced suppression of excitation (DSE) [6]. 2-AG can also activate CB1R's
on astrocytes adjacent to the synapse, causing Ca
2+
concentrations to increase. Eleva-
tion in Ca
2+
stimulates the release of glutamate, which then activates presynaptic type 1
metabotropic glutamate receptors (mGluR) to increase neurotransmitter release in a mech-
anism termed synaptic potentiation (e-SP) [6]. These signaling pathways are illustrated
in Figure 3.1. The specic eects of 2-AG at a synapse have been shown to be location-
dependent. DSE has a local eect, suppressing homoneuronal synapses that are directly
connected to the postsynaptic neuron. On the other hand, e-SP allows widespread, indirect
27
3.1. BACKGROUND
Figure 3.1: Activity in postsynaptic neuron 1 causes DSE at presynaptic axon terminal 1 and
e-SP at presynaptic axon terminal 2. (1) Activity in neuron 1 causes (2) 2-AG to be synthe-
sized and relesed in postsynaptic dendrite 1. (3) 2-AG activates CB1R's on homoneuronal
presynaptic terminal 1. (4) This then inhibits glutamate release by presynaptic terminal 1,
causing DSE. (5) 2-AG can also activate CB1R's on an adjacent astrocyte. (6) This causes
elevations in intracellular Ca
2+
and (7) stimulates the release of glutamate. (8) Astrocytic
glutamate activates mGluR's on heteroneuronal presynaptic terminal 2. (9) This potentiates
glutamate release causing e-SP.
communication between neurons through astrocytic pathways. e-SP potentiates heteroneu-
ronal synapses that are not connected to the neuron producing 2-AG.
Navarrete and Araque demonstrated the eects of DSE and e-SP [6]. Results from their
experiments are shown in Figure 3.2. Figure 3.2(b) shows the setup used in their experiments.
A neuron (green) is stimulated by applying depolarizing pulses that generate spiking, and
responses are measured in surrounding synapses. Responses are recorded from homoneuronal
synapses on the stimulated neuron (green) or from heteroneuronal synapses on a dierent
neuron (blue). The red cells illustrate astrocytes. Figure 3.2(a) shows the relative probability
28
3.1. BACKGROUND
Figure 3.2: Results showing plasticity eects caused by endocannabinoids, from [6]. (a)
Relative probability of neurotransimtter release (Pr) after neural depolarization (ND) plotted
against the distance between somas of the stimulating neuron and recording neuron. (b)
Schematic diagram of the stimulation setup used in the experiment. Stimulation (ND) is
applied to the green neuron and synaptic responses are recorded at a homoneuronal (green)
and heteroneuronal (blue) synapse. (c) EPSC responses and average response before (basal)
and after (ND) stimulation.
of neurotransmitter release (Pr) following neural depolarization (ND) as a function of soma
distance between the stimulating and recording neurons. It can be seen that soma distances
below 60μs tend to get depressed while larger distances tend to get potentiated. Figure
3.2(c) plots EPSCs recorded from 20 heteroneuronal and homoneuronal synapses. The top
traces show the responses overlaid on each other and the bottom traces show the average.
Responses before stimulation (basal) and after stimulation (ND) are plotted for comparison.
It can be seen that heteroneuronal synapses had increased responses following stimulation,
demonstrating potentiation caused by e-SP mechanisms. On the other hand, responses
decreased for homoneuronal synapses. This demonstrated depression caused by DSE.
29
3.1. BACKGROUND
3.1.2 Self-Repair in Astrocyte-Neuron Networks
Wade et al. proposed a system that uses retrograde signaling plasticity mechanisms for
self-repair in computational models of astrocyte-neuron networks [24]. The authors suggest
that the opposing eects of DSE and e-SP balance each other out in homeostasis in order to
maintain stable synaptic weights and ring rates in healthy neurons. They assume that 2-
AG is synthesized and released every time the postsynaptic neuron res an action potential.
Unhealthy neurons are dened as those that have broken synapses whose weights are zero
or very low. An unhealthy neuron would have a low or zero ring rate, meaning that it
would not release 2-AG, and DSE would not occur at its homoneuronal synapses. However
e-SP could still occur at its remaining healthy synapses if other neurons surrounding it are
active. This skews the balance between DSE and e-SP in favor of e-SP so that there is a net
potentiation eect at the synapses of unhealthy neurons. The potentiation could compensate
for the loss of synapses and increase the ring rates of unhealthy neurons so that they are
closer to normal.
Later works from the same group uses the suggested self-repair mechanisms in digital
hardware implementations. The mechanism was applied to an implementation of a robotic
mobile car [73]. The spiking neural network and astrocyte models are implemented on an
FPGA to control the left and right wheels to generate forward motion of the car. The au-
thors claim that functionality is retained when 20% of the synapses in the network are faulty,
and that performance is only degraded slightly when 80% of synapses are faulty. In [74], the
authors applied the retrograde signaling repair mechanism to a novel hardware architecture
for neural networks and measured output spiking frequencies in dierent network cong-
urations. Results from their hardware experiments are compared to results from software
simulations. They found that their network could maintain spiking frequencies when up to
40% of synapses were broken. With 80% of synapses being faulty, performance was degraded
by 20%. In these implementations, faults refer to synapses that no longer respond to action
potential inputs, eectively meaning that the synapse weight is zero.
30
3.2. CMOS CIRCUIT MODELS OF NEURONS AND ASTROCYTES WITH
RETROGRADE SIGNALING MECHANISMS
3.2 CMOS Circuit Models of Neurons and Astrocytes
with Retrograde Signaling Mechanisms
The block diagram of a neuron circuit with retrograde signaling mechanisms presented in
this thesis is shown in Figure 3.3. This type of neuron will be referred to as the Neuron
RG
circuit. It is modied from the BioRC neuron circuit, and the pathway between synapses
and astrocytes are also shown. Brie
y, presynaptic action potentials (AP
pre
) impinge on
synapses. The synapses also respond to retrograde activity. EPSPs output from the synapses
are summed by the dendritic arbor, and the total EPSP is sent to the axon hillock. When the
total EPSP is above the ring threshold, the axon hillock emits an output spike (AP
post
). The
Retrograde Messenger Generation block increases the concentration of retrograde messengers
(RGM ) in the synaptic cleft in response to postsynaptic activity. The amplitude of RGM
increases with more AP
post
spikes. Short-term synaptic plasticity mechanisms mediated by
RGMs are included. The RGM signal is sent back to the excitatory synapses to suppress
activity through RG depression. RGM is also sent to the astrocyte block where it increases
intracellular Ca
2+
. The astrocyte then releases glutamate (Glu
astro
) in response to its Ca
2+
level. Glu
astro
is sent back to the synapses and globally potentiates activity through the RG
potentiation mechanism.
The dendritic arbor and axon hillock components of the circuit are the same as previous
designs from the BioRC group. Three new circuits were designed: (1) the Retrograde Mes-
senger (RGM) Generation Circuit block; (2) the Astrocyte Circuit; and (3) the Retrograde
(RG) Excitatory Synapse Circuit. The RGM Generation Circuit converts postsynaptic ac-
tivity of a neuron into a voltage that represents the concentration of RGM released back into
the synaptic cleft. The Astrocyte Circuit detects neural activity and emulates the release
of glutamate to presynaptic terminals. The circuit for the astrocyte is based on previous
designs from the BioRC group but uses a dierent approach based on RGM concentrations
instead of neurotransmitter concentrations. The RG Excitatory Synapse Circuit is based
31
3.2. CMOS CIRCUIT MODELS OF NEURONS AND ASTROCYTES WITH
RETROGRADE SIGNALING MECHANISMS
Figure 3.3: A block diagram of the Neuron
RG
circuit.
on previous synapse designs from the BioRC group. However the neurotransmitter con-
centration of the synapse can be modulated due to potentiating and depressing eects via
astrocytes and retrograde signaling. CMOS designs for the new circuits will be presented in
this section.
3.2.1 The Retrograde Messenger (RGM) Generation Circuit
In their biophysically-based computational model for astrocyte-neuron systems, Wade et. al
assumed that a postsynaptic neuron releases RGMs every time it res. They described the
dynamics of RGM generation and decay with the following equation [24]:
d(RGM)
dt
=
RGM

RGM
+r
RGM
(tt
sp
)
RGM represents the amount of retrograde messengers in the synaptic cleft.
RGM
is the
decay rate, and r
RGM
is the production rate of RGMs. t
sp
is the time when postsynaptic
spikes are emitted.
A circuit model for RGM production and decay is shown in Figure 3.4. When a post-
32
3.2. CMOS CIRCUIT MODELS OF NEURONS AND ASTROCYTES WITH
RETROGRADE SIGNALING MECHANISMS
Figure 3.4: The RGM Generation Circuit.
synaptic neuron res, AP
post
momentarily goes high, creating a current through transistors
M1-M3. This current is mirrored to the pathway through transistors M4-M5, and some
charge gets stored on the capacitance formed by the gate of transistor M6. The output
of this node (RGM ) represents the amount of RGM in the synaptic cleft. The increase in
RGM 's amplitude every time a spike is red is controlled by the signal r
RGM
and the resistive
properties of transistor M2. When r
RGM
is high, more current is allowed to
ow through the
paths of the current mirror andRGM increases more. RGM decays through transistor M5.
The rate of decay is controlled by the resistance through this path which is set by the bias
voltage
RGM
.
Sample outputs from the RGM Generation Circuit are shown in Figure 3.5(a). The
amplitude of RGM can be tuned by varying the voltage r
RGM
. Higher r
RGM
results in
higher RGM amplitude. The time constant of RGM can also be tuned by varying
RGM
.
Higher
RGM
voltages result in faster decay time constants. Using the resistive and capacitive
properties of the RGM Generation Circuit, RGM can increase even further depending on
the level of postsynaptic activity. Figure 3.5(b) shows the response when the postsynaptic
neuron is very active. The postsynaptic neuron res six action potentials with a period of
10ns. Charge accumulates on transistor M6 in Figure 3.4, and RGM increases with every
spike. It increases to a nal value of 0.92V before decaying back to 0V in the absence of ring
33
3.2. CMOS CIRCUIT MODELS OF NEURONS AND ASTROCYTES WITH
RETROGRADE SIGNALING MECHANISMS
Figure 3.5: Sample outputs from the RGM Generation Circuit. (a) A postsynaptic action
potential (AP
post
) causes a transient increase in RGM. The rate of production r
RGM
was
varied from 0.45V to 0.55V and the RGM signals were plotted. The decay constant,
RGM
,
was 0.4V for the rst spike and 0.45V for the second spike. (b) A train of AP
post
spikes
(black curve) emitted from the postsynaptic neuron can cause RGM (blue curve) to increase
even more. Here, six AP
post
spike were red with a period of 10ns. (c) A train of AP
post
spikes red with a period of 20ns can not cause increased RGM. In (b) and (c),
RGM
was
set to 0.45V and r
RGM
was 0.55V.
activity. Figure 3.5(c) shows the case when activity in the postsynaptic neuron is low. The
neuron res with a period of 20ns. RGM increases due to charge accumulation on transistor
M6 after each spike, but it decays to 0V during quiescent periods through transistor M5
and
RGM
in Figure 3.4. RGM never increases above 0.53V. This shows that sustained,
intense levels of postsynaptic activity are required for RGM to increase signicantly, similar
to results found in biology.
34
3.2. CMOS CIRCUIT MODELS OF NEURONS AND ASTROCYTES WITH
RETROGRADE SIGNALING MECHANISMS
3.2.2 The Retrograde (RG) Excitatory Synapse Circuit
Figure 3.6 shows the circuit for the RG Excitatory Synapse Circuit from Figure 3.3. It is
a modied version of the BioRC Excitatory Synapse Circuit that has been demonstrated
previously. The BioRC Excitatory Synapse Circuit converts a fast input action potential
AP
in
into a slow excitatory postsynaptic potential (EPSP) whose amplitude depends on the
amount of neurotransmitter concentration (NT) in the synaptic cleft. In the RG Excitatory
Synapse Circuit, we have added presynaptic mechanisms that modulate the amount of NT.
The mechanisms arise from the eects of RGMs on presynaptic neurotransmitter release.
In the circuit, NT
base
represents a baseline neurotransmitter concentration when eects of
retrograde signaling are omitted, and NT represents the actual amount of neurotransmitter
in the synaptic cleft. NT represents the change in presynaptic neurotransmitter release
due to RG depression and RG potentiation. When retrograde signaling and astrocytes are
omitted, NT is zero and NT is about equal to NT
base
. When retrograde signaling and
astrocyte mechanisms are included, NT varies and is added to NT
base
through an analog
adder in order to modulate NT. NT is the sum of two signals representing RG Depression
and RG Potentiation mechanisms. The glu
astro
signal represents glutamate released from an
adjacent astrocyte, and the circuit generating this signal will be presented later in the next
section.
In this model, it was assumed that the eects of RG depression on presynaptic neuro-
transmitter release are proportional to the amount of RGM released by the postsynaptic
neuron, similar to the model presented by Wade et. al [24]. The RG Depression Circuit
module converts a positive RGM signal from Figure 3.4 into a proportional negative sig-
nal RG dep. RG dep eectively decreases the value of NT, emulating the suppression of
presynaptic neurotransmitter release by activation of retrograde messenger receptors. The
value for VSS in the experiments shown here was -0.4V. The magnitude of RG depression is
controlled by the signal RG dep control.
A demonstration of the RG Depression Circuit is shown in Figure 3.7. Postsynaptic
35
3.2. CMOS CIRCUIT MODELS OF NEURONS AND ASTROCYTES WITH
RETROGRADE SIGNALING MECHANISMS
Figure 3.6: The Retrograde (RG) Excitatory Synapse Circuit.
action potentials (AP
post
) generate the RGM signal. The RGM signal is converted into a
negative signal (RG dep) whose value is proportional to RGM.
3.2.3 The Astrocyte Circuit
The circuit used to model interactions between astrocytes and neurons is loosely based on
previous BioRC circuits designs from Joshi and Irizarry [5, 57, 58]. A brief description of
these designs were presented earlier in the Chapter 2. The circuit model presented here is
dierent from previous works since it models the in
uence of RGMs on astrocytic Ca
2+
.
Previous designs consider astrocytic Ca
2+
concentrations to be increased from activation
by neurotransmitters released from presynaptic neurons, but this design considers eects
caused by the activation of RGM receptors. This design also uses a dierent model for Ca
2+
microdomains in astrocytes. In previous designs, spatial variation of Ca
2+
concentrations
were included in the astrocyte microdomain model. Ca
2+
levels at each location of a mi-
crodomain was dependent on the neurotransmitter concentration in two adjacent synapses,
and the amount of gliotransmitter released at each location was controlled in a ne-grained
manner by the Ca
2+
concentration. In this design, it is assumed that the Ca
2+
concentra-
tion is the same at all locations within a microdomain. It is assumed that microdomains
36
3.2. CMOS CIRCUIT MODELS OF NEURONS AND ASTROCYTES WITH
RETROGRADE SIGNALING MECHANISMS
Figure 3.7: Sample results from the RG Depression Circuit block when RG dep control =
0:4V and VSS =0:4V .
37
3.2. CMOS CIRCUIT MODELS OF NEURONS AND ASTROCYTES WITH
RETROGRADE SIGNALING MECHANISMS
ensheath small groups of functionally-related synapses, and the microdomain concentration
re
ects the average Ca
2+
level caused by the activity at all synapses connected to the mi-
crodomain. When the Ca
2+
in a microdomain is high enough, it can propagate and aect
concentrations in adjacent microdomains.
A diagram illustrating the design methodology for the Astrocyte Circuit is shown in Fig-
ure 3.8. It shows an astrocyte process that contains two microdomains. Each microdomain
ensheathes three synapses in this example. Neural activity causes each synapse to release
RGMs that are taken up by the microdomains. It is assumed that increases in RGM cause
a proportional increase in Ca
2+
. The Ca
2+
concentration in each microdomain can then
be represented by averaging the RGM signals from each of its synapses. The amount of
neurotransmitter (glutamate) that is released from each microdomain depends on the Ca
2+
level, and it is the same at each synapse in the microdomain's territory. Ca
2+
signaling also
allows microdomains to communicate with each other so that the synaptic activity in one
microdomain can aect the activity in an adjacent microdomain. The Astrocyte Circuit is
comprised of three subcomponents: (1) the Microdomain Ca
2+
Circuit; (2) the Microdomain
Coupling Circuit; and (3) the Astrocytic Glutamate Release Circuit. The designs for these
subcomponents are presented below.
The Microdomain Ca
2+
Circuit is shown in Figure 3.9. The RGM signals for each of the
synapses connected belonging to the microdomain are connected to non-inverting, amplifying
delay blocks (D). The outputs of the delay blocks are sent to a resistive averaging network,
and Ca
microdomain
models the intracellular level of Ca
2+
in the microdomain.
The Microdomain Coupling Circuit is shown in Figure 3.10. Ca
microdomain
signals from
adjacent astrocytic microdomains are linked through NMOS pass transistors. When the
Ca
microdomain
i
signal for a microdomain is above a threshold, the output (thr
i
) of the Coupling
Threshold Circuit block goes high and turns on the pass transistor connecting it to an
adjacent microdomain. Intracellular Ca
2+
can propagate through an astrocyte when the
concentration is high enough. The threshold for propagation can be controlled by precise
38
3.2. CMOS CIRCUIT MODELS OF NEURONS AND ASTROCYTES WITH
RETROGRADE SIGNALING MECHANISMS
Figure 3.8: Design methodology for the Astrocyte Circuit. Astrocytes are divided into mi-
crodomains that ensheathe groups of synapses. Microdomain
1
and Microdomain
2
ensheathe
three synapses each in this example. Each synapses releases an amount of retrograde mes-
senger depending on its activity level. The RGM
i
signals from each synapse get sent to their
associated microdomains. The microdomain Ca
2+
concentration (Ca
microdomain,i
) is repre-
sented by the average of RGM signals (1). Ca
microdomain,i
signals from adjacent microdomains
can in
uence each other (2). Microdomains release glutamate (glu
astro
) in a Ca
microdomain
-
dependent manner. Glu
astro
is the same for all synapses in the same microdomain. Synapses
in Microdomain
1
receive glu
astro,1
, and synapses in Microdomain
2
receive glu
2
.
Figure 3.9: Microdomain Ca
2+
Circuit.
39
3.2. CMOS CIRCUIT MODELS OF NEURONS AND ASTROCYTES WITH
RETROGRADE SIGNALING MECHANISMS
Figure 3.10: Astrocyte Microdomain Coupling Circuit.
sizing of transistors in the Coupling Threshold Circuit blocks.
The Astrocytic Glutamate Release Circuit is shown in Figure 3.11(a). It is a bio-inspired
circuit based on the model proposed by Wade et. al [24]. Their model included complex,
biophysically-based dynamics that created Ca
2+
waves in astrocytes. They assumed that
astrocytes release a pulse of glutamate whenever the intracellular Ca
2+
concentration rises
above a threshold from below. The circuit model proposed in Figure 3.11 is a simplied view
of Wade's model that omits the complicated dynamics of Ca
2+
waves and glutamate release.
In the circuit models, the astrocyte Ca
2+
signals represent time-averaged concentrations.
It is assumed that an astrocyte periodically releases glutamate when its intracellular Ca
2+
level is suciently high. In the circuit, the frequency of glutamate release is set by the
control voltage f
glu
, the amplitude is set by r
glu
, and the decay rate is set by
glu
. The
Ca
2+
for glutamate release is controlled by the sizing of transistors M1 and M2. Initially
input Ca
microdomain
is below the threshold and glu thr is high at VDD. Transistor M3 is
40
3.3. SELF-REPAIR BY RGM-MEDIATED SYNAPTIC PLASTICITY IN AN
ASTROCYTE-NEUROMORPHIC NETWORK
o and glu pulse is held at ground through M5, so the output glu
astro
is at ground. Once
Ca
microdomain
exceeds the threshold, glu thr falls to ground, turning on M3 and increasing
glu pulse to VDD. M8 turns on and the left side of the capacitor (C) falls to 0V. This causes
the right side of the capacitor to also fall to 0V, and the output of the inverter formed by
M11 and M12 rises to VDD. This is sent through a non-inverting delay block (D) that turns
on M5 and turns o M4 after a short period of time, and glu pulse quickly falls back to
0V. M6 then turns on and the capacitor slowly charges up to VDD at a rate controlled by
f
glu
. Once the capacitor is suciently charged, the output of the M11-M12 inverter falls
to 0V, turning o M5 and turning on M4. If Ca
microdomain
is still high, this process can
start over and another quick voltage pulse is generated at glu pulse. glu pulse is input to a
current mirror formed by transistors M13-M17. Whenever glu pulse goes high, a quick pulse
of current
ows through M16 and M17, and charged is stored on the transistor capacitances
connected to glu
astro
.
Sample results from the Astrocytic Glutamate Release Circuit are shown in Figure
3.11(b). At 52ns, Ca
microdomain
rises above the threshold of 0.49V and glu
astro
begins to
increase. During the time that Ca
microdomain
is above the threshold, glu
astro
increases every
20ns. At 202ns, Ca
microdomain
falls below 0.49V. glu
astro
is increased one last time before it
decays back to 0V.
3.3 Self-Repair by RGM-Mediated Synaptic Plasticity
in an Astrocyte-Neuromorphic Network
The RGM signaling circuits were implemented in a feed-forward astrocyte-neuron network.
The conguration when is shown in Figure 3.12(a). The network consists of ve neurons (N
1
-
N
5
), eight synapses (S
1
-S
8
), and an astrocyte with two microdomains (Microdomain
1
and
Microdomain
2
). Input action potentials, AP
in,1
-AP
in,4
, connect to N
1
-N
4
through synapses
S
1
-S
4
. The strengths of these synapses are adjusted such that one input action potential
41
3.3. SELF-REPAIR BY RGM-MEDIATED SYNAPTIC PLASTICITY IN AN
ASTROCYTE-NEUROMORPHIC NETWORK
Figure 3.11: (a) The Astrocytic Glutamate Release Circuit. (b) Example output from the
circuit when f glu = 1V, r glu = 0.32V, and glu = 0.35V. The circuit output, glu
astro
,
starts to increase when Ca
microdomain
is over a threshold of 0.49V.
42
3.3. SELF-REPAIR BY RGM-MEDIATED SYNAPTIC PLASTICITY IN AN
ASTROCYTE-NEUROMORPHIC NETWORK
Figure 3.12: (a) The astrocyte-neuron network used to demonstrate self-repair. (b) Illus-
tration of the expected results during normal operation. (c) The network with one synaptic
fault at S
8
. (d) Illustration of the results when no self-repair is used in the damaged network.
(e) Illustration of the desired results when self-repair is used in the damaged network.
is sucient to cause ring (AP
out
) in the neuron. N5 receives inputs from synapses S
4
-S
8
.
The strengths of the synapses are such that N5 should receive coincident action potentials
AP
out,1
-AP
ou,4
in order to re. The expected behavior of the network when it is functioning
normally is shown in Figure 3.12(b). N5 emits AP
out,5
when all four inputs AP
in,1
-AP
in,4
are
given.
The situation when a synaptic fault occurs is shown in Figure 3.12(c). Here, S8 is broken
(red cross mark) so N5 does not receive input from N4. If no self-repairing mechanisms
are used, N5 will not be able to re regardless of the inputs as shown in Figure 3.12(d).
Using the circuit designs presented in the previous section, this would correspond to the case
43
3.3. SELF-REPAIR BY RGM-MEDIATED SYNAPTIC PLASTICITY IN AN
ASTROCYTE-NEUROMORPHIC NETWORK
where RGM signaling mechanisms are disconnected. When self-repair by RGM signaling is
implemented, we expect the network to regain functionality similar to its normal state as
shown in Figure 3.12(e). When large activity is detected in astrocyte Microdomain
1
, it should
couple to Microdomain
2
through Ca
2+
signaling and stimulate the release of glutamate that
potentiates S
5
-S
7
. When S
5
-S
7
are suciently strong, N5 regains functionality and is able
to emit action potentials.
Circuit simulation results are shown in Figure 3.13. In all simulations, VDD=1.8V,
VSS=-0.4V, and input action potentials are triangular pulses with an amplitude of 1.8V
and width of 2ns. The circuit was designed and simulated in Cadence Virtuoso using 180nm
CMOS technology. The network was stimulated by simultaneous trains of inputs AP
in,1
-AP
4
with a period of 30ns. Other relevant parameters were r
RGM
=0.45V, rg dep control=0.4V,
and f
glu
=1V. The output signals during normal operation are shown in Figure 3.13(a). AP
out,5
emits spikes after each input as expected. Figure 3.13(b) shows results when S
8
is discon-
nected from the circuit to model a synaptic fault and RGM signaling mechanisms are turned
o by setting RGM =0V and glu
astro
=0V for all synapses in the network. This eectively
removes RGM generation and disconnects the astrocyte circuit. Since S
1
-S
4
are not broken,
action potentials are still seen in AP
out,1
-AP
out,4
. However, no spikes are seen in AP
out,5
since N5 does not receive the input AP
out,4
.
Next, RGM signaling mechanisms are turned on and the output signals are plotted in
Figure 3.13(c). Initially N5 does not re since the network is damaged. However it starts to
spike at 120ns when the fourth input spike is given. To explain why this happens, we can
look at the neurotransmitter (NT) signals that represent synapse weights as shown in Figure
3.13(d). The green curve plots NT for S
1
-S
4
. At these synapses, decreases and increases
in neurotransmitter concentration due to RG depression and RG potentiation balance each
other out, and the NT signal stays relatively constant, representing stable synaptic strengths.
Ca
2+
increases in Microdomain
1
and propagates to Microdomain
2
, inducing glutamate re-
lease and potentiation. At synapses connected to N5, the eects of RG potentiation will
44
3.4. SUMMARY
be greater than that of RG depression, resulting in an increase in synaptic weights. This is
shown in the blue curve that plots NT for S
5
-S
7
. The NT signal slowly increases and after
120ns it is large enough to allow N5 to re.
The amount of neural activity required before self-repair occurs can be tuned by varying
r
RGM
, the signal that represents the rate of RGM production. The number of coincident
input spikes before self-repair occurs is plotted as a function of r
RGM
in Figure 3.13(e).
It can be seen that higher r
RGM
values will need less network activity in order to initiate
self-repair.
Simulation results for a network with two broken synapses (S
7
and S
8
) are shown in Figure
3.13(f). Self-repair occurs after seven input spikes have been given, showing that more neural
activity is required when more faults are present. This is because more astrocytic Ca
2+
needs
to build up for sucient amounts of glutamate to be released.
3.4 Summary
Circuit designs that model RGM signaling were presented in this chapter. The circuits
include eects on synaptic plasticity in CMOS astrocytes and neurons. Furthermore it has
been demonstrated how the circuit models could be used to repair networks with synaptic
faults. Healthy synapses are strengthened in order to compensate for broken synapses that
do not contribute to network behavior. Repair occurs autonomously in an activity-dependent
manner. This type of self-repair would be good for highly active networks with low numbers
of faults. If activity levels are insucient, the necessary amount of potentiation at healthy
synapses would not occur.
45
3.4. SUMMARY
Figure 3.13: Circuit simulation results for network. (a) Results during normal operation.
(b) Results when RGM signaling is omitted and one synapse (S
8
is broken. (c) Results when
RGM signaling is included and S
8
is broken. (d) Neurotransmitter (NT) signals for the
synapses when S
8
is broken. (e) Number of input spikes required before self-repair occurs as
a function of r
RGM
when S
8
is broken. (f) Results when two synapses (S
7
and S
8
) are broken.
46
Chapter 4
Astrocyte Mechanisms for
Homeostatic Plasticity through
Modulation of Postsynaptic AMPA
Receptors
In this chapter we present a view of astrocytes as cells that regulate homeostasis in neu-
ral networks. Astrocytes monitor neural ring rates and respond by initiating plasticity
mechanisms when rates go outside of a desired range. We present circuits that aim to em-
ulate the gross behavior and in
uence of astrocytes on short-term and long-term synaptic
weights. The goal here is to generate circuits that can be used restructure synaptic weights
when neural activity levels go out of balance following damage to a a neuromorphic network
or when input representations have changed. The circuits could also be used for network
development.
47
4.1. BACKGROUND
4.1 Background
4.1.1 Glutamate Receptors at Excitatory Synapses
Glutamate receptors are important for the generation of excitatory postsynaptic potentials
(EPSP) and plasticity in the brain. Glutamate released by presynaptic dendrites activate
receptors, allowing an in
ux of ions into the postsynaptic axon terminal. Selectivity of
ions, time scales, and response amplitudes depend on the type of glutamate receptor that is
involved. Permeability to calcium is an important property of receptors since calcium has
been found to initiate dierent form of synaptic plasticity [75]. The main glutamate receptors
at excitatory synapses in the brain are N-methyl-D-aspartate (NMDA) receptors and -
amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA) receptors. NMDA receptors
(NMDAR) and AMPA receptors (AMPARs) vary in composition and activation mechanisms,
and they have dierent roles in synaptic plasticity.
NMDARs are ionotropic glutamate receptors that allow an in
ux of positive ions. Open-
ing of these channels require: (1) Sucient membrane depolarization; (2) Stimulation by
glutamate; and (3) Binding of glycine or D-serine. Typically Mg
2+
from the extracellular
space binds to the receptor, blocking ion
ow through the channel. When the cell's mem-
brane potential is large enough, the ion is repelled and the Mg
2+
block is removed. Activation
of the NMDAR channel also requires co-activation at its two ligand binding sites, the glu-
tamate binding site and the glycine binding site. Glutamate in the synaptic cleft following
presynaptic activity fullls the glutamate binding site requirement. Glycine from neurons
or D-serine from astrocytes can bind to the glycine binding site.
Once the requirements for activation are met, NMDAR channels at a synapse open,
allowing a non-selective in
ux of positive ions into the neuron. The positive in
ux increases
the postsynaptic membrane potential, making a small, delayed contribution to the EPSP
generated by the synapse. NMDARs also permit an in
ux of Ca
2+
ions.
In contrast to NMDARs, AMPAR channel opening does not depend on the membrane
48
4.1. BACKGROUND
Figure 4.1: AMPARs can be permeable or impermeable to calcium [7].
potential. Typically responses to AMPARs are faster and have higher amplitudes compared
with NMDAR responses. AMPAR channels are tetramers that consist of four subunits called
GluA1, GluA2, GluA3, and GluA4. Specic subunit composition of an AMPAR determines
its behavior. Here we focus on two types of AMPARs: (1) Calcium-permeable AMPARs (CP-
AMPAR); and (2) Calcium-impermeable AMPARs (CI-AMPAR). The types of AMPARs are
illustrated in Figure 4.1. The receptors on the left lack GluA2 and are permeable to calcium.
The receptors in the middle have undergone mRNA processes that edited them to contain
GluA2. They are not permeable to calcium. The receptors on the right contain GluA2 but
have not undergone processes that make them impermeable to calcium.
The calcium-permeable type of AMPARs are typically found during early development
of the central nervous system (CNS) [76], and they have also been found in adults [77]. CP-
AMPARs lack the GluA2 subunit, and they are permeable to ions such as Na
2+
, K
2+
, and
Ca
2+
. On the other hand, CI-AMPARS contain the GluA2 subunit and are impermeable to
calcium. They are typically found in the adult CNS.
It is thought that the number of CI-AMPARs at the postsynaptic side of a synapse
is responsible for stable, long-term synaptic strengths. However CP-AMPARs have also
been found to play important roles in long-term potentiation [78]. During development,
CP-AMPARs can be tracked in and out of the cell membrane. Receptors that have been
tracked into the membrane permit Ca
2+
in
ux in actively-stimulated synapses. Large
49
4.1. BACKGROUND
Figure 4.2: Basic plasticity mechanisms caused by NMDARs and AMPARs. Adopted from
[7].
amounts of Ca
2+
in the cell may initiate an mRNA-editing process that converts the receptor
into a stable, GluA2-containing CI-AMPAR [7]. Unstimulated receptors degenerate with a
half-life of 10 minutes.
Basic mechanisms of plasticity caused by NMDARs and AMPARs are illustrated in Figure
4.2. NMDARs on the synapse terminals are stable while AMPARs can be mobilized on and
o the membrane through short-term potentiation (STP) and degradation. NMDARs and
CP-AMPARs allow in
ux of Ca
2+
, leading to LTP and LTD. High Ca
2+
in
ux generally leads
to stabilization of CI-AMPARs and LTP while low or moderate increases in Ca
2+
generally
lead to breakdown of surface AMPARs and LTD.
4.1.2 Role of Astrocytes in Homeostatic Plasticity
Astrocyte cells are widespread and can contact a large number of synapses. A single human
astrocyte has been found to connect to up to 2,000,000 synapses [79]. Thus it is possible that
chemical factors released by an astrocyte may produce a global response in a large number
of synapses in its territory. Through bi-directional communication at the tripartite synapse,
50
4.1. BACKGROUND
astrocyte processes can both detect and respond to neural activity. The spatial relation-
ship between astrocytes and neurons make astrocytes a potential candidate for regulating
homeostatic plasticity.
Astrocytes respond to neuronal activity through calcium levels. Chemical transmitters
released by neurons, such as glutamate and 2-AG, stimulate gradual, long-lasting elevations
in intracellular Ca
2+
. The timescale of astrocyte calcium signaling (seconds to minutes) is
much slower than neurotransmission (milliseconds). Due to their slow time course, astrocytes
have been proposed as memory elements in neuronal networks [8]. Repeated stimulation can
modulate both the amplitude and frequency of calcium signals in an astrocyte.
Figure 4.3 illustrates how an astrocyte can store information about neural activity. In
this example, correlated presynaptic and postsynaptic activity (grey vertical lines) cause
the release of neurotransmitters that induce elevations in the astrocyte Ca
2+
level (purple
trace). The elevations decay over a time period much longer than the duration of an action
potential. When the Ca
2+
level goes above a threshold (dashed line), the astrocyte may
be triggered to release gliotransmitters, initiating homeostatic processes. In this way, the
amplitude of astrocyte Ca
2+
may represent the average neural activity over time. It can be
used to determine when neural activity deviates from the set point.
It has been suggested that astrocytes behave as thresholding units that secrete glio-
transmitters in response to temporal and spatial summations of neural activity levels [10].
Although the complexities of astrocytic calcium signaling are not yet fully understood, it
is possible that the release of gliotransmitters from astrocytes may require specic calcium
signals with certain amplitudes, frequencies or shape. The pattern of calcium signals are
aected by the spatial location of receptors and calcium release sites in the astrocyte's en-
doplasmic reticulum. Intracellular propagation of calcium between astrocyte microdomains
can also aect the shape of calcium signals. Thus astrocytes may release gliotransmitters
only when a sucient number of receptors at the specic locations are activated following
neural activity.
51
4.2. CIRCUIT MODEL
Figure 4.3: Astrocyte as a memory element [8].
4.2 Circuit Model
In this section, we introduce a bio-inspired circuit that emulates homeostatic behaviors found
in biological neurons and astrocytes. Our synapse includes models of postsynaptic NMDARs
and AMPARs that are used to control the weight. The synapse weight consists of a short-
term and long-term factor.
We assume that each neuron and its associated synapses are connected to an astrocyte.
We assume that each synapse is connected to an astrocytic microdomain and that this type
of microdomain responds to neurotransmitters released from the presynaptic terminal in re-
sponse to presynaptic stimulation. We also assume that the soma of each neuron is connected
to a microdomain. This type of microdomain can respond to somatically-released neuro-
transmitters, such as serotonin [80], that are secreted following neural activity. Presynaptic
activity received by synapses and postsynaptic activity output by the neuron are measured
52
4.2. CIRCUIT MODEL
by elevations in Ca
2+
in the corresponding microdomain. We assume that the characteristics
of the intracellular Ca
2+
signal depends on a combination of related microdomain signals.
The astrocyte circuits have two main functionalities: (1) They measure the average level
of neural and synaptic activity over time; and (2) They determine when, where, and what
types of homeostatic plasticity should be implemented. An astrocyte integrates neural ring
rates over a long time scale through its intracellular Ca
2+
signal. The astrocyte is also used as
a threshold element that determines when neural ring rates are above or below the desired
range. When rates are outside of the normal range, the astrocyte initiates homeostatic
plasticity mechanisms to bring rates into the normal range.
Signals produced by the astrocyte are used to enable homeostatic plasticity mechanisms
at the synapse. When neural activity levels are too low, it induces short-term potentiation
(STP) in its associated synapses in order to bring neural activity up into the normal range.
We assume that astrocytes secrete Tumor necrosis factor alpha (TNF) in response to low
intracellular Ca
2+
. In biology, TNF has been shown to increase the number of AMPARs at
a synapse and it has been implicated in forms of homeostatic plasticity [79]. In our model, we
assume that TNF activates receptors on a synapse, causing the transient insertion of CP-
AMPARs in the membrane and STP. Repetitive activation of CP-AMPARs by presynaptic
activity generates an in
ux of Ca
2+
into the synapse that can translate the CP-AMPAR into
a CI-AMPAR. In our circuit model, large excitatory drive during an STP phase potentiates
the synapse's long-term weight (CI-AMPAR). STP is disabled at a synapse when neural ring
rates go above the low-activity threshold and if the synapse receives sucient stimulation.
Synapses in our circuit also include NMDAR elements. The NMDAR is enabled when
neural activity is in the normal range. It causes LTP and LTD through Hebbian-like forms
of plasticity. In Hebbian plasticity, neurons that are active around the same time tend to
be associated so their connections are strengthened. This is in contrast to spike-timing de-
pendent plasticity (STDP), which determines the direction of plasticity based on the precise
timing between spikes. In STDP, a synapse is potentiated when it receives a presynaptic
53
4.2. CIRCUIT MODEL
spike before a postsynaptic spike is emitted within a specic window of time. The synapse
is depressed if it emits a postsynaptic spike before a presynaptic spike is received. In our
circuit model, when neural depolarization, represented by the postsynaptic soma potential,
is large enough, the NMDAR opens and Ca
2+
in
ux is emulated by integrating the number
of presynaptic spikes received in a short time period. If the level of Ca
2+
is above a thresh-
old, the long-term weight is potentiated. If it is below a threshold, we long-term weight is
depressed.
When neural activity is too high, potentiation mechanisms are turned o and synapse
weights are homeostatically depressed by LTD.
4.2.1 An Astrocyte Circuit that Integrates Neural Activity
The circuit compartment that integrates neural activity at each astrocyte microdomain is
shown in Figure 4.4. Action potentials (AP) stimulate elevations in the astrocyte's intra-
cellular Ca
2+
level (AstroCa). In the circuit, action potentials turn on transistor M2 for a
brief period of time. The current mirror made by transistors M1-M3 puts charge on the
gate of M5. M5 acts as a capacitor whose voltage represents the intracellular Ca
2+
level
in the astrocyte. The capacitance can be varied by tuning the large transistor length and
width of M5. V
leak
is a control voltage that represents the uptake of Ca
2+
back into the
astrocyte's endoplasmic reticulum, eectively decreasing the amount of intracellular Ca
2+
.
The amplitude of V
leak
controls the time period over which the astrocyte integrates neural
activity. Low values of V
leak
increase the integration window while high values decrease it.
V
leak
should be low enough so that the integration time is 1000 times the duration of a neural
action potential. We chose this factor because astrocyte Ca
2+
signals in biology operate with
time constants on the order of 1-10s while action potentials have durations around 1ms. The
circuits in this chapter use a V
leak
voltage of 0.35V.
The AstroCa compartment can be used to integrate postsynaptic output activity or presy-
naptic activity stimulating a synapse. To use the circuit to model an astrocyte microdomain
54
4.2. CIRCUIT MODEL
Figure 4.4: AstroCa circuit.
at a synapse, spikes that stimulate the synapse are used as the AP input to model neuro-
transmitters released from the presynaptic terminal. When the circuit is used to model an
astrocyte microdomain connected to the soma of a neuron, spikes output from the neuron
are used as the AP input to model the eect of neurotransmitters postsynaptically-released
from the soma.
4.2.2 Astrocyte Circuit that Determines when Neural Activity
Levels Are In a Stable Range
The astrocyte thresholding circuit is shown in 4.5. It determines whether the average level of
neural activity near an astrocyte microdomain is in a low, high, or stable operating range. It
takes the AstroCa signal from the corresponding astrocyte compartment (Figure 4.4) as an
input. When neural activity is below a low threshold, transistors M6-M7 pull up the signal
Low AstroCa. When neural activity is above a high threshold, the signal High AstroCa is
pulled up by transistors M1-M5. The thresholds can be controlled by tuning the sizes of
the transistors. In our design, we sized M6 to be much more resistive than M7 in order to
obtain a low-activity threshold closer to GND. The value of the high threshold is controlled
by adjusting the resistance of the pull-down path made by transistors M2-M3. M2 acts as a
resistor that can be made more resistive by increasing its channel length. We sized M2 with
a large length in order to obtain a high value closer to VDD for the high-activity threshold.
When neither Low AstroCa nor High AstroCa are on, we assume that the neural activity is
55
4.2. CIRCUIT MODEL
Figure 4.5: AstroCa Threshold circuit.
at a stable level.
Sample results from the AstroCa Threshold circuit are shown in Figure 4.6. The tran-
sistor sizes were tuned to obtain a low-activity threshold around 0.28V and a high-activity
threshold of 0.61V. The segments in green indicate dierent behaviors of operation. The
astrocyte Ca
2+
level (AstroCa, black) starts low at 0V in segment 1 (0-2.3μs). Since it is
below the low-activity threshold, Low AstroCa is on at VDD and High AstroCa is o at 0V.
In segment 2 (2.3-3.8μs, Astro Ca is above 0.28V and below 0.61V. Since it is between the
low- and high-activity thresholds, we consider the neuron to be ring at a normal rate. Sig-
nals Low AstroCa and High AstroCa both remain at 0V. In segment 3 (3.8-7.5μs), Astro Ca
is above the high-activity threshold so High AstroCa goes to VDD while Low AstroCa is at
0V. AstroCa drops and is in a normal range again in segment 4 (7.5-8.9μs). It goes below
the low-activity threshold and Low AstroCa turns on in segment 5 (8.9-17.3μs). Segment 6
(17.3-18.8μs) and segment 8 (22.3-23.9μs) show cases where AstroCa is in the normal range.
Segment 7 (18.8-22.3μs) demonstrates another case where AstroCa is high, and segment 9
(23.9-25μs) shows when AstroCa is in the low-activity range.
56
4.2. CIRCUIT MODEL
Figure 4.6: Sample output of the AstroCa Threshold circuit.
57
4.2. CIRCUIT MODEL
4.2.3 Synapse with Short- and Long-Term Weight
A synapse with long-term weight updates was built using a mixed-signal approach. It is
based on the BioRC group's original excitatory synapse circuit [81]. For our initial design,
we omit eects caused by variations in neurotransmitters released from presynaptic sites.
This circuit models the synapse weight by the number of AMPA receptors (AMPAR) on the
postsynaptic axon terminal. We consider two types of AMPARs: (1) Calcium-permeable
AMPARs (CP-AMPAR) that lack the GluA2 subunit; and (2) Calcium-impermeable AM-
PARs (CI-AMPAR) that contain the GluA2 subunit. The weight of a synapse depends
on the presence of both types of receptors. CP-AMPARs determine the short-term weight
of the synapse while CI-AMPARs determine the long-term weight. Weights modications
are controlled by activity in the presynaptic neuron, postsynaptic neuron, and an adjacent
astrocyte.
The block diagram of the tripartite synapse is shown in Figure 4.7. Presynaptic action
potentials (AP PRE) stimulate the generation of EPSPs from the postsynaptic dendrite.
Components in the postsynaptic dendrite of the synapse are in the yellow rectangle, and
astrocyte components are in the grey rectangle. Blue arrows represent the eects of astro-
cyte signals on the synapse weight. The postsynaptic dendrite is comprised of an NMDAR
component, a CP-AMPAR component that controls the short-term weight (STW), and a CI-
AMPAR component that controls the long-term weight (LTW). The total synaptic weight
is the sum of the STW and LTW. The astrocyte is comprised of multiple microdomains
with Ca
2+
levels generated by the circuit in Figure 4.4. The AstroCa signal in each mi-
crodomain is input to the threshold circuit in Figure 4.5 to generate high and low activity
signals. In Figure 4.7 the i
th
microdomain is connected to the synapse and the i+1
th
mi-
crodomain is connected to the soma of the postsynaptic neuron. We call the Ca
2+
signal
in the microdomain connected to the synapse AstroCaS. The outputs of the thresholding
block for this microdomain are High AstroCaS and Low AstroCaS. We call the signal in the
microdomain connected to the postsynaptic soma AstroCaN, and the thresholding outputs
58
4.2. CIRCUIT MODEL
are High AstroCaN and Low AstroCaN. AstroCaS is obtained by using the presynaptic in-
put to the synapse (AP PRE) as the AP input in Figure 4.4. It can be interpreted as the
average stimulation received by the synapse. AstroCaN is obtained by using spikes output
by the postsynaptic neuron (AP POST) as the AP input in the AstroCa circuit. It can be
interpreted as the average activity level of spikes output by a neuron. AstroCaS is tuned to
have a faster decay rate than AstroCaN in order to mimic fast (1s) astrocyte responses seen
in biology and so that the astrocyte can have quicker in
uences on synaptic behavior. The
astrocyte calcium signals are input to thresholding blocks (Figure 4.5) to obtain signals that
tell whether activity is above or below the desired range of operation. The thresholds can
be varied for the neuron and synapse microdomains.
The long-term weight of a synapse is aected by various mechanisms. The green arrows
in Figure 4.7 represent these eects. CP-AMPARs that are transformed into CI-AMPARs
through mRNA editing processes potentiate the long-term weight (represented by the sig-
nal Up STP in the block diagram). Coincident presynaptic and postsynaptic activity can
induce both potentiating (Up NMDAR) and depressing (Down) eects on the long-term
weight through NMDAR pathways. The astrocyte evaluates neural activity levels and de-
termines what plasticity mechanisms should be used to modulate the long-term weights of
the synapses, as shown by the
owchart in Figure 4.8. The astrocyte connected to a synapse
continuously checks whether the postsynaptic neuron is in a low, stable, or high activity
state. It is in a low activity state when Low AstroCaN is high. In order to increase neural
activity into a stable range, the astrocyte initiates STP as a homeostatic response. In this
state, CP-AMPARs are tracked into the membrane and allow Ca
2+
in
ux. The long-term
weight, controlled by the CI-AMPAR block, can be potentiated by sucient in
ux of Ca
2+
through CP-AMPARs and eects from NMDARs are negligible. In the circuit, the CP-
AMPAR block is transiently activated and the NMDAR block is inactivated during the STP
state. Neural activity is in the stable range when both Low AstroCaN and High AstroCaN
are low. In this state, the synapse can be potentiated or depressed through NMDAR path-
59
4.2. CIRCUIT MODEL
Figure 4.7: Block diagram of the synapse.
ways, and the circuit's NMDAR block is activated. We assume that astrocytes don't release
TNF that tracks CP-AMPARs into the membrane during this state, so the CP-AMPAR
block is inactivated. When neural activity is above the high-activity threshold, as given by
a high voltage on High AstroCaN, homeostatic LTD mechanisms should be used to depress
the weights in the network. The NMDAR component is activated and the CP-AMPAR block
is inactivated. The NMDAR depresses the weights of any synapse that is active during this
state.
The
owcharts in Figure 4.9 show the sequences of events that occur during each synaptic
plasticity mechanism. STP is used to homeostatically potentiate weights during periods of
low activity through CP-AMPARs. As shown in Figure 4.9(a), presynaptic activity poten-
tiates the synapse during STP. When the synapse receives AP PRE spikes, the short-term
60
4.2. CIRCUIT MODEL
weight is transiently potentiated through the CP-AMPAR block in Figure 4.7. The short-
term weight increases with each presynaptic spike and decays quickly. If enough AP PRE
spikes are received and the short-term weight goes above a threshold, V
th,LTP
, the transient
potentiation is converted into a long-term weight increase. This models the mRNA pro-
cess that converts a CP-AMPAR into a permanent CI-AMPAR. The short-term weight in
the CP-AMPAR circuit block is reset since the CP-AMPAR is no longer present. If the
short-term weight doesn't go above the threshold for LTP, the circuit continues to wait for
AP PRE spikes while in the STP state. Figure 4.9(b) illustrates the events that occur when
neural activity is in the stable range. LTP and LTD occur through Hebbian-like mechanisms
based on Ca
2+
through NMDARs that are opened during postsynaptic activity. When the
postsynaptic neurons emits a spike, AP POST, the astrocyte checks the activity level of
the presynaptic neuron. If presynaptic activity was high, as indicated by a high signal in
High AstroCaS, the long-term weight is potentiated. If presynaptic activity was only mod-
erate, indicated by low signals in both High AstroCaS and Low AstroCaS, the long-term
weight is depressed. Figure 4.9(c) shows the homeostatic plasticity process that occurs when
neural activity is too high. LTD occurs through NMDAR pathways in order to curb exci-
tation in the network. The long-term weight of a synapse is depressed when a postsynaptic
spike, AP POST, is emitted.
EPSP Generator Circuit
The EPSP generator circuit is shown in Figure 4.10. Presynaptic action potential (AP PRE)
is converted into an excitatory postsynaptic potential (EPSP). Reuptake of neurotransmit-
ters from the synaptic cleft is represented by the control voltage Reuptake, and the resting
rate of return of the postsynaptic axon terminal potential back to basal values is represented
by the control voltage RR. The amount of neurotransmitter (NT) released in response to a
presynaptic spike is assumed to be constant and was set to a voltage of 0.5V in experiments.
The amplitude of EPSP is controlled by the voltage at the signal Weight, which modulates
61
4.2. CIRCUIT MODEL
Figure 4.8: Flowchart of astrocyte control over synaptic plasticity mechanisms.
62
4.2. CIRCUIT MODEL
Figure 4.9: Flowchart for dierent synaptic plasticity mechanisms. (a) STP during low
activity. (b) LTP/LTD during stable activity. (c) LTD during high activity.
63
4.2. CIRCUIT MODEL
Figure 4.10: The synapse circuit. Includes CP-AMPARs and CP-AMPARs.
the resistance through the pull-up path made by transistors M10-M11. The value of the
weight signal is found by summing short- and long-term weight signals STW and LTW.
Weight signal represents the number of AMPARs that are available at the synapse.
CI-AMPAR Circuit (Long-Term-Weight)
CI-AMPARs at a synapse control its long-term weight. The circuit controlling the persistent
synapse weight is shown in Figure 4.11. A 4-bit digital weight (b3-b0 ) is generated by a digital
up-down counter. Pulses given at the input Up potentiate the weight while pulses given at
Down depress the weight. The 4-bit weight is fed into a digital-to-analog voltage converter
(DAC) to produce an analog signal, LTW, that represents the number of CI-AMPARs present
at the synapse. The signal Up is found by OR'ing the signals Up STP and Up NMDAR.
These signals are generated by the CP-AMPAR and NMDAR circuit blocks, and they will
be discussed in later sections.
The circuit for the 4-bit counter is in Figure 4.12. Inputs Up and Down signal to the
circuit when the weight should be incremented or decremented, respectively. Outputs of the
circuit are binary values b3-b0 with b3 being the most signicant bit and b0 being the least
signicant bit. The weight bits are stored using
ip-
op circuits (FF). Storing the weight in
64
4.2. CIRCUIT MODEL
Figure 4.11: CI-AMPAR circuit. Generates long-term weight of a synapse.
Figure 4.12: 4-Bit Digital Counter.

ip-
ops allows it to be stable and persistent over time. When the value of b3-b0 hits 1111,
it is at its maximum value and it is at its minimum value at 0000. Signals Max and Min are
generated for these outputs and input to the
ip-
ops in order to prevent over
ow when the
weight reaches the maximum or minimum possible value.
The circuit for the
ip-
op is shown in Figure 4.13. Select bits s1 and s0 determine
which of the two inputs, d1 or d0, are passed to the output Q. Turning on the Reset input
forces Q to zero. Turning on Max or Min prevents Q from being updated.
The circuit diagram for the DAC block is shown in Figure 4.14. The digital bits b3-b0
65
4.2. CIRCUIT MODEL
Figure 4.13: Flip-
op circuit used in the digital counter circuit.
Figure 4.14: DAC circuit used in Figure 4.11.
activate resistive transistors M2-M5, and the current through M1 increases as more bits are
set. The current mirrored to the path through M6 is converted into the voltage at LTW
through a resistive voltage divider. Proper sizing of the transistors is required to obtain
values for LTW that re
ect the magnitude of the 4-bit input signal. In our model, we sized
M2-M5 with minimum channel widths and we controlled resistances by varying the channel
lengths. The channel lengths we used wereL(M5) = 2L(M4) = 4L(M3) = 16L(M2).
CP-AMPAR Circuit (Short-Term Weight)
CP-AMPARs in biological synapses transiently potentiate synaptic activity. CP-AMPARs
are tracked into the postsynaptic membrane following neural inactivity. Ca
2+
in
ux
through open CP-AMPAR channels can also cause CP-AMPARs to be converted into per-
66
4.2. CIRCUIT MODEL
Figure 4.15: Short-term weight circuit.
manent CI-AMPARs, causing long-term potentiation.
The Short-Term Weight circuit mimicking activity of biological CP-AMPARs is shown in
Figure 4.15. In the circuit, current
ows through the current mirror made by transistors M1-
M5 when AP PRE and Low AstroCaN are active. The voltage at Ca represents the Ca
2+
in
ux through an open CP-AMPAR channel, and it is used to transform STP into LTP.
The CP-AMPAR can only be activated when the Low AstroCaN signal is on, meaning that
neural activity levels are below the low-activity threshold. Once activated, stimulation by
presynaptic activity (AP PRE) opens the CP-AMPAR, allowing Ca
2+
in
ux. The amount of
Ca
2+
in the postsynaptic dendrite terminal is represented by the signal Ca. Control voltage
V
leak
controls the decay of Ca
2+
. The two inverters are used as a thresholding unit for Ca. If
Ca goes over a threshold, the output of the inverters goes high and triggers a pulse Up STP
at the output of the One-Shot block. The Up STP signal is used to potentiate LTW in the
CI-AMPAR circuit (Figure 4.11), emulating the conversion of a transient CP-AMPAR into
a stable CI-AMPAR. After conversion to a CI-AMPAR, U p resets Ca through transistor
M7.
NMDAR Circuit
The NMDAR circuit is shown in Figure 4.16. It converts presynaptic and postsynaptic
(AP POST) activity into long-term changes in synaptic weight based on Hebbian-like plas-
ticity mechanisms. A pulse output at Up NMDAR is used to increase the synapse's LTW
67
4.2. CIRCUIT MODEL
weight in the CI-AMPAR circuit block and a pulse output at Down decreases the weight
4.11). Activity at either of these outputs can only be generated if the requirements for NM-
DAR activation have been met. Recall that NMDAR channels can only be opened when
the membrane potential is suciently depolarized and with sucient stimulation by gluta-
mate. We assume that the amount of depolarization required for NMDAR activation is large
enough to generate output spiking. Thus we use AP POST to gate output activity. Out-
puts Up NMDAR and Down NMDAR represent LTP and LTD processes that occur during
periods where neural ring rates are in a stable range. Thus, these signals are gated by
Low AstroCaN and High AstroCaN. Output Down homeostatic represents LTD caused
by the astrocyte as a homeostatic response to over-excitation in the network. It is gated by
high neural activity levels (High AstroCaN ).
In order for NMDARs to generate LTP, the synapse should be highly stimulated to allow
a large in
ux of Ca
2+
. This behavior is mimicked by the upper AND gate. LTP (signal
Up NMDAR) requires high presynaptic stimulation (High AstroCaS) at the time that the
membrane is depolarized (AP POST). High AstroCaS represents a large Ca
2+
in
ux. A
third requirement is activation of the glycine binding site. In our model we assume that the
glycine binding site is stimulated by D-serine released by astrocytes, and we assume that the
astrocyte only secretes D-serine when neural activity is suciently high. We model this by
gating the NMDAR output signals with Low AstroCaN.
LTD also requires sucient neuronal depolarization (AP POST) and for neural activity
levels to be above the low-activity point (Low AstroCaN ). The dierence from LTP is that
LTD is caused by moderate increases in Ca
2+
. To model this, we require High AstroCaS
in order for Down NMDAR to go high. We also require a minimum level of stimulation,
represented by Low AstroCaS. The reason for this is so that only synapses that were
moderately active during postsynaptic spiking will be depressed. Synapses that were inactive
will not be modulated.
Additionally, the NMDAR circuit component includes homeostatic eects that down-
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4.3. EXPERIMENTS
Figure 4.16: NMDAR circuit.
regulate synapse weights when neural activity is too high. High levels of neural activity
are found when the signal High AstroCaN is on. Potentiation should be suppressed when
this signal is high, so Up NMDAR is gated with High AstroCaN. We want to depress
synapses in response to high activity. In our model, we assume that postsynaptic action
potentials received during highly active periods will trigger homeostatic depression. An
AND gate is used to check when both High AstroCaN and AP POST are active at the
same time as the condition for homeostatic depression. When this condition is met, the
one-shot circuit generates a constant-duration pulse, Down homeostatic. The logical OR
of Down homeostatic and Down NMDAR generate the nal Down signal used for LTD in
Figure 4.11.
4.3 Experiments
In this section, circuits were simulated in HSPICE using 45nm CMOS technology with a sup-
ply voltage of 0.9V. Input action potential signals were triangular pulses with an amplitude
of 0.9V and duration of 0.1μs.
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4.3. EXPERIMENTS
4.3.1 Inactivity-Induced STP Modulates the Long-Term Weight
The eect of CP-AMPARs on the weight of a single synapse is shown in Figure 4.17. The
synapse is stimulated by action potentials from the presynaptic neuron (AP PRE, second
panel). It is assumed that the neural activity level stays below the high-activity threshold.
The Low AstroCaN signal for the neuron, shown in the rst panel, starts at VDD (0.9V),
meaning that the neural activity level is before the low-activity threshold. At 1.6ms it drops
to 0V to model stable ring rates. At 2.5ms, Low AstroCaN goes back up to VDD. Input
spikes at AP PRE are triangular pulses with an amplitude of 0.9V and duration of 0.1μs.
In order to generate LTP, STW must pass a threshold of 0.4V.
Initially the synapse has zero weight, as seen by the initial value of LTW. From 0-160μs,
the CP-AMPAR circuit component is activated since Low AstroCaN is high, and short-term
potentiation is allowed. Each AP PRE spike opens the CP-AMPAR channel to increase
the Ca
2+
in
ux, as represented by STW (third panel). STW increments with each spike
until it goes above 0.4V, the threshold for CI-AMPAR conversion. In this example, circuit
parameters were tuned so that four 100kHz spikes are sucient to trigger LTP. Transistor
sizes and control voltage amplitudes can be tuned to obtain dierent requirements for LTP.
After four spikes, a pulse is emitted at the signal Up STP (fourth panel) and STW is reset
to 0V. Up STP increases the synapse's long-term weight (LTW, fth panel). From 60-160μs,
the synapse is stimulated by a train of 11 AP PRE spikes at 100kHz. STW builds up but
it is not large enough to generate LTP. Thus LTW remains at 0V and the resulting EPSP
has a low amplitude.
From 200-215μs, the synapse is stimulated with four AP PRE spikes at a frequency of
200kHz. This frequency is large enough to cause STW to go over the threshold for LTP.
After the fourth AP PRE spike, STW goes over the threshold and a pulse is emitted at
Up STP. Up STP stimulates a long-term increase in LTW, and LTW rises to 0.15V. At
400μs, an input spike at AP PRE generates a larger EPSP with amplitude of 58mV due to
the increased LTW amplitude.
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4.3. EXPERIMENTS
Figure 4.17: Short-term potentiation of a synapse by CI-AMPARs.
AP PRE spike trains with frequency 200kHz were input from 600-615μs and 1-1.015ms.
Each of these trains generated LTP in the LTW signal. The EPSP amplitude increases
following these changes. At 800μs, the EPSP amplitude in response to a single input spike is
110mV when LTW is at 0.24V. At 1.2ms, LTW is 0.31V and the EPSP amplitude increased
to 121mV. At 1.4ms, two AP PRE spikes are input at a frequency of 100kHz. This is not
sucient for generating LTP, and LTW remains unchanged.
From 1.6-2.5ms, Low AstroCaN is low. This represents the case where neural ring
rates are in a stable range and homeostatic mechanisms for STP are turned o. Trains of
four 200kHz AP PRE spikes are input at 1.8ms and 2.3ms. However these spike trains do
not potentiate LTW and the EPSP amplitude remains constant. During this time, LTP
requires more than just presynaptic activity. LTP now requires correlated presynaptic and
postsynaptic activity.
At 2.5ms, Low AstroCaN is turned on again. STP through CP-AMPARs is turned on.
Trains of four 200kHz AP PRE spikes generate LTP at 2.6ms and 2.8ms.
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4.3. EXPERIMENTS
This type of circuit could be useful in development of neural networks where synaptic
weights start at low or zero values. In contrast to STDP, this circuit does not rely on
the presence of postsynaptic spikes to trigger potentiation. Instead, it uses an astrocyte
component to integrate activity and detect changes in network behavior. The astrocyte
triggers homeostatic mechanisms that help upregulate synapses when their weights are too
low to generate useful behavior. Once desired levels of neural activity are reached, the
atrocyte can switch o homeostatic mechanisms in favor of other types of plasticity.
4.3.2 Sample Demonstration of Various Plasticity Mechanisms
To demonstrate the functionality of the dierent plasticity mechanisms at a single synapse,
the network in Figure 4.18 was simulated. The network consists of one synapse connecting
presynaptic neuron N1 to postsynaptic neuron N2. The synapse is also connected to two
microdomains of an adjacent astrocyte. Microdomain Astro S detects stimulating activity in
the synapse caused by action potentials AP PRE from N1. Astro S responds to presynaptic
activity with a signal AstroCaS that depends on its intracellular Ca
2+
level. Microdomain
Astro N detects activity output by the postsynaptic neuron N2. AP POST spikes increase
its Ca
2+
level, AstroCaN. The astrocyte communicates information regarding postsynaptic
activity back to the synapse using AstroCaN.
Simulation results are shown in Figure 4.19. The circuit was simulated in HSPICE
using 45nm CMOS technology. Three forms of plasticity that aect long-term changes
in synapse weight are demonstrated. Homeostatic STP caused by neural inactivity and
subsequent conversion to LTP occurs from 0-150μs. Hebbian-like plasticity occurs from 200-
380μs. Homeostatic LTD occurs from 460-520μs. Inputs to the circuit were AP PRE and
AP POST, shown in Figures 4.19(a) and 4.19(b). The long-term synapse weight (LTW )
is shown in Figure 4.19(h), and it represents the number of CI-AMPARs in the membrane.
The weight of the synapse initially starts at 0V. Through homeostatic and Hebbian plasticity
mechanisms, the weight evolves to re
ect the relationship between AP PRE and AP POST.
72
4.3. EXPERIMENTS
Figure 4.18: Experimental network with one synapse and astrocyte components.
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4.3. EXPERIMENTS
The EPSP output by the postsynaptic neuron in response to AP PRE is shown in Figure
4.19. It can be seen that the amplitude of the EPSP changes with the synapse weight.
Astrocyte-related signals from microdomains Astro N and Astro S are shown in Figures
4.19(c) and 4.19(d), respectively. In Figure 4.19(c), the signal AstroCaN represents the
integral of postsynaptic activity over time. Each time a spike is emitted at AP POST,
AstroCaN increases by a small amount followed by a slow decay. With frequent spiking
activity, the amplitude of AstroCaN builds up. In the gure, it can be seen that AstroCaN
starts out at 0V before AP POST becomes active. At 60μs, AP POST starts spiking steadily
with a period of 10μs. Since the spikes occur frequently, AstroCaN is able to charge up
over time. At 490μs, AP POST stops spiking and AstroCaN begins to decay slowly. The
signal Low AstroCaN represents when AstroCaN is below a low-activity threshold, and
High AstroCaN represents when AstroCaN is above a high-activity threshold.
Similar behaviors can be seen for the signals of microdomain Astro S in Figure 4.19(d).
AstroCaS builds up with continuous AP PRE spikes. However the decay rate was set to be
faster than for Astro N. From 0-10μs, AP PRE emits four spikes at a frequency of 1MHz
every 20μs. The activity is high enough to increase AstroCaS levels. From 100-200μs,
AP PRE is stimulated with one spike every 10μs. This ring rate is not large enough to
sustain elevated Ca
2+
levels in the astrocyte and AstroCaS decays a little. At 200μs, AP PRE
res two action potential, slightly increasing the level of AstroCaS. At 220μs, 240μs, and
260μs, trains of four 1MHz spikes are emitted. This increases AstroCaS enough so that
it crosses the high-activity threshold. During this time of elevated AstroCaS, the signal
High AstroCaS turns on. However this elevation is not sustained since AP PRE returns to
ring single spikes every 10μs from 250-300μs. Single spike are red at 400μs, 550μs, 600μs,
and 650μs. Single spikes are not sucient for generated large elevations in AstroCaS, and
the signal decays to 0V.
The direction of change in synapse weight is controlled by signals Up STP, Up NMDAR,
and Down from Figures 4.19(e)-(g). The Up signals induce increases in weight while the
74
4.3. EXPERIMENTS
Down signal decrements the weight. Mechanisms behind the generation of these signals will
be discussed below.
Up STP represents the transient potentiation of a synapse following inactivity and in-
sertion of CP-AMPARs into the membrane. From 0-150μs, postsynaptic activity is very
low. This is represented by the high value of Low AstroCaN. Since neural activity is low,
the synapse allows potentiation based purely on presynaptic activity. If enough AP PRE
spikes are received during a short time period, Up STP turns on and potentiates the synapse
weight. From 0-150μs, AP PRE emits brief trains consisting of four fast spikes. This activity
is high enough for the weight to get potentiated three times to 0.32V.
From 200-380μs, output neural activity is in a stable range. This can be determined
because both Low AstroCaN and High AstroCaN signals are low during this time. During
normal operation, the synapse allows plasticity through Hebbian-like mechanisms. Through
Hebbian plasticity, synapses are potentiated if they are very active around the time its neuron
red. If the synapse is weakly or moderately active, it is depressed. If it is not active during
the ring of an action potential, it is not changed. In our circuit, we determine if a synapse
was very active or moderately active with the signals Low AstroCaS and High AstroCaS. If
High AstroCaS is on, the synapse is highly active and LTP should occur with the generation
of output spikes. If Low AstroCaS is on, we consider the synapse to be inactive, so the
synapse weight should remain unchanged. If both Low AstroCaS and High AstroCaS are
o, this means that the synapse is moderately active so it should be depressed. Results from
Hebbian plasticity can be seen in the Up NMDAR and Down signals from 210-340μs. At
210μs, both Low AstroCaS and High AstroCaS are o, so Down turns on with the arrival
of AP POST and the synapse gets depressed. High AstroCaS is on from 220-300μs. During
this time, eight AP POST spikes arrive and Up NMDAR turns on, potentiating the weight.
From 310-330μs, both threshold signals are o, so AP POST spikes depress the synapse.
At 480μs, AstroCaN goes over the neural high-activity level and High AstroCaN turns
on. This signals that the neuron is overly active and homeostatic mechanisms are imple-
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4.3. EXPERIMENTS
mented to globally down regulate synaptic weights while the neural activity level is still
high. Down LTD turns on to depress the synapse. In this example, the weight is decre-
mented twice.
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4.3. EXPERIMENTS
Figure 4.19: Astrocyte controls type of plasticity at a synapse.
77
Chapter 5
Dendritic Morphology and Plasticity
This chapter introduces electronic circuits that model remapping of neural connections when
damage occurs by overlaying functionality onto neurons by means of dierent spike shapes.
5.1 Motivation
Remapping of cortical neurons following damage has been demonstrated in rodent models
of stroke [9, 54]. Tissue damage and death take place within minutes to hours of the onset
of stroke. However, it has been found that functional recovery of stroke occurs in the
weeks to months following brain injury. During recovery, plasticity mechanisms in surviving
neurons work to strengthen remaining parts of the network and replace damaged synaptic
connections.
The time course of events following stroke for the remapping of rodent contralateral
forelimb sensory maps is shown in Figure 5.1. Initially (pre-stroke), contralateral maps
for the forelimb (cFL) and hindlimb (cHL) are clearly dierentiable. During the rst 1-6
hours of infarct injury, neurons in the stroke core (black circle) die, causing complete loss of
function in the core. In this example the damage occurs in the cFL neural map. 1-2 weeks
after stroke, responses to forelimb activity in the remaining cFL are reduced due to the loss
of intracortical connections from neurons in the stroke core. However the cHL area is still
78
5.2. BACKGROUND: DENDRITE-SPECIFIC ACTION POTENTIAL SHAPES
selective to hindlimb activity. Over the course of several weeks, plasticity mechanisms and
synaptogenesis increase at the borders of the stroke core, and neural connections are rewired
to compensate for reduced neural activity. One month after stroke, neurons in the remaining
cFL (green region) begin to recover functionality. Receptive elds widen and some neurons
at the border between the cFL and cHL (yellow region) begin to respond to stimuli from
both limbs, exhibiting reduced input specicity. After two months, the network stabilizes.
Now some neurons that were initially in the cHL map have been remapped to respond to
the cFL, and the cHL map has reduced in size. Input specicity of neurons increases, and
the number of neurons that respond to both limbs (yellow region) decreases.
In biology, reduced selectivity to stimuli may occur following recovery from stroke since
neurons near the damaged zone need to respond to multiple types of stimuli in order for
plasticity and repair to occur. It has been reported that 50-85% of stroke patients exhibit
reduced ability to discriminate between tactile stimuli [9].
Neuromorphic networks that repair themselves using adaptable plasticity following dam-
age may display similar characteristics of reduced selectivity. In this chapter, we suggest a
method for neuromorphic networks to maintain specicity. We suggest that neurons can en-
code specicity through dierences in spike shapes. Spike shapes output from a neuron can
be controlled through activation of ion channels with precise spatial locations. We use den-
drite morphology as an example in our neuromorphic circuits, and we use astrocyte circuits
to detect damage and initiate repair.
5.2 Background: Dendrite-Specic Action Potential
Shapes
In 2017, Sardi et al. used a new type of recording technique to accurately and consistently
measure neural responses to stimulations from the same location [10]. They found that spike
waveforms from a neuron vary with the spatial location of stimulation. They attributed the
79
5.2. BACKGROUND: DENDRITE-SPECIFIC ACTION POTENTIAL SHAPES
Figure 5.1: Events that occur during remapping of contralateral forelimb sensory maps after
stroke damage. From [9].
80
5.2. BACKGROUND: DENDRITE-SPECIFIC ACTION POTENTIAL SHAPES
Figure 5.2: Adopted from [10]. (a) Illustration of neural stimulation. (b) Spike waveforms
recorded from dierent neurons have shapes that depend on stimulus location.
spike shape variability to activation of dierent dendrites, which act as individual thresh-
olding units for the neuron. Figure 5.2(a) illustrates how neurons were stimulated in exper-
iments. A neuron that was stimulated with above-threshold synaptic inputs from the right
activated the green dendrite (C
1
). Stimulations from the left activated the pink dendrite
(C
2
). Spike waveforms recorded from each side were recorded and plotted in Figure 5.2(b).
Green waveforms plot output spikes recorded from stimuli with the setup in C
1
and pink
waveforms are from stimuli as in C
2
. Each of the panels are from 8 dierent neurons, and
waveforms from 2 recordings for each stimulus conguration were plotted to demonstrate
repeatable spiking shapes.
From Figure 5.2(b) it can be seen that the spike waveforms have repolarizing tails with
dierent durations. For example, the repolarizing tail of the green waveform in the top
81
5.3. A NEURON CIRCUIT WITH INPUT-SPECIFIC SPIKING
left-most panel is much shorter than the pink waveform. In the bottom left-most panel, the
green waveform repolarizes much slower than the pink waveform.
We suggest that the slowly-repolarizing tail may be caused by high-voltage-activated
(HVA) Ca
2+
channels that are localized at specic dendrites. As their name suggests, HVA
Ca
2+
channels require high membrane potential in order to be activated and opened. It has
been shown that activation of HVA Ca
2+
channels generate slow Ca
2+
tail currents evoked
in subicular pyramidal neurons [82]. Action potentials evoked from a neuron activate these
channels. Once activated, the channels deactivate slowly during repolarization, producing a
long after-depolarization in the neuron. It has also been suggested that activation of these
channels is responsible for neural bursting outputs, not implemented here.
5.3 A Neuron Circuit with Input-Specic Spiking
5.3.1 Structure of a Neuron with Multiple Dendrites and HVA
Ca
2+
Channels
The block diagram of a neuron circuit with multiple dendrites and HVA Ca
2+
channels is
shown in Figure 5.3. The neuron has n dendritic branches, B1-Bn, that are connected to
multiple synapses. In the gure, branch B2 connects with m dierent synapses. Each den-
dritic branch sums the EPSPs it receives from its synapses to generate a dendritic potential
DENDi, where i is the dendritic branch. Dendritic potentials are then summed to generate
the total potential, SOMA, at the soma. Similar to other neuron designs, SOMA is fed into
an axon hllock and generates a spike at AP POST. Dendritic potentials DENDi are also
modeled to activate HVA Ca
2+
channels. Activation of HVA Ca
2+
channels aect the shape
of the output action potential, AP POST.
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5.3. A NEURON CIRCUIT WITH INPUT-SPECIFIC SPIKING
Figure 5.3: Block diagram of a neuron with multiple dendrites and HVA Ca
2+
channels.
5.3.2 Axon Hillock Circuit with Eects from Multiple Dendrites
An axon hillock circuit with two dendrites is shown in Figure 5.4. Dierent components in
the design are shown in the dashed boxes. The blue box is a previous design of the axon
hillock demonstrated by the BioRC group [83]. The green box is used to adjust the spiking
frequency at the output. The frequency can be tuned with the control voltage F. Larger
values of F increase the frequency.
The circuit compartments for the HVA Ca
2+
channels are shown in the red boxes (HVA
Ca
2+
Channel). They emulate the opening of channels on the postsynaptic cell following
large membrane depolarization and a subsequent slow in
ow of Ca
2+
ions. In this circuit we
include two dendrites with dendritic branch potentials DEND1 and DEND2. We assume that
each dendrite has a set of HVA Ca
2+
channels with dierent densities and time constants.
When the potential of a dendritic branch is large enough to cause ring, the AP POST
and corresponding DEND signal brie
y turn on the left side of the current mirror in the
associated HVA Ca
2+
Channel module. This pulls up the output of the module, HCa DEND,
to VDD. HCa DEND represents the Ca
2+
that
ows into the postsynaptic cell, causing it to
repolarize slowly. When HCa DEND is high, it pulls up the axon hillock output AP POST
through a resistive NMOS transistor. Here, activation through Dendrite 1 pulls up AP POST
through M11 and activation of Dendrite 2 pulls AP POST through M12. DEND1 must be
high enough to turn on and generate enough current
ow through M3 in order to pull up
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5.3. A NEURON CIRCUIT WITH INPUT-SPECIFIC SPIKING
Figure 5.4: Axon hillock circuit with eects from 2 dendrites.
HCa DEND1. Thresholds for activation can be controlled by tuning the sizes of transistors
M3 and M8. The Decay signals represent the inactivation and closing time constants of each
HVA Ca
2+
channel. They can be tuned to generate dierent action potential shapes for each
dendrite. Although this circuit only demonstrates eects on spiking from two dendrites, it
can be easily be extended to implement more dendrites by adding more HVA Ca
2+
Channel
modules and pull up transistors.
5.3.3 Simulation Results
A neuron with two dendrites is congured using the circuits presented in this section. The
structure of the neuron is shown in Figure 5.5. It has two dendritic branches (Dendritic
Branch 1 and Dendritic Branch 2 ), and each branch is stimulated by input action potentials
at two synapses. Action potentials AP1 and AP2 stimulate Dendritic Branch 1. Dendritic
Branch 2 is stimulated by AP3 and AP4. The neuron, N, emits spikes AP OUT when it
receives at least two coincident input spikes. Two coincident spikes must be received on
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5.3. A NEURON CIRCUIT WITH INPUT-SPECIFIC SPIKING
Figure 5.5: Neuron with 2 dendrites.
the same dendrite in order to generate a dendritic branch potential that is large enough to
activate HVA Ca
2+
channels localized on that branch. The branch is considered to be highly
active when it receives at least two coincident inputs. We congure the HVA Ca
2+
Channel
modules on each dendritic branch with decay values Decay1 =0.22V and Decay2 =0.24V.
Circuits were simulated in HSPICE using 45nm CMOS technology and a supply voltage of
0.9V. Transistors in the axon hillock circuit were sized so that the threshold for ring was
0.45V. Output action potential tail durations were measured from 27% to 5% of VDD on
the falling phase of the signal.
Simulation results for the neuron with two dendrites are shown in Figure 5.6. Input
action potentials were triangular pulses with an amplitude of 0.9V and duration of 0.1μs.
The input spikes, AP1-AP4, are shown on the top four traces, DEND1 and DEND2 show
the dendritic branch potentials for each dendrite, and AP OUT shows the spiking output
on the bottom trace. At 10μs, one action potential is given on input AP1, generating a
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5.3. A NEURON CIRCUIT WITH INPUT-SPECIFIC SPIKING
Figure 5.6: Simulation results for neuron with 2 dendrites.
small potential on DEND1. Since the number of active inputs is less than two, the soma
potential is not greater than the ring threshold and no spike is output on AP OUT. At
20μs, two spikes are input on AP1 and AP2. Since they are on the same dendritic branch,
the potential on DEND1 reaches a high value. DEND2 stays low since its synapses have
not received any input. Since the total number of spikes is at least two, a spike is emitted
at AP OUT (marked by the number 1). The shape of this spike is controlled by the HVA
Ca
2+
channel activated by DEND1. A zoom-in of the spike can be seen in Figure 5.7.1. It
exhibits a tail of duration t
tail
= 0:73μs. This spike particular spike shape is present when
activity in Dendritic Branch 1 is dominant to activity in Dendritic Branch 2.
At 30μs, Dendritic Branch 2 is stimulated with a spike on AP3. No other inputs are
active. DEND2 generates a small potential but it is not large enough to generate output
spiking.
At 40μs, Dendritic Branch 2 is stimulated with two spikes on AP3 and AP4. Now a spike
(numbered 2) is emitted at AP OUT since the soma potential is over the ring threshold.
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5.3. A NEURON CIRCUIT WITH INPUT-SPECIFIC SPIKING
Figure 5.7: Zoom-in of AP OUT in Figure 5.6.
87
5.3. A NEURON CIRCUIT WITH INPUT-SPECIFIC SPIKING
Input activity also generates a large potential on DEND2. It is large enough to activate
the HVA Ca
2+
Channel on Dendritic Branch 2. The specic spike shape generated when
Dendritic Branch 2 is dominant can be seen in Figure 5.7.2. The tail current duration is
t
tail
= 0:33μs. This faster repolarization occurs since the dendrites were programmed with
Dendritic Branch 2 having a larger decay voltage.
At 50μs, the neuron is stimulated with one spike on each branch. Enough inputs are
present for the neuron to emit a spike (numbered 3). However, the DEND potentials at each
dendrite are too small to activate the HVA Ca
2+
Channel modules, and the repolarizing tail
is minimal. The spike shape for this case is shown in Figure 5.7.3. The tail duration is short
at 0.05μs. This spike shape represents the case where neither branch is highly active.
Three input spikes AP1-AP3 stimulate the neuron at 60μs. A spike (numbered 4) is
emitted at AP OUT. Since AP1 and AP2 were input, Dendritic Branch 1 is highly active,
as can be seen by DEND1. However DEND2 is not high since Dendritic Branch 2 only
received one input. So Dendritic Branch 1 is dominant and the spike shape follows the one
that was output at 10μs. Figure 5.7.4 shows the output spike. It has a tail duration of
0.73μs, which is the same as the duration of spike 1.
At 70μs, the neuron is stimulated with all four inputs. Now both dendritic branches are
highly active. DEND1 and DEND2 are high enough to turn on both HVA Ca
2+
channels.
The AP OUT (numbered 5) has a longer duration tail since more HVA Ca
2+
channels were
turned on. From Figure 5.7.5, it can be seen that the duration is 1.10μs. This type of spike
shape occurs when both dendrites are highly active.
The simulation results displayed here demonstrate that an electronic neuron circuit can
output dierent spike shapes to encode dierent types of input stimulation patterns. We
showed that dendritic branches could be used to generate the variations in spike shape. Next
we will demonstrate how spike shape can be used in self-repairing neuronal networks.
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5.4. SIGNALING ASTROCYTE-MEDIATED REPAIR IN A BIO-INSPIRED OCULAR
NETWORK
5.4 Signaling Astrocyte-Mediated Repair in a Bio-Inspired
Ocular Network
In the primary visual cortex, neurons can preferentially respond to activity in one or both
eyes [84]. In this section we demonstrate plasticity mechanisms in a small neural network
inspired by visual cortex neurons. We simulate damage in the network by forcing a neuron
preferential to the left eye to be unresponsive. This causes the network to lose information
regarding stimulation of the left eye. We show that an astrocyte-mediated homeostatic
process can be used to restore functionality in the network. Following recovery, neurons that
were initially preferential to the right eye now respond to stimulation from both eyes. In
order to specify which eye is stimulating, the neuron emits spikes with varying shapes. This
can be useful for downstream neurons in dierentiating the type of response that should be
elicited depending on which eye is signaling.
The experimental network is shown in Figure 5.8. Action potentials AP left and AP right
represent stimulation from the left and right eyes. N1 and N2 represent neurons in the visual
cortex that respond to visual stimulation. Each neuron has two dendritic branches. DB1 N1
and DB2 N1 are the branches of N1, and DB1 N2 and DB2 N2 are branches for N2. Each
neuron has synapses (S1-S4 ) to both eyes. The solid lines to S1 and S3 represent strong
synapses. The dashed lines to S2 and S4 represent silent synapses that have weights too
low to generate ring in their associated neurons. AP left stimulates synapses S1 and S4
while AP right stimulates S2 and S3. Since N1 is strongly excited by the left eye and
weakly excited by the right eye, we say that it is preferential to the left eye. On the
other hand, N2 responds preferentially to the right eye. N1 and N2 emit output spikes
AP POST1 and AP POST2. An astrocyte in the network is excited by AP POST1 and
its Ca
2+
concentration increases when spikes are received. In response to Ca
2+
levels that
are outside of the normal range, the astrocyte secretes gliotransmitters (GT) to synapse S4.
With this conguration, activity in N1 can be propagated to synapses and neurons that are
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5.4. SIGNALING ASTROCYTE-MEDIATED REPAIR IN A BIO-INSPIRED OCULAR
NETWORK
Figure 5.8: Ocular network.
not directly connected to it.
Circuits for the two-dendrite input-specic neuron were presented in the previous sec-
tion of this chapter. Synapse S4 was implemented with a previous BioRC synapse that
implements modulation by an astrocyte. It is shown again in Figure 5.9. The arrival of
the AstroCa
2+
signal pulls up the signal GT to the voltage at V(astro-glut). GT repre-
sented a concentration of gliotransmitters that the astrocyte secretes into the synaptic cleft
in response to astrocyte signaling. GT is added to the Synaptic cleft voltage to increase
the amplitude of the output EPSP (Out(EPSP)). In this circuit, we used a control voltage
of V (astroglut) = 0:3V . For the astrocyte, we use the AstroCa circuit compartment
presented in Chapter 4 (Figure 4.4) with a control voltage Vleak = 0:38V . In this net-
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5.4. SIGNALING ASTROCYTE-MEDIATED REPAIR IN A BIO-INSPIRED OCULAR
NETWORK
Figure 5.9: Previous BioRC excitatory synapse with astrocyte in
uence.
work conguration, we assume that the astrocyte releases gliotransmitters in response to
low intracellular Ca
2+
as a homeostatic response that aims to increase network activity. The
neural activity level is found by putting AstroCa through the AstroCa Threshold block in
Figure 4.5. The Low AstroCa signal is used to initiate homeostatic excitation by activating
the AstroCa
2+
signal (Figure 5.9) on synapse S4.
Simulation results for the network are shown in Figure 5.10(a). It is stimulated with
input spikes AP left and AP right every 20μs. The input action potentials are oset from
each other by 10μs. Neurotransmitter voltages for S1 and S3 were set to 0.75V to represent
strong synapses. Neurotransmitter voltages for S2 and S4 were set to 0.4V to represent
weak synapses. The astrocyte is initialized with an ASTRO CA level of 0.5V to simulate
stable activity in N1.
From 0-200μs, the network functions normally. N1 shows preferential responses to stimu-
91
5.4. SIGNALING ASTROCYTE-MEDIATED REPAIR IN A BIO-INSPIRED OCULAR
NETWORK
lation from the left eye. When spikes are given at AP left, N1 's dendritic branch shows large
activity (DEND1 N1 ), generating spiking in N1 (AP POST1 ). Since synapse S2 is weak,
spikes received from AP right generate small responses in DEND2 N1, and these are not
large enough to cause spiking in AP POST1. On the other hand, N2 shows preferential re-
sponses to the right eye. When activity is present on AP right, large potentials are generated
in DEND1 N2, generating output spiking in AP POST2. Spikes given on AP left generate
only small potentials on DEND2 N2, so AP POST2 does not spike in response to the left
eye. A zoomed-in portion of the waveforms for AP POST1 and AP POST2 from 90-120μs
is shown in Figure 5.10(b). The spike shapes output from each neuron in response to the
preferred eye has a repolarizing tail with duration of 0.73μs. During the period of normal
activity, ASTRO CA remains at a relatively stable level (Figure 5.10(a)) so the astrocyte
does not need to potentiate the network and GT S4 remains low at 0V.
At 200μs we simulate the loss of neuron N1 by forcing its dendritic branch potentials,
DEND1 N1 and DEND2 N2, to 0V. This could model the death of dendrites in a neuron.
Since its dendritic inputs are lost, N1 stops ring and AP POST1 shows no activity. From
200-360μs, the network is in a damaged state and it does not transmit any information
regarding stimulation in the left eye. However, it still communicates information about the
right eye since N2 is intact, and AP POST2 continues responding to spikes from AP right.
During the damage period, ASTRO CA decays since it is no longer receives stimulation from
AP POST1.
At 360μs, ASTRO CA drops below the low-activity threshold that the astrocyte considers
for healthy network behavior. In order to compensate for low activity, the astrocyte begins
to release gliotransmitters at synapse S4 to promote excitability in the network. This can
be seen by the rise in GT S4 from 360-380μs. GT S4 rises maximally to the V(astro-glut)
voltage of 0.3V.
The network recovers functionality and begins to respond to activity in the left eye after
400μs. The voltage at GT S4 provides sucient excitation for S4 to produce large potentials
92
5.4. SIGNALING ASTROCYTE-MEDIATED REPAIR IN A BIO-INSPIRED OCULAR
NETWORK
in N2 's dendritic branch DEND2 N2. Since N1 is broken, N2 becomes responsible for
transmitting information about the left eye in addition to its regular response to the right
eye. This can be seen by the increased output frequency of AP POST2. AP POST2 res
whenever a stimulus is given in either AP right or AP left. A zoomed-in portion of the
waveforms for AP POST1 and AP POST2 are shown in Figure 5.10(c). AP POST2 now
res two types of spikes in response to input activity. Spikes with longer repolarizing tails
of duration 0.73μs are emitted when N2 is stimulated by the preferred right eye. Faster
repolarizing spikes with tail duration of 0.33μs are output when the neuron is stimulated by
the non-preferred left eye.
The conguration of the network following damage recovery is shown in Figure 5.11. N1
is damaged (dashed circle) and no longer responds. N2 is remapped to respond to both the
right and left eye through strong synapses S3 and S4. Specicity of outputs at AP POST2
are signaled through dierent spike shapes.
The original conguration of the network can be recovered if damaged neuron N1 some-
how regains functionality. Figure 5.12 simulation results extended from Figure 5.10. At
700μs, N1 's functionality is restored (black arrow) by reintroducing its dendritic branches.
DEND1 N1 becomes responsive to AP left and spike are emitted at AP POST1. From 700-
920μs, both N1 and N2 respond to AP left. As AP POST1 spikes are emitted, ASTRO CA
begins to build up. At 920μs (blue arrow), ASTRO CA goes above the low-activity thresh-
old and the astrocyte determines that homeostatic plasticity mechanisms can be turned o.
GT S4 drops to 0V and AP POST2 stops responding to activity in AP left. At this point,
the mapping of the original network is restored and each neuron responds preferentially to
a single eye.
93
5.5. SUMMARY
5.5 Summary
In this chapter, we introduced a neuron circuit that exhibits input-specic spiking. We
believe that these types of circuits can be advantageous in signaling when a neuromorphic
network has been damaged and homeostatic repair processes have been initiated. This type of
signaling can help prevent reductions in selectivity in downstream neurons following synaptic
restructuring. Another useful benet could be increased communication bandwidth. For this
type of specialized signaling to be functional requires neurons that can respond selectively
to dierent spike shapes. The circuits presented here are initial designs that we believe can
be useful in increasing the eciency of neuromorphic networks. We leave the design of other
necessary components to future work.
94
5.5. SUMMARY
Figure 5.10: (a) Simulation results from ocular network demonstrating that network can
recover from loss of a neuron. Zoomed-in portions of the waveforms for AP POST1 and
AP POST2 are shown from 90-120μs (b) and 500-530μs (c). AP POST1 is shown in the
upper, blue trace, and AP POST2 is shown in the lower, black trace. Durations of the
repolarizing tail are also shown.
95
5.5. SUMMARY
Figure 5.11: Ocular network remapping after recovery from damage in N1.
96
5.5. SUMMARY
Figure 5.12: Ocular network remaps back to its original conguration if N1 functionality is
restored.
97
Chapter 6
Conclusion and Future Work
This thesis presented novel circuit designs that could be useful for plasticity and repair in
astrocyte-neuromorphic networks. Functionalities of the circuit components were inspired
by behaviors of biological astrocytes and neurons, as described in the neuroscience literature.
The goal of this research was to demonstrate our circuits as a proof of concept to show that
astrocyte-inspired components can provide useful feedback to initiate plasticity and repair
mechanisms in neuromorphic networks, adding to the capabilities of neuron-only networks.
We have implemented our circuits in several small networks that exhibit how they can be used
to recover functionality after damage to neurons. We have also demonstrated how they can
be used to control plasticity during dierent phases of development in a network. We envision
that large-scale neuromorphic networks will benet from the use of multiple mechanisms for
self-repair when deployed in real-world applications. The redundancy of multiple mechanisms
can increase the fault-tolerance of a system, and using multiple types of mechanisms that
check for dierent types of faults can enhance robustness. We believe that the astrocyte-
inspired components presented in this thesis can be utilized as one of multiple forms of
fault-tolerance that are employed in a system. The circuits presented here emulate rst-
order behaviors found in biology and represent initial designs for astrocyte-mediated repair
mechanisms that can be used in larger astromorphic networks. Each chapter demonstrated
98
stand-alone components that model a few biological behaviors. Our future plan is to integrate
the circuits to create an astrocyte circuit that models multiple, more-complicated biological
behaviors related to plasticity and repair. We also plan to create astrocyte components
that model calcium waves and the dynamics of intracellular calcium more faithfully by
considering the amplitude, frequency, and shape of the signals. Intercellular propagation of
calcium waves should be considered as well. Circuit designs presented in this thesis were not
optimized in terms of power and area. Time constants and voltages in the circuit simulations
do not match those found in biological cells. Further work should be done to optimize these
properties.
In Chapter 3, we designed circuit components that model the eects of retrograde mes-
sengers on astrocytes. The circuits allow postsynaptic neurons to signal "backwards" to
presynaptic neurons through an astrocyte. The eects of this retrograde signaling was local
and depressing, reducing the amount of neurotransmitter released by a presynaptic termi-
nal connected to the postsynaptic neuron. An astrocyte also allows indirect communication
between neurons that are not directly connected through a synapse. This type of commu-
nication caused potentiating eects, increasing the amount of neurotransmitters released at
distant synapses. By combining these eects, an astrocyte is able to initiate repair mecha-
nisms when an input to the network is lost. Through a small neural network, we have shown
that the astrocyte compensates for a lost input by strengthening the remaining healthy
synapses in the network.
In Chapter 4, we proposed a bio-inspired model for short- and long-term plasticity in
neuronal networks. Based on evidence from the neuroscience literature, we have proposed
how astrocytes can be used to control the specic types of plasticity that are used in the
network. The astrocyte integrates neural activity over time to determine if the network is in
an under-excited, stable, or over-excited state. The types of plasticity that are implemented
at a synapse depends on the state of the network and the stimulation that is received at
the synapse. Astrocytes control the type of plasticity as a homeostatic response with the
99
goal of shifting neural activity levels into the stable state. These circuits can be used to
strengthen synapse weights during developmental stages of a network when weights are too
low to generate spiking activity. They can be used during initial development or during
synapse restructuring following damage to neurons and synapses. The circuits can also be
used to dampen excitation when activity levels get too high. This can be useful in preventing
damage to the network and reducing energy consumption when faults occur that over-excite
the network or generate detrimental positive feedback loops. Small networks were simulated
to demonstrate an astrocyte's homeostatic control on plasticity. In the future, we plan to
implement and evaluate the circuit models in larger networks with practical applications.
We plan to integrate the circuit with other mechanisms to develop restructured networks
overlaid on existing low-weight synapses to re-route signals and restore some functionality
when parts of a neuronal network are damaged. We also plan to include noise in the synaptic
weights to study how these circuits can help with development when weights are randomly
distributed.
In Chapter 5, we have designed a neuron that exhibits dierent action potential shapes
based on the spatial location of its inputs. The presented circuit components are based
on recent ndings in neuroscience showing that a single neuron emits spikes with dierent
tail shapes depending on which of its dendrites were stimulated. The neuron circuit we
designed includes two dendrites with programmable tail duration. We implemented this
new type of neuron in a sample astromorphic network modeling the visual cortex. When a
neuron in the cortex is damaged, the astrocyte, through homeostatic plasticity mechanisms,
initiates repair that re-routes input sensory signals to the remaining healthy cortical neurons.
Through dendrite-specic spiking, the healthy cortical neurons can retain specicity by using
spike shapes to signal to downstream neurons when repair has occurred. In the future we
plan to create neuron components that can dierentiate between the various types of spiking.
Another plan is to add larger numbers of dendrites with unique spike shapes to the neuron
and to evaluate the optimum number of spike shapes for particular applications such as
100
pattern recognition or directional selectivity. We also plan to incorporate behaviors that
in
uence and are in
uenced by dendritic spikes in the dendritic arbor.
101
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Abstract (if available)

Abstract Electronic circuits inspired by astrocytes can be utilized as mechanisms of plasticity and self-repair in neuromorphic hardware systems. Through their slow, integrative properties, astrocytes can monitor neural activity and trigger plasticity processes that are important for maintaining useful neural activity. Astrocytes also provide indirectly-connected neurons with a widespread form of communication that is not present in neuron-only networks. In this research, we explore biological phenomena related to astrocytes that have not been implemented in other neuromorphic systems. We present CMOS circuit models for these mechanisms and demonstrate applications where they are beneficial to plasticity, homeostasis, fault tolerance, and development in hardware astromorphic systems.

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Creator Lee, Rebecca Kim (author)

Core Title Astrocyte-mediated plasticity and repair in CMOS neuromorphic circuits

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Electrical Engineering

Publication Date 07/26/2018

Defense Date 06/08/2018

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

Tag astrocyte,astrocyte circuits,astrocyte-neuromorphic,astromorphic,astromorphic hardware,fault tolerance,neural encoding,neuromorphic,neuromorphic circuits,neuromorphic engineering,neuromorphic hardware,OAI-PMH Harvest,self-repair,synaptic plasticity

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Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Parker, Alice C. (committee chair), Beerel, Peter A. (committee member), Valero-Cuevas, Francisco (committee member)

Creator Email leerk@usc.edu,rlee1146@gmail.com

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c89-31748

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