Emulation of Bursting Neurons in Neuromorphic Hardware based on Phase-Change Materials
©2015
Textbook
119 Pages
Summary
In the history of computing hardware,Moore’s law, named after Intel co-founder Gordon E. Moore, describes a long-termtrend, whereby the number of transistors that can be placed inexpensively on an integrated circuit doubles approximately every two years [1]. Because the number of transistors is crucial for computing performance, significant performance gains could be achieved simply through complementary metal-oxide-semiconductor (CMOS) transistor downscaling. AlthoughMoore’s law, which was mentioned for the first time in 1965, turned out to persist for almost five decades, the nano era poses significant problems to the concept of downscaling [2]. Upon approaching the size of atoms, quantumeffects, such as quantum tunneling, pose fundamental barriers to the trend. Furthermore, the conventional computing paradigm based on the Von-Neumann architecture and binary logic becomes increasingly inefficient considering the growing complexity of todays computational tasks. Hence, new computational paradigms and alternative information processing architectures must be explored to extend the capabilities of future information technology beyond digital logic. A fantastic example for such an alternative information processing architecture is the human brain. The brain provides superior computational features such as ultrahigh density of processing units, low energy consumption per computational event, ultrahigh parallelism in computational execution, extremely flexible plasticity of connections between processing units and fault-tolerant computing provided by a huge number of computational entities. Compared to today’s programmable computers, biological systems are six to nine orders of magnitude more efficient in complex environments [3]. For instance: simulating five seconds of brain activity takes IBM’s state-of-the-art supercomputer Blue Gene a hundred times as long, i.e. 500 s, during which it consumes 1.4 MWof power, whereas the power dissipation in the human central nervous system is of the order of 10W[4, 5]. Thus, it is not only extremely interesting but in terms of computational progress also highly desirable to understand how information is processed in the human brain. The conceptual idea developed within the framework of this thesis tries to contribute to this intention. In contrast to most recent research dealing with the simulation and emulation of specific connections between nerve cells [5–12], the work of this thesis focuses on investigating, on […]
Excerpt
Table Of Contents
Contents
4.4. Modeling Neuronal Bursting Activity
. . . . . . . . . . . . . . . . . . . . . . . . . 59
4.4.1. The Integrate-and-Fire Model
. . . . . . . . . . . . . . . . . . . . . . . . . 59
4.4.2. The Resonate-and-Fire Model
. . . . . . . . . . . . . . . . . . . . . . . . . 61
4.4.3. The Quadratic Integrate-and-Fire model
. . . . . . . . . . . . . . . . . . . 61
4.4.4. The Simple Model of Choice
. . . . . . . . . . . . . . . . . . . . . . . . . . 62
4.5. An Overall View
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
5. A PCM Bursting Neuron
65
5.1. Voltage-Controlled Relaxation Oscillation in a PCM Device
. . . . . . . . . . . . 66
5.2. The Analogy to Hippocampal Pyramidal Bursting Neurons
. . . . . . . . . . . . 70
5.3. Simulation of a PCM Bursting Neuron
. . . . . . . . . . . . . . . . . . . . . . . . . 77
5.4. An Overall View
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
6. An Outlook on the Future
83
A. Quantification of the Membrane Potential
87
B. Vocabulary
89
List of Figures
I
List of Tables
V
Bibliography
VII
Acknowledgement
XVII
CHAPTER 1
Introduction
In the history of computing hardware, Moore's law, named after Intel co-founder Gordon E.
Moore, describes a long-term trend, whereby the number of transistors that can be placed
inexpensively on an integrated circuit doubles approximately every two years [
1
]. Because
the number of transistors is crucial for computing performance, significant performance
gains could be achieved simply through complementary metal-oxide-semiconductor (CMOS)
transistor downscaling. Although Moore's law, which was mentioned for the first time in 1965,
turned out to persist for almost five decades, the nano era poses significant problems to the
concept of downscaling [
2
]. Upon approaching the size of atoms, quantum effects, such as
quantum tunneling, pose fundamental barriers to the trend. Furthermore, the conventional
computing paradigm based on the Von-Neumann architecture and binary logic becomes
increasingly inefficient considering the growing complexity of todays computational tasks.
Hence, new computational paradigms and alternative information processing architectures
must be explored to extend the capabilities of future information technology beyond digital
logic. A fantastic example for such an alternative information processing architecture is the
human brain. The brain provides superior computational features such as ultrahigh density
of processing units, low energy consumption per computational event, ultrahigh parallelism
in computational execution, extremely flexible plasticity of connections between processing
units and fault-tolerant computing provided by a huge number of computational entities.
Compared to today's programmable computers, biological systems are six to nine orders of
magnitude more efficient in complex environments [
3
]. For instance: simulating five seconds
of brain activity takes IBM's state-of-the-art supercomputer Blue Gene a hundred times as
long, i.e. 500 s, during which it consumes 1.4 MW of power, whereas the power dissipation in
the human central nervous system is of the order of 10 W [
4
,
5
]. Thus, it is not only extremely
interesting but in terms of computational progress also highly desirable to understand how
1
Chapter 1: Introduction
information is processed in the human brain. The conceptual idea developed within the
framework of this thesis tries to contribute to this intention. In contrast to most recent
research dealing with the simulation and emulation of specific connections between nerve
cells [
5
12
], the work of this thesis focuses on investigating, on a purely conceptional basis,
the issue of a possible future emulation of an artificial nerve cell based on the inherent physics
of phase-change materials.
After this introduction, chapter two provides the reader with the necessary biological
background and gives insight into some physiological key processes and functional principles
of the nervous system. At some points in this chapter, detailed explanations of selected
mechanisms are deliberately left out in order to keep the reader focussed on the central
theme of this thesis. Chapter three presents the reader with a selection of recent examples of
current research dealing with the emulation of biological functionality. Chapter four describes
a specific behaviour of nerve cells which is thought to play an important role in the process
of neural information processing and chapter five documents a conceptual idea to emulate
this behaviour in an artificial nerve cell based on a phase-change material. Finally, chapter
six concludes this thesis and gives an outlook on some future ideas that could be investigated
to complement the work of this thesis. Furthermore, keywords that are mentioned for the
first time in the text are typed in italic and can be looked up in the vocabulary in appendix
B
which provides the reader, who might not be deeply familiar with the technical terminology,
with the possibility to quickly refresh key definitions which are repeatedly used throughout
the whole text. The author hopes to inspire every reader who comes in touch with this field of
science for the first time and wishes him to find as much pleasure and excitement in reading
this thesis as the author had working on it and writing it down.
2
CHAPTER 2
A Biological Background
The Human brain is vastly superior to the brain of other animals in its ability to exploit the
physical environment in which the controlled organism has to operate. The remarkable com-
plexity of the environment that humans created for themselves since the beginning of their
existence depends on the connection of highly sophisticated arrays of sensory receptors to an
extremely flexible neural machine - a brain - which provides the possibility to discriminate an
enormous variety of events in the environment. The brain organizes the continuous stream
of information from these receptors into perceptions which are partly stored in memory for
future references. These perceptions are then organized into appropriate behavioral respons-
es. All of this is accomplished by the brain using nerve cells that are connected to each other
via synapses. Even though the nervous system has two classes of cells, nerve cells (neurons)
and glial cells (glia), which outnumber neurons by a factor of 10 - 50, within the framework
of this thesis only structural and functional properties of neurons are dealt with because
neurons are the main signaling units of the nervous system. [
13
]
2.1. The Neuron
The Neuron is the basic processing unit of the brain. The human brain contains an extraordi-
nary number of these morphologically simple units (of the order of 10
11
neurons), each of
which has about 10
3
connections to other units. Although classifiable into at least a thousand
different types, all neurons share the same basic architecture. Different ways in which neu-
rons with basically similar properties are connected to each other can, nevertheless, lead to
quite different characteristics of the resulting entities. The basis for the complexity of human
behaviour is formed by the fact that numerous neurons constitute precise anatomical and
functional entities rather than by the specialization of individual neurons.
3
Chapter 2: A Biological Background
In order to appreciate how information in the nervous system is processed it is necessary
to begin with with the structural and functional properties of neurons and then to deal
with the mechanisms that are responsible for the generation and processing of signals.
[
13
]
2.1.1. Morphology of a Neuron
A typical neuron has four morphologically defined regions, as illustrated in Figure
2.1
: (1)
the cell body (soma), (2) the dendrites, (3) the axon and (4) several presynaptic terminals.
Each region plays a distinct role in the generation of signals and communication between
neurons. The soma is the center of metabolism of the neuron and has usually two types
of extensions: a) several short dendrites and b) one long, tubular axon. Through extensive
branching, the dendrites form a dendritic tree which functions as the main apparatus for
receiving incoming signals from other neurons. In contrast, the axon functions as the main
conducting unit that carries signals away from the soma to other neurons. The axon conveys
electrical signals in form of action potentials (see section
2.1.4
) that are initiated at the axon
hillock, a specialized trigger region at the origin of the axon. The axon itself is partly insulated
by myelin sheathes that are interrupted at regular intervals by the nodes of Ranvier, which
enables the fast transport of APs (see section
2.1.5
). Near its end, the axon splits in a tree-like
fashion into several terminals that form communication sites with other neurons, called
synapses (see section
2.2
). Presynaptic terminals end mostly at the dendrites of a postsynaptic
neuron, however, they may also end at the soma or even at the beginning or the end of the
axon of the receiving neuron.
Every neuron's intracellular space is separated from the extracellular space by the
cell membrane whose membrane potential is determined by ion concentrations inside and
outside the cell. Changes of the membrane potential can be generated by individual sensory
cells in response to smallest stimuli: photoreceptors in the eye respond to a single photon of
light; olfactory neurons detect a single molecule of odorant; and hair cells in the inner ear
respond to tiny movements of atomic dimensions. Neuronal signaling in the brain depends
on the ability of neurons to respond to such small stimuli by producing rapid changes
in the electrical potential difference across their cell membranes. These rapid changes
are mediated by ion channels, therefore ion channels are important for signaling in the
nervous system. [
13
]
2.1.2. Ion channels
Ion channels owe their functional importance to three basic properties: (1) they conduct
ions, (2) they recognize and select specific ions, (3) they open and close in response to
specific electrical, mechanical or chemical signals. Ion channels conduct ions across the cell
4
2.1. The Neuron
Figure 2.1.: A typical neuron's morphology. The cell body (soma) is responsible for
metabolism processes of the neuron and contains the nucleus, the store-
house of genetic information. It has two types of extensions: (1) several
dendrites and (2) the axon. The axon is the signal transmitting element
(or the output element) of the neuron and can vary greatly in length. Some
can extend up to three meters in the body. Most axons have a relatively
thin diameter of about 0.2-20
m compared to the diameter of the so-
ma (about 50
m or more). Many axons are partly insulated by myelin
sheathes that are interrupted at regular intervals by the nodes of Ran-
vier which allows the fast transport of APs (see section
2.1.5
). Once the
signal travelled through the axon it reaches the axon terminals which
can connect to other neurons. Such connections, called synapses, most-
ly appear at the dendrites, the input elements of the neuron and can
occur up to a thousand times at a single neuron. [
13
] [modified from
http://insidethemind.synthasite.com]
membrane between the intracellular and extracellular space at extremely rapid rates: up to
10
8
ions may pass through a single channel per second. Despite the ability to provide high
conductance rates, ion channels also provide sophisticated selective mechanisms, i.e. each
type of ion channel allows only one or a few types of ions to pass. For instance: the resting
potential - the membrane potential of a neuron which is at rest, i.e. the neuron shows no
5
Chapter 2: A Biological Background
activity - is largely determined by ion channels that are selectively permeable to K
+
-cations.
These K
+
-channels are typically 100-fold more permeable to K
+
-cations than to Na
+
-cations.
During depolarization (see section
2.1.3
), however, Na
+
-channels that are 10-20-fold more
permeable to Na
+
-cations than to K
+
-cations are responsible for the value of the membrane
potential. The exact understanding of the underlying mechanisms for the selectivity of ion
channels is not mandatory for the concept of this thesis, thus, further explanations are left
out but can be found elsewhere, e.g. in [
13
].
The activation or deactivation of many ion channels can be caused by different stimuli,
as illustrated in Figure
2.2
: (1) voltage-gated channels are regulated by changes in voltage, i.e.
by changes of the potential across the channel which is determined by the neuron's membrane
potential, (2) ligand-gated channels are regulated by chemical transmitters, i.e. opening
and closing of the channel depends on whether a specific ligand binds at the channel's
receptor or not and (3) mechanically gated channels are regulated by pressure or stretch. In
general, ion channels can enter one of three states under the influence of the above regulating
mechanisms: (1) closed and can be activated (resting state), (2) open (active state) and (3)
closed and can not be activated (refractory state). The most important task of voltage-gated
channels is the generation of APs because the generation and transmission of APs are the
basis for encoding neural information in the nervous system. In order to understand how
an AP is generated, it is necessary to begin with a brief dealing of a neuron's membrane
potential. [
13
]
2.1.3. The Membrane Potential
The electrical signals representing the flow of information in the nervous system are produced
by temporary changes in the current flow into and out of the cell, driving the membrane
potential - the electrical potential across the cell membrane - away from its resting value.
This current flow is controlled by ion channels integrated in the cell membrane, as illustrated
in Figure
2.3
, whereas these ion channels can be one of two types: (1) resting channels and (2)
gated channels. Resting channels are usually opened and are not significantly influenced by
extrinsic factors, i.e. their operational state is not altered by changing e.g. the potential across
the membrane. These channels are primarily important in maintaining the resting potential
of the neuron, i.e. the electrical potential across the membrane in the absence of signaling.
The current that is carried by ion fluxes through resting channels is called leakage current and
the conductivity of the population of resting channels, which is determined by the amount of
ions passing through, is called leakage conductance. On the contrary, most gated channels
are at rest when the neuron is at rest, i.e. gated channels are closed when the membrane
potential is at its resting potential value. In the resting state, the separation of charges across
a neuron's cell membrane consists of a thin cloud of ions spread over the inner and outer
6
2.1. The Neuron
Figure 2.2.: Several types of stimuli control the opening and closing of ion channels.
A) Ligand-gated channels open upon binding of a ligand to the channel's
receptor.
B) Voltage-gated channels open and close upon changes in the cell mem-
brane potential. The change of the potential causes a conformational
change by acting on a component of the channel that has a net charge.
C) Stretch/Pressure-gated channels are activated by stretch or pressure
which mechanically forces gating of the channel through the cytoskeleton.
[modified from [
13
]]
7
Chapter 2: A Biological Background
Figure 2.3.: The ionic permeability of the cell membrane is provided by integrated
ion channels. These ion channels provide a pathway for hydrated ions
to cross the membrane, i.e. ions flow according to their concentration
gradient from the extracellular space to the intracellular space and vice
versa. [modified from [
13
]]
surface of the cell membrane. An excess of positive ions on the outside and negative ions
on the inside of the cell membrane is maintained because its lipid bilayer blocks diffusion
processes of the ions (see Figure
2.4
). The resulting charge separation gives rise to different
electrical potentials inside and outside the cell defining the membrane potential V
m
:
V
m
= V
i n
-V
out
,
where V
i n
and V
out
are the electrical potentials inside and outside the cell, respectively. Since
by convention the potential outside the cell is defined as zero, the resting potential V
r
is equal
to V
i n
and usually ranges from -60 mV to -70 mV which can be calculated with the Goldman
equation (see appendix
A
).
In order to change the resting potential, electric current carried by both, positive cations
(Na
+
and K
+
) and negative anions (Cl
-
and A
-
- organic anions, mostly amino acids and pro-
teins), has to flow into and out of the cell which causes a perturbation of the charge separation
and thus, changes the resting potential. A reduction of charge separation leading to a less neg-
ative membrane potential is called depolarization. An increase in charge separation leading
8
2.1. The Neuron
Figure 2.4.: The membrane potential results from a charge separation across the cell
membrane. The resting potential is characterized by an excess of positive
and negative charges outside and inside the cell, respectively. [modified
from [
13
]]
to a more negative membrane potential is called hyperpolarization. In case of perturbation,
the membrane potential recovers to its resting potential value thanks to a specific distribution
of several resting channels integrated in the cell membrane accompanied by the activity of
ion pumps that balance the passive flux of ions. The resting channels are either permeable
only to potassium (resting channels in glial cells) or permeable to potassium as well as to
sodium and chloride (resting channels in nerve cells). The ion pumps prevent the dissipation
of ionic gradients by moving ions against their net electrochemical gradient. In order to do so,
ion pumps need to generate energy which is achieved through hydrolysis of ATP (Adenosine
Triphosphate, a multifunctional nucleoside triphosphate used as a coenzyme to transport
chemical energy within cells for metabolism) molecules. Thus, the resting potential is not
an equilibrium, but rather a steady state: the continuous passive influx of Na
+
and efflux
of K
+
through resting channels is exactly counterbalanced by the ion pumps. An exception
9
Chapter 2: A Biological Background
poses the distribution of chloride ions whose movement tends toward equilibrium across
the membrane so that there is no net Cl
-
-flux at rest. The exact understanding of the under-
lying mechanisms for the maintenance of the resting potential, especially the mechanism
of ATP hydrolysis which is responsible for the energy extraction of the ion pumps, is not
mandatory for the concept of this thesis, thus, further explanations are left out but can be
found elsewhere, e.g. in [
13
]. When the resting potential is sufficiently perturbed, an action
potential is generated, i.e. the balance of ion fluxes that maintains the resting potential is
abolished. [
13
]
2.1.4. The Action Potential
Depolarization of a neuron's membrane mostly occurs at the dendrites which transport the
input signals to the soma (see section
2.1.5
). The soma acts as an integrator, spatially and tem-
porally adding up all single input signals from all dendrites. When the membrane potential is
depolarized past the threshold potential, i.e. the membrane potential rises past a critical value
which leads to the activation of voltage-gated ion channels, the balance of ion fluxes in the
resting state changes. Voltage-gated Na
+
-channels open rapidly in an all-or-nothing fashion
resulting in an increased membrane permeability to Na
+
-ions. The Na
+
-influx exceeds the K
+
-
efflux which leads to a net influx of positive charge causing further depolarization resulting
in the activation of additional Na
+
-channels which increase the Na
+
-permeability even more
and so fourth. This regenerative, positive feedback cycle develops explosively, driving the
membrane potential toward the Na
+
-equilibrium potential, i.e. toward the equilibrium which
would adjust incase of permanently opened voltage-gated Na
+
-channels, of about +55 mV,
which can be calculated with the Nernst equation (see appendix
A
). After the generation of
such an action potential (AP), two processes lead to repolarization of the membrane potential,
i.e. the AP is terminated and the resting potential will be restored: (1) the voltage-gated Na
channels gradually close, reducing the Na
+
-influx and (2) voltage-gated K
+
-channels that
were opened during the late stage of depolarization increase the K
+
-efflux. The existence of
a threshold potential is based on the fact that small depolarizations do not only lead to an
increase of Na
+
-influx but also to an increase of K
+
-efflux which resists the depolarization
action of the Na
+
-influx up to a certain point. It is important to note that the increase in
K
+
-permeability during depolarization is much slower compared to the explosive increase
in Na
+
-permeability because of the slower rate of opening of K
+
-channels compared to Na
+
-
channels. After the AP peak is reached, the delayed K
+
-efflux combined with the decreasing
Na
+
-influx leads to a net efflux of positive charge which continues until the resting potential
is restored.
In most neurons, the AP is followed by the after potential, a transient hyperpolarization
driving the membrane potential toward the K
+
-equilibrium potential of about -75 mV. The
10
2.1. The Neuron
Figure 2.5.: The change of the membrane potential during the generation of an AP
can be divided into five phases: (1) the neuron is at rest, i.e. shows no
activity. The resting potential is maintained by the balance of ion fluxes
provided by several resting channels and ion pumps; (2) subthreshold
stimuli depolarize the membrane and may add up to one single stimulus
until the threshold voltage is reached. If no superthreshold stimulus is
applied, the resting potential is restored; (3) the membrane potential rises
past its threshold value triggering a regenerative, positive feedback cycle of
inward Na
+
-flux generating the actual AP; (4) the closing of Na
+
-channels
and delayed opening of voltage-gated K
+
-channels drive the membrane
potential back to its resting value; (5) the delayed closing of K
+
-channels
lead to hyperpolarization after which the resting potential is restored.
Note that each AP is followed by a period of refractoriness during which
the neuron is insensitive to stimuli and can not be excited. [modified from
[
14
]]
11
Chapter 2: A Biological Background
after potential occurs because the K
+
-channels, which opened during the later phase of the
AP, need a few milliseconds to close and are still opened even though the membrane potential
has already reached its resting value. Simultaneously, the AP is also followed by a brief period
of refractoriness (refractory period), i.e. a period during which it is impossible or exceedingly
difficult to excite the neuron, that can be divided into two phases: (1) the absolute refractory
period immediately follows the AP. During this period the neuron is not at all excitable no
matter how great the applied stimulating current is. (2) the relative refractory period directly
follows the absolute refractory period. During this period it is again possible to excite the
neuron but the stimuli must be stronger than those usually required to trigger the neuron, i.e.
to rise the membrane potential past the threshold value. Both periods of refractoriness are
the result of the residual inactivation of Na
+
-channels and increased opening of K
+
-channels.
It takes a few milliseconds for the voltage-gated Na
+
-channels that are responsible for the
generation of APs to be closed during which they are insensitive to opening signals, thus, lead-
ing to the period of refractoriness. Figure
2.5
illustrates how the membrane potential changes
during the generation of an AP which is a so called all-or-nothing event, i.e. the underlying
mechanisms for the generation are always the same, thus, every AP of a particular neuron
looks the same. A neuron's sole ability to generate APs is not enough to process information
in the nervous system. For communication purposes, the neuron has to transport the AP
through its axon to the axon terminals, where it can be transmitted to other neurons. [
13
]
2.1.5. Propagation of the Action Potential
In order to communicate with other neurons, a neuron has to transport its informational
content, i.e. an AP, to its output apparatus, the axon terminals. Every neuron has three
relatively constant, passive electrical properties that affect the electrical signaling: (1) the
resting membrane resistance r
m
(units of
·cm) represents the resistance of ion channels for
ions passing through a channel from the extracellular space to the intracellular space and
vice versa. The current that is carried by ions passing a channel, i.e. the electrical current
passing the resting membrane resistance, is called ionic membrane current; (2) the membrane
capacitance c
m
(units of farads) represents the capacitive characteristic of a neuron's cell
membrane to separate charges inside and outside the cell (see Figure
2.4
). The current that
is carried by ions that change the net charge stored on the membrane is called capacitive
membrane current; (3) the intracellular axial resistance r
a
(units of
/cm) represents the
resistance for a current that flows along the axon and the dendrites. In electric signaling
along dendrites and axons, the non spherical geometry of both compartments causes a
subthreshold voltage signal to decrease in amplitude with distance from its site of initiation.
The propagation of electrical signals along dendrites and axons can be best understood
with the help of an equivalent electrical circuit (see Figure
2.6
) that shows how the geometry of
12
2.1. The Neuron
the compartments influence the distribution of current flow. If ions flow from the extracellular
Figure 2.6.: Equivalent electrical circuit representing a neuronal extension, e.g. a
neuron's axon. The extension is divided into unit lengths with an own
membrane resistance r
m
and a membrane capacitance c
m
. The single
circuits are connected by resistors r
a
, representing the axial resistance of
the cytoplasm and a short circuit with negligible resistance representing
the extracellular fluid. [modified from [
13
]]
fluid into the cytoplasm through ion channels, i.e. if a current is injected into the cell and
flows through the electrical circuit, which represents a unit length, the current flows out of
the cell through several parallel pathways across successive cylinders along the length of
the extension. The total resistance r
t ot
for each of these pathways is made of all resistive
components in series that the current has to go through on its way into the cell, through the
cytoplasm and out of the cell again, i.e.
r
t ot
= 2 · r
m
+ x · r
a
,
where x is the number of segments along the pathway in the cytoplasm. (Here, for reasons of
simplicity, it is assumed that the duration of the current injection is large compared to the
time the membrane potential needs to change, i.e. t
c
m
, so that the capacitive current is
zero). Because the resistance of the pathways with a greater distance from the site of current
injection is bigger, the current I
m
decreases along the extension and with it the membrane
potential V
m
= I
m
· r
m
. Thus, the change of the membrane potential
V (x) depends on the
distance from the site of current injection x:
V (x) = V
0
· e
-x/
,
where
is the membrane length constant and V
0
is the change in membrane potential
produced by the current flow at the injection site, i.e. at x
= 0. The membrane length constant
13
Chapter 2: A Biological Background
Figure 2.7.: The change in membrane potential in a passive neuronal extension decays
with distance. The distance at which
V
m
has decayed to 37 % if its initial
value is defined by the membrane length constant
. [modified from [
13
]]
is determined by the resistances of the cell,
= (r
m
/r
a
),
and defines the distance after which the change in membrane potential has decayed to 1/e,
i.e. 37% of its initial value (see Figure
2.7
). This means that the better the insulation of the
membrane, i.e. the greater r
m
, and the better the conducting properties of the cytoplasm,
i.e. the lower r
a
, the greater the length constant of the extension. The resistances of the
cell depend on the cells geometry, more precisely on its diameter, leading to transformed
expressions for r
a
and r
m
:
r
a
= /a
2
,
where
(in units of · cm) is the specific resistance of a 1 cm
3
cube of cytoplasm and a is the
radius of the extension and
r
m
= R
m
/2
a,
where R
m
(in units of
·cm
2
) is the specific resistance of a unit area of membrane, which leads
to an expression for the membrane length constant in terms of the intrinsic (size invariant)
properties R
m
and
:
=
R
m
·
a
2
.
Thus, thicker axons and dendrites have longer length constants than thinner cell extensions
and hence, carry electrical signals over longer distances. With the properties of a cell extension
14
2.1. The Neuron
Figure 2.8.: APs in myelinated fibers are periodically refreshed at the nodes of Ranvier.
Capacitive and ionic membrane current densities are much higher at the
nodes of Ranvier than in the internodal regions which is represented by
the thickness of the arrows. Because of the much higher membrane capac-
itance at the nonmyelinated nodes, the AP slows down as it approaches
each node and thus, appears to jump from node to node. [modified from
[
13
]]
and their influence on electrical signaling as discussed above, the propagation of an AP
through the axon can be understood.
If the membrane at any point of an axon has been depolarized beyond threshold,
an AP is generated at this point. The local change in membrane potential spreads down
the axon causing the adjacent region to be depolarized past the threshold which leads to
the generation of another AP at that adjacent point. The depolarization spreads along the
whole axon by local-circuit current resulting from the potential difference between the active
15
Chapter 2: A Biological Background
and inactive regions of the membrane. This current has a great spread in cells with longer
length constants leading to a more rapid propagation of APs, whereas there are two ways
of increasing the conduction velocity of APs through the axon: (1) an increase in the axons
diameter increases the length constant (note the dependence of
on a) and (2) myelination
of the axon, i.e. wrapping of insulating glial cells around the axon, increases the thickness
of the axonal membrane and hence, decreases its capacitance. Since the time it takes for a
depolarization to spread along the axons is determined by
= r
m
· c
m
, partly insulating the
axon, i.e. decreasing its membrane capacitance, results in a more rapid propagation of APs. A
neuron triggered at the nonmyelinated axon hillock will generate an AP at this point which
discharges the capacitance of the myelinated axon ahead of it. The AP is prevented from
dying out by the nodes of Ranvier which interrupt the insulation of the axon every 1-2 mm by
bare patches of the axon membrane, about 2
m in length. At these nodes, the AP is refreshed
because of the richness of voltage-gated Na
+
-channels that generate an intense depolarizing
Na
+
-inward current in response to the passive spread of depolarization. Figure
2.8
illustrates
the propagation of an AP down the axon. Note that the propagation speed of an AP is much
faster in the myelinated areas due to the low membrane capacitance. The AP basically jumps
from node to node which is called saltatory conduction.
In summary, myelination is not only extremely important in terms of conduction speed
but it is also favorable from a metabolic standpoint: Because ion channels are integrated
only in nonmyelinated parts of the membrane, ionic membrane currents flow only at the
nodes in myelinated fibers which means that less energy must be expended by ion pumps in
restoring the ion concentration gradients (see section
2.1.3
). After an AP travelled through
the axon, it reaches the axon terminals which form communication sites with other neurons.
The point at which one neuron communicates with another is called a synapse which is a
fundamental element for information processing in the nervous system. [
13
]
2.2. The Synapse
Synapses are the connections between the basic units of the nervous systems, the neurons.
Synaptic transmission - the transmission of signals from one neuron to another - is the
fundamental basis for communication in the nervous system. The human brain contains
about 10
11
neurons, each of which forms about a thousand synaptic connections with other
neurons and receives up to a hundred thousand connections, as e.g. the Purkinje cell in
in the cerebellum, thus, about 10
14
or more connections are formed in the human brain.
There are more neurons and synapses in one single brain than the several billion stars in our
galaxy, fortunately, however, only a few basic mechanisms underlie synaptic transmission
at these many connections. A typical synapse consists of a presynaptic axon apposed to a
postsynaptic neuron via an axon terminal. Based on the structure of the apposition, synapses
16
2.2. The Synapse
can be divided into either electrical synapses, i.e. the transmission of signals is of electrical
nature, or chemical synapses, i.e. that the transmission of signals is of chemical nature. At elec-
trical synapses the presynaptic terminal is not completely separated from the postsynaptic
neuron so that the current generated by a presynaptic action potential (PSAP) flows directly
into the postsynaptic neuron through specialized channels called gap-junction channels
which physically connect the pre- and postsynaptic cytoplasms. In contrast, at chemical
synapses the two neurons are physically separated by the synaptic cleft. The transmission
of signals is provided by the release of neurotransmitters upon the arrival of PSAPs at the
presynaptic terminals. These transmitters diffuse into the synaptic cleft and bind to postsy-
naptic receptors, evoking a postsynaptic signal. Several steps that are involved in chemical
transmission are the reason for a synaptic delay compared to electrical transmission. Both
forms of synaptic transmission can have either inhibitory or excitatory effect on the postsy-
naptic cell, i.e. that both forms can either facilitate or impede the generation of a postsynaptic
AP. Moreover, the strength of both forms can be either enhanced or diminished which is
called synaptic plasticity and is crucial to memory and other higher brain functions. Table
2.1
summarizes the properties of electrical and chemical synapses. In the following section,
the focus lies on chemical synaptic transmission because, although slower in transmis-
sion speed, chemical synapses provide the possibility to amplify signals, unlike electrical
synapses, therefore, chemical synaptic transmission is thought to be crucial for emergent
phenomena such as memory and learning. [
13
]
Type of synapse
Distance
be-
tween pre- and
postsynaptic
cell membrane
Cytoplasmic con-
tinuity
between
pre- and postsy-
naptic cells
Ultrastructural
components
Agent
of
transmis-
sion
Synaptic
delay
Direction
of transmis-
sion
Electrical
3.5 nm
Yes
Gap-junction
channels
Ion current
Virtually
absent
Usually bidi-
rectional
Chemical
20-40 nm
No
Presynaptic
vesicles
and
active
zones;
postsynaptic
receptors
Chemical
transmit-
ter
Significant:
at
least
0.3 ms,
usually
1.5 ms or
longer
Unidirectional
Table 2.1.: Properties of electrical and chemical synapses. [taken from [
13
]]
2.2.1. Synaptic Transmission at Chemical Synapses
Synaptic transmission at chemical synapses involves several steps, as illustrated in Figure
2.9
,
starting with the arrival of an AP at the presynaptic terminal. During discharge of a PSAP,
voltage-gated Ca
2+
-channels integrated in the active zone of the presynaptic terminal's cell
17
Chapter 2: A Biological Background
membrane are opened facilitating a Ca
2+
-inward current. The resulting rise in intracellular
Ca
2+
-concentration causes synaptic vesicles to fuse with the presynaptic cell membrane which
causes neurotransmitters stored inside the vesicles to be released into the synaptic cleft, a
process called exocytosis. The neurotransmitter molecules diffuse across the synaptic cleft
until they reach their receptors integrated in the postsynaptic cell membrane. Upon arrival
at their receptors, the binding of transmitter molecules causes ligand-gated Na
+
-channels
to be opened facilitating a postsynaptic inward Na
+
-current which depolarizes the postsy-
naptic membrane, thereby generating a postsynaptic potential (PSP). After binding to their
receptors, the transmitter molecules must be removed from the synaptic cleft in order to ter-
minate synaptic transmission. In case of no transmitter removal, the synapse would become
refractory, i.e. no new presynaptic signals would be transmitted due to receptor desensiti-
zation resulting from continuous exposure to transmitter molecules. The understanding of
the mechanisms underlying the removal of neurotransmitter from the synaptic cleft is not
mandatory for the concept of this thesis, thus, further explanations are left out but can be
found elsewhere, e.g. in [
13
].
The several steps of chemical synaptic transmission are responsible for the synaptic
delay which does not occur at electrical synapses. However, the lack of speed at chemical
synapses compared to electrical synapses is compensated by the highly important property
of amplification: A single synaptic vesicle contains several thousand molecules of neuro-
transmitter, although typically only two molecules of transmitter are required to open a
postsynaptic ion channel. Consequently, just a single synaptic vesicle can open thousands
of ion channels in the postsynaptic cell. In this way even weak electrical currents generated
by small presynaptic nerve terminals of chemical synapses can have much greater impact
on the postsynaptic neuron as it would be the case at electrical synapses. After exocytosis,
the presynaptic terminal membrane is slightly enlarged, precisely about the size of all vesicle
membranes that fused with the terminal membrane, and the number of vesicles inside the
cell is decreased. In order to prevent this trend, synaptic vesicle membranes added to the
terminal membrane are recycled generating new synaptic vesicles. This recycling process is
called endocytosis and has not yet been completely understood [
13
]. Figure
2.10
illustrates
the cycling of synaptic vesicles at nerve terminals which involves several distinct steps: (1)
free vesicles must be targeted to the active zone and then (2) dock at the active zone after
which they (3) become primed in order to undergo exocytosis, i.e. (4) they fuse with the
terminal membrane and release the contained neurotransmitter. (5) At last, the fused vesicles'
membranes are taken up to the endosome in the interior of the cell by endocytosis where
they are regenerated completing the recycling process. A variety of proteins are involved in
the recycling process but the exact understanding of the underlying mechanisms for the
processes of exocytosis and endocytosis is not mandatory for the concepts of this thesis, thus,
further explanations are left out but can be found elsewhere, e.g. in [
13
].
18
2.2. The Synapse
Figure 2.9.: Chemical synaptic transmission involves several steps: An AP arriving
at the presynaptic terminal causes voltage-gated Ca
2+
-channels at the
active zone to be opened which facilitates a Ca
2+
-influx. The increased
concentration in Ca
2+
-ions inside the cell leads to the process of exocytosis:
synaptic vesicles containing neurotransmitters fuse with cell membrane
at the active zone causing the transmitter molecules to be released into the
synaptic cleft. The transmitter molecules diffuse across the cleft and bind
to specific receptors on the postsynaptic cell membrane causing ligand-
gated ion channels to open (or close), thereby changing the postsynaptic
membrane potential. [modified from [
13
]]
19
Chapter 2: A Biological Background
Figure 2.10.: The cycling of synaptic vesicles at nerve terminals involves several dis-
tinct steps: Free vesicles are in a first step targeted to the active zone then
dock at this active zone in a second step. The docked vesicles become
primed in the third step so they can undergo exocytosis. In response to a
rise in Ca
2+
-concentration the vesicles can fuse with the terminal mem-
brane in the fourth step to release the neurotransmitter. After transmitter
release, in the fifth step the fused vesicle membrane is taken up into the
interior of the cell by endocytosis. The endocytosed vesicles fuse with the
endosome (an internal membrane compartment) which regenerates the
vesicles completing the recycling process. [modified from [
13
]]
Postsynaptic neurons usually receive input from about a thousand synaptic connections, all
of which can affect the neuron in a different way or with different efficacy. The neuron has to
process all this input simultaneously in order to produce a subsequent reaction, i.e. the
neuron has to decide if an AP is generated or not. [
13
]
2.2.2. Synaptic Integration
The synaptic input of neurons in the brain, i.e. the postsynaptic currents (PSPs) evoked by
PSAPs that facilitate synaptic transmission, can affect the postsynaptic neuron in two ways:
(1) synaptic input can be excitatory, i.e. an excitatory postsynaptic current (EPSC) is generated
in the postsynaptic cell. This current is typically carried by Na
+
-ions flowing inside the cell
through ligand-gated ion channels that are opened after binding neurotransmitter molecules
20
2.2. The Synapse
at their specific receptors. This inward current depolarizes the postsynaptic membrane in the
subthreshold regime generating an excitatory postsynaptic potential (EPSP); (2) synaptic input
can be inhibitory, i.e. an inhibitory postsynaptic current (IPSC) is generated in the postsynaptic
cell. This current is typically carried by Cl
-
-ions flowing inside the cell through ligand-gated
ion channels. This inward current hyperpolarizes the postsynaptic membrane generating an
inhibitory postsynaptic potential (IPSP). Consequently, the effect of a synaptic potential is not
determined by the type of transmitter released from the presynaptic neuron but rather by the
type of ion channels in the postsynaptic neuron gated by these transmitters. Nevertheless,
some transmitters act predominantly on receptors that are of one or the other type. For
instance: in the vertebrate brain, glutamate (glutamic acid, C
5
H
9
NO
4
) as a neurotransmitter
typically acts on receptors that produce excitation, whereas GABA (
-Aminobutyric acid,
C
4
H
9
NO
2
) and glycine (NH
2
CO
2
COOH) typically act on receptors that produce inhibition,
however, an exception is found in the vertebrate retina and many others can be found in
invertebrates [
13
].
Interestingly, a synapses morphology seems to be correlated to its functionality: two
common morphological types of synaptic connections can be found in the brain, Gray type
I and type II synapses (named after E.G. Gray). Type I synapses are often glutamatergic, i.e.
the presynaptic terminal releases glutamate as neurotransmitter, and therefore excitatory,
whereas type II synapses are often GABA-ergic, i.e. the presynaptic terminal releases GABA as
neurotransmitter, and therefore inhibitory. Furthermore, excitatory and inhibitory synapses
have favored docking sites at postsynaptic cells: Gray type I synapses, often excitatory, prefer-
ably form communication sites at postsynaptic somas or dendrites, either at the dendritic
shaft itself or at a dendritic spine, a fine specialized input zone of the dendrite, whereas Gray
type II synapses, often inhibitory, preferably form communication sites at the postsynaptic
neuron's axon. Therefore axosomatic synapses and axodendritic synapses are often excitatory,
whereas axoaxonic synapses are often inhibitory. Figure
2.11
and Figure
2.12
illustrate the mor-
phological difference between Gray type I and type II synapses which are also summarized
in Table
2.2
and their preferred docking sites at a postsynaptic neuron. A neuron receives
synaptic input from about a thousand connections, each of which may be different from the
other in terms of whether the input is excitatory or inhibitory, in terms of input strength and
in terms of input frequency. In order to decide whether a postsynaptic AP is generated in
response to the various competing inputs from all synaptic connections, the inputs are inte-
grated by the postsynaptic neuron which is called neuronal integration, a decision-making
process which the neurophysiologist and noble laureate Charles Sherrington regarded as
the brain's most fundamental operation. Neuronal integration involves the summation of
synaptic potentials that passively spread to the trigger zone, the axon hillock, whereas this
summation is spatial as well as temporal. Spatial summation is the integrative process of
summing up synaptic inputs at different communication sites of the postsynaptic neuron,
21
Chapter 2: A Biological Background
Figure 2.11.: Synaptic contact can occur at the soma, the dendrites or the axon of
postsynaptic neurons. The names of the various kinds of synapses iden-
tify the docking regions of the presynaptic terminal at the postsynaptic
neuron. Note that axodendritic synapses can either dock at the main
shaft of the dendrite or at a specialized input zone, the spine. [modified
from [
13
]]
whereas temporal summation is the integrative process of summing up consecutive synaptic
potentials at the same communication site. If the integrative processes of both, temporal and
spatial summation result in a superthreshold depolarization of the postsynaptic neuron, an
AP would be generated. A remarkable feature of synapses is their ability to undergo functional
22
2.2. The Synapse
Figure 2.12.: The two most common morphologic types of synapses in the brain are
Gray type I and type II. Type I synapses are usually glutamatergic and
therefore excitatory whereas type II synapses are usually GABA-ergic and
therefore inhibitory. Both types have differences in width of the synaptic
cleft, total area of the active zone, prominence of presynaptic densities,
shape of vesicles, and presence of a dense basement membrane. Type I
synapses commonly contact dendritic spines and sometimes the den-
dritic shaft, whereas type II synapses commonly contact the postsynaptic
soma. [modified from [
13
]]
23
Chapter 2: A Biological Background
Type of
synapse
width of
synaptic
cleft
area
of
active
zone
density of vesi-
cle release sites
vesicle shape
density of base-
ment membrane
Gray
type I
about
30 nm
1
-2m
2
dense
regions
on presynaptic
membrane;
predominant
tends
to
as-
sume a charac-
teristic round
shape
amorphous
dense basement-
membrane
ma-
terial appears in
synaptic cleft
Gray
type II
about
20 nm
< 1
m
2
less
obviously
distinct;
clus-
tered
tends
to
as-
sume a rather
oval shape
little or no base-
ment membrane
in synaptic cleft
Table 2.2.: Summary of the morphological differences between Gray type I and type II
synapses.
and structural changes depending on their history in a neural network. This ability is called
synaptic plasticity and is crucial to memory, learning and other higher brain functions.
[
13
]
2.2.3. Synaptic Plasticity
"What fires together, wires together." - attributed to C.J. Shatz [
15
].
In 1949, the psychologist Donald Olding Hebb introduced the Hebbian theory which explains
the adaption of neurons in the brain during the process of learning [
16
]. The theory states
that an increase in synaptic weight, i.e. an increase in synaptic efficacy in response to PSAPs,
arises from repeated and persistent stimulation of the postsynaptic neuron through a presy-
naptic neuron. Hebb's theory is often summarized as "What fires together, wires together"
and attempts to explain associative learning, an ability of the nervous system to adjust the
connection strength of neural pathways, or more precisely the mechanisms by which simul-
taneous activation of neurons leads to a pronounced increase of synaptic strength between
those neurons. This method of learning, named after its originator Donald O. Hebb, is called
Hebbian learning. Synapses that are affected by Hebbian learning undergo functional and
structural changes, called synaptic plasticity, which can be temporary or permanent. A tem-
porary change in synaptic efficacy lasting a few seconds or less is categorized as short-term
plasticity (STP). Short-term synaptic enhancement is often differentiated into three categories
depending on their timescales: (1) short-term facilitation (STF), also called pulsed pair facili-
tation (PPF) usually lasts for tens of milliseconds while (2) short-term augmentation (STA)
24
Details
- Pages
- Type of Edition
- Erstausgabe
- Year
- 2015
- ISBN (eBook)
- 9783954898442
- ISBN (Softcover)
- 9783954893447
- File size
- 7.4 MB
- Language
- English
- Publication date
- 2015 (January)
- Keywords
- emulation bursting neurons neuromorphic hardware phase-change materials
