Emulation of Bursting Neurons in Neuromorphic Hardware based on Phase-Change Materials

Contents

1. Introduction

2. A Biological Background
2.1. The Neuron
2.1.1. Morphology of a Neuron
2.1.2. Ion channels
2.1.3. The Membrane Potential
2.1.4. The Action Potential
2.1.5. Propagation of the Action Potential
2.2. The Synapse
2.2.1. Synaptic Transmission at Chemical Synapses
2.2.2. Synaptic Integration
2.2.3. Synaptic Plasticity
2.2.4. Spike-Timing-Dependent Plasticity (STDP)
2.3. An Overall View

3. Experimental Emulations
3.1. Modeling STP and LTP in a CMOS Spiking Neural Network Chip
3.2. Implementation of STDP based on Phase-Change Material Synapses
3.2.1. Phase-Change Materials
3.2.2. A Phase-Change Cross-Point Structure emulating STDP
3.3. Phase-Change Materials for Artificial Neural Networks
3.4. An Overall View

4. Bursting Neurons
4.1. Physiological Mechanisms of Bursting
4.2. Bursts as a Unit of Neuronal Information
4.3. Bursting for Selective Communication
4.4. Modeling Neuronal Bursting Activity
4.4.1. The Integrate-and-Fire Model
4.4.2. The Resonate-and-Fire Model
4.4.3. The Quadratic Integrate-and-Fire model
4.4.4. The Simple Model of Choice
4.5. An Overall View

5. A PCM Bursting Neuron
5.1. Voltage-Controlled Relaxation Oscillation in a PCM Device
5.2. The Analogy to Hippocampal Pyramidal Bursting Neurons
5.3. Simulation of a PCM Bursting Neuron
5.4. An Overall View

6. An Outlook on the Future

A. Quantification of the Membrane Potential

B. Vocabulary

List of Figures

List of Tables

Bibliography

Acknowledgement

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 years¹. 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 downscaling². 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 environments³. 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 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.

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 responses. 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 1011 neurons), each of which has about 103 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.

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

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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 μ m compared to the diameter of the so- ma (about 50 μ 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 108 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 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. in¹³.

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

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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 ]]

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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 ]]

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 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:

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where V _in 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 _in and usually ranges from -60 mV to -70 mV which can be calculated with the Goldman equation (see appendix A).

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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 ]]

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 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 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. in¹³. 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.

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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 ]]

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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 ]]

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 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 Ω · 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 Ω/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.

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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 ]]

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 the compartments influence the distribution of current flow. If ions flow from the extracellular 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 tot 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.

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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. [illustration not visible in this excerpt], 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 [illustration not visible in this excerpt] decreases along the extension and with it the membrane potential [illustration not visible in this excerpt]. Thus, the change of the membrane potential Δ V (x) depends on the distance from the site of current injection x:

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where λ is the membrane length constant and Δ 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

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Figure 2.7.: The change in membrane potential in a passive neuronal extension decays with distance. The distance at which Δ V_m has decayed to 37 % if its initial value is defined by the membrane length constant λ . [modified from [ 13 ]]

is determined by the resistances of the cell,

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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:

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where ρ (in units of Ω · cm) is the specific resistance of a 1 cm³ cube of cytoplasm and a is the radius of the extension and

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where r _m (in units of Ω · cm2) 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 ρ:

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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

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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 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 λ 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 [illustration not visible in this excerpt], 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, about²⁺ μ 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 1011 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 1014 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 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 transmission 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

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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 Ca²⁺ -channels integrated in the active zone of the presynaptic terminal’s cell

Chapter 2: A Biological Background

membrane are opened facilitating a Ca²⁺ -inward current. The resulting rise in intracellular Ca²⁺ -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. in¹³. 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 understood¹³. 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. in¹³.

2.2. The Synapse

Figure 2.9.: Chemical synaptic transmission involves several steps: An AP arriving at the presynaptic terminal causes voltage-gated Ca²⁺ -channels at the active zone to be opened which facilitates a Ca²⁺ -influx. The increased concentration in Ca²⁺ -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 ]]

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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 Ca²⁺ -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 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, C5H9NO4) as a neurotransmitter typically acts on receptors that produce excitation, whereas GABA (γ -Aminobutyric acid, C4H9NO2) and glycine (NH2CO2COOH) typically act on receptors that produce inhibition, however, an exception is found in the vertebrate retina and many others can be found in invertebrates¹³.

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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 ]]

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, 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 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

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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 ]]

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Table 2.2.: Summary of the morphological differences between Gray type I and type II synapses.

2.2.3. Synaptic Plasticity

“What fires together, wires together.” - attributed to C.J. Shatz¹⁵.

In 1949, the psychologist Donald Olding Hebb introduced the Hebbian theory which explains the adaption of neurons in the brain during the process of learning¹⁶. 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) acts on the timescale of seconds and (3) short-term potentiation (STP - not to be confused with short-term plasticity) which has a time course of tens of seconds up to several minutes ¹⁷. Each form of temporary enhancement of synaptic strength is an exclusively presynap- tic mechanism and results from an increased probability to release vesicles in response to a PSAP as a consequence of an increased Ca²⁺ -concentration in the presynaptic terminal. Consequently, the synaptic connection will be strengthened for a short time because of either an increase in size of the readily releasable pool of vesicles that contain neurotransmitter molecules or because of an increase in the amount of neurotransmitter molecules stored in the vesicles released in response to an AP. The type of synaptic enhancement present at a given synapse depends on its input: a single AP leads to facilitation, whereas a short train of consecutive APs generally causes augmentation while longer trains lead to potentiation ¹⁸,¹⁹. The inset in Figure 2.13 illustrates how paired pulse facilitation affects the PSCs in a way that two consecutive APs separated by a time Δ t evoke PSCs with the second response larger than the first, while the amplitude of facilitation depends on the temporal structure of synaptic input. The opposed effect to STF is short-term depression (STD) which decreases the amplitude of PSCs and occurs due to a decrease in the probability to release vesicles in response to a PSAP as a consequence of a decreased Ca²⁺ -concentration in the presynaptic terminal²⁰.

Complementary to STP, synaptic plasticity lasting several minutes or longer is catego- rized as long-term plasticity (LTP), an exclusively postsynaptic mechanisms which is found to require the binding of glutamate and glycine for the activation of the specific receptors responsible for LTP, so called NMDA receptors²¹. Similar to STP, LTP is differentiated into long-term potentiation (LTP - not to be confused with long-term plasticity), and long-term depression (LTD). Although oppositional in their effects on synaptic transmission, both LTP as well as LTD are induced by a rise in the intracellular Ca²⁺ -concentration Ca ²⁺ + i inthe postsynaptic neuron. The brief activation of an excitatory pathway can produce LTD only at a minimum level of postsynaptic depolarization caused by a rise in postsynaptic Ca ²⁺ + i.LTP on the other hand requires much stronger postsynaptic depolarization and consequently a much higher postsynaptic Ca ²⁺ + i,hence,itispossibletofirstinduceLTDandthenLTPat the same synapse²². The amplitude of Ca²⁺ -surge is critical for the induction of LTD and LTP rather than the source of Ca²⁺ since the activation of voltage-gated Ca²⁺ -channels and ligand-gated Ca²⁺ -channels as well as the release from intracellular stores have been shown to contribute to the induction of both LTD and LTP. Figure 2.14 illustrates the dependence of whether LTD or LTP is induced on the postsynaptic membrane potential V_m. Note that there are two ranges of V_m within which synapses do not undergo any long-term modifications. A moderate rise in Ca ²⁺ + i leadstoapredominantactivationofphosphatases,whileastronger depolarization favorably leads to the activation of kinases, which has the opposing effect to the activation of phosphatases²⁴.

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