Population Effects on the Dynamics of a Cortical Network of Pyramidal Cells and FSN Interneurons

Transcription

1 Population Effects on the Dynamics of a Cortical Network of Pyramidal Cells and FSN Interneurons Björn Svennenfors TRITA-NA-E04002

2 NADA Numerisk analys och datalogi Department of Numerical Analysis KTH and Computer Science Stockholm Royal Institute of Technology SE Stockholm, Sweden Population Effects on the Dynamics of a Cortical Network of Pyramidal Cells and FSN Interneurons Björn Svennenfors TRITA-NA-E04002 Master s Thesis in Computer Science (20 credits) at the School of Engineering Physics, Royal Institute of Technology year 2004 Supervisor at Nada was Anders Lansner Examiner was Anders Lansner

3 Population Effects on the Dynamics of a Cortical Network of Pyramidal Cells and FSN Interneurons In layer 2/3 of rat neocortex, recent studies have found low connectivity between pyramidal cells, in terms of both the number of unitary connections and the strength of individual connections. In contrast, pyramidal FSN interneuron (fast-spiking nonaccommodating) connectivity was found high, with reciprocal connections to the majority of pyramidal cells in the vicinity. This makes the local interneuron ideally poised to both coordinate and expand the local pyramidal cell network via pyramidal interneuron pyramidal communication. An earlier study of this network examined interneurons capability to alter the behavior of the local pyramidal cells using a subsampled network, a microcircuit consisting of one interneuron and one pyramidal cell. The study focused on a conditioning dependent synaptic plasticity that reduced the inhibitory effect of the interneuron on the pyramidal cell. In this master s project, that network was extended, and a pronounced increase in the effect of the plasticity on the activity of the pyramidal cell activity was found. Further experiments showed that the networks synchronization tendency among the pyramidal cells was reduced when the number of pyramidal cells was increased, approaching the number estimated in the founding biological experiments. Populationseffekter på dynamiken i ett kortikalt nätverk av pyramidceller och FSN-interneuron Nyligen har studier av lager 2/3 i råttans neocortex funnit en låg sannolikhet för kopplingar pyramidceller emellan, och de kopplingar man funnit har varit svaga. Däremot har kopplingarna pyramidcell FSN-interneuron (snabbfyrande icke-ackommoderande) uppvisat stor sannolikhet för starka, ömsesidiga kopplingar till pyramidceller. Det ger interneuronet en ideal position för att både koordinera och expandera nätverket av pyramidceller via kommunikation pyramidcell interneuron pyramidcell. En tidigare studie av detta nätverk undersökte interneuronets förmåga att påverka beteendet av de lokala pyramidcellerna med hjälp av ett subsamplat nätverk; en mikrokrets bestående av ett interneuron och en pyramidcell. Studien fokuserade på en konditioneringsberoende synaptisk plasticitet som reducerade interneuronets inhibitoriska effekt på pyramidcellen. I det här exjobbet expanderades nätverket, och en uttalad ökning av plasticitetens genomslagskraft på pyramidcellaktiviteten observerades. Ytterligare experiment visade att pyramidcellernas tendens att synkronisera minskade när antalet pyramidceller ökades, och på så vis närmade sig de antal som uppskattats i de biologiska experiment som det här arbetet baserats på.

4 Preface My interest for neuroscience begun in earnest a few years ago, when I had the pleasure of taking part in the work of Dr Yuri Zilberter and Carl Holmgren for a year at the Department of Neuroscience, Karolinska Institute. The incredible nerve they showed in their work has been an inspiration to me ever since, and Yuri gave me an introduction to neuroscience that no books could replace. Thanks for taking time for discussions whenever I bothered you, and for providing me with data whenever I asked for it. This master s thesis is the final stage of my undergraduate studies at the Engineering Physics programme of the Royal Institute of Technology, Stockholm. My supervisor and examiner Anders Lansner has a great part in this work by letting me take part of his knowledge and experience of the field. I also want to show my gratitude to Erik Fransén for bringing me to the ground when I lost the grip, and my precursor David Eriksson for his great support. I would like to thank my roommates at Nada for making work happier. To you who have shared your knowledge of neuroscience with me: I will never stop harassing my nearest by paying it forward!

5 Contents Introduction 1 1 Background 2 The Nervous System... 2 Sensory Input... 2 The Central Nervous System... 2 Neocortex... 3 The Neuron... 3 Synaptic Plasticity... 6 Experimental Background... 7 Experimental Methods... 7 Experimental Results... 9 Hypotheses... 9 Cortical Modeling Single Cell and Synapse Level The Compartmental Cell Model Network Level Example of a Similar Model Project Goals Network Extension Methods 14 Founding Model The Modeled Neurons The Modeled Synapses The Conditioning Dependent Synaptic Plasticity Previous Network Model Previous Results... 15

6 Network Scaling Problems Arising Solutions Inter-Cell Synaptic Conductance Variability Model Network Design Construction Input to the Network Network Implementation Additional Specialized Objects Data Presentation and Analysis The Random Search Method Results 24 The Effect of the Conditioning Dependent Synaptic Plasticity Scaling Up of the Network Discussion 27 Possible Importance of the Conditioning Dependent Plasticity Comparisons of the Conditioning Dependent Plasticity Effect The Synchronization Tendencies Proposed Improvements of the Model Conclusions 30 The Effect of the Conditioning Dependent Plasticity The Synchronization Tendencies Bibliography 31

7 Introduction This report is addressed to a reader with a background corresponding to a graduate engineer s degree. For those to which neuroscience is unfamiliar, the field is surveyed in the first part of the Background chapter, The Nervous System. That section is thought to give enough knowledge of the nervous system for the not initiated reader to profit from the remaining parts of the report. To give a more complete picture of the project, the experimental background has a section of its own in the Background chapter. Here is the actual performance of the experiments described, that constitute the founding statistics of this project. The results and the hypotheses supported by these experiments are also reviewed. This work is a study of a specific kind of synaptic plasticity in cortex. Since this is a too complex task to study analytically, a computer model of a cortical network has been set up, and simulations were performed on it to study its behavior. The model of this project was based on a previous model from another project, consisting of only two cells (Eriksson 2002). We have studied differences in the plasticity related behavior of that minimal network model and the larger one implemented in this project. For the readers that are not familiar with neural modeling, the section Cortical Modeling of the Background chapter gives some insight into the principles. The explicit objectives of my Master s project are stated in the final section of the Background chapter; Project Goals. Pleasant reading! 1

8 Chapter 1Equation Chapter 1 Section 1 Background The Nervous System For those who are not familiar with neuroscience, this section gives the reader an overall understanding of the basics, to have as a starting point when reading the rest of the report. The prospective reader is referred to Neuroscience, edited by Purves et al. (2001), a textbook giving a rigorous exposition of the field. Sensory Input Information we get about the surrounding world is passed to us by our sensory inputs. A basic and to most people familiar division of the senses into five major modalities was performed by Aristotle: seeing, hearing, taste, olfaction (smell) and physical feeling. Without the sensory inputs, we would not be aware of the surrounding world; all information we get about our surroundings and interaction with other human beings is passed via the senses. Hence, the senses provide us with all raw information about the world. For a creature, however, to be successful, gathering information is not enough. The behavior produced is of course essential. That is why the central nervous system has evolved. The Central Nervous System In the central nervous system, all sensory input is compiled, processed and evaluated. Ultimately a decision how to react if at all to a certain situation is made, based on the apprehension of the present situation and previous experience. The ability to make a successful such decision is an aspect of what we define as intelligence. Intelligence is a concept very difficult to delimit; nevertheless is it a factor of undisputed importance for the success of a species in the competition with others. Intelligence is the cause of mans complete dominance of earth, and master s theses like this one. All processing of considerable complexity is performed by the brain (cerebrum) where cortex (from now on, when speaking of cortex, the cerebral cortex is concerned) is responsible for all higher mental functions. The principles behind its enormous processing capability is yet to be discovered, but we are at least able to observe 2

9 some of the mechanisms underlying the information processing in the basic functional element of the brain; the neuron, and the organ used by neurons for communication; the synapse. An introduction of both is found below, but first we will briefly review the part of the brain where the synaptic and neuronal complexity is at its highest: neocortex. Neocortex In the most distal parts of our brain, evolutions latest contribution to it, neocortex, is found. Below it, the phylogenetically older paleocortex is found. Together they compose the mammalian cerebral cortex, though neocortex represents the main part of it. Mammals are considered the highest developed of species, at least in terms of the central nervous system, and they solely prove to have a neocortex. Other, more proximal parts of the brain provide neocortex with preprocessed data, which in turn has been collected further down in the neural system hierarchy, ultimately coming from the sensory systems. However, that is a rather severe simplification, but there are indeed different levels of data processing in the central nervous system, where neocortex is at the top. Accordingly, the most complex tasks, being too complex for other cerebral areas, are handled by neocortex. The results are then passed by neocortex to the appropriate neural motor region to perform whatever actions decided to be taken. Neocortex is built up in a structure with six layers, organized with layer one at the outermost level of the brain, and the other following in an ascending order in the proximal direction. Each layer comprises more or less distinctive populations of cells, based on their different densities, sizes, shapes, physiology, inputs and outputs. In this report, layer 2/3 is in focus. The layers 2 and 3 are normally treated in combination, since the separation of the two is difficult and they are functionally very close. Layer 2/3 is thought to be the major step of final processing of sensory information coming via afferents (incoming axons) in layer 1 and layer 6. The Neuron Nervous tissue, like all other organs, is made up of cells. Though, already by a visual examination, it is clear that they differ from other cells. Nerve cells are clearly distinguished by their extraordinary shapes and complexity. There are two broad categories of cells in the nervous system: neurons and a variety of supporting cells; the glial cells. In this thesis all focus is on the neurons; in fact two special kinds of neurons: the pyramidal cell and the fast spiking non-accommodating (FSN) interneuron (see Figure 1.1) (Zilberter 2000; Wang et al. 2002). The latter is one out of about ten different kinds of inhibitory interneurons found in neocortex (Gupta et al. 2000). Pyramidal cells and interneurons are the two major cell types in cortex. Approximately % are of pyramidal type, and the remaining cells are mainly inhibitory interneurons (Braitenberg & Schuz 1998). Neurons are, unlike the supporting (glial) cells, specialized for electrical signaling over long distances. Special signaling characteristics of both considered cell types will be described below. We start with a survey of the neurons in focus in a morphological order. There are three general structures of the pyramidal cell and the FSN interneuron: dendrites, soma and axon. The exposition will follow the way of a neural signal through such a cell; from the entrance of the neuron and all the way to the terminus, where the signal continues to the next neuron. 3

10 Figure 1.1. A representative pyramidal cell (left) and interneuron after reconstruction using confocal laser-scanning microscopy Images were taken over a µm µm surface area. Scalebar = 200 µm. Dendrites and Receiving of Signals A particularly prominent structure of most nerve cells is the elaborate arborization of dendrites that arise from the cell body (soma). In the dendrites, incoming signals from other neurons are received via synapses, where a chemical signal is converted to an electrical signal (an introduction to synapses is given below). Electrochemical mechanisms in the surface of the cell (cell membrane) provide for the signals propagation in the dendritic branches. In branch conjunctions, signals are accumulated and disseminated. Important is that the electrotonic properties of dendrites vary with the local membrane potential, i.e. the electric potential difference over the cell membrane, and the sectional diameter, which varies along the dendrite, typically increasing in the direction towards the soma. Adding the temporal aspect, the complexity of the propagation of signals in the dendrites becomes obvious. Soma and All or Nothing Dynamics Eventually the dendritic signal might reach the soma. Here all signals are accumulated, positive (excitatory) signals raising the somatic potential and negative (inhibitory) signals lowering it. If the aggregate input is excitatory and strong enough, the soma reaches the threshold. That is when axon hillock, situated in the soma at the root of the axon, is activated. Axon hillock is responsible for the neurons all or nothing dynamics in its signaling. While the somatic potential remains under a certain threshold, axon hillock stays inactive; but once exceeding the threshold, no matter to what extent, it emits a strong positive electric impulse; the neuron fires. This electric impulse is called action potential. Axon and Action Potential Neuronal firing is what carries a neuron s interpretation of its input to the next neuron on the way of information. The axon is the structure of the neuron, specialized for passing information to other neurons. When axon hillock fires, the axonal mechanism responsible for signal propagation, the action potential, evokes. Once activated, the action potential, a self-regenerating wave of electrical activity, propagates throughout the axon with undiminished strength to the terminus of the axon. 4

11 Hence, the strength of a neurons output is unaffected by the degree to which the threshold was exceeded, and by the many divisions in the axon. Importantly, this uniformity is crucial in an analogue device such as the brain, where small errors can accumulate in an avalanche like fashion, and where error correction is more difficult than in a digital system. At last we have reached the final break on our journey on a signals way through a neocortical network: the synaptic terminal, passing the signal on to the next neuron, somewhere into its dendritic arborization. Backpropagating Action Potential The concept of backpropagating action potentials (BAP) is believed to be essential in memory formation. Basically a BAP arises when an ordinary AP is generated. As axon hillock emits the strong electrical pulse that starts up the AP, the sudden raise in potential does not only propagate to the axon, but also into the dendrites. The dendrites do not, as the case is with the axon, actively mediate the potential raise, at least not to the extent of the axon does; so the signal decays on its way up the dendrites. But yet the signal is strong enough to reach far in the dendrites, and modify synaptic signaling and the propagation of incoming signals. Synapses and Signal Transmission For a neuron to be able to transmit signals, synapses have developed. They are the main functional element for communication between neurons and each neuron receives many synapses. For example, a typical neocortical pyramidal cell has about 8000 input synapses. The most frequently occurring type of synapses is the chemical one. Among the chemical synapses there is a broad variation, with different signaling properties, but here we will confine to their basic principles. As mentioned above, the synaptic transmission begins when the signal reaches a synaptic terminal. The neuron in question is designated presynaptic, as that one comes before the synapse, from a signals point of view. Consequently, the neuron reached by the signal after the synapse is denoted postsynaptic. When an action potential invades the presynaptic terminal, which means a substantial depolarization of the membrane potential; voltage-gated ion channels permeable to calcium ions are opened. Because of the steep concentration gradient of Ca 2+ across the membrane in the presynaptic terminal, the opening of these channels causes a rapid influx of Ca 2+ into the terminal. The following high concentration of Ca 2+ allows synaptic vesicles to fuse with the membrane. A synaptic vesicle is a small membrane bubble, containing neurotransmitter. At a high enough calcium concentration, mechanisms cause the vesicle to fuse with the presynaptic membrane, letting its contents into the synaptic cleft. The released neurotransmitters carry the signal over the synaptic cleft, which is the space between the presynaptic terminal and the postsynaptic specialization. Once reaching the postsynaptic specialization, the transmitter molecules bind to receptors in the postsynaptic membrane, which in turn opens ion channels in the membrane (see Figure 1.2). Ions flowing through an ion channel are, as mentioned, driven by a concentration gradient, and to that comes the electrical gradient. The ion flow strives to level the resulting gradient, and finally it might be eliminated. The membrane potential at which this occurs is called the reversal potential, since above that limit the ion flow is redirected. The bigger the difference is between the actual membrane potential and its reversal potential, the bigger the impact is of the synapse s activation. If the aggregated reversal potential for all ions of the postsynaptic specialization is above the firing threshold of a neuron, that synapse is called excitatory; otherwise inhibitory. An inhibitory synapse is called so because the ion flow through it, if it is active, will counteract the neuron reaching the threshold, while an excitatory synapse will have the opposite effect. 5

12 Figure 1.2. Schematic picture describing the function of a typical chemical synapse The cellular activation of a synapse, leading to a postsynaptic membrane depolarization, i.e. a raise in the intracellular potential, is called an EPSP (excitatory postsynaptic potential). Consistently the contrary is denoted IPSP (inhibitory postsynaptic potential). EPSPs and IPSPs are summarizing called PSPs (post synaptic potentials). When the synapse has brought about a potential alteration in the postsynaptic neuron, the circle is closed; and the process described above starts all over again in the postsynaptic cell. Note that this is not the process of all signaling in neocortex, but for the type of network in this article it is, and generally it is a good description for cortex signaling. Synaptic Plasticity Synaptic plasticity is the term used for the ability of synapses to change their characteristics over time. This is believed to be the basic mechanism responsible for the establishing of memories, and to have an essential role in data processing as a kind of working memory, when operating over shorter time periods. As mentioned, plasticity can operate on both shorter and longer time periods, ranging from milliseconds to several hours, or even longer. The plasticity is consequently divided into two major classes; the long-term and the short-term types of plasticity. Synaptic plasticity can also be divided up by its effect. On one hand, the plasticity can have a potentiating effect, i.e. an enhancing effect; and on the other hand it can have a depressing effect, i.e. a moderating effect. Combining these concepts gives the four major classes of plasticity: Long-Term Potentiation (LTP), Long Term Depression (LTD), Short-Term Potentiation (STP) and Short Term Depression (STD). 6

13 Experimental Background The subject of this master s thesis is a neocortical layer 2/3 network consisting of pyramidal cells and about one FSN interneuron. Important is that the network studied is built upon the statistics of what is seen from a cell in the center of a cylindrical volume of 200 µm 200 µm (height diameter). An explanation of this demarcation follows. Below is a presentation of the experiments and the results and hypotheses that make this network of special interest. The experiments were performed by Holmgren et al. at the Karolinska Institute, Stockholm, Sweden (Holmgren et al. 2003). Experimental Methods To be able to get the information necessary about neurons and synapses, sophisticated methods have been elaborated. Below follows an account for the methods used in the experiments constituting the base for the model building. The animal used in the analysis is the Sprague-Dewley rat (Markram et al. 1997), days old. Experiments were performed at the Karolinska Institute in Dr Zilberter's group, were the undersigned has taken part in the work the preceding year. Preparing the Brain Slices Animals were killed by rapid decapitation, all performed by a veterinary surgeon in accordance with the ethical guidelines of the Karolinska Institute. Quickly the brain was placed in an oxygenized synthetic extracellular solution. Using a razorblade equipped device, parasagital or coronal 300 µm slices were prepared. The slices are placed in a vitrum, yet surrounded by synthetic, oxygenized extracellular solution. Recording and Controlling of Membrane Potential Neurons in layer 2/3 were selected on the basis of morphological features using infrared-differential interference contrast video microscopy. Subsequent characterization of the neuron firing properties was performed as a final identification of the cell type. To connect to the cells, micropipettes of glass were used, manufactured by controlled heating and stretching of for the purpose specialized thin wall glass tubes, resulting in a pipette with a point of about one micron diameter. The pipette was filled with a synthetic intracellular ionic solution, and a thin silver wire was put in contact with the solution, making electric contact to it. Controlled by a mechanical stage for micro positioning, the pipette tip was moved towards the cell soma, under visual control using the microscope. Once touching the soma slightly with the pipette, a natural seal is soon formed, detected by a dramatically increased pipette resistance. After the seal was formed, a gentle suction was applied to the pipette; just enough to cause the cell membrane immediately under the tip to tear lose. At Figure 1.3. Recorded cell firing in neocortical layer 2/3 Somatic potential traces under similar input as in the model. The two on top show FSN interneuron and the following two pyramidal cell. Scalebar = 200 µm. 7

14 this point, the pipette is electrically connected to the neuron, and both recording and control is possible through the silver wire. Using this technique, information about single cells and synaptic connections can be acquired. In Figure 1.3 somatic recordings with the described technique (patch clamp) from both pyramidal cell and FSN interneuron are shown. Estimating the Network Connectivity By connecting to multiple neurons in the way described above, normally two at a time, statistics about synaptic connectivity were collected. Connections in cell pairs can be detected by applying a depolarizing current to one of the cells, letting it fire, and simultaneously recording the somatic potential of the other one to disclose a synaptic connection between the cells. Further information about connections is gained in a similar way. This technique provides a way to detect connections, but additional methods are needed to estimate the total number of connections in the variety of pair formations possible in the delimited volume. A possible way of doing this would be to simply try all connections within such a volume. However, that is not possible for two reasons. First, it is not practically viable to keep a check on which pairs have been tested and which ones have not. Secondly, the time for which a brain slice and a neuron connected to can be kept functioning is limited, which in turn limits the number of recordings possible on one and the same slice and neuron. This problem was overcome by mapping the connection probability instead of going straight to the number of connections. Since there were strong suspicions that the connection probability would to a great extent be dependent on the inter cell distance, at least for some types of connections, the mapping was divided into several separate volumes of different distances. The inter cell dependent connection probability mapping was achieved by keeping one of the glass pipettes connected to one cell (the central cell), and letting the other one connect to other cells while keeping track of their relative positions. Finally, the total numbers of connections in each volume from a specific cell type to a central cell were calculated by multiplying the calculated probability of connection with the volume and the density of the non-central cell type. Further on, other network properties such as the total number of some specific connection type within a volume can be calculated out of those numbers. This detection of connection probability as a function of distance has an upper limit of the distance between the central cell and the other, for natural causes. Based on experimental experience, a division of the connection probability was made in a cylinder shaped form with a layer structure, where the layers have the same height but are located at different radii (see Figure 1.4). For the network of this study, the upper limit of the radius was set to 100 µm, and the height 200 µm. It is very important to notice this restriction; the statistics that the model network is built upon reflect that. Figure 1.4. Layer structure in the connection probability division Layer distribution: 0-25, 25-50, (µm). 8

15 Experimental Results To conclude, the model network in focus of this thesis is made up of the pyramidal cells and one FSN interneuron in neocortical layer 2/3, where each cell only connects to the amount of cells that a corresponding biological cell would connect to from the middle of a 200 µm 200 µm (height diameter) cylinder. Here follows a resume of the results from experiments on this specific network. Notice that all statistics only yields for this special restriction. Statistics Within the described volume, there are about 600 pyramidal cells and on average one FSN interneuron at most. One individual pyramidal cell receives synaptic inputs from about 30 of those pyramidal cells, reciprocal connections being rare. Local FSN interneuron pyramidal cell connections are about fifteen times more numerous, with the very majority of connections being reciprocal. The probability of pyramidal pyramidal cell connections decreases quickly with distance; consequently the major part of the input to a pyramidal cell by its equals comes from cells in the very vicinity of itself. On the other hand, within the same volume, the probability of FSN interneuron pyramidal cell connections decreases only slightly with distance. FSN interneurons give inhibitory connections to pyramidal cells, while pyramidal cells give excitatory connections to both interneurons and other pyramidal cells. Generally, connections from a pyramidal cell to another are relatively weak, while in contrast connections both ways between pyramidal cells and FSN interneurons are strong. All used data on the inter cell connections are displayed in Table 1.1. Hypotheses Below are the hypotheses presented by Dr Zilberter s group after considering the above described results and performing additional experiments, closer investigating the conditions in neocortical layer 2/3. Those hypotheses are the reasons for this thesis, which is an initial investigation of the considered network. The rhetoric and conclusions are all elaborated in Dr Zilberter s group. What is the driving force of the pyramidal cell firing? At first, the limited excitatory synaptic signaling received by each pyramidal cell from other network members, in terms of both quantity and strength, is striking. This raises the question of how activity of the network during information processing influences the pattern of firing in the output of a pyramidal cell. Table 1.1. Properties of synaptic connections in pyramidal pyramidal and pyramidal FSN cell pairs Connection EPSP/IPSP at RP (mv) Pyramidal pyramidal 0.65 ± 0.64 (n=83) Pyramidal FSN 3.48 ± 2.52 (n=79) FSN pyramidal 2.96 ± 2.52 (n=109) % rise time (ms) 5.28 ± 1.88 (n=15) 2.32 ± 1.00 (n=17) 6.50 ± 3.67 (n=32) Width at half amplitude (ms) ± (n=15) ± 5.78 (n=17) ± (n=32) Paired-pulse ratio 0.92 ± 0.42 (n=70) 0.70 ± 0.14 (n=20) 0.70 ± 0.15 (n=22) IPSPs were recorded with 20 mm Cl in the pipette solution. Paired-pulse ratio measured with 100 ms interpulse interval. 9

16 Dual recordings from pyramidal cells in the same layer of rat neocortex (Mason et al. 1991; Markram et al. 1997; Thomson & Deuchars 1997; Gibson et al. 1999; Reyes & Sakmann 1999; Thomson et al. 2002) (in agreement with the present results) or different cortical layers (Thomson & Deuchars 1997; Reyes & Sakmann 1999; Thomson et al. 2002) indicated that pyramidal cells have low local interconnectivity, why a significant contribution from those is questionable. A more likely hypothesis suggested is that the pyramidal cell firing is generated on the strong background of synaptic signaling from extra-layer 2/3 sources (Azous & Gray 1999; Destexhe & Paré 1999; Ho & Destexhe 2000). How is the computation performed? If we suggest that computation in the local network is produced by pyramidal cells, their interaction should lead to a modulation of output firing rates. Following that hypothesis, the logical question is how they interact. To investigate this, Dr Zilberter's group has performed the following test, among other things. The effect of a synaptic input is, as described above, highly dependent on the membrane potential of the postsynaptic cell. Hence, the impact of a PSP during resting membrane potential do not (necessarily) reflect that of a PSP in the same postsynaptic cell when it is close beneath or above its firing threshold. Consequently, the power of a neuron to modulate the firing of another by a unitary input (the presynaptic cell firing once) while the postsynaptic cell is firing at rates detected during in vivo experiments, i.e. experiments performed on living animals, would be a realistic measure of the synaptic impact of the presynaptic cell. To enable such a measure, the firing pattern of the postsynaptic cell was measured twice, with identical stimulus to layer 1 and layer 6 afferents given. One trial the presynaptic cell is kept silent, and the other it is fired once. The difference in the two firing patterns of the postsynaptic neuron mirrors the actual synaptic strength. Experiments on pyramidal pyramidal cell pairs did not show any difference in the postsynaptic firing patterns, even when the efficacy of unitary connection was relatively large at resting potential. On the other hand, in experiments with FSN interneuron pyramidal cell and pyramidal cell FSN interneuron pairs, there was a difference. In the former case, the difference was more pronounced, but in the latter case the numerous presynaptic cells make a very strong ensemble excitation possible. Thus, there are good reasons to believe that pyramidal cells not only communicate directly, but also via pyramidal interneuron pyramidal connections. This is not only an effective way to affect other pyramidal cells, but also to considerably increase the number of interacting pyramidal cells, at least ten fold higher. A local interneuron incorporated in the pyramidal cell network receives strong excitatory background from extra-layer 2/3 sources concurrently with pyramidal cells, and interneuron firing is determined to a considerable extent by the mutual activity of a large fraction of these pyramidal cells. Accordingly, the interneuron output carries information on the common activity of the network and this information is delivered back to a number of network members affecting their firing patterns, thereby coordinating the network activity. Cortical Modeling A lot has been done in the neural modeling field, and there are many ways of designing such a model. This section gives an apprehension of the questions that arise during the construction of a cortical model. Finally an example of a model similar to the one in this project is described. See Founding Models and Model Network Design for details and techniques of the model in this project. 10

17 Single Cell and Synapse Level When modeling a neuron, you need to choose one out of several ways of doing that. The morphology can be treated in different ways, and the functionality, such as ion channel types implemented for example, can also be modeled in several ways. Depending on the purpose of the model, the best modeling method on the different levels should be chosen. The same yields for synapses, except in that case morphology is not modeled, rather the functionality is described in the synapse model. Many components of the synaptic signal transmitting and modulation have been identified, and a synapse can be modeled at many different levels of complexity. For a good review of modeling at single cell and synapse level the reader is referred to Spiking Neuron Models (Gerstner & Kistler 2002). The Compartmental Cell Model When modeling cells, the Compartment Cell model is perhaps the most common way of doing it, and it is used for the cell models in this project. Therefore this technique will be described a bit closer here. Building a cell model, there are especially two matters that need to be considered. First, the complexity of the cell model can not be too high, and secondly the model has to show good significance, despite its simplifications. These conditions are fulfilled by the Compartment Model (Bush & Sejnowski 1993). The first condition is satisfied by an adjustable number of compartments, and the selected functional complexity of each compartment. The second is satisfied by the methods of setting the compartment parameters. Additionally it is attractive to have a low detail model, since this allows us to isolate and more in detail study a property of the model. Reducing Morphology Using the compartment model, the cell is as the name indicates divided into small compartments. Each compartment is treated as an isopotential element that exchange currents axially with neighboring compartments, and radial currents are cross membrane. Treating the compartments as isopotential elements is a first step in reducing the overall complexity of the cell, but we need to decrease the morphological complexity of the model, where the dendritic tree is the major factor. The methodology is to collapse many small compartments to one bigger. This can be done in many ways; one is to do straightforward simulations in order to find which parts are not necessary (Bush & Sejnowski 1993). Another, perhaps more elaborate way to collapse compartments is to conserve various attributes of the subtree to be collapsed, such as the electrotonic length (Carnevale et al. 1999). For the attributes to be exactly preserved, however, the child branches (which are collapsed) of the father branch (which is preserved) must follow Rall s rule: d 3/2 3/2 father dchild i i = (1.1), where d is the diameter of the branch. In fact, experiments have shown that Rall s rule often is fulfilled with good accuracy in the dendritic tree of neurons. Reducing Physical Attributes All the physical attributes a cell show can not be included in the model. The properties of interest, and the additional ones that considerably affect them, are advisably considered. Such things can be specific ion channels distributed over the cell mem- 11

18 brane and ion types included in the model. Important is that the cell over all behavior is generally conserved. Network Level There is a multitude of various types of neural networks, and roughly they can be divided into two groups based on the purpose of the model. First, many types are specialized for one or several specific tasks, in functional purpose. For example, a neural network can be used to interpret voice commands. Secondly, a network can also be implemented to primary resemble nature, to investigate the principle mechanisms responsible for computation in cortex. The distinction is not always that clear, since the two variants preferably are combined. In Neural Networks and Brain Function (Rolls & Treves 1998), the reader can find a survey of different neural networks. Example of a Similar Model As an example of previous work on similar models, a network simulation described by Fransén and Lansner (1997) will be briefly reviewed here. The cell models in that article are, just like in this report, the pyramidal cell and a type of interneuron. Cells are arranged in columns, with a higher connection probability within a column. The columns are in turn connected to each other with a lower connection probability, via connections between cells in different columns. The network in the article has less detailed cell models than the network in this project, but in turn the article presents a much bigger network of 750 cells arranged in 50 columns, 15 cells in each. The network operates as an associative memory, while at the same time showing a connectivity that is sparse and asymmetric at the cell-to-cell level. Project Goals These were the goals set up in the beginning of the project. The entire project revolved around the scaling up of the micro circuit; set up and examined in a previous project at the Sans group of Nada, KTH (Eriksson 2002). Network Extension The main task was to extend the network constructed by Eriksson, consisting of only one pyramidal cell and one FSN interneuron, forming the smallest neural network possible; the microcircuit. My intention was to do it in a general manner, to facilitate future manipulations and further extension of the network. The size of the network was bounded by the simulation time, which had to be kept on a reasonable level running on the workstation I was allotted (1.5 GHz Intel Pentium 4 processor with 256 Mb RAM). Network Properties Extending the network inevitably arouses the problem of setting the network properties. The properties should be set in a way that makes the network reflect reality (see section Network Scaling in the Methods chapter). For example, there should be a balance between connectivity and synaptic strengths, when adjusting the activity in 12

19 the network. Then again; what is an appropriate level of network activity? In this way subsequent reasoning should finally end up in a network of biological significance. Network Evaluation Once the extended network was implemented and working as intended, its behavior was to be examined. What general characteristics of a neural network did it show, such as spike synchronization and bursting? Would the effect of the special conditioning dependent plasticity that was studied by Eriksson change, and if so; in what way? 13

20 Chapter 2Equation Chapter (Next) Section 2 Methods Founding Model The network I have modeled in this master s thesis is built upon cell models previously implemented by David Eriksson, in his master s thesis (2002). Eriksson s work was, as mine was as well, based on results from Dr Zilberter s lab. His aim was to create a network consisting of two cells: one pyramidal cell and one FSN interneuron, reciprocally connected. My task was to extend that network model to consist of multiple pyramidal cells, in that way approaching reality. Therefore, I will give a summary of Eriksson s work, on which my work is founded, but for details Eriksson s work is referred to. The Modeled Neurons There are two cell models implemented by Eriksson, on which my model is built: the pyramidal cell and the FSN interneuron. Eriksson used an eight compartment pyramidal cell model (Bush & Sejnowski 1993) and then adjusted the model to fit his purposes. The same pyramidal cell model was used for both the pyramidal cell and the FSN interneuron in the absence of a better model for the interneuron; though the two models were separately adjusted to well mimic the properties of their biological counterparts. Characteristics To begin with, a visual examination of the two cell types makes the morphological differences known (see Figure 1.1). The different morphologies have consequences for the function of the cell. The different functioning of the two cells is what is of most concern in this context. Unlike the pyramidal cell, the FSN interneuron displays a high frequency firing and shows no adaptation, while the pyramidal cell proves to have pronounced adaptation. This is a well studied phenomenon of neurons. It means that, due to underlying mechanisms that will not be taken up for discussion here, the cell adapts to an excitatory supra-threshold stimulus. In other words; given a constant input depolarizing current strong enough to make the cell fire, the cell fires faster in the beginning, to eventually adapt to the input, firing at lower intensity. 14

21 The Modeled Synapses All synapse models used were based on Varela s short-time facilitation and depression model (Varela et al. 1997). All synapses were implemented with short-time depression and no facilitation (Zilberter 2000). The short-time depression time constants were set to 200 ms, and the strengths of the depression were set to 70 percent for two pulses separated by 200 ms (the time constant). The Conditioning Dependent Synaptic Plasticity In this project there is a certain type of plasticity that is of special interest. That is the conditioning dependent plasticity. As mentioned above, plasticity is a mechanism responsible for a neurons ability to alter its properties over time. There are different ways of triggering plasticity, and in this case the trigger is a conditioning signal to the post synaptic cell; a pyramidal cell, which in turn generates BAPs in the postsynaptic cell, that modify the properties of the synaptic specialization. The plasticity is implemented for the FSN interneuron pyramidal cell synapse. The plasticity depends on the concentration of Ca 2+ in the dendrites of the postsynaptic cell; the pyramidal cell. This was implemented by introducing a calcium pool in pyramidal cell dendrites. When a BAP reaches the calcium pool, an L-channel connected to the calcium pool is activated, and mediate a calcium influx to the pool. The calcium pool approaches its steady state concentration of 50 nm with a time constant of 100 ms (Kaiser et al. 2001), and the L-channel conductance was set to µs for the calcium transient after a single AP (Kaiser et al. 2001). The depression of the synapse was related to the calcium concentration in the pool with a Michaels-Menten function (Zilberter et al. 1999): D K = (2.1) 1 + [ ] max 2 Cahalf Ca +, where D is the depression. K max and Ca half were derived from the relation between number of APs in the conditioning signal and the amount of depression (Zilberter 2000). Previous Network Model The previously modeled network with the above described cell models is the smallest possible, the so called microcircuit. That is simply two cells reciprocally connected to each other, in this case one pyramidal cell and one FSN interneuron. The cells were driven by a virtual accumulated layer 1 and layer 6 stimulus, and as mentioned the FSN to pyramidal synapse was implemented with the conditioning dependent synaptic plasticity described above. Previous Results The main focus of Eriksson s thesis was the plasticity in the FSN interneuron pyramidal cell synapse. Since that synapse is inhibitory, and the plasticity decrease the efficacy of the synaptic transmission; an increase in the pyramidal cell activity was to expect when the plasticity was activated, compared to the case without its activation. It was found that the plasticity managed to increase the pyramidal spiking, though the effect was rather weak. This occurred by the manner of unblocking action 15

22 potentials that previously were blocked by the inhibitory influence of the FSN interneuron. Network Scaling Because of computational limitations, compromises were unavoidable while modeling the biological network. At the detail level of the model used, a network of biological sizes would not be within the computational limits that had to be obeyed, as mentioned. To get down to reasonable simulation times, a network consisting of 10 pyramidal cells and one FSN interneuron was suitable for the numerous simulations that had to be run during the parameter search. However the experiments also included simulations of a much bigger network with 100 pyramidal cells and one FSN interneuron. For the scaling up of the 10 pyramidal cell network, the following scaling model was used. Both used model networks are what one usually calls sub-sampled networks. The decrease in the number of cells in the model, compared to reality, reduced its complexity to an adequate level. Reasonable computational times were reached that way, but the solution caused new troubles; with such a scaling of the model, some problems came up that had to be dealt with. Problems Arising Keeping the other properties in the network to those estimated in biological experiments, simply decreasing the number of cells, would result in an activity in the network that is far too low. Some properties can even be impossible to achieve, such as the number of synapses given to an FSN interneuron from the surrounding pyramidal cells. Biological experiments show that there are about 400 pyramidal cells out of about 600 within the volume of consideration, connected to the one FSN interneuron. In the present network there was a total of 10 to 100 pyramidal cells, so having 400 pyramidal cells connecting to the FSN interneuron was of course impossible. The number and strengths of the synapses must on the whole be dramatically decreased. This is just one among many other problems that turn up when a network is scaled down. Below follows a survey of this problem and others that had to be overcome, in order to get a network model that hopefully reflects the behavior of the biological full scale network. At first the questions will be presented separately, and then the solutions. Fewer Cells This is where it all begun; the number of cells needed to be reduced, so that the network complexity in turn would be reduced. But when diminishing the number of cells in the network, can the cell properties really be preserved? Number of Synapses The question how the number of synapses scales with the number of cells in the network is a question that needs to be treated. The number of synapses in the network is very important for the degree of correlation in the cell population. Synaptic Activity When running simulations on the model network, the activity in the network should reasonably reflect the activity found in a corresponding biological network. But what does that mean in terms of individual cell firing? In the model network the number of 16

23 cells is strongly reduced, and a direct comparison between individual cell firing patterns in biology and model would not be appropriate. Constant Input A first criterion when a model is scaled is that the aggregate input current to any cell in the network should be kept approximately the same, regardless of the network size. As mentioned above, in this case a decrease in the number of synapses was inevitable; and obviously it would also be irrational to try keeping the number of synapses while reducing the number of cells. A decrease in the number of synapses a cell receives most certainly affects the total input current to that cell. Solutions This is a presentation of the solutions to the above described problems that we have come up with. This is not the only way to solve the scaling related problems, but they do seem to suit their purpose. Fewer Cells At the single cell level, the scaling does not impinge on the cell properties. These are kept as close to biology as possible, but with a lower variance; when the number of cells in this case the number of pyramidal cells is subject to such a substantial reduction as here, the cells can not be described with the same variation as in nature. One cell of considerable discrepancy would stand out of the group in an unacceptable way in its behavior. The model cells can be regarded as representing several biological cells. The variation of the means in a group of elements is always smaller than for individual elements, and the variations decrease with increasing size of the group. Hence, the model neurons had to be implemented with a lower mutual variation than what is found in biological neurons. This is the only direct consequence with regard to the single cell properties due to the scaling. Number of Synapses An intuitive solution to the scaling of the number of synapses is to try keeping the fraction of presynaptic neurons connecting to the postsynaptic neuron. A closer look reveals that things are not that easy. To facilitate things, we use the following way of thinking. All cells can be regarded as being connected by synapses, some of them being active, and some inactive. This is not a restriction, since the effect of an inactive synapse is the same as if the synapse did not exist, and we are now only interested in the functionality. In the following reasoning it is important to distinguish between two concepts. First, there is the biological synapse (BS). That is a synapse representative for those observed in biological experiments. Secondly there is the model synapse (MS), a synapse of the model. With that approach we let each MS represent a proper number of BSs, which are randomly chosen. All MSs represent the same number of BSs. The fraction of MSs containing one or more active BS would most likely exceed the fraction of active synapses among the BSs. This probability increases with increasing number of BSs we let each MS represent. Keeping the observed fraction of active BSs in the model, still fulfilling the requirement of preserving the input strength to each cell (see Constant Input below), is on the analogy of exclusively collecting either active or inactive BSs in each of their model counterparts. Hence, a way to deal with this problem is to let a larger fraction of the neurons Letting some of the active BSs end up in an inactive MS, would mean they were silenced. Then to preserve the activity in the network, the active model synapses would have to increase their activity or/and strength. That leaves us with the same result as if those silenced biological synapses were a part of the active model synapses from the start. 17