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Simulation with NEST, an Example of a Full-Scale Spiking Neuronal Network Model - Seminar Paper

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Simulation with NEST, an Example of a Full-Scale Spiking Neuronal Network Model - Seminar Paper Simulation with NEST, an example of a full-scale spiking neuronal network model - seminar paper Till Schumann, CES, 293576 Computational and Systems Neuroscience (INM-6) 1 Introduction to Computational Neuroscience 1.1 Motivation Computational neuroscience is part of the computational biology, which, besides other meth- ods, relies on modeling to understand various aspects of biological systems. Computational neuroscience itself focuses on the nervous system. It is a growing field of research. With the fast development of computer systems and the growing availability of experimental data, computational simulations get more important. The computational power, which is available now and will be available in the next years, allows simulations of mammalian brains. Even a simulation of the human brain seems to be doable in the upcoming years. Modeling nervous systems helps us to understand the functionality of the human brain. It can help us to un- derstand different kinds of diseases like Alzheimer's and can help to develop novel therapies. Since the human brain is not accessible to direct experimental studies models of the brain are essential to understand its functionality. Computational modeling allows to construct neuron models that are based on cell-level data obtained from experiments. In contrast to the human, brain experimental data from animal experiments are widely available. Because of related structures these data is used to improve and validate models of the brain. In combination with neuronal simulations these data allows a first look into the functionality of nervous sys- tems. The paper The cell-type specific cortical microcircuit: relating structure and activity in a full-scale spiking network model shows the usability of current models and simulation tools. It shows that simulations using measurements from rats and cats can reproduce dynamic behaviors of brain cells. 1.2 Anatomy of the brain The human brain is the main part of the central nervous system which consists of the spinal cord, sensory organs and all of the nerves that connect these organs with the rest of the body. These organs are responsible for the control of the body and communication between its parts. The nervous system is the most complex system of our body with respect to functionality. It contains billions of nerve and glia cells. The nerve cells are connected via synapses to a complex network. Electrical pulses from neuron to neuron transmit information through the network. Glia cells help to maintain the right concentration of chemical substances in the extracellular space around neurons and provide supporting structures for the growth of neurons and for their spatial arrangement. 1 1.2.1 Macroscopic structure The anatomy of the brain as depicted in Figure 1(a), shows that different parts vary in cell density and functionality. Figure 1(a) shows a cross-section of the human brain. The outer layer is called the gray matter, due to the color caused by the high density of nerve cells. The white matter, which is underneath the gray matter, consists most of connection fibers of the nerve cells. The thalamus is situated in the middle of the brain and functions as a relay station between the sensory system and the cortical systems for cognition and motor control. Because of the high density of nerve cells the gray matter is the main part of information (a) A cross-section of the human (b) A general map of the human brain (c) The vertical struc- brain shows different densities of assigns parts of the gray matter to fuc- ture of the gray matter nerve cells [11]. tionalities [11]. shows six layers [11]. Figure 1: The macroscopic structure of the human brain. processing of the brain. The number of nerve cells (neurons), the number of connections (synapses) and the struc- ture differs from person to person. The connections of each neuron are dynamic and change over time. Some parts of the brain can still be assigned roughly to functionality as shown in Figure 1(b). Having a look at the vertical structure of the cortex, the gray matter can be partitioned in six layers as shown in figure 1(c). The cells in each layer have similarities like cell type, connections to other layers and connections to the thalamus and other parts. 2 1.2.2 Microscopic structure The nerve cells are tiny structures which are connected to each other. For an understanding of the brain a deeper look at the nerve cells is necessary. There are different cell types in a brain. They vary in structure and size. Pyramidal, spiny stellate and smooth stellate cells occur most often. For each layer there are types which occur more frequent. In Figure 2 a typical neuron is depicted. It contains the soma (the cell body) dendrites and axons. Electrical pulses are transported from the dendrites to the soma. In case of a spike an electrical impulse is forwarded through the axon. These axons are connected via synapses to further dendrites. The electrical impulse is transmitted via a chemical reaction in the synapse to the dendrites of connected cells. There are excitatory and inhibitory neurons. Figure 2: Microscopic structure of a neuron. [13] The excitatory neurons excite the following neurons, in contrast the inhibitory neurons inhibit the following neurons. Via electrical currents the connected neurons influence the membrane potential of each neuron. The membrane potential can be measured. As an example the membrane potential is plotted over time in Figure 3(a). Chemical processes inside the neu- ron generate a spike if the membrane potential reaches a specific electrical level called the threshold. As shown in Figure 3(a) spikes are peaks in the membrane potential. 3 (a) The plot shows the membrane potential of a neuron (b) The dot plot shows spikes of each neuron over the time. The peaks are called spikes. There are over time. On the y-axis there are the neurons four spikes in the time span shown. The firing threshold number. The histogram in the lower panel sums of the cell is at about 58 mV [11]. up all spikes for each time bin. [11] Figure 3: The activity of a single neurons is displayed using its membrane potential. For multiple neurons the information is reduced to spike timings. In order to analyze the membrane potential more objectively it is reduced to timings of the spikes. For multiple neuron the spike timings in a dot plot can be visualized as in Figure 3(b). One can get an overview of the activity in a whole neuronal network if the spike sums are plotted (summed up spikes for each time bin) in a so-called histogram. 1.3 Neuron models To understand the behavior and functionality of spiking neurons, various models have been developed over the last years, which focus on the electrical and chemical interactions. There are two main types of spiking neuron models: single compartment models and multi compartment models. The single compartment models reduce the whole dentric tree, the axon and the soma of the nerve cell to a single point. Synapse models are used as connections between these point neurons. A range of single compartment models have been developed, which vary in accuracy and complexity. The goal of each model is to reproduce the spiking activity. The Hodgkin Huxley model is one of the most accurate single compartment models available. _ 4 3 CV = I − g¯K+ n (V − EK+ ) − g¯Na+ m (V − ENa+ ) − gL(V − EL) (1) n (V ) − n) n_ = 1 (2) τn(V ) m1(V ) − m) m_ = (3) τm(V ) h (V ) − h) h_ = 1 (4) τh(V ) 4 (a) A picture of a pyra- (b) The neuron can be di- (c) Reducing the midal cell with soma, den- vided into soma, dendrites neuron to a point drites and cell body. and cell body. neuron. Figure 4: The partioning of a neuron for a single compartment model. The dendrites are the connection inputs of the neuron and the axons are the connection output of the neuron. 4 The three ordinary differential equations (ODE) consider the ion currents of sodium (¯gK+ n (V − 3 EK+ )), potassium (¯gNa+ m (V − ENa+ )) and leak (gL(V − EL)) in a synapse. The Izhikevich and the MAT model are simplifications of the Hodgkin Huxley model [11]. Further information can be found in the neuroscience literature [9]. The simplest one is the Integrate-and-fire model, which is based on one ODE: dν τ = −ν(t) + RI(t) (5) m dt The equation can be solved explicitly in one step. From the perspective of computational costs, this is very important if a large amount neurons have to be simulated. This is the case for most complex neuronal network models. Neuronal networks are described in section 1.4. The multi compartment models partition the dendrites, soma and axons in smaller bits. Therefore a multi compartment model is more accurate but also more complex. Each com- partment is modeled similar to a single compartment model, while the different compartments are coupled in an electrical cable equation. Further details are available in the neuroscience literature [9]. 5 1.4 Neuronal networks The nervous system in the human brain is a complex neuronal network. It contains around 1011 neurons and each neuron has on average 7,000 synaptic connections to other neurons. Estimates of the total number vary between 100 to 500 trillion connections [7]. Figure 5 shows axons in the cortical tissue in a micro meter scale. It gives an idea of how complex the neuronal networks are. The most important external drive of the neuronal network is the Figure 5: Axons in cortical tissue [1] thalamus (1.2.1). It is connected to several neurons in the network.
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