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 understand 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 systems. 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 structure 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 neuron 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˙ = ∞ (2) τn(V ) m (V ) − m) m˙ = ∞ (3) τm(V ) h (V ) − h) h˙ = ∞ (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 compartment 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. Via signals from other parts of the human body it stimulates the network and can be seen as its input. Figure 6(a) shows Golgi-stained neurons form somatosensory cortex in the macaque monkey. It is just a small slice of the monkey brain but gives an idea of its structure. Reducing the neurons in the nervous system to single compartment models allows to represent it as a graph (Figure 6(b)). The graph stores point neurons and connections with their strengths and delays. The behavior of a neuronal network depends on the size of the inhibitory and excitatory populations and on the connections as well as the external drives. The balanced states of these networks is characterized by fluctuations of population activity about an attractive fixed point[14]. If there is a fix point, such a network is called balanced network.

6 (a) Golgi-stained neurons from (b) Neurons are connected to (c) A neuronal network con- somatosensory cortex in the each other. A graph allows tains excitatory and inhibitory macaque monkey on micro meter to store the connection informa- neurons. They are connected scale. [4] tion. to each other. Additionally there are external drives which are connected to the populations.

Figure 6: For a point neuron model, the brain cells are reduced to a graph of point neurons.

2 Simulation tools

There are a few simulation tools for neuronal networks available. The focus of these tools are varying to a great extent. CSIM [15], NEST [10] and NCS [3] are using mostly single- compartment neuron models. These tools focus on the functionality of the whole neuronal network and not the chemical processes. Neuron [5], Genesis [2] and SPLIT [6] are supporting multi-compartment neuron models. They allow a deeper look into the processes inside each neuron. Neuron is used for the simulation of empirically-based models of biological neurons and neuronal circuits, especially for models with complex branched anatomy. Genesis is a general simulation system for the realistic modeling of neuronal and biological systems and NEST is focused on large neuronal networks with biologically realistic connectivity. In the paper The cell-type speciﬁc cortical microcircuit: relating structure and activity in a full-scale spiking network model. , the NEST simulator is used. Therefore it is described in more detail below.

2.1 NEST The NEST Initiative (http://nest-initiative.org) has developed the neuronal simulation tool NEST over the past 20 years [8]. It supports the simulation of large-scale neuronal networks with diﬀerent types of neuron models and focuses on the dynamics, size and structure of neuronal systems rather than on the exact morphology [10]. NEST supports models of information processing in the visual or auditory cortex of mammals, models of network activity dynamics, laminar cortical networks or balanced random networks, and models of learning and plasticity. The complexity of the simulations reaches form small networks computed on local machines up to ones using the full capabilities of the world’s leading supercomputers. To cover this big range NEST is a hybrid parallel application using threads locally and message passing over the compute nodes. For large networks of integrate-and-ﬁre neurons, the communication dominates the computation costs. Large scale simulations with NEST were tested on K and JUQUEEN. K and JUQUEEN are two of the fastest supercomputers available. Besides

7 high computational power spread over a huge amount of cores they have high interconnection speed (See Figure 7). The results of scalability benchmarks are plotted below. The maximum

K JUQUEEN compute nodes 88,128 28,672 cores per compute node 8 16 architecture SPARC64 VIIIfx IBM PowerPC A2 clock speed 2 GHz 1.6 GHz interconnect network six-dimensional ﬁve-dimensional mesh/torus network mesh/torus network interconnection speed per link 5 GB/s 2 GB/s

Figure 7: Main characteristics of K and JUQEEN. number of neurons is around 109 which is at the scale of a mouse brain. To provide enough computation power and storage for a human brain simulation computers have to be at least a factor 100 bigger than they currently are.

JUQUEEN

neurons JUQUEEN K K ressources

number of virtual processes (comp. time * number of virtual proc.) number of neurons (a) Maximum network size and corresponding run (b) Required resources to simulate a network of size time as a function of number of virtual processes N [12] [12]

3 Example of a full-scale spiking network model

3.1 Motivation Simulation in neuroscience is an important tool to test hypothesis inspired from anatomical and functional data. Experiments on humans are diﬃcult to perform and even the possibilities to do experiments with animals are restricted. However there are connection measurements available from species like rats and cats. Exact measurements of the human brain are not yet available on this level of detail and constructing a human brain model is thus not possible at the moment. In order to understand the behavior of neuronal networks statistical measurements from cats and rats are used to build up meaningful neuronal networks. These neuronal networks can be tested with diﬀerent stimuli to understand their functionality.

8 In the following sections the paper The cell-type specific cortical microcircuit: relating structure and activity in a full-scale spiking network model is presented which shows whether this is possible. This paper mainly focuses on the questions: Can a meaningful network be created from these measurements? Can we use this network to understand the functionality of the brain? Which connectivity data and which level of abstraction are adequate to reproduce the reported differences in cell-type specific activity?

3.2 Model A neuronal network is constructed, which contains different layers as shown in Figure 1(c). As described in section 1.2.1 the properties of nerve cells in one layer are similar. Cell types and the connection patterns are related. The network is defined by 8 neuronal populations repre- senting the excitatory and inhibitory cells in L2/3, L4, L5, L6. The cell types are taken from neuroscientific literature. Cell type specific connectivity and activity at local cortical networks are characterized experimentally. The characteristics can be traced back to stochastic values. For the connection probability they assume that the synapses are randomly distributed. They get 8 cell types with 64 connection probabilities. Furthermore a connectivity map containing all connection probabilities is generated. The results are shown in Figure 8.

Figure 8: Model deﬁnition. Layers 2/3, 4, 5, and 6 are each represented by an excitatory (triangles) and an inhibitory (circles) population of model neurons. Input to the populations is represented by thalamo-cortical input targeting layers 4 and 6 and other external background input to all populations. The model size corresponds to the cortical network under a surface of 1mm2. [16]

With an integrated connectivity map a full-scale spiking network model of the local cortical microcircuit is generated. Current-based leaky integrate-and-ﬁre model neurons with expo- nential synaptic currents are randomly connected with connection probabilities according to the integrated connectivity map used. The generated model contains over 80,000 neurons and 0.3 billion synapses.

3.3 Simulation The simulation was executed on 24 nodes compute each with two quad core AMD Opteron 2834 processors and interconnected by a 24-port Voltaire InﬁniBand switch ISR9024D-M. The resulting simulation was running close to real time.

9 3.4 Analysis The output of the simulation are spike trains of the neurons in the layers. The spike trains contain spike timings of neurons. A plot of the spike timings can be seen in Figure 9(a). In the first and third column there are spike timings plotted for each neuron as a dot when they occur. The firing rate (spikes per second) is summed in the second column for two simulations. The fourth column shows histograms of the firing rates for each layer. These results are compared to real values measured from cats and rats. At first the model is tested for robustness. Therefore the external inputs are varied to compare the resulting activity of different layers. Constant input currents and poissonian background inputs yields similar activity. Reducing the input of specific layers produces zero activity in these layers, which is in agreement with real measurements. Comparing frequencies of simulation and experimental results also provide good matches for most of the layers. All in all the model predicts the cell-type specific activity very well, if compared with data from awake animals.

(a) Dot plot of the spike timings of the neurons in (b) The dots show the main activities in the network. layers is in the ﬁrst and third column. The sec- The arrows visualize the activation and deactivation dy- ond and fourth column shows the ﬁring rates of namics of the network. Excitatory neurons are visualized each layer. Excitatory neurons are visualized with with dark dot/bar/line. Inhibitory neurons are visual- dark dot/bar/line. Inhibitory neurons are visualized with bright dot/bar/line. [16] ized with bright dot/bar/line. [16]

Figure 9(b) shows the dynamics of the neuronal network. Confronted wit transient thala- mic input, the model exhibits a particular propagation of activity from the input layers to the output layers [16]. The diﬀerent layers activate and deactivate each other with feed-forward and feedback loops. The layer L4 activates L2/3. L6 deactivates L4. L2/3 activates L5 and L2/3 deactivates L4 and so on. The propagation pattern is comparable to in vivo experiments of awake rats [16]. The simulation successfully reproduces prominent features of cortical activity, even though just simple point integrate-and-ﬁre neuron models were used. This suggests that the connectivity structure is enough to reproduce the activity reliably, and the exact features of the neurons only play a minor role[16].

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