Client-Server Architecture for a Neural Simulation Tool

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1 Client-Server Architecture for a Neural Simulation Tool Olga Kroupina and Raúl Rojas Institute of Computer Science Free University of Berlin Takustr. 9, D Berlin Germany ABSTRACT NeuroSim is a simulator of biological neural networks based on a client-server architecture. The program is platform-independent and provides a comfortable graphical user interface (GUI) for all aspects of model definition and control of simulation results. The client is designed for entering a model description and connections to a server which solves the differential equations arising in the modelling. The client has been developed in Java and can be started on any microcomputer; it accesses a powerful server available through the network. The results of numerical integration of differential equations are uploaded to the user s computer for visual presentation and evaluation of the simulation. The system has been coupled with the Genesis simulator, used as a server on the remote computer. The numerical integration can be also performed with our own server implemented in C++. KEY-WORDS Neuronal Simulator, Hodgkin-Huxley equations, compartmental modelling. 1 Introduction Recently, there has been a dramatic increase in the number of neurobiologists using computational methods as an aid to their empirical studies. As more experimental data is accumulated, it becomes clear that detailed physiological data alone is not enough to infer how neural circuits work. A quantitative modelling approach helps to understand the functional consequences of particular neural elements. Therefore, computer simulations are an important tool for neuroscience research. Biologically detailed simulations of single neurons and neural networks are typically based on the approach of compartmental modelling; that is, each cell is divided into many isopotential compartments, joined by conductances, and activated via simulated ion channels and current stimuli. Each compartment is then modelled with equations describing electrical currents []. The advantage of this approach is that it places no restrictions on the membrane properties. The influence of the diversity of activated channels can be taken into account by including additional equations describing the channel dynamics. The mathematical result of this approach is a system of ordinary differential equations, one for either a compartment or for an ionic channel. For modelling this on the computer, one needs to solve the equations arising from model elements in parallel. In case of a model with a huge number of neurons, or with a complicated structure of activated channels, large computational power is required. 2 Important features of neural simulation systems Modelling has become important in neuroscience research and neurobiologists are using simulation programs as any other peace of lab equipment. In this case easiness of use can be quite essential. This includes simple installation, platform-independence, no extensive computer knowledge required, an easy to use interface, etc. Some well-known simulation systems, such as Genesis [7] and Neuron [4], are Unix-based. They have their own interpreted scripting language, in which users define components and running parameters for their simulation. In the hands of experienced users with access to a compatible computer system, these modelling packages are powerful research tools. However, they do suffer several drawbacks for novice users. Firstly, it is difficult and time consuming to learn the formal structure of the scripting language. Secondly, they do not provide a graphical user interface (GUI) or do it only for common model experiments. The difficulty of constructing a GUI for each model has an explanation from the origin of these packages. They were developed as an attempt to create a general simulation system, that is, with the capability of solving problems at many levels of detail (i.e, from parts of neurons to large neural systems). However, the large spectrum of application requires flexible modes of specifying selections of single elements for editing and display.

2 3 Client-Server Architecture Detailed simulations of single neurons and neural networks are made applying compartmental modelling. Large computational power can be necessary for solving the system of the differential equations which mathematically describe the spread and interaction of electrical and chemical signals in neuronal networks. A client-server architecture of the application software is an alternative for performing intensive calculation on a high-power compute server, while control and visual results presentation are left to a personal computer (see Fig. 1). This was the motiva- Java Client Model Description Java Client 4 NeuroSim User Interface 4.1 Model definition and modelling elements The user interface for the modeler is a thin client that can be started either as an application on the user s computer with any operating system, or as a Java applet from the internet. The client GUI is simple to learn. New elements for a model can be added to the simulation just with a mouse click. The corresponding kind of model and mode of operation are chosen from the main menu. The parameters of elements (neurons, compartments, ionic and synaptic channels, neuron connections, etc.) can be viewed and edited in the separate windows (see Fig. 2). Thus, no extra programming code is needed to be written for model definition. Integration Results Own C++ Server Genesis Java Client Figure 1: The Client-Server architecture. tion behind our development of a new simulation system, NeuroSim. It was realized in Java; thus, it can run on virtually any computer and with most operating systems. The connection mechanism between a client and server is made with a Java tool Remote Method Invocation (RMI), which supports distributing run-time objects across multiple computers. After definition of an experimental model on the client side, the data with model description are transferring to a server, accessible through a network. The Genesis simulator is used as server on the remote computer for solving the corresponding differential equations. Numerical integration can be performed also with our own server implemented on C++. The model properties necessary for numerical integration are sent to the server in the XML format. They are transformed to a Genesis format or to a format of C++ server input file with available Java techniques for parsing XML documents the Extensible Style Sheet Language for Transformations (XSLT). The data from a server are sent for the client in the standard output stream and can be played back. A client makes it possible to view the curves of simulated parameters. One can also start an animation of the transfer of pulses through the networks connections and of the neurons activations. Figure 2: Example of the network structure and neuron parameters in the main window. Drag-and-drop operations allows one to change the positions of neurons and establish the connections between them. The neurons with the same physiological and anatomical parameters can be copied, and this simplifies their definition. The structure of neuronal networks is presented in the main panel, so that all elements of model as neurons, channels and inserting mechanisms are marked with a single symbol. The program can be used to simulate the flow of current in multi-compartmental models of a cell. The electrical properties of individual neurons are described with Hodgkin-Huxley type voltage-dependent ionic channels [5]. The connections among neurons can be made by a chemical synapse. The standard inserting mechanisms as spike generator and synaptic-activated channel can be bound into the model. Electrical excitation can be implemented with different type of cell stimulus: pulsed stimuli, randomized stimuli, or constant injection.

4.2 Client-Server connection The client program automatically creates the files with the model description necessary for the server for solving the differential equations.

3). Moreover, an animation of the network activations can be started. It shows the transfer of pulses through the network connection and the neurons excitations.

3 4.2 Client-Server connection The client program automatically creates the files with the model description necessary for the server for solving the differential equations. The data is sent to the server in the standard XML format. The connection to the server can be established from menu Simulation after setting up method and step size of numerical integration (see Fig. 3). Moreover, an animation of the network activations can be started. It shows the transfer of pulses through the network connection and the neurons excitations. It was implemented as a thread with two modes asynchronous and synchronous. The asynchronous mode allows to execute a task from an action event handler into a background thread, so that GUI remains responsible. The synchronous mode allows one to schedule the periodic actions with just one thread. Both of these modes was developed with Java utility classes SwingWorker and the Timer classes [6]. The files of models description as well as the results of simulation can be saved on the disk for use in the next working session. They are specified in the standard XML model description format for extensibility. Also, the elements of simulation with their states can be saved as a serializable objects provided by Java serialization facility. 5 Simulation Examples In this section we show with examples how NeuroSim works. Figure 3: Setting up the step size and numerical method for simulation. The available numerical methods range from the crude explicit forward Euler method until highly stable implicit methods [8], [3]. The user can interactively define step size and interval of simulation depending on the speed and accuracy of the simulation. 4.3 Results of the Simulation The results of a simulation are uploaded on the user s computer automatically. The graphic output of membrane voltage and channel conductances can be represented visually. The graphs can be observed in the windows with scrolling panels and list of optional variables for visualization (see Fig. 4). Figure 4: The model structure and the potential curves resulting from the simulation. 5.1 The simulation of a neural network with Hodgkin-Huxley channels First we review the simulation principles of neural network with Hodgkin-Huxley voltage-activated channels. Hodgkin and Huxley estimated activation and inactivation functions for the sodium and potassium current, using the voltage clamp technique. This allowed them to devise the mathematical model which describes an action potential resembling experiments. This model remains the formalism of choice for most neuroscientists. When Hodgkin-Huxley channels are present, the ionic current is the sum of the sodium (Na) and potassium (K) channel currents: I i = I Na + I K (1) The sodium current is the product of a maximal conductance ḡ Na, the activation variable m, the inactivation variable h, and a driving force (V m V Na ): I Na = ḡ Na m 3 h (V m V Na ) (2) The potassium current is the product of a maximal conductance ḡ K, the activation variable n and a driving force (V m V K ): I K = ḡ K n (V m V K ) (3) The variables m, n, and h are called gating variables. They evolve according to the differential equations dm dn dh = α m (V m )(1 m) β m (V m )m (4) = α n (V m )(1 n) β n (V m )n = α h (V m )(1 m) β h (V m )h

The functions α and β are empirical functions of V m that were adjusted by Hodgkin and Huxley to fit the data of the giant axon of the squid: α m (V m ) = 0.

125 exp ( V m 60) 80 We illustrate the simulation of two realistic neurons in a feedback configuration. Each cell is composed of two compartments corresponding to a soma and dendrite.

The dendritic channels are synaptically activated and responsible for the cell connections. The output of each cell is a spike event, which reach its destinations after a specific delay.

4 The functions α and β are empirical functions of V m that were adjusted by Hodgkin and Huxley to fit the data of the giant axon of the squid: α m (V m ) = 0.1( 35 V m ) exp ( 35 V m) 1 β m (V m ) = 4 exp ( V m 60) 18 α h (V m ) = 0.07 exp ( V m 60) 18 1 β h (V m ) = exp ( 30 V m) + 1 α n (V m ) = 0.01( 50 V m) exp ( 50 V m) 1 β n (V m ) = exp ( V m 60) 80 We illustrate the simulation of two realistic neurons in a feedback configuration. Each cell is composed of two compartments corresponding to a soma and dendrite. A soma in each compartment is composed of two variable conductance ionic channels for sodium (Na), and potassium (K), described with Hodgkin-Huxley dynamics. The dendritic channels are synaptically activated and responsible for the cell connections. The output of each cell is a spike event, which reach its destinations after a specific delay. After that the synaptic channels is activated. The conductance change the synaptic channels activation described with alpha function form for τ 1 τ 2 : G(t) = G max weight t (exp ( t/τ 1 ) exp ( t/τ 2 )), (6) where the G max weight is the peak value of the voltage change. The change of the membrane potential of a single compartment is described with equation (7), a consequence from the compartmental modelling. C m dv m = E m V m R m (5) + V m V m + I R i + I inject (7) a In (7 C m is the membrane capacitance, R m is the membrane resistance and the E m is the membrane rest potential. V m presents the membrane potentials of the adjacent compartment and R a is the axial resistance between the simulated and adjacent compartments. I i is the ionic current and I inject is an injected current. In Fig. 5 we see the model structure, where the modeler, after setting the model elements, can observe the neuron structure. One can see the compartments, voltage- and synaptically-activated channels as well the neurons connections. In this figure, it is also shown the properties of a connection that can be edited. The injection current into the soma of the first cell will activate the Hodgkin- Huxley channels, that corresponds to spike initiation in the first cell. The spike event activates the excitative synaptical channel in the dendrite of the second cell. It gives the stimulus to activation of the Hodgkin-Huxley channels in the Dendrite and soma HH channels(rot polygon) Connections Synapses Figure 5: The structure of two-cell model with Hodgkin- Huxley channels. soma of the second cell, which accordingly activate the inhibitory synaptically channel in the dendrite of the second cell. After starting the server, there is a possibility to see an animation of the simulation results. The spike events in the main window with the structure of model can be observed together with the graphs of voltage spread and synaptic channels conductance change (see Fig. 6). Neuron activation Spike spread Figure 6: The animation of simulation results of two-cell model with Hodgkin-Huxley channels. 5.2 Example of spike initiation in the sensory neuron of Aplysia The second example will illustrate the simulation process of B21 cell in Aplysia. This model was taken to learn the mechanism of spike regulation. The neuron for neurobiological study, B21, is a bipolar mechanoafferent that innervates a muscle, the subradula tissue (SRT). This muscle is used to move food into the buccal cavity of Aplysia (see Fig. 7). One concentrates in the study on one of the output connection of B21, its excitatory connections with a radula-closer motor neuron (B8) [1] [2]. Experiments has shown, that when B21 is peripherally activated at its resting membrane potential, postsynaptic potentials (PSPs) are not observed in B8. In contrast,

5 if B21 is centrally depolarized and then peripherally activated, PSPs are observed in B8 [11]. Subradula tissue B21 To B8 The important feature of B21 sensory neuron for neurobiologists is that it is easily reidentifiable, because its soma is centrally rather than peripherally located. The model for the simulation based on this form of cell structure can be suggested. It was assumed that the peripheral part of dendritic tree contains ten passive compartments, that are longitudinally connected with the soma. The soma is connected with the lateral dendrites that are inhomogeneous with Hodgkin-Huxley type ionic channels. The neuron was modelled with the compartmental approach. We obtained the parameters of cell morphology from neurobiological studies. It was assumed that the compartments in the peripheral part have cm radius, cm length. The soma is modelled as a cylindrical compartment with radius cm and length 0.02 cm. The lateral dendritic compartments have radius cm and length cm. The specific membrane resistance of the cell RM = 00 Ωcm 2, specific axial resistance RA = 0 Ωcm, specific membrane capacitance CM = 1 µf/cm 2. The resting membrane potential of the cell is E rest = 65 mv. As a first experiment, the peripheral activation of the cell was simulated. Because the peripheral part of dendrites serve as a passive dendritic tree, one-dimensional cable theory can be used to understanding the voltage spread with the space. The compartmental approach is derived from cable theory, which describes current flow in a continuous passive dendritic tree using partial differential equations. The analytical solution for current inputs of cable equations has a form of voltage spread depending both from time and space position. One can calculate the constants influencing the form of the cable equation solution. The length constant λ = 0.09 provides the information about the capability of the dendritic tree to integrate inputs in space. In our case, the peripheral part of dendrite has the electronic length X = L = 0.1, where X was calculated at the end of the dendrite. Thus, the change of the voltage in peripheral dendrite has a form of of decrease through the cable. It can be observed from the graphs of voltage. The pulsed current was injected in the first peripheral segment. The voltage in the first compartment after current activation gets the value that could be enough for action potential initiation (above threshold). But in the compartments closer to the soma the voltage decreases and in the soma its value is under threshold for the spike initiation (see Fig. 8). So, the ionic channels in the lateral part of the cell could be opened and no action potential is observed. Medial dendrites Lateral dendrites Figure 7: The B21 cell, schematically represented. Voltage Vm0 Vm1 Vm2 Vm3 Vm4 Vm5 Vm6 Vm7 Vm8 Vm9 VmSoma time Figure 8: The graphs of the voltage spread in the peripheral dendrite and soma of the B21 cell. V mi is the voltage of i-th compartment. The second experiment performs additionally a soma depolarization. A constant current was injected into the soma. The increase in soma voltage influences on the voltage in the segments of the lateral dendritic tree. So, in this case the ionic channels are opened and the action potentials are observed (see Fig. 9). One can conclude that than B8 neuron can be synaptically activated and the PSPs are observed. The results of this simulation showed the cause of the PSPs initiation in the B8 motor neuron just by the depolarization in soma and peripheral activation of B21 cell. 6 Discussion NeuroSim, our system for simulation of real networks has an effective client-server architecture. In the first phase of the project, the Genesis simulator was used as a server on the remote computer. It solves the differential equations describing spread of electrical currents in the neural networks. In the second phase of the project, we have been developing our own server for numerical integration. The model of B21 cell in Aplysia was considered as the simulation example. The simulation showns no action potential in lateral dendrites of the B21 cell when it is peripherally activated. In contrast, if the B21 cell is centrally depolarized and peripherally activated, the spike initiation in the lateral dendrites is observed. It could explain why

6 Voltage time Vmlat0 Vmlat1 Vmlat2 Vmlat3 Vmlat4 Vmlat5 Vmlat6 Vmlat7 Vmlat8 Vmlat9 [4] M. Hines. A program for simulation of nerve equations with branching geometries. International Journal of Biomedical Computing, 24:33 68, [5] A. Hodgkin and A. Huxley. The components of membrane conductance in the giant axon of Loligo. J. Physiol., 116: , [6] C. S. Horstmann and G. Cornell. Core Java 2. Sun Microsystems Press, [7] M. A. Wilson, U. S. Bhalla, J. D. Uhley and J. M. Bower. GENESIS: A system for simulating neural networks. In Advances in Neural Information Processing Systems, pages Morgan Kaufman, San Mateo, Figure 9: The spike initiation in the lateral part of the B21 cell. V mlati refers to the i-th lateral compartment. the PSPs in excitatory connected with B21 cell B8 neuron are observed just in the second case, as the neurobiological experiments have shown. In the current phase of the project, we are integrating NeuroSim with the electronic chalkboard, E-Chalk, our E- Learning system [9]. The GUI has been adapted that it is possible to draw free-hand a model of neurons and connections, after that the simulation is started. It can be effectively used in the lectures for the educational purposes. NeuroSim has been designed as the tool for research modelling experiments as well as the powerful education software. [8] M. Mascagni. Numerical methods for neuronal modelling. In C. Koch and I. Segev, editors, Methods in Neuronal Modeling. MIT Press, Cambridge, Mass, [9] R. Rojas and G. Friedland and L. Knipping and W. L. Raffel. Elektronische Kreide: Eine Java-Multimedia- Tafel für den Präsenz- und Fernunterricht. Technical Report B-00-17, FU Berlin, Institut für Informatik, October [] W. Rall. Branching dendritic trees and motoneuron membrane resistivity. Exp. Neurol., 1: , [11] S. C. Rosen, M. W. Miller, C. G. Evans, E. C. Cropper, I. Kupfermann. Diverse synaptic connections between peptidergic radula mechanoafferent neurons and neurons in the feeding system of Aplysia. J. Neurophysiol, 83: , Acknowledgments Olga Kroupina thanks the Graduiertenkolleg GRK 120 Signal cascades in living systems, Deutsche Forschungsgemeinschaft, for its support during her Ph.D. studies. References [1] C. G. Evans, S. C. Rosen, E. C. Cropper. Regulation of spike initiation and propagation in an Aplysia sensory neuron. J. Neuroscience, 23(7): , April [2] E. C. Cropper, C. G. Evans, S. C. Rosen. Multiple mechanisms for peripheral activation of the peptidecontaining radula mechanoafferent neurons B21 and B22 of Aplysia. J. Neurophysiol, 76: , [3] M. Hines. Effecient computation of branched nerve equations. J. Biomed. Comp., 15:69 76, 1984.

80% of all excitatory synapses - at the dendritic spines.

80% of all excitatory synapses - at the dendritic spines. Dendritic Modelling Dendrites (from Greek dendron, tree ) are the branched projections of a neuron that act to conduct the electrical stimulation received from other cells to and from the cell body, or