{"title": "Hybrid Circuits of Interacting Computer Model and Biological Neurons", "book": "Advances in Neural Information Processing Systems", "page_first": 813, "page_last": 819, "abstract": null, "full_text": "Hybrid Circuits of Interacting Computer Model \n\nand Biological Neurons \n\nSylvie Renaud-LeMasson(cid:173)\nDepartment of Physics \n\nBrandeis University \nWaltham. MA 02254 \n\nEve Marder \n\nDepartment of Biology \n\nBrandeis University \nWaltham. MA 02254 \n\nGwendal LeMasson' \nDepartment of Biology \n\nBrandeis University \nWaltham. MA 02254 \n\nL.F. Abbott \n\nDepartment of Physics \n\nBrandeis University \nWaltham. MA 02254 \n\nAbstract \n\nWe demonstrate the use of a digital signal processing board to construct \nhybrid networks consisting of computer model neurons connected to a \nbiological neural network. This system operates in real time. and the \nsynaptic connections are realistic effective conductances. Therefore. \nthe synapses made from the computer model neuron are integrated \ncorrectly by the postsynaptic biological neuron. This method provides \nus with the ability to add additional. completely known elements to a \nbiological network and study their effect on network activity. \nMoreover. by changing the parameters of the model neuron. it is \npossible to assess the role of individual conductances in the activity of \nthe neuron. and in the network in which it participates. \n\n\"Present address. \n\nl-Enserb. \nCNRSURA 846. 351 crs de la Liberation. 33405 Talence Cedex. \nFrance. \n\nlXL. Universit6 de Bordeaux \n\n'Present address. LNPC. CNRS. Universite de Bordeaux 1. Place \n\nde Dr. Peyneau. 33120 Arcachon. France \n\n813 \n\n\f814 \n\nRenaud-LeMasson, LeMasson, Marder, and Abbott \n\n1 INTRODUCTION \n\nA primary goal in neuroscience is to understand how the electrical properties of \nindividual neurons contribute to the complex behavior of the networks in which they \nare found. However, the experimentalist wishing to assess the contribution of a given \nneuron or synapse in network function is hampered by lack of adeq.uate tools. For \nexample, although pharmacological agents are often used to block synaptic \nconnections within a network (Eisen and Marder, 1982), or individual currents within \na neuron (Tierney and Harris-Warrick, 1992), it is rarely possible to do precise \npharmacological dissections of network function. Computational models of neurons \nand networks (Koch and Segev, 1989) allow the investigator the control over \nparameters not possible with pharmacology. However, because realistic computer \nmodels are always based on inadequate biophysical data, the investigator must always \nbe concerned that the simulated system may differ from biological reality in a critical \nway. We have developed a system that allows us to construct hybrid networks \nconsisting of a model neuron interacting with a biological neural network. This \nallows us to work with a real biological system while retaining complete control over \nthe parameters of the model neuron. \n\n2 THE MODEL NEURON \n\nBiophysical data describing the ionic currents of the Lateral Pyloric (LP) neuron of \nthe crab stomatogastric ganglion (STG) (Golowasch and Marder, 1992) were used to \nconstruct an isopotential model LP neuron using MAXIM. MAXIM is a software \npackage that runs on MacIntosh systems and provides a graphical modeling tool for \nneurons and small neural networks (LeMasson, 1993). The model LP neuron used \nuses Hodgkin-Huxley type equations and contains a fast Na+ conductance, a Ca+ \nconductance, a delayed rectifier K+ conductance, a transient outward current (iJ and \na hyperpolarization-activated current OJ, as well as a leak conductance. This model \nis similar to that reported in Buchholtz et al. (1992) but because the raw data were \nrefit using MAXIM, details are slightly different. \n\n3 ARTIFICIAL SYNAPSES \n\nArtificial chemical synapses are produced by the same method used in Sharp et at. \n(1993). An axoclamp in discontinuous current clamp (DCC) mode is used to record \nthe membrane potential and inject current into the biological neurons (Fig. 1). The \npresynaptic membrane potential is used to control current injection into the \npostsynaptic neuron simulating a conductance change (rather than an injected current \nas in Yarom et al.). The synaptic current injected into the postsynaptic neuron \ndepends on the programmed synaptic conductance and an investigator-determined \nreversal potential. The investigator also specifies the threshold and the function \nrelating \"transmitter release\" to presynaptic membrane potential, as well as the time \ncourse of the synaptic conductance. \n\n\fHybrid Circuits of Interacting Computer Model and Biological Neurons \n\n815 \n\nparameters \n\nMac IIfx \n\nDSP \n\ndata \n\n,...------, V m & Is \n\n.... Vl--m----4 Axoclamp \nt--~ D. C. C. \n\nSTG \n\nFigure 1: Schematic diagram of the system used to establish hybrid circuits. \n\n4 HARDWARE \nOur system uses a Digital Signal Processor (DSP) board with built-in AID and DI A \n16 bit-precision converters (Spectral Innovations MacDSP256KNI), with DSP32C \n(AT&T) mounted in a Macintosh II fx (MAC) computer. A block diagram of the \nsystem is shown Fig. 1. The parameters describing the membrane and synaptic \nconductances of the model neuron are stored in the MAC and are transferred to the \nDSP board RAM (256x32K) through the standard NuBus interface. The DSP \ntranslates the parameter files into look-up tables via a polynomial fitting procedure. \nThe differential equations of the LP model and the artificial synapses are integrated by \nthe DSP board, taking advantage of its optimized arithmetic functions and data access. \nIn this system, the computational model runs on the DSP board, and the Mac IIfx \nfunctions to store and display data on the screen. \n\nThe computational speed of this system depends on the integration time step and the \ncomplexity of the model (the number of differential equations implemented in the \nmodel). For the results shown here, the integration time step was 0.7 msec, and \nunder the conditions described below, 10-15 differential equations were used. The \ncurrent system is limited to two real neurons and one model neuron because the DSP \nboard has only two input and two output channels. A later generation system with \nmore input and output channels and additional speed will increase the number of \nneurons and connections that can be created. During anyone time step, the membrane \npotential of the model neuron is computed, the synaptic currents are determined, and a \nvoltage command is exported to the Axoclamp instructing it to inject the appropriate \ncurrent into the biological neuron (typically a few nA). During each time step the \nAxoclamp is used to measure the membrane potential of the biological neurons \n(typically between -80mV and OmV) used to compute the value of the synaptic inputs \nto the model neuron. The computed and measured membrane potentials are \nperiodically (every 500 time steps) sent to the computer main memory to be displayed \nand recorded. \n\nTo make this system run in real time, it is necessary to maintain perfect timing among \nall the components. Therefore in every experiment we first determine the minimum \ntime step needed to do the integration depending on the complexity of the model being \nimplemented. For complex models we used the internal clock of the MacII to drive \nthe board. Under some conditions it was preferable to drive the board with an external \nclock. It is critical that the Axoclamp sampling rate be more than twice the board time \nstep if the two are not synchronized. In our experiments, the Axoclamp switching \n\n\f816 \n\nRenaud-LeMasson, LeMasson, Marder, and Abbott \n\nA \n\nB \n\nModel LP \n\n~ real synapses \n\n-\n\n\u2022 ..,~ artificial synapses \n\nC: increaseofglh \n\n0.5 sec \n\nISOmV \n\nFigure 2: Hybrid network consisting of a model LP neuron connected to a PD neuron of \na biological stomatogastric ganglion. A: Simplified connectivity diagram of the pyloric \ncircuit of the stomatogastric ganglion. The AB/PD group consists of one AB neuron \nelectrically coupled to two PD neurons. All chemical synapses are inhibitory. B: \nSimultaneous intracellular recordings from two biological neurons (PD and LP) and a plot \nof the membrane potential of the model LP neuron connected to the circuit. The \nparameters of the synaptic connections and the model LP neuron were adjusted so that \nthe model LP neuron fired in the same time in the pyloric cycle as the biological LP \nneuron. C: Same recording configuration as Bt but maximal conductance of ih in the \nmodel neuron was increased. \n\n\fHybrid Circuits of Interacting Computer Model and Biological Neurons \n\n817 \n\nA \n\nB \n\npy \n\nModel LP \n\n~ real synapses \n\n~ artificial synapses \n\n110 mV \n\n150 mV \n\n110 mV \n\n0.5 sec \n\nFigure 3: Hybrid network in which the model LP neuron is connected to. two diffe~ent \nbiological neurons. A: Connectivity diagram showing the pattern of synaptic connections \nshown in part B. B: Simultaneous recordings from the biological AB neuron, the model \nLP neuron, and a biological PY neuron. \n\ncircuit was running about three times faster than the board time step. However, if \nexperimental conditions force a slower Axoclamp sampling rate, then it will be \nimportant to synchronize the Axoclamp clock with the board. \nS RESULTS \nThe STG of the lobster, Panulirus interruptus contains one LP neuron, two Pyloric \nDilator (PO) neurons, one Anterior Burster (AB), and eight Pyloric (PY) neurons \n(Eisen and Marder, 1982; Harris-Warrick et al., 1992). The connectivity among \nthese neurons is known, and is shown in Figure 2A. The PD and LP neurons fire in \nalternation, because of the reciprocal inhibitory connections between them. Figure 2B \nshows a model LP neuron connected with reciprocal inhibitory synapses to a \nbiological PD neuron. The parameters controlling the threshold, activation curve, \ntime course, and reversal potential of the model neuron were adjusted until the model \nneuron fired at the same time within the rhythmic pyloric cycle as the biological LP \nneuron (Fig. 2B). Once these parameters were set, it was then possible to ask what \neffect changing the membrane properties of the model neuron had on emergent \nnetwork activity. Figure 2C shows the result of increasing the maximal conductance \nof one of the currents in the model LP neuron, it,. Note that increasing this current \n\n\f818 \n\nRenaud-LeMasson, LeMasson, Marder, and Abbott \n\nincreased the number of LP action potentials per burst. The increased activity in the \nLP neuron delayed the onset of the next burst in the PO neurons because of the \ninhibitory synapse between the model LP neuron and the biological PO neuron, and \nthe cycle period therefore also increased. Another effect seen in this example, is that \nthe increased conductance of ~ in the LP neuron delayed the onset of the model LP \nneuron's firing relative to that of the biological LP neuron. \n\nIn the experiment shown in Figure 3 we created reciprocal inhibitory connections \nbetween the model LP neuron and two biological neurons, the AB and a PY (Fig. \n3A). (The action potentials in the AB neuron are higbly attenuated by the cable \nproperties of this neuron). This example shows clearly the unitary inhibitory \npostsynaptic potentials (IPSPs) in the biological neurons resulting from the model LP's \naction potentials. During each burst of LP action potentials the IPSPs in the AB \nneuron increase considerably in amplitude, although the AB neuron's membrane \npotential is moving towards the reversal potential of the IPSPs. This occurs \npresumably because the conductance of the AB neuron is higher right at the end of its \nburst, and decreases as it hyperpolarizes. The same burst of LP action potentials \nevokes IPSPs in the PY neuron that increase in amplitude, here presumably because \nthe PY neuron is depolarizing and increasing the driving force on the artificial \nchemical synapse. These recordings demonstrate that although the same function is \ncontrolling the synaptic -release- properties in the model LP neuron, the actual \nchange in membrane potential evoked by action potentials in the LP neuron is affected \nby the total conductance of the biological neurons. \n\n6 CONCLUSIONS \n\nThe ability to connect a realistic model neuron to a biological network offers a unique \nopportunity to study the effects of individual currents on network activity. It also \nprovides realistic, two-way interactions between biological and computer-based \nnetworks. As well as providing an \u00b7important new tool for neuroscience, this \nrepresents an exciting new direction in biologically-based computing. \n\n7 ACKNOWLEDGMENTS \n\nWe thank Ms. Joan McCarthy for help with manuscript preparation. Research \nsupported by MH 46742, the Human Science Frontier Program, and NSF DMS-\n9208206. \n\n8 REFERENCES \n\nBuchholtz, F., Golowasch, J., Epstein, I.R., and Marder, E. (1992) Mathematical \nmodel of an identified stomatogastric ganglion neuron. 1. Neurophysiology 67:332-\n340. \n\nEisen, J.S., and Marder, E. (1982) Mechanisms underlying pattern generation in \nlobster stomatogastric ganglion as determined by selective inactivation of identified \nneurons. III. Synaptic connections of electrically coupled pyloric neurons. 1. \nNeurophysiology 48: 1392-1415. \n\nGolowasch, J. and Marder, E. (1992) Ionic currents of the lateral pyloric neuron of \n\n\fHybrid Circuits of Interacting Computer Model and Biological Neurons \n\n819 \n\nthe stomatogastric ganglion of the crab. J. Neurophysiology 67:318-331. \n\nHarris-Warrick. R.M .\u2022 Marder, E .\u2022 Selverston, A.I.. and Maurice, M .\u2022 eds. (1992) \nDynamic Biological Networks. Cambridge. MA: MIT Press. \n\nKoch. C .\u2022 and Segev. I.. eds. (1989) Methods in Neuronal Modeling. Cambridge, \nMA: MIT press. \n\nLeMasson, G. (1993) Maxim: A software system for simulating single neurons and \nneural networks, in preparat~on. \n\nSharp, A.A .\u2022 O'Neil, M.B., Abbott, L.F. and Marder. E. (1993) The dynamic \nclamp: Computer-generated conductances in real neurons. J. Neurophysiology, in \npress. \n\nYarom, Y. (1992) Rhythmogenesis in a hybrid system interconnecting an olivary \nneuron to an network of coupled oscillators. Neuroscience 44:263-275. \n\n\f", "award": [], "sourceid": 640, "authors": [{"given_name": "Sylvie", "family_name": "Masson", "institution": null}, {"given_name": "Gwendal", "family_name": "Le Masson", "institution": null}, {"given_name": "Eve", "family_name": "Marder", "institution": null}, {"given_name": "L.", "family_name": "Abbott", "institution": null}]}