{"title": "Neural Network Analysis of Distributed Representations of Dynamical Sensory-Motor Transformations in the Leech", "book": "Advances in Neural Information Processing Systems", "page_first": 28, "page_last": 35, "abstract": "", "full_text": "28 \n\nLockery t Fang and Sejnowski \n\nNeu.\u00b7al Network Analysis of \n\nDistributed Representations of Dynamical \n\nSensory-Motor rrransformations in the Leech \n\nShawn R. LockerYt Van Fangt and Terrence J. Sejnowski \n\nComputational Neurobiology Laboratory \n\nSalk Institute for Biological Studies \nBox 85800, San Diego, CA 92138 \n\nABSTRACT \n\nInterneurons in leech ganglia receive multiple sensory inputs and make \nsynaptic contacts with many motor neurons. These \"hidden\" units \ncoordinate several different behaviors. We used physiological and \nanatomical constraints to construct a model of the local bending reflex. \nDynamical networks were trained on experimentally derived input-output \npatterns using recurrent back-propagation. Units in the model were \nmodified to include electrical synapses and multiple synaptic time \nconstants. The properties of the hidden units that emerged in the \nsimulations matched those in the leech. The model and data support \ndistributed rather than localist representations in the local bending reflex. \nThese results also explain counterintuitive aspects of the local bending \ncircuitry. \n\nINTRODUCTION \n\nNeural network modeling techniques have recently been used to predict and analyze the \nconnectivity of biological neural circuits (Zipser and Andersen, 1988; Lehley and \nSejnowski, 1988; Anastasio and Robinson, 1989). Neurons are represented as simplified \nprocessing units and arranged into model networks that are then trained to reproduce the \ninput-output function of the reflex or brain region of interest. After training, the \nreceptive and projective field of hidden units in the network often bear striking similarities \nto actual neurons and can suggest functional roles of neurons with inputs and outputs that \nare hard to grasp intuitively. We applied this approach to the local bending reflex of the \nleech, a three-layered, feed-forward network comprising a small number of identifiable \n\n\fNeural Network Analysis of Distributed Representations in the Leech \n\n29 \n\nneurons whose connectivity and input-output function have been determined \nphysiologically. We found that model local bending networks trained using recurrent \nback-propagation (pineda, 1987; Pearlmutter, 1989) to reproduce a physiologically \ndetennined input-output function contained hidden units whose connectivity and temporal \nresponse properties closely resembled those of identified neurons in the biological \nnetwork. The similarity between model and actual neurons suggested that local bending \nis produced by distributed representations of sensory and motor infonnation. \n\nTHE LOCAL BENDING REFLEX \n\nIn response to a mechanical stimulus, the leech withdraws from the site of contact (Fig. \nla). This is accomplished by contraction of longitudinal muscles beneath the stimulus \nand relaxation of longitudinal muscles on the opposite side of the body, resulting in a U(cid:173)\nshaped local bend (Kristan, 1982). The fonn of the response is independent of the site of \nstimulation: dorsal, ventral, and lateral stimuli produce an appropriately oriented \n\na \n\nRutlng .-/\n~~\\ \n\n\"\",,-\n\n\" \n\n. ,\n\nDorsal \n\nb \n\nSensory \nneurons \n\nInterneurons \n\nLeft \n\nRight \n\n~~ , \n\n, \n0000-\n\nMotor \nneurons \n\nDorsal \n\n~ 0 0 ~ -local bending \ninterneurons \n\nUnidentifi8d \n0000- local bending \ninterneurons \n\n-\n\n-\n\nexcitatory \n\ninhib~ory \n\nFigure 1: a. Local bending behavior. Partial view of a leech in the resting position \nand in response to dorsal, ventral, and lateral stimuli. b. Local bending circuit. The main \ninput to the reflex is provided by the dorsal and ventral P cells (PD and PV). Control of \nlocal bending is largely provided by motor neurons whose field of innervation is restricted \nto single left-right, dorsal-ventral quadrants of the body; dorsal and ventral quadrants are \ninnervated by both excitatory (DE and VE) and inhibitory (DI and VI) motor neurons. \nMotor neurons are connected by electrical and chemical synapses. Sensory input to motor \nneurons is mediated by a layer of intemeurons. Intemeurons that were excited by PD and \nwhich in tum excite DE have been identified (hatched); other types of intemeurons \nremain to be identified (open). \n\n\f30 \n\nLockery, Fang and Sejnowski \n\nwithdrawal. Major input to the local bending reflex is provided by four pressure sensitive \nmechanoreceptors called P cells, each with a receptive field confined to a single quadrant \nof the body wall (Fig. Ib). Output to the muscles is provided by eight types of \nlongitudinal muscle motor neurons, one to four excitatory and inhibitory motor neurons \nfor each body wall quadrant (Stuart, 1970; Ort et al., 1974). Motor neurons are connected \nby chemical and electrical synapses that introduce the possibility of feedback among the \nmotor neurons. \n\nDorsal. ventral. and lateral stimuli each produce a pattern of P cell activation that results \nin a unique pattern of activation and inhibition of the motor neurons (Lockery and \nKristan, 1990a). Connections between sensory and motor neurons are mediated by a layer \nof interneurons (Kristan, 1982). Nine types of local bending interneurons have been \nidentified (Lockery and Kristan, 1990b). These comprise the subset of the local bending \ninterneurons which contribute to dorsal local bending because they are excited by the \ndorsal P cell and in turn excite the dorsal excitatory motor neuron. There appear to be no \nfunctional connections between interneurons. Other interneurons remain to be identified, \nsuch as those which inhibit the dorsal excitatory motor neurons. \n\nInterneuron input connections were determined by recording the amplitude of the \npostsynaptic potential in an interneuron while each of the P cells was stimulated with a \nstandard train of impulses (Lockery and Kristan, 1990b). Output connections were \ndetennined by recording the amplitude of the postsynaptic potential in each motor neuron \nwhen an interneuron was stimulated with a standard current pulse. Interneuron input and \noutput connections are shown in Figure 2, where white squares are excitatory \nconnections, black squares are inhibitory connections, and the size of each square indicates \nconnection strength. Most interneurons received substantial input from three or four P \ncells, indicating that the local bending network fonns a distributed representation of \nsensory input. \n\ndorsal \nventral \n\nc \n\nFigure 2: \nInput and output connections of the nine types of dorsal local bending \ninterneurons. Within each gray box, the upper panel shows input connections from \nsensory neurons, the middle panel shows output connections to inhibitory motor \nneurons, and the lower panel shows output connections to excitatory motor neurons. \nSide-length of each box is proportional to the amplitude of the connection detennined \nfrom intracellular recordings of interneurons or motor neurons. White boxes indicate \nexcitatory connections and black boxes indicated inhibitory connections. Blank spaces \ndenote conections whose strength has not been detennined for technical reasons. \n\n\fNeural Network Analysis of Distributed Representations in the Leech \n\n31 \n\nNEURAL NETWORK MODEL \n\nBecause sensory input is represented in a distributed fashion, most interneurons are active \nin all forms of local bending. Thus, in addition to contributing to dorsal local bending, \nmost interneurons are also active during ventral and lateral bending when some or all of \ntheir output effects are inappropriate to the observed behavioral response. This suggests \nthat the inappropriate effects of the dorsal bending interneurons must be offset by other as \nyet unidentified interneurons and raises the possibility that local bending is the result of \nsimultaneous activation of a population of interneurons with multiple sensory inputs and \nboth appropriate and inappropriate effects on many motor neurons. It was not obvious, \nhowever, that such a population was sufficient, given the well-known nonlinearities of \nneural elements and constraints imposed by the input-output function and connections \nknown to exist in the network. The possibility remained that intemeurons specific for \neach form of the behavior were required to produce each output pattern. To address this \nissue, we used recurrent back-propagation (Pearl mutter, 1989) to train a dynamical \nnetwork of model neurons (Fig 3a). The network had four input units representing the \n\na \n\nSensory \nneurons \n\nInterneuron. \n\nMotor \nneuron. \n\nLeft \n\nRIght \n\n@@ \n\nIJ \n\nBefore \n1 -\n\n2 -\n\nc \n0 \n~ 4 -\n:s \nCD \n\u00a3: \n~ \n0 \n'-\n\n-0 \n\n5 ---\n\n3 -\n\n6 -\n\nI \n\n7 -\n\n8 -\n\n~ \u2022\u2022 clatory \n\n-\n\nInPllbaory - - - electrical \n\nStlm ~ \n\nAfter Target \n\ny-\n\nJ>--\n\nf.-\n\ny-\n\ny-\n\nJ---\n\nf.-\n\ny-\n\n-\"'\"-\n\n\"-\ny-\n\ny-\n\n-\"'\"-\n\n\"-\ny-\n\ny-\n~ ---=-110 mV \n\n5 sac \n\nFigure 3: a. The local bending network model. Four sensory neurons were connected to \neight motor neurons via a layer of 10 interneurons. Neurons were represented as single \nelectrical compartments whose voltage varied as a function of time (see text). Known \nelectrical and chemical connections among motor neurons were assigned fixed connection \nstrengths (g's and w's) determined from intracellular recordings. Interneuron input and \noutput connections were adjusted by recurrent back-propagation. Chemical synaptic \ndelays were implemented by inserting s-units between chemically connected pairs of \nneurons. S-units with different time constants were inserted between sensory and \ninterneurons to account for fast and slow components of synaptic potentials recorded in \ninterneurons. b. Output of the model network in response to simultaneous activation of \nboth PDs (stirn). The response of each motor neuron (rows) is shown before and after \ntraining. The desired response contained in the training set is shown on the right for \ncomparison (target). \n\n\f32 \n\nLockery, Fang and Sejnowski \n\nfour P cells, and eight output units representing the eight motor neuron types. Between \ninput and output units was a single layer of 10 hidden units representing the intemeurons. \nNeurons were represented as single electrical compartments with an input resistance and \ntime constant. The membrane potential (V j) of each neuron was given by \n\nwhere Ti and Ri are the time constant and input resistance of the neuron and Ie and Ie are \nthe sum of the electrical and chemical synaptic currents from presynaptic neurons. \nCurrent due to electrical synapses was given by \n\nwhere gij is the coupling conductance between neuron i and j. To implement the delay \nassociated with chemical synapses, synapse units (s-units) were inserted between between \npairs of neurons connected by chemical synapses. The activation of each s-unit was given \nby \n\nwhere Tij is the synaptic time constant and f(Vj) was a physiologically determined \nsigmoidal function (0 S f S 1) relating pre- and postsynaptic membrane potential at an \nidentified monosynaptic connection in the leech (Granzow et al., 1985). Current due to \nchemical synapses was given by \n\nwhere Wij is the strength of the chemical synapse between units i and j. Thus, synaptic \ncurrent is a graded function of presynaptic voltage, a common feature of neurons in the \nleech (Friesen, 1985; Granzow et al., 1985; Thompson and Stent, 1976) and other \ninvertebrates (Katz and Miledi, 1967; Burrows and Siegler, 1978; Nagayama and Hisada. \n1987). \n\nChemical and electrical synaptic strengths between motor neurons were determined by \nrecording from pairs of motor neurons and were not adjusted by the training algorithm. \nInterneuron input and output connections were given small initial values that were \nrandomly assigned and subsequently adjusted during training. During training, input \nconnections were constrained to be positive to reflect the fact that only excitatory \ninterneuron input connections were seen (Fig. 2), but no constraints were placed on the \nnumber of input or output connections. Synaptic time constants were assigned fixed val(cid:173)\nues. These were adjusted by hand to fit the time course of motor neuron synaptic \npotentials (Lockery and Kristan, 1990a), or determined from pairwise motor neuron \nrecordings (Granzow et al., 1985). \n\n\fNeural Network Analysis or Distributed Representations in the Leech \n\n33 \n\na \n\nleft \n\\ \n\ndorsal \nventral -\n\nright \nI \n\nData \n\nModel \n\nb \n\nSlow \n\nFast \n\n~l-ttL----------\n\nStirn \n\n110mV \n--=---1100 mV \n\nStirn \n\n400ms \n\nFigure 4: Q. Input and output connections of model local bending intemeurons. Model \ninterneurons, like the actual interneurons, received substantial inputs from three or four \nsensory neurons and had significant effects on most of the motor neurons. Symbols as in \nfigure 2. o. Actual (data) and simulated (model) synaptic potentials recorded from three \ntypes of interneuron. Actual synaptic potentials were recorded in response to a train of P \ncell impulses. Simulated synaptic potentials were recorded in response to a pulse of \ncurrent in the P cell which simulates a step change in P cell firing frequency. \n\nRESULTS \n\nModel networks were trained to produce the amplitude and time course of synaptic \npotentials recorded in all eight motor neurons in response to trains of P cell impulses \n\n\f34 \n\nLockery t Fang and Sejnowski \n\n(Lockery and Kristan. 1990a). The training set included the response of all eight motor \nneurons when each P cell was stimulated alone and when P cells were stimulated in pairs. \nAfter 6.000 - 10.000 training epochs. the output of the model closely matched the desired \noutput for all patterns in the training set (Fig. 3b). To compare intemeurons in the model \nnetwork to actual interneurons. simulated physiological experiments were performed. \nInterneuron input connections were determined by recording the amplitude of the \npostsynaptic potential in a model interneuron while each of the P cells was stimulated \nwith a standard current pulse. Output connections were detennined by recording the \namplitude of the postsynaptic potential in each motor neuron when an interneuron was \nstimulated with a standard current pulse. Model interneurons. like those in the real \nnetwork. received three or four substantial connections from P cells and had significant \neffects on most of the motor neurons (Fig. 4a). Most model interneurons were active \nduring each form of the behavior and the output connections of the interneurons were only \npartially consistent with each fonn of the local bending response. Thus. the appropriate \nmotor neuron responses were produced by the summation of many appropriate and \ninappropriate interneuron effects. This result explains the appropriate and inappropriate \neffects of interneurons in the leech. \n\nThere was also agreement between the time course of the response of model and actual \ninterneurons to P cell stimulation (Fig. 4b). In the actual network. interneuron synaptic \npotentials in response to trains of P cell impulses had a fast and slow component. Some \ninterneurons showed only the fast component. some only the slow. and some showed \nboth components (mixed). Although no constraints were placed on the temporal response \nproperties of interneurons. the same three types of interneuron were found in the model \nnetwork. The three different types of interneuron temporal response were due to different \nrelative connection strengths of fast and slow s-units impinging on a given interneuron \n(Fig. 3a). \n\nCONCLUSION \n\nOur results show that the network modeling approach can be adapted to models with more \nrealistic neurons and synaptic connections. including electrical connections. which occur \nin both invertebrates and vertebrates. The qualitative similarity between model and actual \ninterneurons demonstrates that a population of interneurons resembling the identified \ndorsal local bending interneurons could mediate local bending in a distributed processing \nsystem without additional interneurons specific for different forms of local bending. \nInterneurons in the model also displayed the diversity in temporal responses seen in \ninterneurons in the leech. Clearly. the training algorithm did not produce exact matches \nbetween model and actual intemeurons. but this was not surprising since the identified \nlocal bending interneurons represent only a subset of the intemeurons in the reflex. More \nexact matches could be obtained by using two pools of model interneurons. one to \nrepresent identified neurons, the other to represent unidentified neurons. Model neurons in \nthe latter pool would constitute testable physiological predictions of the connectivity of \nunidentified local bending intemeurons. \n\nAcknowledgements \n\nSupported by the Bank of America-Giannini Foundation. the Drown Foundation. and the \nMathers Foundation. \n\n\fNeural Network Analysis of Distributed Representations in the Leech \n\n3S \n\nReferences \n\nAnastasio. T. and Robinson. D. A. (1989) Distributed parallel processing in the \n\nvestibulo-oculomotor system. Neural Compo 1:230-241. \n\nBurrows, M., and M.V.S. 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Andersen (1988) A back-propagation programmed network that \nsimulates response properties of a subset of posterior parietal neurons Nature \n331:679-684. \n\n\f", "award": [], "sourceid": 249, "authors": [{"given_name": "Shawn", "family_name": "Lockery", "institution": null}, {"given_name": "Yan", "family_name": "Fang", "institution": null}, {"given_name": "Terrence", "family_name": "Sejnowski", "institution": null}]}