{"title": "Extraction of Temporal Features in the Electrosensory System of Weakly Electric Fish", "book": "Advances in Neural Information Processing Systems", "page_first": 62, "page_last": 68, "abstract": null, "full_text": "Extraction of temporal features in the \nelectrosensory system of weakly electric \n\nfish \n\nFabrizio Gabbiani(cid:173)\nDivision of Biology \n\n139-74 Caltech \n\nPasadena, CA 91125 \n\nWalter Metzner \n\nDepartment of Biology \nUniv. of Cal. Riverside \nRiverside, CA 92521-0427 \n\nRalfWessel \n\nDepartment of Biology \nUniv. of Cal. San Diego \nLa J oBa, CA 92093-0357 \n\nChristof Koch \n\nDivision of Biology \n\n139-74 Caltech \n\nPasadena, CA 91125 \n\nAbstract \n\nThe encoding of random time-varying stimuli in single spike trains \nof electrosensory neurons in the weakly electric fish Eigenmannia \nwas investigated using methods of statistical signal processing. At \nthe first stage of the electrosensory system, spike trains were found \nto encode faithfully the detailed time-course of random stimuli, \nwhile at the second stage neurons responded specifically to features \nin the temporal waveform of the stimulus. Therefore stimulus infor(cid:173)\nmation is processed at the second stage of the electrosensory system \nby extracting temporal features from the faithfully preserved image \nof the environment sampled at the first stage. \n\n1 \n\nINTRODUCTION \n\nThe weakly electric fish, Eigenmannia, generates a quasi sinusoidal, dipole-like elec(cid:173)\ntric field at individually fixed frequencies (250 - 600 Hz) by discharging an electric \norgan located in its tail (see Bullock and Heilgenberg, 1986 for reviews). The fish \nsense local changes in the electric field by means of two types of tuberous electrore(cid:173)\nceptors located on the body surface. T-type electroreceptors fire phase-locked to \nthe zero-crossing of the electric field once per cycle of the electric organ discharge \n\n-email: gabbiani@klab.caltech.edu, wmetzner@mail.ucr.edu, rwessel@jeeves.ucsd.edu, \n\nkoch@klab.caltech.edu. \n\n\fExtraction of Temporal Features in Weakly Electric Fish \n\n63 \n\n(EOD) and are thus able to encode phase changes. P-type electroreceptors fire in \na more loosely phase-locked manner with a probability smaller than 1 per EOD. \nTheir probability of firing increases with the mean amplitude of the field thereby \nallowing them to encode amplitude changes (Zakon, 1986). \n\nThis information is used by the fish in order to locate objects (electrolocation, \nBastian 1986) as well as for communication with conspecifics (Hopkins, 1988). One \nbehavior which has been most thoroughly studied (Heiligenberg, 1991), the jamming \navoidance response, occurs when two fish with similar EOD frequency (less than \n15 Hz difference) approach close enough to sense each other's field . In order to \nminimize beat patterns resulting from their summed electric fields, the fish with \nthe higher (resp. lower) EOD raises further (resp. lowers) its own EOD frequency. \nThe resulting frequency difference increase reduces the dis torsions in the interfering \nEODs. The fish is known to correlate phase differences computed across body \nregions with local amplitude increases or decreases in order to determine whether \nit should raise or lower its own EOD. \n\nAt the level of the first central nervous nucleus of the electrosensory pathway, the \nelectrosensory lateral line lobe of the hindbrain (ELL), phase and amplitude in(cid:173)\nformation are processed nearly independently of each other (Maler et al., 1981). \nAmplitude information is encoded in the spike trains of ELL pyramidal cells that \nreceive input from P-receptor afferents and transmit their information to higher \norder levels of the electrosensory system. Two functional classes of pyramidal cells \nare distinguished: E-type pyramidal cells respond by raising their firing frequency \nto increases in the amplitude of an externally applied electric field while I-type pyra(cid:173)\nmidal cells increase their firing frequency when the amplitude decreases (Bastian, \n1981). \n\nThe aim of this study was to characterize the temporal information processing \nperformed by ELL pyramidal cells on random electric field amplitude modulations \nand to relate it to the information carried by P-receptor afferents. To this end \nwe recorded the responses of P-receptor afferents and pyramidal cells to random \nelectric field amplitude modulations and analyzed them using two different methods: \na signal estimation method characterizing to what extent the neuronal response \nencodes the detailed . time-course of the stimulus and a signal-detection method \ndeveloped to identify features encoded in spike trains. These two methods as well \nas the electrophysiology are explained in the next section followed by the result \nsection and a short discussion. \n\n2 METHODS \n\n2.1 ELECTROPHYSIOLOGY \n\nAdult specimens of Eigenmannia were immobilized by intramuscular injection of \na curare-like drug (Flaxedil). This also strongly attenuated the fish's EODs. The \nfish were held in place by a foam-lined clamp in an experimental tank and an EOD \nsubstitute electric field was established by two electrodes placed in the mouth and \nnear the tail of the fish. The carrier frequency of the electric field, fcarrier, was \nchosen equal to the EOD frequency prior to curarization and the voltage generating \nthe stimulus was modulated according to \n\nVet) = Ao(1 + set)) cos (27rfcarrier) , \n\nwhere Ao is the mean amplitude and set) is a random, zero-mean modulation having \na flat (white) spectrum up to a variable cut-off frequency fc and a variable standard \ndeviation u. The modulation set) was generated by playing a blank tape on a tape \n\n\f64 \n\nA \n\nF. Gabbiani, W. Metzner, R. Wessel and C. Koch \n\nB \n\n} \n\n-200m. \n\nFigure 1: A. Schematic drawing of the experimental set-up. Tape recorder (T), \nvariable cutoff frequency Bessel filter (BF) and function generator (FG). B. Sample \namplitude modulation set) and intracellular recording from a pyramidal cell (I-type, \nIe = 12 Hz) . Spikes occurring in bursts are marked with an asterisk (see sect. 2.3.2). \nThe intracellular voltage trace reveals a high frequency noise caused by the EOD \nsubstitute signal and a high electrode resistance. \n\nrecorder, passing the signal through a variable cut-off frequency low-pass filter before \nmUltiplying it by the frequency carrier signal in a function generator (fig. 1A). \n\nExtracellular recordings from P-receptor afferents were made by exposing the an(cid:173)\nterior lateral line nerve. Intracellular recordings from ELL pyramidal cells were \nobtained by positioning electrodes in the central region of the pyramidal cell layer . \nIntracellular recoroing electrodes were filled with neurotracer (neurobiotin) to be \nused for subsequent intracellular labeling if the recordings were stable long enough. \nThis allowed to verify the cell type and its location within the ELL . In case no intra(cid:173)\ncellular labeling could be made the recording site was verified by setting electrolytic \nlesions at the conclusion of the experiment. In the subsequent data analysis, data \nfrom E- and I-type pyramidal cells and from two different maps (centromedial and \nlateral, Carr et al., 1982) were pooled. For further experimental details, see Wessel \net al. (1996), Metzner and Heiligenberg (1991), Metzner (1993). \n\n2.2 SIGNAL ESTIMATION \n\nThe ability of single spike trains to carry detailed time-varying stimulus information \nwas assessed by estimating the stimulus from the spike train. The spike trains, \nx(t) = E 6(t - ti), where ti are the spike occurrence times, were convolved with a \nfilter h (Wiener-Kolmogorov filtering; Poor, 1994; Bialek et al. 1991), \n\nSe3t(t) = J dtl h(tl)X(t - t 1) \n\nchosen in order to minimize the mean square error between the true stimulus and \nthe estimated stimulus, \n\nf2 = (s(t) - Se3t(t\u00bb2}. \n\nThe optimal filter h(t) is determined in Fourier space as the ratio of the Fourier \ntransform of the cross-correlation between stimulus and spike train, R X3 ( r) = \n(x(t)s(t + r)} and the Fourier transform of the autocorrelation (power spectrum) of \nthe spike train, Rxx(r) = (x(t)x(t + r)}. The accuracy at which single spike trains \ntransmit information about the stimulus was characterized in the time domain by \nthe coding fraction, defined as 'Y = 1 -\nflu, were u is the standard deviation of \nthe stimulus. The coding fraction is normalized between 1 when the stimulus is \nperfectly estimated by the spike train \u00ab( = 0) and 0, when the estimation perfor(cid:173)\nmance of the spike train is at chance level (f = u). Thus, the coding fraction can be \n\n\fExtraction a/Temporal Features in Weakly Electric Fish \n\n65 \n\ncompared across experiments. For further details and references on this stimulus \nestimation method in the context of neuronal sensory processing, see Gabbiani and \nKoch (1996) and Gabbiani (1996). \n\n2.3 FEATURE EXTRACTION \n\n2.3.1 General procedure \n\nThe ability of single spikes to encode the presence of a temporal feature in the stim(cid:173)\nulus waveform was assessed by adapting a Fisher linear discriminant classification \nscheme to our data (Anderson, 1984; sect. 6.5). Each random stimulus wave-form \nand spike response of pyramidal cells (resp. P-receptor afferents) were binned. The \nbin size ~ was varied between ~min = 0.5 ms, corresponding to the sampling ra(cid:173)\ntio and ~max, corresponding to the longest interval leading to a maximum of one \nspike per bin. The sampling interval yielding the best performance (see below) was \nfinally retained. Typical bin sizes were ~ = 7 ms for pyramidal cells (typical mean \nfiring rate: 30 Hz) and ~ = 1 ms for P-receptor afferents (typical firing rate: 200 \nHz). The mean stimulus preceding a spike containing bin (m1) or no-spike con(cid:173)\ntaining bin (mO) as well as the covariances eEl, 'Eo) of these distributions were \ncomputed (Anderson, 1984; sect. 3.2). Mean vectors (resp. covariance matrices) \nhad at most 100 (resp . 100 x 100) components. The optimal linear feature vector \nf predicting the occurrence or non-occurrence of a spike was found by maximizing \nthe signal-to-noise ratio (see fig. 2A and Poor, 1994; sect. IIIB) \n\nSNR(f) = [f \u00b7 ~ml - mo)]2 . \nf\u00b7 2('EO + 'El)f \n\n(1) \n\nThe vector f is solution of (m1 - mO) = ('EO + 'E1)f. This equation was solved by \ndiagonalizing 'EO + 'E 1 and retaining the first n largest eigenvalues accounting for \n99% of the variance (Jolliffe, 1986; sect . 6.1 and 8.1) . The optimal feature vector \nf thus obtained corresponded to up- or downstrokes in the stimulus amplitude \nmodulation for E- and I-type pyramidal cells respectively, as expected from their \nmean response properties to changes in the electric field amplitude (see sect. 1). \nSimilarly, optimal feature vectors for P-receptor afferents corresponded to upstrokes \nin the electric field amplitude (see sect. 1) . \n\nOnce f was determined, we projected the stimuli preceding a spike or no spike onto \nthe optimal feature vector (fig. 2A) and computed the probability of correct clas(cid:173)\nsification between the two distributions so obtained by the resubstitution method \n(Raudys and Jain, 1991). The probability of correct classification (Pee) is obtained \nby optimizing the value of the threshold used to separate the two distributions in \norder to maximize \n\n(2) \n\nwhere the probabilities of false alarm (PFA) and correct detection (PeD ) depend \non the threshold. \n\n2.3.2 Distinction between isolated spikes and burst-like spike patterns \n\nA large fraction (56% \u00b1 21%, n = 30) of spikes generated by pyramidal cells in \nresponse to random electric field amplitude modulations occurred in bursts (mean \nburst length: 18 \u00b1 9 ms, mean number of spikes per burst : 2.9 \u00b1 1.3, n = 30, \nfig . 1B). In order to verify whether spikes occurring in bursts corresponded to \na more reliable encoding of the feature vector, we separated the distribution of \nstimuli occurring before a spike in two distributions, conditioned on whether the \n\n\f66 \n\nA \n\nB \n\nF. Gabbiani, W. Metzner, R. Wessel and C. Koch \n\n\u00b71000 \n\n0 \n\n\u00b72000 \nprojection onto the feature vector \n\n1000 2000 \n\nFigure 2: A. 2-dimensional example of two random distributions (circles and \nsquares) as well as the optimal discrimination direction determined by maximiz(cid:173)\ning the signal-to-noise ratio of eq. 1. The I-dimensional projection of the two \ndistributions onto the optimal direction is also shown (compare with B). B. Exam(cid:173)\nple of the distribution of stimuli projected onto the optimal feature vector (same cell \nas in fig. 1B). Stimuli preceding a bin containing no spike (null), an isolated spike \n(isolated) and a spike belonging to a burst (burst). Horizontal scale is arbitrary \n(see eq. 1). \n\nspike belonged to a burst or not. The stimuli were then projected onto the feature \nvector (fig. 2B), as described in 2.3.1, and the probability of correct classification \nbetween the distribution of stimuli occurring before no spike and isolated spike bins \nwas compared to the probability of correct classification between the distribution \nof stimuli occurring before no spike and burst spike bins (see sect. 3). \n\n3 RESULTS \n\nThe results are summarized in fig. 3. Data were analyzed from 30 pyramidal cells \n(E- and I-type) and 20 P-receptor afferents for a range of stimulus parameters \n(Ie = 2 - 40 Hz, (J' = 0.1 - 0.4, Ao was varied in order to obtain \u00b120 dB changes \naround the physiological value of the mean electric field amplitude which is of the \norder of 1 m V / cm). Fig. 3A reports the best probability of correct classification \n(eq. 2) obtained for each pyramidal cell (white squares) / P-receptor afferent (black \ndots) as a function of the coding fraction observed in the same experiment (note \nthat for pyramidal cells only burst spikes are shown, see sect. 2.3.2 and fig. 3B). \nThe horizontal axis shows that while the coding fraction of P-receptors afferents \ncan be very high (up to 75% of the detailed stimulus time-course is encoded in a \nsingle spike train), pyramidal cells only poorly transmit information on the detailed \ntime-course of the stimulus (less than 20% in most cases). In contrast, the vertical \naxis shows that pyramidal cells outperform P-receptor afferent in the classification \ntask: it is possible to classify with up to 85% accuracy whether a given stimulus \nwill cause a short burst of spikes or not by comparing it to a single feature vector \nf. This indicates that the presence of an up- or downstroke (the feature vector) \nis reliably encoded by pyramidal cells. Fig. 3B shows for each experiment on \nthe ordinate the discrimination performance (eq. 2) for stimuli preceding isolated \nspikes against stimuli preceding no spike. The abscissa plots the discrimination \nperformance (eq. 2) for stimuli preceding spikes occurring in bursts (white squares, \nfig. 3A) or stimuli preceding all spikes (black squares) against stimuli preceding \n\n\fExtraction o/Temporal Features in Weakly Electric Fish \n\n67 \n\n1.0 \n\nA \nc \n0 \n;:; \ntJ \n!E \n= 0.9 \n- 0.8 \nl1li \nU \nU \n- 0 \n~ \n0 \nu \n0 \n~ \n:a \n.! \n2 \n0. \n\n0.5 \n\n0.0 \n\n0.6 Do \n\no \n\nD \n\n0.7 D.p, \n\n'\\, \n\nB \nc \n.2 \n'tii \nu \n!E \n\n1.0 \n\n0.9 \n\nCD \n\nD \n\n0.8 \n\nD D \n\nDD \n\nD burst spikes \n\n.... \nill\u00b7 \n\n. all spikes \n. . . \u2022 \n.. \n.. \n.D \nD J' , \n. . . \n. .. \n0.6 ~ ~~ . \" \n\n= \nl1li \nU \n~ \\ \n. \n. u \n. . \n.. ' \n0 \n. \n. \n'0 \n~ \n:a \n1.0 \nl1li \n.a \n2 probability of correct classification \n0. \n\nlill\" \n. .. \n\n0.6 \n\n0.8 \n\n0.6 \n\n0.7 \n\n0.7 \n\n0.5 \n\n0.5 \n\n0.9 \n\nD \n\nD \n\n.\n\n'~ \n\no \n\no \n\n0.8 \n\nD \n\n. \n\npyramidal cells \nPreceptors \n\nD '\" \n\nII DtiJ D \n\nD \n\no D \n\n0.2 \n\n0.4 \n\ncoding fraction \n\nFigure 3: A. Coding fraction and probability of correct classification for pyramidal \ncells (white squares, burst spikes only) and P-receptor afferents (black circles). B. \nProbability of correct classification against stimuli preceding no spikes for stimuli \npreceding burst spikes or all spikes vs. stimuli preceding isolated spikes. Dashed \nline: identical performance. \n\nno spike. The distribution of stimuli occurring before burst spikes (all spikes) is \nmore easily distinguished from the distribution of stimuli occurring before no spike \nthan the distribution of stimuli preceding isolated spikes. This clearly indicates that \nspikes occurring in bursts carry more reliable information than isolated spikes. \n\n4 DISCUSSION \n\nWe have analyzed the response of P-receptor afferents and pyramidal cells to random \nelectric field amplitude modulations using methods of statistical signal processing. \nThe previously studied mean responses of P-receptor afferents and pyramidal cells \nto step amplitude changes or sinusoidal modulations of an externally applied elec(cid:173)\ntric field left several alternatives open for the encoding and processing of stimulus \ninformation in single spike trains. We find that, while P-receptor afferents encode \nreliably the detailed time-course of the stimulus, pyramidal cells do not. In con(cid:173)\ntrast, pyramidal cells perform better than P-receptor afferents in discriminating the \noccurrence of up- and downstrokes in the amplitude modulation. The presence of \nthese features is signaled most reliably to higher order stations in the electrosen(cid:173)\nsory system by short bursts of spikes emitted by pyramidal cells in response to the \nstimulus. This code can be expected to be robust against possible subsequent noise \nsources, such as synaptic unreliability. The temporal pattern recognition task solved \nat the level of the ELL is particularly appropriate for computations which have to \nrely on the temporal resolution of up- and downstrokes, such as those underlying \nthe jamming avoidance response. \n\n\f68 \n\nAcknowledgments \n\nF Gabbiani, W. Metzner, R. Wessel and C. Koch \n\nWe thank Jenifer Juranek for computer assistance. Support: UCR and NSF grants, \nCenter of Neuromorphic Systems Engineering as a part of the NSF ERC Program, \nand California Trade and Commerce Agency, Office of Strategic Technology. \n\nReferences \n\nAnderson, T.W. (1984) An introduction to Multivariate Statistical Analysis. Wiley, \nNew York. \nBastian, J. (1981) Electrolocation 2. The effects of moving objects and other elec(cid:173)\ntrical stimuli on the activities of two categories of posterior lateral line lobe cells in \napteronotus albifrons. J. Compo Physiol. A, 144: 481-494. \nBialek, W., de Ruyter van Steveninck, R.R. & Warland, D. (1991) Reading a neural \ncode. Science, 252: 1854-1857. \nBullock, T .H. & Heiligengerg, W. (1986) Electroreception. Wiley, New York. \n\nCarr, C.C., Maler , L. & Sas, E. (1982). Peripheral Organization and Central Pro(cid:173)\njections of the Electrosensory Nerves in Gymnotiform Fish. J. Compo Neurol., \n211:139-153 . \nGabbiani, F. & Koch , C. (1996) Coding of Time-Varying Signals in Spike Trains of \nIntegrate-and-Fire Neurons with Random Threshold. Neur. Comput., 8: 44-66. \n\nGabbiani, F. (1996) Coding of time-varying signals in spike trains of linear and \nhalf-wave rectifying neurons. Network: Compo Neur. Syst., 7:61-85 . \nHeiligenberg, W . 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Springer \nVerlag, New York. \nRaudys, S.J. & Jain, A.K. (1991) Small sample size effects in statistical pattern \nrecognition: Recommendations for practitioners. IEEE Trans. Patt. Anal. Mach. \nIntell., 13: 252-264. \nWessel, R., Koch, C. & Gabbiani F. (1996) Coding of Time-Varying Electric Field \nAmplitude Modulations in a Wave-Type Electric Fish J. Neurophysiol. 75:2280-\n2293 . \n\nZakon, H. (1986) The electroreceptive periphery. In: Bullock, T .H. & Heiligenberg, \nW. (eds) , Electroreception, pp. 103-156. Wiley, New York. \n\n\f", "award": [], "sourceid": 1222, "authors": [{"given_name": "Fabrizio", "family_name": "Gabbiani", "institution": null}, {"given_name": "Walter", "family_name": "Metzner", "institution": null}, {"given_name": "Ralf", "family_name": "Wessel", "institution": null}, {"given_name": "Christof", "family_name": "Koch", "institution": null}]}