Extraction of temporal features in the 
electrosensory system of weakly electric 
fish 
Fabrizio Gabbiani* 
Division of Biology 
139-74 Caltech 
Pasadena, CA 91125 
Walter Metzner 
Department of Biology 
Univ. of Cal. Riverside 
Riverside, CA 92521-0427 
Ralf Wessel 
Department of Biology 
Univ. of Cal. San Diego 
La Jolla, CA 92093-0357 
Christof Koch 
Division of Biology 
139-74 Caltech 
Pasadena, CA 91125 
Abstract 
The encoding of random time-varying stimuli in single spike trains 
of electrosensory neurons in the weakly electric fish Eigenmannia 
was investigated using methods of statistical signal processing. At 
the first stage of the electrosensory system, spike trains were found 
to encode faithfully the detailed time-course of random stimuli, 
while at the second stage neurons responded specifically to features 
in the temporal waveform of the stimulus. Therefore stimulus infor- 
mation is processed at the second stage of the electrosensory system 
by extracting temporal features from the faithfully preserved image 
of the environment sampled at the first stage. 
1 INTRODUCTION 
The weakly electric fish, Eigenmannia, generates a quasi sinusoidal, dipole-like elec- 
tric field at individually fixed frequencies (250 - 600 Hz) by discharging an electric 
organ located in its tail (see Bullock and Heilgenberg, 1986 for reviews). The fish 
sense local changes in the electric field by means of two types of tuberous electrore- 
ceptors located on the body surface. T-type electroreceptors fire phase-locked to 
the zero-crossing of the electric field once per cycle of the electric organ discharge 
*emMl: gabbianiklab.cMtech.edu, wmetznermail.ucr.edu, rwesseljeeves.ucsd.edu, 
koch@klab.cMtech.edu. 
Extraction of Temporal Features in Weakly Electric Fish 63 
(EOD) and are thus able to encode phase changes. P-type electroreceptors fire in 
a more loosely phase-locked manner with a probability smaller than 1 per EOD. 
Their probability of firing increases with the mean amplitude of the field thereby 
allowing them to encode amplitude changes (Zakon, 1986). 
This information is used by the fish in order to locate objects (electrolocation, 
Bastian 1986) as well as for communication with conspecifics (Hopkins, 1988). One 
behavior which has been most thoroughly studied (Heiligenberg, 1991), the jamming 
avoidance response, occurs when two fish with similar EOD frequency (less than 
15 Hz difference) approach close enough to sense each other's field. In order to 
minimize beat patterns resulting from their summed electric fields, the fish with 
the higher (resp. lower) rOD raises further (resp. lowers) its own rOD frequency. 
The resulting frequency difference increase reduces the distorsions in the interfering 
EODs. The fish is known to correlate phase differences computed across body 
regions with local amplitude increases or decreases in order to determine whether 
it should raise or lower its own EOD. 
At the level of the first central nervous nucleus of the electrosensory pathway, the 
electrosensory lateral line lobe of the hindbrain (ELL), phase and amplitude in- 
formation are processed nearly independently of each other (Maler et al., 1981). 
Amplitude information is encoded in the spike trains of ELL pyramidal cells that 
receive input from P-receptor afferents and transmit their information to higher 
order levels of the electrosensory system. Two functional classes of pyramidal cells 
are distinguished: E-type pyramidal cells respond by raising their firing frequency 
to increases in the amplitude of an externally applied electric field while I-type pyra- 
midal cells increase their firing frequency when the amplitude decreases (Bastian, 
1981). 
The aim of this study was to characterize the temporal information processing 
performed by ELL pyramidal cells on random electric field amplitude modulations 
and to relate it to the information carried by P-receptor afferents. To this end 
we recorded the responses of P-receptor afferents and pyramidal cells to random 
electric field amplitude modulations and analyzed them using two different methods: 
a signal estimation method characterizing to what extent the neuronal response 
encodes the detailed.time-course of the stimulus and a signal-detection method 
developed to identify features encoded in spike trains. These two methods as well 
as the electrophysiology are explained in the next section followed by the result 
section and a short discussion. 
2 METHODS 
2.1 ELECTROPHYSIOLOGY 
Adult specimens of Eigenmannia were immobilized by intramuscular injection of 
a curare-like drug (Flaxedil). This also strongly attenuated the fish's EODs. The 
fish were held in place by a foam-lined clamp in an experimental tank and an EOD 
substitute electric field was established by two electrodes placed in the mouth and 
near the tail of the fish. The carrier frequency of the electric field, feartier, was 
chosen equal to the EOD frequency prior to curarization and the voltage generating 
the stimulus was modulated according to 
V(t) = Ao(1 + S(t))COS(2rfcarrir), 
where A0 is the mean amplitude and s(t) is a random, zero-mean modulation having 
a fiat (white) spectrum up to a variable cut-off frequency fc and a variable standard 
deviation a. The modulation s(t) was generated by playing a blank tape on a tape 
64 E Gabbiani, W. Metzner, R. Wessel and C. Koch 
A 
B 
Figure 1: A. Schematic drawing of the experimental set-up. Tape recorder (T), 
variable cutoff frequency Bessel filter (BF) and function generator (FG). B. Sample 
amplitude modulation s(t) and intracellular recording from a pyramidal cell (I-type, 
fc = 12 Hz). Spikes occurring in bursts are marked with an asterisk (see sect. 2.3.2). 
The intracellular voltage trace reveals a high frequency noise caused by the EOD 
substitute signal and a high electrode resistance. 
recorder, passing the signal through a variable cut-off frequency low-pass filter before 
multiplying it by the frequency carrier signal in a function generator (fig. 1A). 
Extracellular recordings from P-receptor afferents were made by exposing the an- 
terior lateral line nerve. Intracellular recordings from ELL pyramidal cells were 
obtained by positioning electrodes in the central region of the pyramidal cell layer. 
Intracellular recording electrodes were filled with neurotracer (neurobiotin) to be 
used for subsequent intracellular labeling if the recordings were stable long enough. 
This allowed to verify the cell type and its location within the ELL. In case no intra- 
cellular labeling could be made the recording site was verified by setting electrolytic 
lesions at the conclusion of the experiment. In the subsequent data analysis, data 
from E- and I-type pyramidal cells and from two different maps (centromedial and 
lateral, Carr et al., 1982) were pooled. For further experimental details, see Wessel 
et al. (1996), Metzner and Heiligenberg (1991), Metzner (1993). 
2.2 SIGNAL ESTIMATION 
The ability of single spike trains to carry detailed time-varying stimulus information 
was assessed by estimating the stimulus from the spike train. The spike trains, 
x(t) =  6( - ti), where ti are the spike ocurrence times, were convolved with a 
filter h (Wiener-Kolmogorov filtering; Poor, 1994; Bialek et al. 1991), 
chosen in order to minimize the mean square error between the true stimulus and 
the estimated stimulus, 
((40- 
The optimal filter h(t) is determined in Fourier space as the ratio of the Fourier 
transform of the cross-correlation between stimulus and spike train, R,(r) = 
(x(t)s(t + r)) and the Fourier transform of the autocorrelation (power spectrum) of 
the spike train, R(r) = ((t)x(t + r)). The accuracy at which single spike trains 
transmit information about the stimulus was characterized in the time domain by 
the coding fraction, defined as 7 = 1 - e/r, were r is the standard deviation of 
the stimulus. The coding fraction is normalized between 1 when the stimulus is 
perfectly estimated by the spike train ( = 0) and 0, when the estimation perfor- 
mance of the spike train is at chance level ( = r). Thus, the coding fraction can be 
Extraction of Temporal Features in Weakly Electric Fish 65 
compared across experiments. For further details and references on this stimulus 
estimation method in the context of neuronal sensory processing, see Gabbiani and 
Koch (1996) and Gabbiani (1996). 
2.3 FEATURE EXTRACTION 
2.3.1 General procedure 
The ability of single spikes to encode the presence of a temporal feature in the stim- 
ulus waveform was assessed by adapting a Fisher linear discriminant classification 
scheme to our data (Anderson, 1984; sect. 6.5). Each random stimulus wave-form 
and spike response of pyramidal cells (resp. P-receptor afferents) were binned. The 
bin size A was varied between Amin = 0.5 ms, corresponding to the sampling ra- 
tio and Amax, corresponding to the longest interval leading to a maximum of one 
spike per bin. The sampling interval yielding the best performance (see below) was 
finally retained. Typical bin sizes were A = 7 ms for pyramidal cells (typical mean 
firing rate: 30 Hz) and A -- 1 ms for P-receptor afferents (typical firing rate: 200 
Hz). The mean stimulus preceding a spike containing bin (ml) or no-spike con- 
taining bin (m0) as well as the covariances (1, 0) of these distributions were 
computed (Anderson, 1984; sect. 3.2). Mean vectors (resp. covariance matrices) 
had at most 100 (resp. 100 x 100) components. The optimal linear feature vector 
f predicting the occurrence or non-occurrence of a spike was found by maximizing 
the signal-to-noise ratio (see fig. 2A and Poor, 1994; sect. IIIB) 
[f. (rn 1 - m0)] 2 
SNR(f) = : x . 
(r0 + rl)f (1) 
The vector f is solution of (m I - m0) = (Z0 + Z1) f. This equation was solved by 
diagonalizing Z0 + Z1 and retaining the first n largest eigenvalues accounting for 
99% of the variance (Jolliffe, 1986; sect. 6.1 and 8.1). The optimal feature vector 
f thus obtained corresponded to up- or downstrokes in the stimulus amplitude 
modulation for E- and I-type pyramidal cells respectively, as expected from their 
mean response properties to changes in the electric field amplitude (see sect. 1). 
Similarly, optimal feature vectors for P-receptor afferents corresponded to upstrokes 
in the electric field amplitude (see sect. 1). 
Once f was determined, we projected the stimuli preceding a spike or no spike onto 
the optimal feature vector (fig. 2A) and computed the probability of correct clas- 
sification between the two distributions so obtained by the resubstitution method 
(Raudys and Jain, 1991). The probability of correct classification (Pcc) is obtained 
by optimizing the value of the threshold used to separate the two distributions in 
order to maximize 
Pcc = (1- PFA)q- PcD, (2) 
where the probabilities of false alarm (PFA) and correct detection (PcD) depend 
on the threshold. 
2.3.2 Distinction between isolated spikes and burst-like spike patterns 
A large fraction (56% q- 21%, n = 30) of spikes generated by pyramidal cells in 
response to random electric field amplitude modulations occurred in bursts (mean 
burst length: 18 q- 9 ms, mean number of spikes per burst: 2.9 q- 1.3, n = 30, 
fig. lB). In order to verify whether spikes occurring in bursts corresponded to 
a more reliable encoding of the feature vector, we separated the distribution of 
stimuli occurring before a spike in two distributions, conditioned on whether the 
66 F. Gabbiani, W. Metzner, R. Wessel and C. Koch 
A B 
0'021 
o ' / burt 
projtlon onto the feature vtor 
Figure 2: A. 2-dimensional example of two random distributions (circles and 
squares) as well as the optimal discrimination direction determined by maximiz- 
ing the signal-to-noise ratio of eq. 1. The 1-dimensional projection of the two 
distributions onto the optimal direction is also shown (compare with B). B. Exam- 
ple of the distribution of stimuli projected onto the optimal feature vector (same cell 
as in fig. lB). Stimuli preceding a bin containing no spike (null), an isolated spike 
(isolated) and a spike belonging to a burst (burst). Horizontal scale is arbitrary 
(see eq. 1). 
spike belonged to a burst or not. The stimuli were then projected onto the feature 
vector (fig. 2B), as described in 2.3.1, and the probability of correct classification 
between the distribution of stimuli occurring before no spike and isolated spike bins 
was compared to the probability of correct classification between the distribution 
of stimuli occurring before no spike and burst spike bins (see sect. 3). 
3 RESULTS 
The results are summarized in fig. 3. Data were analyzed from 30 pyramidal cells 
(E- and I-type) and 20 P-receptor afferents for a range of stimulus parameters 
(fc = 2 - 40 Hz, a = 0.1 - 0.4, A0 was varied in order to obtain :k20 dB changes 
around the physiological value of the mean electric field amplitude which is of the 
order of I mV/cm). Fig. 3A reports the best probability of correct classification 
(eq. 2) obtained for each pyramidal cell (white squares) / P-receptor afferent (black 
dots) as a function of the coding fraction observed in the same experiment (note 
that for pyramidal cells only burst spikes are shown, see sect. 2.3.2 and fig. 3B). 
The horizontal axis shows that while the coding fraction of P-receptors afferents 
can be very high (up to 75% of the detailed stimulus time-course is encoded in a 
single spike train), pyramidal cells only poorly transmit information on the detailed 
time-course of the stimulus (less than 20% in most cases). In contrast, the vertical 
axis shows that pyramidal cells outperform P-receptor afferent in the classification 
task: it is possible to classify with up to 85% accuracy whether a given stimulus 
will cause a short burst of spikes or not by comparing it to a single feature vector 
f. This indicates that the presence of an up- or downstroke (the feature vector) 
is reliably encoded by pyramidal cells. Fig. 3B shows for each experiment on 
the ordinate the discrimination performance (eq. 2) for stimuli preceding isolated 
spikes against stimuli preceding no spike. The abscissa plots the discrimination 
performance (eq. 2) for stimuli preceding spikes occurring in bursts (white squares, 
fig. 3A) or stimuli preceding all spikes (black squares) against stimuli preceding 
Extraction of Temporal Features in Weakly Electric Fish 67 
o pyramidal cells ._ 1.0- 
'- 1.0-  Preceptors 
0.9- 
0.9' o= 
0.8- 
0.8' o 
o  
0.7' 
t.} 
0,6' 
 ' ' 0.6- 
   
 0.5 
burst spikes .. 
all spikes o == .... 
0.5 .... 0'.6 0'.7 018 0'.9 ' 
0.0 0'.2 0'.4 0'.6 0'.8 as 0.5 1.0 
. probability of correct classification 
coding fraction 
Figure 3: A. Coding fraction and probability of correct classification for pyramidal 
cells (white squares, burst spikes only) and P-receptor afferents (black circles). B. 
Probability of correct classification against stimuli preceding no spikes for stimuli 
preceding burst spikes or all spikes vs. stimuli preceding isolated spikes. Dashed 
line: identical performance. 
no spike. The distribution of stimuli occurring before burst spikes (all spikes) is 
more easily distinguished from the distribution of stimuli occurring before no spike 
than the distribution of stimuli preceding isolated spikes. This clearly indicates that 
spikes occurring in bursts carry more reliable information than isolated spikes. 
4 DISCUSSION 
We have analyzed the response of P-receptor afferents and pyramidal cells to random 
electric field amplitude modulations using methods of statistical signal processing. 
The previously studied mean responses of P-receptor afferents and pyramidal cells 
to step amplitude changes or sinusoidal modulations of an externally applied elec- 
tric field left several alternatives open for the encoding and processing of stimulus 
information in single spike trains. We find that, while P-receptor afferents encode 
reliably the detailed time-course of the stimulus, pyramidal cells do not. In con- 
trast, pyramidal cells perform better than P-receptor afferents in discriminating the 
occurrence of up- and downstrokes in the amplitude modulation. The presence of 
these features is signaled most reliably to higher order stations in the electrosen- 
sory system by short bursts of spikes emitted by pyramidal cells in response to the 
stimulus. This code can be expected to be robust against possible subsequent noise 
sources, such as synaptic unreliability. The temporal pattern recognition task solved 
at the level of the ELL is particularly appropriate for computations which have to 
rely on the temporal resolution of up- and downstrokes, such as those underlying 
the jamming avoidance response. 
68 E Gabbiani, W. Metzner, R. Wessel and C. Koch 
Acknowledgments 
We thank Jenifer Juranek for computer assistance. Support: UCR and NSF grants, 
Center of Neuromorphic Systems Engineering as a part of the NSF ERC Program, 
and California Trade and Commerce Agency, Office of Strategic Technology. 
References 
Anderson, T.W. (1984) An introduction to Multivariate Statistical Analysis. Wiley, 
New York. 
Bastian, J. (1981) Electrolocation 2. The effects of moving objects and other elec- 
trical stimuli on the activities of two categories of posterior lateral line lobe cells in 
apteronotus albifrons. J. Comp. Physiol. A, 144: 481-494. 
Bialek, W., de Ruyter van Steveninck, R.R. & Warland, D. (1991) Reading a neural 
code. Science, 252: 1854-1857. 
Bullock, T.H. & Heiligengerg, W. (1986) Electroreception. Wiley, New York. 
Carr, C.C., Maler, L. & Sas, E. (1982). Peripheral Organization and Central Pro- 
jections of the Electrosensory Nerves in Gymnotiform Fish. J. Comp. Neurol., 
211:139-153. 
Gabbiani, F./z Koch, C. (1996) Coding of Time-Varying Signals in Spike Trains of 
Integrate-and-Fire Neurons with Random Threshold. Neut. Cornput., 8: 44-66. 
Gabbiani, F. (1996) Coding of time-varying signals in spike trains of linear and 
half-wave rectifying neurons. Network: Comp. Neut. Syst., 7:61-85. 
Heiligenberg, W. (1991) Neural Nets in electric fish. MIT Press, Cambridge, MA. 
Hopkins, C.D. (1976) Neuroethology of electric communication. Ann. Rev. Neu- 
rosci., 11:497-535. 
Jolliffe, I.T. (1986) Principal Component Analysis. Springer-Verlag, New York. 
Maler, L., Sas, E.K.B./z Rogers, J. (1981) The cytology of the posterior lateral line 
lobe of high-frequency weakly electric fish (gymnotidae): Dendritic differentiation 
and synaptic specificity. J. Comp. Neurol., 255: 526-537. 
Metzner, W. (1993) The jamming avoidance response in Eigenmannia is controlled 
by two separate motor pathways. J. Neurosci., 13:1862-1878. 
Metzner, W. & Heiligenberg, W. (1991). The coding of signals in the electric 
communication of the gymnotiform fish Eigenmannia: From electroreceptors to 
neurons in the torus semicircularis of the midbrain. J. Comp. Physiol. A, 169: 
135-150. 
Poor, H.V. (1994) An introduction to Signal Detection and Estimation. Springer 
Verlag, New York. 
Raudys, S.J. & Jain, A.K. (1991) Small sample size effects in statistical pattern 
recognition: Recommendations for practitioners. IEEE Trans. Part. Anal. Mach. 
Intell., 13: 252-264. 
Wessel, R., Koch, C./z Gabbiani F. (1996) Coding of Time-Varying Electric Field 
Amplitude Modulations in a Wave-Type Electric Fish J. Neurophysiol. 75:2280- 
2293. 
Zakon, H. (1986) The electroreceptive periphery. In: Bullock, T.H. & Heiligenberg, 
W. (eds), Electroreception, pp. 103-156. Wiley, New York. 
