To measure baseline activity rates, we recorded extracellular spontaneous activity from the sensory receptors of five species (Figure 1). This sample included two species with broadly distributed spiking receptors, as well as Petrocephalus microphthalmus, whose receptor physiology was previously unknown. P. microphthalmus is behaviorally sensitive to EOD waveform variation, but it evolved this ability independently of other species with broadly distributed receptors (Carlson et al., 2011). We found that the receptors of P. microphthalmus indeed fire spikes (Figure 1A), just like other mormyrids with broadly distributed receptors and EOD waveform sensitivity. We also recorded spontaneous oscillations from rosette receptors of two species (Figure 1C,D). Spontaneous interspike intervals and spontaneous oscillation periods varied across species (Figure 1B,D).

Figure 1

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Oscillating receptors are organized into three rosettes on each side of the head (Figure 2A) (Harder, 1968b; Lavoue et al., 2004, 2010; Carlson et al., 2011). To study how spontaneous activity varied within a rosette, we obtained spontaneous recordings from every receptor in a single rosette in one Petrocephalus tenuicauda (Figure 2B). Spontaneous oscillation amplitude was largest in the center of the rosette and progressively decreased towards the periphery. Oscillation frequency and amplitude were not significantly correlated (Spearman R = 0.27, t₍₂₂₎ = 1.3, p = 0.21), although frequencies tended to be highest near the center of the rosette (Figure 2B).

Figure 2

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To determine whether the oscillations of receptors in different rosettes were synchronized with one another, we collected simultaneous recordings from pairs of receptors, each located in a different rosette (see Figure 2C, top). We then determined the phase of the oscillations throughout each pair-wise recording using a Hilbert transform (see Figure 2C, bottom). Next, we constructed probability distributions of the phases for each receptor in pair-wise recordings. If the phases are truly independent, then the joint probability histogram should be similar to the product of the individual probability distributions. Indeed, the joint probability histograms (e.g., Figure 2E) closely resembled the product of the individual probability distributions (e.g., Figure 2D). We also computed the joint probability histogram for surrogate data consisting of non-simultaneously recorded oscillations (e.g., Figure 2F). These histograms should match those of the simultaneous recordings if the oscillations are truly independent. Indeed, the joint probability distributions of non-simultaneous recordings closely resembled those of the simultaneous recordings (compare Figure 2F with Figure 2E).

To evaluate statistically the possibility of phase coupling between receptors in different rosettes, we determined the circular correlation coefficient (r) of the instantaneous oscillatory phases between each receptor pair (Berens, 2009). We averaged the resulting r over five 1-s recordings from each pair. Across 14 receptor pairs in one P. tenuicauda, the mean r was 0.05 + 0.05. For comparison, we generated non-simultaneously recorded surrogate data sets consisting of the first of five 1-s recordings from one receptor in the pair and the fifth recording from the other pair, and vice versa. There was no significant difference between the r of simultaneous recordings and the r (mean = 4 × 10⁻⁴ + 7 × 10⁻⁴) of non-simultaneous recordings (Wilcoxon matched-pairs test, Z₍₁₄₎ = 1.7, p = 0.084). In another P. tenuicauda, we recorded from six pairs of receptors and found similar results, with no differences in the circular correlation coefficient for phases of simultaneous (mean r = −0.06 + 0.04) and non-simultaneous (mean r = 0.001 + 0.001) recordings (Wilcoxon matched-pairs test, Z₍₆₎ = 1.8, p = 0.075). Therefore, oscillatory phase was independent across receptors in different rosettes.

To determine whether the individual receptors within rosettes oscillated at the same frequency, we recorded spontaneous activity with a differential electrode pair centered over a single rosette. The differential electrode allowed us to record local field potentials resulting from the combined oscillations of multiple receptors. If the receptors near our electrodes were oscillating independently at different frequencies, we should see beats, or amplitude modulations, in the field potentials due to constructive and destructive interference. Indeed, beats were present in these recordings (see example in Figure 2G), indicating that our electrode was in fact recording activity from multiple sources with different frequencies. Accordingly, at least three distinct peaks were present in the power spectrum of this recording (black trace in Figure 2H). Recording activity at a position 2 mm posterior to this location led to the loss of two of these peaks and the addition of two new peaks, suggesting that the electrode was recording activity from a distinct, but overlapping population of receptors compared to the previous location (red traces in Figure 2G,H). Qualitatively similar results were seen in differential recordings from additional rosettes. Therefore, in agreement with a previous report (Harder, 1968b), oscillatory activity of individual receptors is not correlated within or across rosettes.

To understand sensory encoding by these receptors, we recorded responses to focal stimulation with monopolar square pulses (Figure 3). We delivered both positive- and negative-polarity pulses to mimic the stimulation that receptors at different locations on the fish's body would experience during a natural global stimulus (Hopkins and Bass, 1981). As shown previously, spiking receptors responded with a single time-locked spike in response to inward current transients (Bennett, 1965), which occur at the onset of a positive-polarity pulse and at the offset of a negative-polarity pulse (Figure 3A,B). Spike probability depended on pulse duration (Figure 3C) but was high for stimulus durations within the range of total durations of conspecific EODs (horizontal bars in Figure 3C).

Figure 3

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Oscillating receptors responded to square pulses with phase resets and amplitude increases (Figure 3E,F), which occurred both in receptors with high-amplitude spontaneous oscillations as well as in receptors with little to no spontaneous oscillatory activity. The degree of amplitude enhancement relative to prestimulus amplitudes depended on pulse duration (Figure 3G). At the stimulus duration that elicited the maximum oscillation amplitude in each receptor, there was a positive correlation between spontaneous and stimulus-evoked oscillation amplitudes (Spearman R = 0.90, t₍₃₎ = 3.6, p = 0.037).

Spiking receptors encode square pulse duration into differences in spike times between receptors (Hopkins and Bass, 1981; Lyons-Warren et al., 2012). For instance, the differences in spike times elicited by each polarity of a square pulse of durations 0.10 and 0.20 ms were exactly 0.10 and 0.20 ms, respectively (Figure 3A,B). Across all spiking receptors, this spike-timing difference perfectly matched pulse duration for pulses longer than ∼0.1 ms (Figure 3D). Importantly, spike-timing differences accurately represented pulse duration over the behaviorally relevant ranges for total EOD duration in each species (horizontal bars in Figure 3D). Such precise coding of stimulus-timing cues mediates the demonstrated ability of species with spiking receptors to detect EOD waveform variation (Hopkins and Bass, 1981; Arnegard et al., 2006; Machnik and Kramer, 2008; Feulner et al., 2009; Carlson et al., 2011).

In oscillatory receptors, positive- and negative-polarity square pulses elicited phase resets that differed by ∼180° (Figure 3E,F). This phase difference was constant regardless of pulse duration (Figure 3L). To determine whether oscillating receptors could encode pulse duration in a manner similar to the spike-timing differences of spiking receptors, we measured the difference in times of oscillatory peaks evoked by opposite-polarity pulses (Figure 3E,F). For pulse durations exceeding receptors' intrinsic oscillation periods (∼0.5 ms), the phase could be reset in response to each stimulus edge. In these instances, we measured the oscillation-timing difference elicited by the onset of a positive-polarity pulse and the offset of a negative-polarity pulse. However, pulses of shorter durations did not elicit phase resets to each stimulus edge, since these durations are shorter than receptors' intrinsic oscillation periods. For these stimulus durations, we measured the oscillation-timing differences after stimulus offset (e.g., Figure 3E,F). Oscillation-timing differences did not accurately encode pulse durations shorter than ∼1 ms (Figure 3H), reflecting phase resets to the leading edge of the pulse that differ by ∼180° regardless of pulse duration (Figure 3E,F,L). This means that oscillatory responses could not encode pulse durations found in conspecific EODs (black bar in Figure 3H). Therefore, species with oscillating receptors cannot behaviorally detect waveform variation at least in part because the precise timing cues are not encoded at the periphery. However, oscillating receptors would be able to encode the location of the stimulus based on which receptors reset to a peak first, owing to differences in stimulus polarity.

To confirm that natural EOD waveforms also elicit oscillatory phase differences of ∼180°, we presented conspecific EODs at varying intensities to oscillating receptors (Figure 3I,J). We measured the vector strength and phase differences for responses to opposite-polarity stimuli. The vector strength is a measure of phase-locking that ranges from 0 (phase is random across repetitions) to 1 (identical phase across repetitions). At each intensity, we compared the phases elicited by each polarity using the parametric second-order Hotelling test for paired circular data (Zar, 1999). At intensities for which the phase resets evoked by opposite polarity EODs were significantly different, phase differences were always ∼180° (filled circles in Figure 3K).

Spiking receptors have been reported to be most sensitive to the frequencies occurring in conspecific EOD waveforms (Hopkins, 1981; Bass and Hopkins, 1984; Lyons-Warren et al., 2012). To confirm this finding in our test species, we compared the frequency sensitivity of individual spiking receptors to the power spectra of conspecific EODs (Figure 4A,B,D). We collected threshold frequency tuning curves as described previously (Lyons-Warren et al., 2012). We defined a receptor's best frequency as the frequency with the lowest threshold. In general, spiking receptors had best frequencies that were close to the frequencies with the highest power in conspecific EODs (compare Figure 4D with Figure 4B). On average, the best frequencies of spiking receptors were within one octave of the peak power frequencies of conspecific EODs (filled symbols in Figure 4F).

Figure 4

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To determine the frequency sensitivity of oscillating receptors, we also collected frequency tuning curves from oscillating receptors. Due to the oscillatory nature of both stimulus artifact and response, we could not use the same constant-frequency stimuli that we used to characterize frequency tuning in spiking receptors. Instead, we presented single-cycle bipolar sine waves at three intensities and measured the vector strength of phase resets at stimulus offset. We defined an oscillating receptor's best frequency as the frequency that elicited the largest vector strength.

Oscillating receptors were most sensitive to frequencies well below the peak power frequency in conspecific EODs (compare Figure 4E with black trace in Figure 4C). On average, the best frequencies of oscillating receptors were more than two octaves below the peak power frequencies of conspecific EODs (open symbols in Figure 4F).

At the stimulus intensity where tuning was sharpest (10 nA), the best frequencies (0.8–2.5 kHz) of oscillating receptors roughly corresponded to their intrinsic oscillation frequencies (1.5–2.0 kHz), suggesting that their frequency tuning resulted from resonance with their spontaneous oscillations. To test this hypothesis, we also delivered single-cycle bipolar sine waves of durations equal to multiples of each receptor's intrinsic oscillation period. Oscillatory phase-locking was strongest for stimulus durations matching each receptor's spontaneous oscillation period (Figure 4G).

Electric communication signals consist of the EOD produced at variable IPIs. Whereas the stereotyped EOD waveform can contain identifying information, such as species and sex, the IPIs convey behavioral state (see Carlson, 2002 for review). To investigate IPI coding in the three species with spiking receptors included in this study, we presented receptors with a pair of 0.2-ms duration monopolar square pulses at a range of IPIs (Figure 5A,B).

Figure 5

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The probability that a receptor fired a spike in response to both pulses in the pair decreased at the shortest intervals tested (Figure 5B,C). However, receptors of all species reliably fired spikes at the reported minimum IPIs produced by individual fish (∼8 ms) (Hopkins, 1986; Carlson, 2002).

In agreement with previous studies (Bell and Grant, 1989; Baker et al., 2013), spiking receptors encoded IPIs into interspike intervals within receptors, with the interspike intervals exactly matching the IPI (Figure 5A,D). IPIs shorter than 1 ms in Pollimyrus adspersus and P. microphthalmus failed to evoke spikes in response to the second pulse due to receptors' refractory periods (Figure 5B,C), which is why data points below these values are missing from Figure 5D. Spiking receptors can therefore faithfully encode the IPIs generated by individual signaling fish into interspike intervals within receptors.

To understand IPI coding by oscillatory receptors, we analyzed the amplitude and phase of oscillations as a function of the interval between pulse pairs (e.g., Figure 5E,F). At the shortest intervals tested, the stimulus artifact of the second pulse obscured the oscillatory response to the first pulse (Figure 5F). Thus, to investigate how oscillating receptors encode IPIs, we measured interoscillation intervals as the time between the first oscillatory peak following a single-pulse stimulus and the first oscillatory peak following the second pulse in the paired stimulus (Figure 5E,F). This method was equivalent to measuring the time interval between oscillatory peaks evoked by each pulse in the pair, but it allowed us to measure the interoscillation intervals at the shortest IPIs where the oscillatory response was obscured by stimulus artifact. Interoscillation intervals accurately represented the IPI for intervals of ∼1 ms and longer (Figure 5E,G). Importantly, interoscillation intervals accurately encoded IPIs over the range produced by individual fish (>8 ms) (Hopkins, 1986; Carlson, 2002).

Although interoscillation intervals accurately represent IPIs longer than ∼1 ms, how would the system disambiguate these stimulus-evoked oscillatory peaks from ongoing oscillations? Phase resets in oscillatory receptors serve to transiently synchronize the population in response to a stimulus (Figure 6). Because oscillation frequency varies across receptors, responses rapidly desynchronize (Figure 6). For instance, in response to a single square pulse, across-receptor synchrony is greatest for the first poststimulus oscillatory peak (Figure 6A). In response to a pair of pulses, across-receptor synchrony is high immediately following each pulse and rapidly decreases (Figure 6B). To further illustrate this, we recorded responses to a single conspecific EOD of normal and reversed polarities from all 36 receptors in a single rosette of one P. tenuicauda (same receptors illustrated in Figure 2B). Responses from four of these receptors are shown in Figure 6C. Notice that again, across-receptor synchrony is greatest for the first poststimulus oscillation, but then rapidly declines. Summing responses across all 36 receptors resulted in a single, distinct peak immediately following the stimulus (Figure 6D), due to a transient synchronization across receptors followed by increasing asynchrony of receptors oscillating at different frequencies. In this way, the electrosensory system could use synchrony across the population of receptors to distinguish between stimulus-evoked and spontaneous oscillation cycles.

Figure 6

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Oscillating receptors also encoded IPI into amplitude changes (Figure 7A,B). At the highest intensity tested, oscillation amplitudes were attenuated relative to single-pulse responses for IPIs below 1 ms (black curve in Figure 7C). As stimulus intensity decreased, however, oscillation amplitudes became selectively enhanced in response to 0.5-ms IPIs (Figure 7C). Phase-locking, as measured by the vector strength of oscillatory responses to the second pulse in the pair, also depended on IPI and stimulus intensity (Figure 7E). As the intensity decreased, responses became more sharply selective for IPIs around 0.5 ms, which is near the intrinsic oscillation periods (0.47–0.99 ms) of receptors in this species. This is suggestive of resonance in which stimulating an oscillating receptor with a pair of pulses separated by the receptor's intrinsic oscillation period results in stronger responses.

Figure 7

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To test this hypothesis, we presented receptors with IPIs equal to multiples of their intrinsic oscillation periods. As stimulus intensity decreased, oscillatory responses became more selective for IPIs equal to the intrinsic oscillation period (Figure 7D). At the lowest intensity tested, the phase-locking was also greatest for IPIs matching receptors' intrinsic oscillation periods (light gray curve in Figure 7F).

These results reveal that oscillating receptors produce the largest responses for IPIs matching their intrinsic oscillation periods. These periods, however, are at least one order of magnitude shorter than the IPIs that single fish produce. Therefore, signals arriving at submillisecond IPIs will be easier to detect, even though these IPIs are too short for each individual pulse within the train to be encoded with a phase reset. Why would some species of mormyrids have receptors that are maximally sensitive to signals too short to be produced by individual fish?

Even though the minimum IPI a single fish produces is approximately 8 ms, a large group of signaling fish may collectively produce much shorter IPIs. Could the oscillations in rosette receptors be tuned to these shorter IPIs? To test this hypothesis, we first recorded 20 min of electric signaling from individual fish of a species with spiking receptors (P. microphthalmus) (e.g., Figure 8A) and from individual fish of a congeneric species with oscillating receptors (P. tenuicauda) (e.g., Figure 8D). Next, we recorded electrical activity from group tanks of each of the same two species (Figure 8B,E). Indeed, group signals contained much shorter IPIs than single-fish signals (compare Figure 8B with Figure 8A, and Figure 8E with Figure 8D; note different time scales).

Figure 8

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To determine whether spiking and oscillating receptors could encode the very short IPIs in group signals, we compared the magnitude of receptor responses with the IPIs recorded from a group of the corresponding species (Figure 8C,F). The spiking receptors of P. microphthalmus could not respond to the submillisecond intervals present in collective conspecific group signals (Figure 8C). In contrast, oscillating receptors responded most strongly to 0.5-ms IPIs, which are found only in group signals (Figure 8F). Thus, one advantage for species with high-frequency oscillating receptors may be the ability to detect very short IPIs in group communication signals that spiking receptors cannot encode due to refractoriness.

If oscillating receptors facilitate detection of communication signals produced by a group of individuals, then species with oscillating receptors should exhibit selective behavioral responses to submillisecond IPIs, and species with spiking receptors should not. To test this hypothesis, we performed behavioral playback experiments in which we presented a single fish with a train of 10 conspecific EODs at constant IPIs (Figure 9).

Figure 9

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In general, mormyrids respond to electric signals by increasing or decreasing their rate of EOD production (Moller et al., 1989; Post and von der Emde, 1999; Carlson et al., 2011; Lyons-Warren et al., 2012). Increases in EOD rate have been interpreted to be an orienting response to a novel stimulus (Post and von der Emde, 1999). Decreases in EOD rate, or social silence, have been hypothesized to allow the silent fish to attend to another fish's signals or to make the silent fish electrically ‘invisible’ to other fish (Moller et al., 1989). As previously described in another species (Post and von der Emde, 1999), the same fish often produced both an increase and a decrease in response to a stimulus (Figure 9). In general, P. tenuicauda tended to respond with a decrease followed by an increase (Figure 9A), whereas P. microphthalmus tended to respond with an increase followed by a decrease (Figure 9B). Regardless of an individual's response pattern, we measured the maximum increase and decrease in EOD rate in response to each stimulus and compared the fish's electric signaling activity evoked by IPI stimuli to that evoked by a single conspecific EOD. A species with oscillating receptors produced the strongest EOD rate increases at the shortest and longest IPIs tested (P. tenuicauda in Figure 9C). The shortest IPIs (≤5 ms) correspond to those found only in signals recorded from groups of fish.

A congeneric species with spiking receptors (P. microphthalmus in Figure 9D) responded differently to IPIs than the species with oscillating receptors (repeated-measures ANOVA, interaction between species and IPI, F_(6,12) = 3.4, p = 0.0048). The species with spiking receptors produced the greatest EOD rate increases for IPIs in the intermediate range of those tested, which roughly correspond to the minimum IPI produced by individual fish.

In general, the species with oscillating receptors tended to produce weaker EOD rate decreases in response to the IPI stimuli than to single pulses (negative y-values in Figure 8B). In contrast, the species with spiking receptors tended to produce stronger EOD rate decreases for IPI stimuli than for single EODs (positive y-values in Figure 9B). Accordingly, there was a significant effect of species in a repeated-measures ANOVA (F₍₁₎ = 18, p = 0.0012), but no interaction effect between species and IPI (F_(6,12) = 1.0, p = 0.43). The potential social implications of variation in the strength of EOD rate increases and decreases across this range of IPIs are unknown.

These results lend support to our hypothesis that the frequency tuning of oscillating receptors may mediate detection of submillisecond IPIs that are only present in the communication signals produced by a large group of individuals. These very short IPIs elicit stronger responses in oscillating receptors and greater EOD rate increases in species with oscillatory receptors. Since spiking receptors cannot encode these submillisecond IPIs, we propose that oscillations are an adapation for detecting large groups of conspecifics.

15 B. niger (standard length [SL] = 5.9–8.6 cm), 17 P. adspersus (SL = 6.2–8.6 cm), 20 P. microphthalmus (SL = 6.3–8.0 cm), 20 P. tenuicauda (SL = 5.5–9.0 cm), and 5 P. soudanensis (SL = 8.0–10.0 cm) contributed data to this study. We used fish of both sexes. All fish were acquired through the aquarium trade except for P. microphthalmus, which were obtained from Lac Zilé, Gabon. EODs and receptor frequency tuning data from B. brachyistius came from a previously published study (Lyons-Warren et al., 2012). In the laboratory, we housed fish in conspecific-only group tanks with 12 hr:12 hr light:dark cycle, water conductivity of 200–400 μS/cm, and temperature of 25–29°C. We fed the fish live black worms four times per week. Species of the genus Petrocephalus are extremely difficult to obtain. Therefore, to minimize the number of fish used in our physiological recordings, we collected just enough data to detect a robust pattern, which in some cases happened at a low sample size (e.g., n = 3 in Figures 5, 7). All procedures were in accordance with the guidelines established by the National Institutes of Health and were approved by the Institutional Animal Care and Use Committee at Washington University in St. Louis.

Extracellular recordings from single receptors were obtained using previously reported methods (Bennett, 1965; Hopkins and Bass, 1981; Lyons-Warren et al., 2012). Briefly, we anesthetized fish in 300 mg/l tricaine methanesulfonate (MS-222, Sigma–Aldrich, St. Louis, MO) and then paralyzed and electrically silenced fish with 20–80 μl of 0.1 mg/ml gallamine triethiodide (Flaxedil, Sigma–Aldrich). We then placed the fish in a 20 × 12.5 × 45 cm chamber filled with freshwater and positioned the fish on a plastic platform with lateral supports. We respirated the fish with freshwater through a pipette tip in the fish's mouth while monitoring the fish's electromotor output using a pair of electrodes placed next to the fish's tail (Carlson, 2002). Flaxedil silences the EOD, but external electrodes can record fictive EOD motor commands from spinal electromotor neurons. After the fish had completely recovered from anesthesia, as indicated by the return of fictive EODs, we began the recording session. After receptor recordings, fish were allowed to recover completely from paralysis before being returned to their home tank.

We used electrodes made from borosilicate capillary glass (o.d. = 1 mm, i.d. = 0.5 mm; A-M Systems, Everett, WA, USA). We bent the last ∼1 cm of the electrode to a 30° angle and polished the tip using the flame from a Bunsen burner. We filled the electrode with tank water and placed it in an electrode holder with a Ag-AgCl wire connected to the headstage of the amplifier. We placed the electrode next to, but not quite touching, individual receptors. The fish remained completely under water for the entire recording session. Extracellular activity was referenced to ground, amplified 10 times (Neuroprobe Model 1600, A-M Systems), digitized at a rate of 97.7 kHz (RP2.1, Tucker–Davis Technologies, Alachua, FL, USA), and saved using custom software in Matlab 7.0 (MathWorks, Natick, MA, USA). Spiking responses and some oscillating responses were also low-pass filtered (cut-off frequency = 100 kHz) during recording.

We obtained simultaneous recordings from pairs of oscillating receptors using the same glass electrodes as single-receptor recordings. Extracellular activity was referenced to ground, amplified 100 times, band-pass filtered (0.3–20 kHz) (Model 1800, A-M Systems), digitized at a rate of 97.7 kHz (RP2.1, Tucker–Davis Technologies), and saved in Matlab. We selected one spontaneously oscillating receptor in each rosette, for a total of 14 possible pairs across six rosettes. In one P. tenuicauda, we collected five 1-s simultaneous recordings of spontaneous activity in 13 pairs of rosettes. We were unable to see the left and right nackenrosettes at the same time under our microscope in this fish, so we could not obtain simultaneous recordings from this pair of rosettes. In another P. tenuicauda, we obtained simultaneous recordings from six pairs of rosettes.

To assess whether receptors within a rosette oscillate at the same frequency, we recorded local field potentials with a differential electrode consisting of a pair of Ag-AgCl wires separated by 5 mm. This method allowed us to record the collective activity of several receptors located closer to one another than separate glass electrodes would allow. Each wire had a diameter of 0.635 mm and uninsulated tip length of 2 mm. We oriented the electrode pair perpendicular to the skin, with the recording electrode next to the skin and reference electrode farther away. Electrical activity was amplified 100 times and band-pass filtered (0.3–5 kHz) (Model 1800, A-M Systems), digitized at a rate of 97.7 kHz (RP2.1, Tucker–Davis Technologies), and saved using custom software in Matlab 7.0.

All stimuli were generated in Matlab, digital-to-analog converted at a rate of 195.31 kHz (RP2.1, Tucker–Davis Technologies), and attenuated (PA5, Tucker–Davis Technologies) before delivery to the current input of the amplifier (Neuroprobe Model 1600, A-M Systems). The amplifier then delivered constant-current stimuli through the monopolar recording electrode referenced to ground (Lyons-Warren et al., 2012). We used a bridge balance to minimize the stimulus artifact.

To study how receptors encode electric pulse waveform, we recorded responses to 10 or 25 repetitions of monopolar square pulses of durations ranging from 0.01 to 5 ms. We used both positive and negative polarities at an intensity within the behaviorally relevant range that reliably elicited responses from each receptor (10–18 nA in P. adspersus, 18 nA in B. niger, 32 nA in P. microphthalmus, and 45–100 nA in P. tenuicauda).

We also delivered previously recorded conspecific EOD waveforms. For each receptor, we randomly selected an EOD stimulus from a library of 10 conspecific EOD waveforms. We presented 10 repetitions of both normal- (head-positive) and reversed-polarity waveforms at intensities ranging from 6 to 312 nA.

To measure frequency tuning in spiking receptors, we presented 15 repetitions of 90-ms duration sinusoidal stimuli of frequencies ranging from 0.1 to 50 kHz with 5 ms cosine-squared on- and off-ramps. Because we could not separate a continuously oscillating response from a continuously oscillating stimulus artifact, we had to use different stimuli to measure frequency tuning in oscillating receptors. We presented 10 repetitions of single-cycle bipolar sine wave stimuli of frequencies ranging from 0.2 to 84 kHz to measure frequency tuning of oscillating receptors. We also delivered single-cycle bipolar sine wave stimuli at durations equal to multiples (¼, ½, 1, 2, 4) of each receptor's spontaneous oscillation period. We used both positive (peak leading trough) and negative (trough leading peak) polarities at three stimulus intensities (10, 32, and 100 nA) in P. tenuicauda. In P. soudanensis, we used positive- and negative-polarity stimuli at 32 nA.

To study how spiking and oscillating receptors encode IPIs in communication signals, we presented 10 repetitions of a pair of monopolar square pulses, with each pulse 0.2 ms in duration. We used IPIs ranging from 0.3 to 13 ms. For oscillatory receptors, we also used IPIs equal to multiples (¼, ½, 1, 2, 4, 8) of each oscillating receptor's intrinsic oscillation period. We used both positive and negative polarities at an intensity that reliably elicited responses in each receptor (6–10 nA in P. adspersus, 7–10 nA in B. niger, 18 nA in P. microphthalmus, and 10–100 nA in P. tenuicauda).

To quantify the responses of spiking receptors, we detected spikes by finding the peak voltage that crossed a manually set threshold specific to each receptor. We measured interspike intervals as the difference in time between consecutive spikes. To measure the responses of oscillating receptors, we first median filtered the recordings using a filter width of 0.1 ms. Next, we detected the first seven oscillatory peaks after stimulus offset on each stimulus sweep, which allowed us to measure the first six poststimulus oscillation periods. Imperfections in artifact balancing had no impact on the detection and measurement of spiking responses. However, sometimes it was unclear whether the first poststimulus oscillatory peak was contaminated by artifact. To assess whether the stimulus artifact affected the first poststimulus oscillation peak, we compared the first poststimulus period to the average of the following five poststimulus periods. If the first period was less than 85% or more than 115% of the average of the next five periods, we concluded that the artifact interfered with the first poststimulus peak and instead used the second poststimulus peak for all measurements.

The time between the first and second poststimulus peaks represented the poststimulus oscillation period. We measured the oscillation amplitude by first averaging the voltage values of the first two poststimulus oscillatory peaks, and then subtracting the voltage value at the intervening oscillatory trough. Next, we calculated the angle (φ, in radians) of the oscillatory phase reset as

where lat is the latency of the first poststimulus peak (time of peak minus time of stimulus offset) and p is the first poststimulus period. We then used these values across repetitions to calculate the vector strength (r), a measure of phase-locking, according to

where n is the number of stimulus repetitions. The vector strength is a normalized measure of phase-locking that equals 1 when the constituent angles are perfectly in phase with one another across stimulus repetitions, and 0 when the constituent angles are completely random across stimulus repetitions.

We recorded spontaneous activity of each receptor five times for 1 s each. For a given spiking receptor, we measured the interspike intervals on each repetition and then averaged across recordings. For oscillating receptors, we averaged the fast Fourier transform (FFT) of the oscillatory activity across five repetitions, and then used the peak of the averaged FFT as the receptor's spontaneous oscillation frequency. We used the inverse of the spontaneous oscillation frequency as the spontaneous oscillation period. We measured the spontaneous oscillation amplitude of each receptor by subtracting the voltage at each oscillatory trough from the voltage of the preceding oscillatory peak, and then averaging these amplitude values across the spontaneous recordings. If spontaneous activity was recorded more than once from the same receptor, we averaged measurements across all recordings.

To determine whether the oscillatory activity of different receptors was correlated, we obtained the instantaneous phase of oscillations of two receptors recorded simultaneously using a Hilbert transform in Matlab. We then computed the circular correlation coefficient between the phases of two simultaneous recordings (Berens, 2009). For each pair of receptors, we generated two surrogate data sets of non-simultaneous recordings. The first data set consisted of the first 1-s recording from one receptor and the fifth 1-s recording from the other receptor. The second data set consisted of the fifth 1-s recording from one receptor and the first 1-s recording from the other receptor.

We measured frequency tuning in spiking receptors following previously described methods (Lyons-Warren et al., 2012). We defined a response as at least one more spike/sweep during the 90-ms stimulus period than during the 90-ms prestimulus period. We determined a receptor's threshold by finding the lowest intensity at which the receptor responded to a given frequency. The frequency with the lowest threshold was defined as the receptor's best frequency. We generated normalized tuning curves by setting threshold intensities as dB relative to the threshold intensity at the best frequency. For oscillating receptors, we generated tuning curves by plotting vector strength vs stimulus frequency. We defined the best frequency as the frequency with the highest vector strength. In three of eight oscillating receptors, the best frequencies in response to positive- and negative-polarity stimuli differed slightly. In these cases, we determined the receptor's best frequency by averaging the best frequencies to each stimulus polarity.

To study how spiking receptors encode electric pulse waveform, we averaged the time of the first spike that occurred after stimulus onset (positive-polarity stimuli) or stimulus offset (negative-polarity stimuli). The difference in average spike times elicited by stimuli of opposite polarities was defined as the spike-timing difference. Since receptors on opposite sides of the body experience stimuli of opposite polarities, this procedure is equivalent to measuring the difference in spike times between receptors at different locations on the body evoked by the same stimulus (Hopkins, 1981). For a comparable measurement in oscillatory responses, we subtracted the average time of the first peak that occurred after the offset of the negative-polarity pulse from the average time of the first peak that occurred after the onset of the positive-polarity pulse for pulse durations longer than 0.5 ms. For shorter stimulus durations (≤0.5 ms), we measured the difference in the times of the first oscillatory peaks that occurred after stimulus offset for each stimulus polarity. This procedure is equivalent to measuring the difference in oscillatory peak times between receptors on opposite sides of the body evoked by the same stimulus. To quantify the degree of oscillation amplitude enhancement, we first measured all prestimulus oscillation amplitudes on each recording trace, and then averaged across all repetitions of the same stimulus. Next, we measured the poststimulus oscillation amplitude on each recording trace and averaged across all repetitions of the same stimulus. Lastly, we divided the mean poststimulus oscillation amplitude by the mean prestimulus oscillation amplitude for each pulse duration.

Since the peak power frequency of a single-cycle bipolar sine wave is slightly lower than the inverse of the wave's duration, we used Welch's power spectral density in Matlab to compute the power spectrum of each single-cycle sine wave. We took the peak of the power spectrum as the frequency of each stimulus.

We measured the difference in the phases of oscillatory resets evoked by opposite-polarity stimuli by first averaging the recorded potential across stimulus repetitions, and then measuring the first poststimulus period and the latency of the first poststimulus peak. We used these values to calculate the difference in the phase (Δφ) of oscillatory reset between responses to opposite-polarity pulses according to

where lat_N is the latency of the first peak, and p_N is the first period, respectively, evoked by the negative-polarity stimulus, and lat_P is the latency of the first peak, and p_P is the first period, respectively, evoked by the positive-polarity stimulus.

To measure spiking responses to paired pulses, we measured the interspike intervals between the spikes elicited by the onset (positive-polarity stimuli) or offset (negative-polarity stimuli) of each pulse. If no spikes occurred in response to the second pulse, no interspike intervals were recorded. For clarity, stimulus artifacts were removed from the recording traces shown in Figure 5A,B by drawing a straight line from the times of stimulus onset or offset plus 0.03 ms. In oscillating receptors, the stimulus artfact at the shortest IPIs tested obscured responses to the first pulse in the pair. To circumvent this issue, we first averaged oscillatory responses across stimulus presentations. Next, we measured the time interval between the first oscillatory peak that followed a single pulse and the first oscillatory peak that followed the second pulse in the pair. This method is equivalent to measuring the time interval between the first peaks following each pulse in the pair. We also measured the vector strength and poststimulus oscillation amplitude following the second pulse in the pair. We normalized mean poststimulus oscillation amplitudes by dividing by the mean poststimulus oscillation amplitude following a single pulse of 0.2 ms with the same polarity.

EODs were amplified 20–100 times, band-pass filtered (1 Hz–50 kHz) (BMA-200, Odmore, PA, USA), digitized at a rate of 195 kHz (RP2.1, Tucker Davis Technologies), and saved using custom software in Matlab 7.0. We measured total EOD durations using previously defined criteria (Carlson et al., 2000). EOD power spectra were computed using Welch's power spectral density estimate in Matlab.

To measure the IPIs generated by single fish and groups of fish, we recorded 20 min of electrical activity from a species with spiking receptors (P. microphthalmus) and a congeneric species with oscillating receptors (P. tenuicauda). For single-fish recordings, fish were removed from their home tank and placed into a 15 × 17 × 31 cm plastic chamber with a single recording electrode in which the positive and negative terminals were separated by 20 cm. Fish were allowed to acclimate for at least 10 min before the recordings. For group recordings, we placed four vertically oriented electrodes suspended with the reference terminal up (16.5 cm from the top of the tank) in the home tank (61 × 76 × 61 cm) of each species. Each electrode was located one-third of the distance between tank walls (i.e., at the vertices of nine equally sized rectangles). We placed the electrodes in the tank and allowed fish to acclimate to them overnight before starting the recordings. We amplified electrical activity 100 times before band-pass filtering (0.1 Hz–20 kHz) (Model 1700, A-M Systems) and digitizing at 97.7 kHz (RX8, Tucker–Davis Technologies). We detected EODs as points where the rectified recorded potential exceeded a threshold of 0.6 mV. Data were saved using custom Matlab software. For the histograms shown in Figure 8B,C,E,F, we used the recording from just one of the four electrodes. Single-fish and group tank recordings took place between 1700 and 1900.

To test whether species with different receptor physiologies exhibited different behavioral responses to IPIs, we recorded fish's EOD output in response to a train of 10 conspecific EODs at a constant IPI (0.3–100 ms) using previously described methods (Carlson et al., 2011). Briefly, we removed one fish from its group tank and placed it into a 10 gallon tank with a cylindrical plastic chamber (5 cm diameter × 13.2 cm) in the middle of the tank. If the fish was not inside the chamber at the end of a 30-min acclimation period, we guided the fish into the chamber with nets. Netted caps were then placed over each end of the chamber to keep the fish inside during the experiment. Fish were then allowed an additional 5-min acclimation period before starting the experiment. A pair of electrodes oriented horizontally along the inside walls of the chamber delivered the stimulus, and a pair of electrodes oriented vertically at either end of the chamber recorded the fish's EOD output. For each fish, we randomly selected a conspecific EOD waveform stimulus from a library. To generate the IPI train stimuli, we first defined the start and end of the EOD as the first and last points, respectively, where the absolute value of the waveform exceeded 0.5% of the maximum peak-to-peak amplitude. We then concatenated 10 identical EODs together, adding zero padding as necessary in between EODs to achieve the desired IPIs. If the duration of the EOD was longer than the IPI, we truncated the EOD at the IPI. We presented only normal-polarity (head-positive) stimuli. All stimuli were generated in Matlab, digital-to-analog converted at a rate of 195.31 kHz (RX8, Tucker–Davis Technologies), and attenuated (PA5, Tucker–Davis Technologies) before delivery to the analog stimulus isolator (Model 2200, A-M Systems).

To record fish's EOD output, we amplified electrical activity 100 times before band-pass filtering (0.1 Hz–20 kHz) (Model 1700, A-M Systems) and digitizing at 97.7 kHz (RX8, Tucker–Davis Technologies). We collected a fish's responses to 20 repetitions of each IPI train and to a single EOD stimulus, with 1 min between trials to reduce habituation. We randomized stimulus order. To quantify responses, we recorded the time of each EOD produced by the fish, and then computed the spike-density function (SDF) by convolving each EOD time with a Gaussian of 200-ms width (Carlson and Hopkins, 2004). We then averaged the SDF across stimulus repetitions. Next, we measured the fish's baseline response by averaging the resulting EOD rate over a window starting 0.2 s after the start of the 5-s prestimulus period and ending 0.2 s before stimulus onset. Because mormyrids can respond to electric stimuli with increases or decreases in their EOD rate (Moller et al., 1989; Post and von der Emde, 1999; Carlson et al., 2011), we measured the maximum and minimum of the SDF that occurred between 0.2 s before stimulus onset and 1.2 s following stimulus offset. We subtracted the baseline discharge rate from these two values to get the maximum increase in EOD rate and the maximum decrease in EOD rate in response to the stimulus. Because response patterns varied across individuals (Moller et al., 1989), we used a normalized measure of response strength. To compare responses across individuals, we subtracted the single-pulse response from the response to the IPI stimulus, and then we divided by the sum of the single-pulse and IPI response. We performed the same analysis on EOD rate increases and decreases.

We used circular statistics to measure mean angles ± S.E.M. of phase modulations of oscillatory receptor responses (Batschelet, 1981). We used the parametric second-order Hotelling test for paired circular data to compare oscillatory phase modulations elicited by normal- and reversed-polarity EODs (Zar, 1999). We used repeated-measures ANOVA in Statistica 6.1 (StatSoft, Tulsa, OK, USA) to compare behavioral responses to IPI stimuli across two species. We used Wilcoxon's matched-pair test in Statistica to compare circular correlation coefficients of simultaneous and non-simultaneous recordings. We used Spearman's rank test in Statistica 6.1 to compare spontaneous oscillation amplitudes and frequencies, as well as spontaneous and stimulus-evoked oscillation amplitudes in response to square pulses in oscillatory receptors. For all tests, significance level was defined as α = 0.05.

All of the data and all of the custom-written Matlab software used for data analysis are available at the Dryad Digital Repository (Baker et al., 2015).

The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.

We thank Tim Holy and Barani Raman for helpful discussions. This research was supported by the National Science Foundation (IOS-1255396 to BAC) and the National Institutes of Health (DC012452 to CAB).

Animal experimentation: All procedures were in strict accordance with the guidelines established by the National Institutes of Health and were approved by the Institutional Animal Care and Use Committee (Animal Welfare Assurance Number: #A-3381-01) at Washington University in St. Louis. The protocol was approved by the Animal Studies Committee at Washington University in St. Louis (Approval Number: 20130265). Every effort was made to minimize pain and stress. No surgical procedures were performed.

© 2015, Baker et al.

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