Coding conspecific identity and motion in the electric sense

Abstract

Interactions among animals can result in complex sensory signals containing a variety of socially relevant information, including the number, identity, and relative motion of conspecifics. How the spatiotemporal properties of such evolving naturalistic signals are encoded is a key question in sensory neuroscience. Here, we present results from experiments and modeling that address this issue in the context of the electric sense, which combines the spatial aspects of vision and touch, with the temporal aspects of audition. Wave-type electric fish, such as the brown ghost knifefish, Apteronotus leptorhynchus, used in this study, are uniquely identified by the frequency of their electric organ discharge (EOD). Multiple beat frequencies arise from the superposition of the EODs of each fish. We record the natural electrical signals near the skin of a "receiving" fish that are produced by stationary and freely swimming conspecifics. Using spectral analysis, we find that the primary beats, and the secondary beats between them ("beats of beats"), can be greatly influenced by fish swimming; the resulting motion produces low-frequency envelopes that broaden all the beat peaks and reshape the "noise floor". We assess the consequences of this motion on sensory coding using a model electroreceptor. We show that the primary and secondary beats are encoded in the afferent spike train, but that motion acts to degrade this encoding. We also simulate the response of a realistic population of receptors, and find that it can encode the motion envelope well, primarily due to the receptors with lower firing rates. We discuss the implications of our results for the identification of conspecifics through specific beat frequencies and its possible hindrance by active swimming.

Figure 1. Electric organ discharge (EOD) from weakly electric fish in different situations.

(A) Experimental recordings of two isolated individual fish. (B) An example compound EOD recording from two fish in close proximity. The interference of electric fields generated by each fish evokes a time-varying beating amplitude modulation (AM) which is a first order envelope E1 (red trace), as well as a second order envelope E2 (here a flat line, blue trace). (C) The EOD signal with a sinusoidal amplitude modulation (SAM, red trace) or a narrowband random amplitude modulation (RAM, red trace) are common ways to experimentally mimic or computationally simulate electrosensory signals arising from social interactions.

Figure 2. Analysis of experimental recordings.

(A) Experimental setup: the fish in the middle of the tank is restrained in a hammock; another one or two fish swim freely. The compound electric organ discharge (EOD) signals due to all fish were recorded through two electrodes (red dots) 1 cm apart and very close to the skin of the head of the restrained “receiving” fish. The line joining the electrodes was perpendicular to the skin in order to measure the normal component of the electric field. (B) Raw electric field (black) recorded from two static fish (both were held in hammocks), and its corresponding first envelope E1 (red) and second envelope E2 (blue). Their EOD frequencies (EODf) are 827 and 763 Hz, respectively. (C) A stretch of data of 1.2 sec long (black, only the positive part is shown) from one restrained fish (EODf at 827 Hz) with one other fish (763 Hz) freely swimming, and the corresponding E1 (red) and E2 (blue). (D) E2 extracted from the recording in (C) over a 10 second duration. The dip around the middle of this trial (marked by “*”, same event as in (E)) indicates a chirp. (E) 3D spectrogram of the data in (D). The amplitude of the spectral density (ASD) of the restrained fish is almost constant at 827 Hz, but the ASD of the freely swimming fish at 763 Hz varies with a very similar pattern as E2 shown in (D).

Figure 3. Characterization of the recorded social signal and comparison to the model signal described in Equation (1).

(A) Averaged auto-correlation of E2 calculated from five-minute recordings from 8 pairs of fish (each pair labeled by a different color), and from an artificial signal in Equation (1) with  = 2 (dotted line). The Ornstein-Uhlenbeck process (OUP) is generated using (black dotted curve). (B) Mean contrasts standard deviations (STD) of the raw data from the same 8 pairs using the same color scheme as in (A); numerical results calculated directly from Equation (1) (black lines) and approximate theoretical results (circles, see Materials and Methods) showing how the mean contrast (solid black line and solid circles) of the simulation signal and the mean STD contrast with  = 0.6 (dashed black lines and open circles) increase with ; Inset: STD/mean contrast for eight pairs of fish. Note that timeplots in Figure 2C, 2D and 2E, the green curve in Figure 3A and the green data point in Figure 3B are from the same recording of a pair of fish, and it will be used as representative data in the later analysis and figures in the case of two fish. (C) Based on the parameter values provided by this representative data, an example of the artificial signal (see Equation (1); black, only the upper part shown here) is shown and its envelopes E1 (red) and E2 (blue) over 1.2 seconds. Its parameter values are  = 827 Hz,  = 763 Hz,  = 0.143,  = 0.08,  = 1. (D) A comparison between E2 (blue) and the amplitude of the second sinusoidal wave: (orange) over 10 seconds.

Figure 4. Spectral analysis of sensory signals and their envelopes.

Power spectral densities (PSD) of the signal recorded at the receiving fish (A), and its envelopes E1 (B) and E2 (C) from 12-second recordings (green) and the simulated signal (black) for two fish (left column) and three fish (right column). The simulated signal in the swimming state (0, black solid curves) is scaled so that its total energy is equal to that of the raw data. The same scaling factor (18000) is used to simulate the signal corresponding to the “static” mode ( = 0, black dashed curves). Note that the rising power in the low frequency range (0–20 Hz) related to the motion disappears. In the case of two fish, the EODfs of the receiving fish and its neighbour were  = 827 Hz and  = 763 Hz, respectively, causing a beat frequency of 64 Hz. For three fish, the EODfs of the receiving fish and its two neighbours were  = 831 Hz,  = 740 Hz and  = 889 Hz, respectively, with beat frequencies of 91 Hz and 58 Hz. The secondary beat frequency (i.e. the difference between two beat frequencies, ) are highlighted by E2. The parameters used for the simulated signal are  = 0.143,  = 0.08 for the two fish case, and  = 0.03,  = 0.08,  = 0.5 for the three fish case;  = 1 in both cases.

Figure 5. The mean amplitude and standard deviation of the EOD of the swimming fish influence the spectral characteristics of E1.

(A, B) The height (solid line), width (measured at 310⁻⁹, dashed line) and (C, D) resolution (defined as the ratio of height to width) of the peak of at the beat frequency, , with increasing and fixed  = 0.1 (left column), or increasing and fixed  = 0.2 (right column). Increasing improves this resolution, whereas the increases in decreases this resolution. Other parameters here are the same as those in the case of two fish in Figure 3. 50 independent OU process realizations were used to produce theses averaged plots.

Figure 6. The fluctuations in the period of E1 received by the stationary fish vary with the motion of the neighboring fish.

Probability density function (PDF) of the periods of E1 when and changes (A), or when and changes (B). The binwidth is 0.02 msec. A larger produces more periods at precisely ; a higher disperses the periods over a broader time interval. (C) The coefficient of variation (CV, the ratio between STD and mean) of the periods of E1 increases with , but decreases with . Combinations of and corresponding to experimental trials are marked by dots with the same color scheme as in Figure 2B.

Figure 7. The response of electroreceptors (P-units) to the motion stimuli.

(A) Three examples of spike trains generated by the P-unit model (P-value = 0.12, 0.26 and 0.4) in response to the sensory input of the recording plotted in Figure 2C with E1 (red) and E2 (blue). (B) With as input ( is constant), the firing rate of the P-unit increases with increasing . The range of the envelope, , is mainly ] as indicated in equation (6) in Material and Methods. (C) Within a time window of 0.1 second, the number of spikes increases with increasing E2. These data are extracted from recordings (as in Figure 2D) and simulations (as in Figure 3D). (D) Mean time-dependent firing rate (black trace) obtained from 200 independent P-units, each with its own internal noise and baseline firing rate set by the parameter (see panel E), exhibits a time-varying curve similar to E2 (blue trace, as in Figure 2D) of the recording that was used as input to all 200 P-units. The colored trace is an example of the time-varying firing rate of a single P-unit with a P-value of 0.23. (E) Varying in the P-unit model (equation (7) in Material and Methods) according to the density shown on the top generated a good approximation to the experimentally observed heterogeneity in P-values shown on the bottom (the latter being well-fitted to a log-normal density in [29]). It also leads to a good agreement with the experimental observed envelop-coding ability of P-units in (see Figure S1).

Figure 8. The information extracted from spike trains of P-units.

(A) Averaged PSD of the simulated P-unit response . (B) Cross-spectra between E1 and the P-unit response, and cross-spectra between E2 and the P-unit response. (C) Coherence between E1 and the P-unit response, and coherence between E2 and the P-unit response; we compare the coherence functions of P-units with different P-values over 0–20 Hz in the inset, showing that P-units with low P-values can better encode motion-related information than those with high P-values. Results are shown for two fish (left column) and three fish (right column) and P-unit model with P-value of 0.26 (green and black curves), P-value of 0.12 (cyan curves) and a population of 200 P-units with variable P-values as shown in Figure 7E (magenta curves). The recordings in Figure 3 were used as input to the P-unit model (green, cyan, magenta traces); the same parameter values in Figure 3 were used for simulation input (black traces).

Figure 9. A higher mean amplitude or lower standard deviation of the EOD of the swimming fish facilitates estimation of beat frequency at the receptor level.

(A) The height (solid line) of the peak of at the beat frequency, , and the width (dashed line) of this peak at the coherence value of 0.15 increase and slightly decrease, respectively, with (with fixed  = 0.1). However (B), the above height and width slightly decrease and strongly increase, respectively, with (with fixed  = 0.2). Therefore (C), the height-to-width ratio of this peak slightly increases with , while (D) it decreases rapidly with . The curves in this figure and next figure are the average results over five artificial signals with  = [827,737], [827,760], [827,792], [827,704], [740,807]Hz; 50 independent OU processes were used to calculate the average for each artificial signal.

Figure 10. Increasing or enhances the motion-related information gained by the electroreceptors in the case of two fish.

(A–B) The maximum (solid line) of over the 0–20 Hz range and the width (dashed line, measured at 0.15) increase, with (and fixed  = 0.1), as well as with (and fixed  = 0.2). Higher mutual information (MI) rate, , could be obtained over 0–20 Hz with increasing (C) and (D). The numerical method to obtain the height and width of is described in Figure 9.