Sparse and dense coding of natural stimuli by distinct midbrain neuron subpopulations in weakly electric fish

Abstract

While peripheral sensory neurons respond to natural stimuli with a broad range of spatiotemporal frequencies, central neurons instead respond sparsely to specific features in general. The nonlinear transformations leading to this emergent selectivity are not well understood. Here we characterized how the neural representation of stimuli changes across successive brain areas, using the electrosensory system of weakly electric fish as a model system. We found that midbrain torus semicircularis (TS) neurons were on average more selective in their responses than hindbrain electrosensory lateral line lobe (ELL) neurons. Further analysis revealed two categories of TS neurons: dense coding TS neurons that were ELL-like and sparse coding TS neurons that displayed selective responses. These neurons in general responded to preferred stimuli with few spikes and were mostly silent for other stimuli. We further investigated whether information about stimulus attributes was contained in the activities of ELL and TS neurons. To do so, we used a spike train metric to quantify how well stimuli could be discriminated based on spiking responses. We found that sparse coding TS neurons performed poorly even when their activities were combined compared with ELL and dense coding TS neurons. In contrast, combining the activities of as few as 12 dense coding TS neurons could lead to optimal discrimination. On the other hand, sparse coding TS neurons were better detectors of whether their preferred stimulus occurred compared with either dense coding TS or ELL neurons. Our results therefore suggest that the TS implements parallel detection and estimation of sensory input.

Fig. 1

In vivo recordings and stimulus ensemble used in this study. A: schematic side view of the brain of Apteronotus leptorhynchus based on Maler et al. (1991). Scale bar, 1 mm. Recordings were obtained from neurons in the hindbrain electrosensory lateral line lobe (ELL) and in the midbrain torus semicircularis (TS). B: cartoon illustrating the behavioral context of chirp production in weakly electric fish. Top: the 2 fish produce electric organ discharges (EODs) at different frequencies, creating a beat phenomenon that can be perceived by both fish. The oval rings represent the field lines from each fish. Bottom: the upper fish produces a small chirp—a transient rise in its EOD frequency that briefly increases the beat frequency, which is best seen by looking at the time course of each fish’s EODs. Note that the chirp features were exaggerated for illustration purposes. C, top: instantaneous EOD frequency of the 2 fish in B. Bottom: amplitude modulation (AM, black line) of the carrier wave (gray line) due to the ongoing interference between 2 EODs. Note that the small chirps act as a phase reset of the beat. Small chirps used in this study were defined by the beat frequency (bf), the chirp excursion frequency (cf), and the phase of the beat at which the chirp occurred (cp). D: AM components of natural and artificial stimuli used in this study. Small chirps characterized by 5 different beat frequencies, 5 different chirp excursion frequencies, and 4 different phases of the beat were used in this study. Only 1 variant of a big chirp was used. Pure beat stimuli were given at 9 different frequencies. The noise stimulus consisted of zero mean Gaussian white noise that was low-pass filtered at 120 Hz.

Fig. 2

Transformation of the neural code between the ELL and TS. Aligned raster diagrams of spike responses to a set of 24 stimuli comprising 12 small chirps, 1 big chirp, 9 pure beats, a step, and a noise stimulus are shown. Stimulus parameters are everywhere, as indicated in A. Time 0 marks the chirp/step onset. Noise and beat stimuli start at time −0.1 s and last throughout the entire time segment. Response rasters to beats were built by cutting and wrapping around the spike times in response to 1 ongoing beat stimulus of several seconds duration. The same applies to the frozen noise that consisted of 5 identical pieces. Since chirps were interspersed into a beat, the prestimulus time comprises the ongoing beat stimulus. Between 10 and 30 trials are represented for each stimulus and 5 for the noise stimulus. Gray response windows indicate significant responses as determined by comparing the response entropy to surrogate data sets as described in METHODS under Testing response significance. Note that not all trials are shown for each stimuli. A: typical ELL neuron displaying strong phase-locking behavior during most beat stimuli and firing bursts of spikes in response to most chirps. B: example TS neuron. The neuron had very little activity during beat stimuli and responded exclusively to 3 chirps. C: another example TS neuron that showed a significant decrease in firing in response to the step and phase-locking behavior during most beat stimuli and increased its firing rate in response to most chirps.

Fig. 3

Comparing sparse coding in ELL and TS. A and B: population activity for a set of 24 stimuli measured in 17 ELL neurons (A) and 29 TS neurons (B). Black squares mark stimuli for which a significant response was obtained. Cells were sorted as a function of their response probability. C: response probabilities for TS (black bars) and ELL (gray bars) neurons computed as the fraction of the stimuli each cell responded to. Response probabilities were included from neurons tested with a minimum of 12 different stimuli. The response probability of TS neurons was significantly lower than that of ELL neurons (U-test, P < 0.01). Response probability was distributed normally in ELL (Lilliefor test, ELL: P = 0.5, TS: P = 0.04) and uniformly in TS (χ²-test, ELL: P < 0.01, TS: P = 0.23). D: baseline (i.e., in the absence of stimulation) firing rates were correlated with response probability for TS neurons (r = 0.5, P < 0.01), not for ELL neurons (r = 0.34, P = 0.09). Note that spontaneous firing rates reached much lower values in TS neurons than in ELL neurons (U-test, P < 0.01). Different markers label sparse TS neurons with lifetime sparseness index > 0.5 (triangles), dense TS neurons with lifetime sparseness index ≤ 0.5 (black filled circles), and dense ELL neurons with lifetime sparseness index ≤ 0.5 (gray filled circles). E: lifetime sparseness indices were consistent with data drawn from a normal distribution in ELL (Lilliefor test, P = 0.37) but were significantly different than data drawn from a unimodal distribution in TS neurons (Hartigan’s dip test, P = 0.017). On average TS neuron responses were sparser than ELL neuron responses (U-test, P < 0.01). The sparseness is quantified based on the firing rate distribution (see METHODS). Insets: firing rate distributions corresponding to the same neurons as in Fig. 2, A and B. L_S, lifetime sparseness. F: population sparseness was higher across TS neurons than across ELL neurons (U-test, P < 0.01). Insets: firing rate distributions for responses to a small chirp (bf = 5 Hz, cf = 60 Hz, cp = 75) for ELL and TS. P_S, population sparseness.

Fig. 4

TS neurons are highly selective to natural communication signals. Maximal selectivity to small and big chirps was smaller in ELL (A, C) than in TS (B, D). Each example is taken from a different neuron and shows the stimulus waveform (top), the raster plot (middle), and the peristimulus time histogram (PSTH; bottom). The chirp selectivity index (CSI) quantifies the contrast in maximal firing rates during the response window (gray rectangles) and before chirp onset. E and F, left: maximum CSI values obtained in each cell across all chirp stimuli were more variable in TS than in ELL (Ansari-Bradley test, P < 0.01). A subpopulation of TS neurons reached CSIs of >0.8 that were never observed in ELL. Right: best CSI values observed in each neuron were correlated with lifetime sparseness in TS (r = 0.47, P = 0.01, marked by asterisk), not in ELL (r = 0.19, P = 0.48). G and H: histograms of maximum CSI value for big chirps as a function of the maximum CSI value for small chirps measured in 24 ELL neurons (G) and 146 TS neurons (H). We only included neurons for which CSI > 0.2 for at least 1 stimulus. Although a few TS neurons were highly selective for both small and big chirps, there was a general trend for TS neurons to be selective either to small or to big chirps. This was reflected in the fact that the fraction of data falling onto the axes was significantly larger than expected from random data for the TS population (Monte Carlo test, P < 0.01) but not for the ELL population (P = 0.08).

Fig. 5

TS neurons are selective to moving objects and communication signals. A: example TS neuron that was responsive to a small dipole moved alongside the fish when the dipole was at a specific location on the animal’s rostro-caudal axis. The movement selectivity index (MSI) was defined in analogy to the CSI. The gray rectangle marks the window of movement cycle to which the maximal firing rate is being compared. B: this same example neuron was not responsive to small chirps (nor to big chirps, CSI = 0; not shown). C: example TS neuron that was not responsive to the moving dipole. D: this same neuron responded to big chirps (best CSI for small chirps was 0). E: the maximum value of MSI as a function of maximum value of CSI for TS neurons (n = 27) showed a strong trend for selectivity for either chirps or moving objects. This is a consequence of the data points falling significantly more often on the axes than expected from random data (Monte Carlo test, P < 0.01). F: response profiles for a set of 6 stimuli including the moving object sorted as a function of response probability. Note that most neurons responded to ≤2 stimuli.

Fig. 6

Discrimination of chirps based on spike trains of single TS and ELL neurons. A: example ELL neuron that responded to most chirps. Left: raster plots obtained with 13 different chirps. Response windows were 100 ms long and started at chirp onset. The 4 raster plots at the bottom (dark gray fill) indicate responses to 4 small chirps with identical beat and chirp frequencies presented at different phases of the beat. Top right: confusion matrix for the restricted stimulus set consisting of these 4 chirps occurring at different phases. The confusion matrix shows the probability of assigning a spike train that was actually elicited by the stimulus corresponding to the column as being elicited by the stimulus corresponding to the row. Such elements on the main diagonal correspond to correct classification and off-diagonal elements to incorrect classification. Bottom right: confusion matrix for the full stimulus set consisting of all 13 chirps. B: example TS neuron that responded selectively to only a few chirps, notably small chirps presented at 3 different phases plus the big chirp. Left: raster plots obtained with 13 different chirps. Top right: confusion matrix for the restricted stimulus set. Bottom right: confusion matrix for the full stimulus set consisting of all 13 chirps. C: example TS neuron that responded to most chirps. Left: raster plots obtained with 13 different chirps. Top right: confusion matrix for the restricted stimulus set. Bottom right: confusion matrix for the full stimulus set consisting of all 13 chirps. Note that stimulus attributes could be best discriminated by using the activity of the dense TS neuron, followed by that of the ELL neuron, and followed by that of the sparse TS neuron. MI, mutual information in % of the maximal mutual information available in the stimulus set. Cost measures the time precision of the decoder at best performance.

Fig. 7

Discrimination of chirps based on pooling of the activities of sparse TS, dense TS, and ELL neurons. A: average mutual information (error bars represent SD) as a function of population size for the restricted stimulus set. Chirp discrimination was enhanced by combining the activities of multiple neurons for all 3 groups (analysis as in Fig. 6; Kruskal-Wallis test, P < 0.01 for all groups). It is seen that all 4 chirps can be optimally discriminated by the dense coding TS population. B: mutual information as a function of population size for the full stimulus set. The discrimination performance of dense TS neurons was significantly greater than that of ELL neurons. Moreover, the discrimination performance of ELL was significantly greater than that of sparse TS neurons. C: cost values indicating the precision that led to the maximal mutual information for the restricted stimulus set. D: cost values for the full stimulus set. Precision decreased with increasing group size in ELL and sparse TS neurons but increased for dense TS neurons (Kruskal-Wallis test, P < 0.01 for all groups). Brackets labeled “ns” indicate pairs that were not significantly different based on pairwise group comparisons; all other groups displayed significant differences (Kruskal-Wallis test with Tukey-Kramer correction for multiple comparisons, P < 0.05).

Fig. 8

Detecting the presence of a chirp stimulus. A: raster plots obtained from an example sparse TS neuron in response to 13 different chirps. B, top: spike count distributions in a 100-ms window preceding and following chirp onset (white and black bars, respectively) for the restricted stimulus set of 4 chirps occurring at 4 different phases of the beat. B, bottom: the receiver-operator characteristic (ROC) curve was built by varying a threshold criterion for spike counts for the restricted stimulus set. The fraction of spike counts above the criterion and occurring before chirp onset represents the probability of false alarm [p(FA)]; the fraction of spike counts above the criterion and occurring after chirp onset is referred to as the probability of correct detection [p(CD)]. The ROC area is given in the bottom right corner of the ROC plot; 0.5 indicates chance level, 1 indicates perfect detection. C, top: spike count distributions in a 100-ms window preceding and following chirp onset (white and dark gray bars, respectively) for the full stimulus set consisting of all 13 chirps. C, bottom: ROC curve for the full stimulus set. D: raster plots obtained from an example dense TS neuron in response to 13 different chirps. E and F are organized analogously to B and C, respectively. G: raster plots obtained from an example ELL neuron in response to 13 different chirps. H and I are organized analogously to B and C, respectively. J: population-averaged area under the ROC curve computed from the joint spike count distributions of sparse TS, dense TS, and ELL neurons as a function of population size for the restricted stimulus set. K: population-averaged area under the ROC curve computed from the joint spike count distributions of sparse TS, dense TS, and ELL neurons as a function of population size for the full stimulus set. In both cases, chirp detection performance increased with the number of combined neurons (Kruskal-Wallis test, P < 0.01 for all groups). Chirp detection performance reached superthreshold values for both stimulus sets in sparse TS neurons only (the dashed line shows the ROC area threshold of 0.76) and was significantly better in sparse TS neurons than in both dense TS neurons and ELL neurons. Brackets labeled “ns” indicate pairs that were not significantly different based on pairwise group comparisons; all other groups displayed significant differences (Kruskal-Wallis test with Tukey-Kramer correction for multiple comparisons, P < 0.05).