Fig 1.
The simultaneous activity of a population of neurons is recorded with a Neuropixels probe while the fish is stimulated locally with a 4 Hz prey-mimic amplitude modulation (upper right: EOD black, AM orange). Example raw voltage traces, with the spiking activity of each neuron labeled in a different color, is shown on the left. The dipole delivering the stimulus is placed at positions along the length of the fish within the receptive fields of the neurons being recorded (schematic receptive field on fish’s skin: center in dark blue, surround in lighter blue). The electric image of the stimulus delivered through the dipole electrode projects onto the surface of the fish’s skin diffusely (white circle). The electrosensory circuitry of the brain (bottom right) is composed of feedforward (black arrows) and feedback pathways (red arrows), with the ELL highlighted in yellow. EAs, electrosensory afferents; ELL, electrosensory lateral line lobe; TS, torus semicircularis; nP, nucleus praeeminentialis; EGP, eminentia granularis posterior.
Fig 2.
Mapping the receptive fields of ON and OFF-type pyramidal cells.
(A) Schematic of a receptive field with the center (blue)—surround (red) organization and stimulation paradigm. A dipole delivering a local stimulus (white circles) is systematically moved from rostral to caudal positions to map the receptive fields of the recorded neurons. (B) Top: Neural responses from an example ON-type pyramidal cell to stimulation at different locations on the rostro-caudal axis (spike train, green). The positive half-cycle of each repetition, or trial, of the stimulus (orange) was analysed. The grey bands cover the negative half-cycle of the stimulus. Bottom: Trial-averaged firing rate (green) as a function of stimulus position (i.e., the receptive field) for this example cell, with shaded error bars indicating the SEM. The responses corresponding to the three positions shown in (A) are marked by arrows and black dots. The receptive field center and surround were defined as the regions in space for which the firing rate was either greater or lesser than the baseline firing rate (horizontal black line), respectively. (C) Same as (B), but for an example OFF-type pyramidal cell (purple). In this case the receptive field center and surround were defined as the regions in space for which the firing rate was either lesser or greater than the baseline firing rate, respectively.
Fig 3.
Example receptive fields from ON and OFF-type ELL pyramidal cell populations.
Color plot showing the receptive fields of 32 simultaneously recorded neurons (14 ON-type neurons listed first, followed by 17 OFF-type neurons) visualized as the change (Δ) in normalized firing rate as a function of stimulus position.
Fig 4.
ELL pyramidal cells display spatially dependent covariance.
Covariance matrices (bottom panels) obtained for three different positions (top; receptive field schematic for two overlapping neurons: centers in blue, surrounds in red). Pairwise covariances at stimulus positions near the edges of where the receptive fields overlap (left and right panels), where the surrounds of most neurons are activated, are larger than in the middle of the receptive field overlap (center panel), where the centers of most neurons are activated. (Note: the variances along the diagonal are not shown to emphasize the spatial dependence of the covariances.) Center inset: The distribution of covariance magnitudes is significantly different across the three stimulus positions (Kruskal-Wallis: p = 1.4·10−52; left-center: p = 3.5 · 10−51; left-right p = 4.8 · 10−6; center-right p = 1.7 · 10−24). “*” indicates statistical significance.
Fig 5.
Spatial modulation of spike-count correlations depends on the level of baseline correlations.
(A) Magnitude of pairwise baseline correlations (|rBL|; black circles) as a function of the relative distance between neurons with a fitted exponential curve (black line). A threshold of |rBL| = 0.15 (red line) was used to separate neural pairs into high and low |rBL| pairs. (B) The spatial depth of modulation (max.-min.) of the spike-count correlations (|rSC|) is significantly higher for high |rBL| pairs than for low |rBL| pairs across recording sessions (Wilcoxon rank sum test for b: p = 2.1 · 10−128; outliers were removed as detailed in the Materials and Methods section). (C) Spatial dependence of the |rSC| is shown for four example pairs, two same-type pairs (OFF-OFF type pairs) and two opposite-type pairs (ON-OFF type pairs) each with low and high |rBL|. For high |rBL| pairs (left column), the spatial dependence of the |rSC| (black) is determined by the region of receptive field overlap (receptive field neuron 1 blue, receptive field neuron 2 purple): in regions where the surrounds of both neurons overlap, the |rSC| approaches |rBL| (green background); in regions where the surround of one neuron overlaps the center of the other, the |rSC| is intermediate (pink background); and in regions where there is center-center overlap, the |rSC| approaches zero (blue background). In contrast, for low |rBL| pairs of either type (right column), there is minimal or no spatial modulation and the magnitude hovers near zero. (D) Distributions of |rSC| for regions of center-center (blue), center-surround (pink) and surround-surround overlap (green) pooled over all pairs across all recording sessions: for high |rBL| pairs (left) the three distributions are significantly different (Kruskal-Wallis: p = 1.8 · 10−131; cc-cs: p = 9.7 · 10−10; cc-ss: p = 9.6 · 10−10; cs-ss: p = 9.6 · 10−10); however, they are not significantly different for low |rBL| pairs (right; Kruskal-Wallis: p = 0.89; cc-cs: p = 0.94; cc-ss: p = 0.89; cs-ss: p = 0.99). “*” indicates statistical significance; ns, not significant; c, center; s, surround.
Fig 6.
Redundancy reduction by spatially dependent spike-count correlations.
(A) Schematic for calculating Fisher information (FI) from the neural responses (i.e., the derivative of the neural receptive fields and the covariance matrices). (B) Schematic of the different correlation scenarios used when calculating the Fisher information: the intact data which includes spatially dependent rSC (SD: left, blue), the independent case where all correlations are set to zero (I: middle, red) and the spatially independent case where the correlation values at all stimulus positions for a given pair are set to the baseline correlation for that pair (SI: right, purple). (C) Fisher information as a function of stimulus position for the three correlation scenarios, averaged over recording sessions with a population size of 28 neurons. The dip in Fisher information at position zero is caused by the slopes of many neurons in the population approaching zero as the firing rates reach their maximum. The light grey bar indicates the region of peak information and the stimulus positions over which the mean Fisher information is calculated for (D). (D) Fisher information (<FI>) increases linearly with population size for all three correlation scenarios over recording sessions. Inset: The boxplot of the Fisher information at a population size of 28 neurons, normalized by the Fisher information at a population size of one neuron for each recording session, shows that the three different correlation scenarios are significantly different (one-way ANOVA: df = 12, p = 3.8 · 10−6; SD—I: p = 6 · 10−4; SD—SI: p = 6.3 · 10−3; I—SI: p = 2.8 · 10−6). (E) By transforming the Fisher information to the root Cramér-Rao bound (, blue), the standard deviation of the prey location estimate can be compared to the radius of the average prey captured by the fish (0.15 cm, green line). The grey box indicates the range of positions over which averaging is done for (F). (F) The averaged root Cramér-Rao bound (<
>) vs neural population size decreases to below the average radius of prey at a population of ~19 neurons. Shaded error bars indicate the SEM in (C-F).
Fig 7.
Modeling receptive field heterogeneities and spatially dependent spike-count correlations.
(A) Schematic of the model in which modeled neural receptive fields (left, colored curves) and spatially dependent pairwise spike-count correlations (right, grey curves) are used to calculate the spatially dependent Fisher information. (B) Fisher information visualized as a function of stimulus position for spatially dependent (SD: blue), independent (I: red) and spatially independent correlation scenarios (SI: purple). (C) Fisher information (<FI>) as a function of neural population size (averaged between -0.5 and 0.5 cm). Though quite small, the shaded error bars indicate the SEM in (B & C). Inset: Fisher information at the neural population size of 28 neurons, normalized by the Fisher information at a population size of one neuron, is significantly different for the three correlation scenarios: spatially dependent, independent, and spatially independent (Kruskal-Wallis: p = 8 · 10−17; SD—I: p = 3.3 · 10−6; SD—SI: p = 6.2 · 10−4; I—SI: p = 2.7 · 10−17). “*” indicates statistical significance.
Fig 8.
Receptive field heterogeneities can optimize information transmission.
(A) The level of heterogeneity in terms of the receptive field position was varied from low (left) to high (middle), emphasized by the black arrows. The right panel shows the Fisher information as a function of receptive field position heterogeneity with (blue) and without (red) spatially dependent spike-count correlations, as well as with spatially independent spike-count correlations (purple). Heterogeneity was quantified as the standard deviation of the distribution from which the receptive field position for each neuron is drawn. Though small, the shaded error bars indicate the SEM. In all three correlation scenarios, the Fisher information clearly goes through a maximum as the level of receptive field position heterogeneity is increased. (B) Same as (A) but varying the level of receptive field width heterogeneity. In this case the Fisher information increases in a monotonic fashion with increasing receptive field width heterogeneity. (C) Same as (A) but varying the level of receptive field amplitude heterogeneity. In this case the Fisher information was largely independent of the level of receptive field amplitude heterogeneity.