Nonlinear response properties of combination-sensitive electrosensory neurons in the midbrain of Gymnarchus niloticus

Abstract

The jamming avoidance response of the weakly electric fish Gymnarchus niloticus relies on determining the sign of the frequency difference (Df) between the fish's own electric organ discharge (EOD) and that of a neighbor, which is achieved by comparing modulations in amplitude (AM) and phase (PM) that result from the summation of their EODs. These two stimulus features are processed in separate pathways that converge in the torus semicircularis on combination-sensitive neurons, many of which are selective for the sign of Df. We recorded extracellular single-unit responses to independent stimulation with AM and PM and combined AM-PM stimulation to determine how sign selectivity is established. Responses to AM and PM frequently summated nonlinearly, leading to sign-selective responses as a result of facilitation to the preferred sign of Df and/or suppression to the nonpreferred sign of Df. Facilitation typically occurred when responses to AM and PM were aligned, whereas suppression typically occurred when they were offset. By experimentally manipulating the degree of alignment between these two responses, we found that the summed response was dependent on their relative timing. In addition, we found a unique class of units that were sensitive to differences in amplitude between two body surfaces. This sensitivity rendered such units immune to the problem of orientation ambiguity, in which the sign selectivity of a single neuron reverses with changes in stimulus orientation. We discuss potential synaptic mechanisms for driving nonlinear responses in these and other combination-sensitive neurons.

Figure 1.

Sensory cues for the JAR. A, Combining two sinusoidal signals results in amplitude and phase modulation at a frequency equal to the frequency difference between the two sinusoids. The vertical ticks on the time axis mark the timing of zero crossings in the uncontaminated signal. B, The fish's own EOD is generated internally, leading to current flow perpendicular to the skin surface at every point (black arrows), whereas the neighbor's EOD is generated externally, leading to current flow through the fish in a single direction (gray arrows). Because the electroreceptors are sensitive to current flow that is oriented perpendicular to the body surface, the fish's EOD will be more strongly contaminated at body surface A compared with B. C, Modulations in amplitude and phase at body surfaces A and B for opposite signs of Df. The vertical lines mark zero crossings. D, Amplitude at body surface A and differential phase of body surface A relative to B for opposite signs of Df. The temporal relationship between amplitude and differential phase is reversed when switching the sign of Df, which results in a different direction of rotation in a Lissajous graph. Adv., Advance; Del., delay.

Figure 2.

A, The phase chamber electrically isolates the head from the trunk, allowing one to independently manipulate AM and PM. Peristimulus time histograms of single-unit activity are constructed in relation to the modulation cycle. AM is shown as a solid line, and PM is shown as a dashed line with delays indicated by positive values and advances by negative values. A vertical line is included for all histograms with a significant VS_Df at a value equal to the mean vector angle of the response. B-D, Responses of four different combination-sensitive units to AM, PM, Df >0, and Df <0 in both the head and trunk compartments as well as no modulation. The units in B and C were sensitive to head AM and DPM. Both gave an I/advance-type response in the head and were Df >0 selective (B,t₈₂ = 5.11,p<0.0001; C, t₄₀ = 4.05, p < 0.001). The units in D and E were sensitive to DAM and DPM. The unit in D gave an E/advance-type response in the head and an I/delay-type response in the trunk and was nonselective in both the head (t₄₀ = 1.99; p > 0.05) and the trunk (t₄₀ = 0.48;p > 0.63). The unit in E gave an I/delay-type response in the head and an E/advance-type response in the trunk and was Df <0 selective in both compartments (head, t₄₁ = 8.65, p < 0.000000001; trunk, t₄₂ = 4.34, p < 0.001). Vertical scale: B, 54 spikes/sec; C, 45 spikes/sec; D, 40.5 spikes/sec; E, 36 spikes/sec. Adv., Advance; Del., delay; No Mod, no modulation.

Figure 3.

Responses of five different units to head AM, trunk AM, joint AM, head PM, and trunk PM. A, This AM-DPM-sensitive unit gave identical responses to head AM and joint AM, gave no response to trunk AM, and responded to head advances and trunk delays. Vertical scale, 114 spikes/sec. B, This DAM-sensitive unit gave an I-type response in the head, an E-type response in the trunk, a weakened response to joint AM, and no response to PM in either compartment. Vertical scale, 20.1 spikes/sec. C, This DAM-DPM-sensitive unit gave an E/delay-type response in the head, an I/advance-type response in the trunk, and a weakened response to joint AM. Vertical scale, 61.8 spikes/sec. D, This unit was DAM and DPM sensitive, giving an I/delay-type response in the head, an E/advance-type response in the trunk, and a weakened response to joint AM. Vertical scale, 44.4 spikes/sec. E, This unit was DAM and DPM sensitive, giving an I/delay-type response in the head, an E/advance-type response in the trunk, and a weakened response to joint AM. Vertical scale, 37.2 spikes/sec.

Figure 4.

Verification of DAM sensitivity. A, This AM-sensitive unit responded to head AM, regardless of whether there was any signal in the trunk compartment, but gave no response to trunk AM. Vertical scale, 51 spikes/sec. The units in B-D were all DAM sensitive and responded to AM in both compartments under a variety of different stimulus conditions, including no signal in the other compartment, signals of different carrier frequencies (diff. carr. freq.) in the two compartments, and signals in the two compartments with 180° phase differences. Vertical scale: B, 132 spikes/sec; C, 30 spikes/sec; D, 96 spikes/sec.

Figure 5.

Examples of nonlinear responses in combination-sensitive units. Response histograms are shown in black, and the expected linear summation of AM and PM responses for Df >0 and Df <0 are shown in gray. Two histograms are shown for the PM responses of each unit, one shifted by 90° to align the response with the Df >0 stimulus and one shifted by 270° to align the response with the Df <0 stimulus. Note that these two histograms are identical except for their time bases. A, An E/advance-type unit that showed a linear summation for both signs of Df and is nonselective (t₄₀ = 0.01; p > 0.98). Vertical scale, 54 spikes/sec. B, An I/delay-type unit that was Df >0 selective (t₁₆₆ = 12.2; p < 0.000000001), resulting from facilitation in response to Df >0, and a linear combination in response to Df <0. Vertical scale, 102 spikes/sec. C, An E/advance-type unit that was Df <0 selective (t₁₆₆ = 4.71; p < 0.0001), resulting from suppression in response to Df >0, and a linear combination in response to Df <0. Vertical scale, 150 spikes/sec. D, An E/delay-type unit that was Df >0 selective (t₈₂ = 12.7; p < 0.000000001), resulting from suppression in response to Df <0, and a linear combination in response to Df >0. Vertical scale, 93 spikes/sec. E, An E/delay-type unit that was Df >0 selective (t₈₂ = 13.6; p < 0.000000001), resulting from facilitation in response to Df >0, and suppression in response to Df <0. Vertical scale, 90 spikes/sec. No Mod, No modulation.

Figure 6.

Responses to various start angles of PM relative to AM in sign-selective units. A, This unit was Df <0 selective and responded most strongly when PM was offset by values near that of a natural Df <0 stimulus (270°). The fitted function is of the form y = M + Acos(t - t₀) (r² = 0.44; p < 0.01). B, This unit was Df >0 selective and responded most strongly when PM was offset by values near that of a natural Df >0 stimulus (90°). The fitted function is of the same form in A (r² = 0.72; p < 0.00001). C, Ten responses from nine units to the same start angles shown in A and B, shifted to show the relative distance between the AM and PM mean vector angles and then binned into 20° segments. Spike rate is normalized to the spike rate in response to AM alone (mean ± SEM), with a fitted function of the same form in A and B (r² = 0.91; p < 0.0000001).

Figure 7.

Sign selectivity in three units that gave no observable response to PM presented alone. A,Df >0-selective unit (t₈₂ = 6.80; p < 0.00000001). Vertical scale, 46.2 spikes/sec. B, Df <0-selective unit (t₅₆ = 2.24; p < 0.05). Vertical scale, 9 spikes/sec. C, Df >0-selective unit (t₈₂ = 2.10; p < 0.05). Vertical scale, 77.4 spikes/sec.

Figure 8.

Orientation ambiguity in AM-DPM-sensitive units and DAM-DPM-sensitive units. Sign selectivity of responses from five AM-DPM-sensitive units and four DAM-DPM-sensitive units (1 unit from each group was stimulated with 2 different modulation rates) in response to joint stimulation of the head and trunk with identical signs of Df but with the modulation depth of one chamber set at 30% of the other.