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Department of Biology, University of Virginia, Charlottesville, Virginia
Submitted 10 August 2006; accepted in final form 25 September 2006
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSREFERENCES |
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSREFERENCES |
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; Marr 1982). At each subsequent level of processing, individual sensory neurons become increasingly selective, often responding preferentially to specific combinations of different stimulus features. These combination-sensitive neurons play a critical role in sensory processing because they provide information that cannot be obtained by analyzing any one stimulus feature in isolation (Schnupp and King 2001). For example, the visual system must obtain information about multiple stimulus attributes such as shape, size, color, orientation, speed, and direction of motion, and then combine information about each of these different features to detect, identify, and discriminate among different visual stimuli. Certain visual neurons in the mammalian cortex display remarkable selectivity for complex stimuli, providing explicit representations of faces, individuals, landmarks, animals, objects, or spatial scenes (Ewert 1997; Fujita et al. 1992; Logothetis and Sheinberg 1996; Quiroga et al. 2005; Tanaka 1996; Tsao et al. 2006). Similarly, vertebrate auditory neurons are often highly selective for particular sounds that are defined by relative intensity, temporal sequence, and spectral characteristics (Fuzessery and Feng 1983; Margoliash 1983; Margoliash and Fortune 1992; Misawa and Suga 2001; Peña and Konishi 2001). However, the complexity of vertebrate visual and auditory systems has made it difficult to precisely characterize the mechanisms underlying the transformation from raw sensory input to single-neuron combination sensitivity.
The weakly electric fish Gymnarchus niloticus generates a nearly sinusoidal electric organ discharge (EOD) that is monitored using an array of electroreceptors distributed throughout the skin, allowing them to communicate and electrolocate (Lissman 1958). When two fish with similar EOD frequencies meet, their electrolocation abilities are impaired by electrical interference (Heiligenberg 1975). To avoid this, both fish shift their EOD frequencies away from each other, a behavior called the "jamming avoidance response" (JAR) (Bullock et al. 1975). To perform the JAR, a fish determines the sign of the frequency difference (Df) between its own EOD and its neighbor's EOD (Df = neighbor's EOD frequency – own EOD frequency) by comparing the temporal patterns of sinusoidal amplitude modulation (AM) and sinusoidal phase modulation (PM) that result from the interference (Kawasaki 1993). By themselves, both AM and PM are identical for opposite signs of Df, but the temporal relationship between them differs: when Df is positive (Df >0), PM is advanced by 90° relative to AM, but when Df is negative (Df <0), PM is delayed by 90° relative to AM (Carlson and Kawasaki 2004).
AM and PM are processed in separate electrosensory pathways that converge in the midbrain torus semicircularis (Kawasaki and Guo 1998), where a number of neurons are selective for the sign of Df (Kawasaki and Guo 2002). In response to sinusoidal AM, these sign-selective neurons typically fire during either the rising or falling portion of the stimulus and, in response to sinusoidal PM, they typically fire during either the advanced or delayed portion of the stimulus (Carlson and Kawasaki 2004). Sign selectivity is generally characterized by a nonlinear summation of the spiking responses to AM and PM that depends on their relative timing; for the preferred sign of Df, the responses to AM and PM are typically aligned, leading to a linear to supralinear summation of spike rates, but for the nonpreferred sign of Df, these responses are typically offset, leading to a linear to sublinear summation (Carlson and Kawasaki 2004).
Experimental and theoretical studies on synaptic integration by single neurons suggest that several possible mechanisms could be responsible for this nonlinear processing, such as inhibitory shunting (Borg-Graham et al. 1998; Torre and Poggio 1978), presynaptic inhibition (Rudomin et al. 1998), and voltage-dependent ion channels, including both ligand-gated channels with voltage dependency (Mel 1992, 1993) and ion channels that are regulated exclusively by voltage (Magee 1999). Alternatively, a nonlinear summation of spike rates can result from a linear summation of the underlying postsynaptic potentials (PSPs) because of a nonlinear relationship between membrane potential and spike rate (Jagadeesh et al. 1993; Srinivasan and Bernard 1976). In the current study, we made whole cell recordings in vivo from sign-selective midbrain neurons in Gymnarchus to explore these possibilities and determine how the PSP responses to AM and PM interact to confer selectivity for the sign of Df.
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METHODS |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSREFERENCES |
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We used 38 Gymnarchus niloticus of both sexes (10–20.5 cm in total length). They were collected in West Africa at lengths of 5 to 6 cm and raised to the experimental size in our laboratory under conditions identical to those described earlier (Kawasaki 1994). After anesthesia with tricaine methanesulfonate (MS-222, 1:10,000; Sigma, St. Louis, MO), we immobilized fish with an intramuscular injection of flaxedil (gallamine triethiodide: 8 to 20 µl of a 0.1% solution; Sigma), which greatly attenuated EOD amplitude. Activity of the EOD pacemaker command signal was recorded from the tail to monitor the fish's condition throughout each experiment.
Fish were placed inside a Plexiglas chamber, gently held with a sponge-lined clamp, and submerged in water except for a small area along the dorsal surface of the head. Oxygen-saturated water was provided to the gills with a tube inserted in the mouth. After local application of Xylocaine (2%; Barber Veterinary Supply, Richmond, VA), we removed a small portion of the skull and meninges above the midbrain. The valvula cerebelli, which lies above the torus semicircularis (Bass and Hopkins 1982), was gently displaced using the grounding wire to expose the dorsal surface of the torus. At the conclusion of experiments, fish were killed by deep anesthesia in MS-222 (1:1,000). These procedures are in accordance with the guidelines established by the National Institutes of Health and were approved by the University of Virginia Animal Care and Use Committee.
Whole cell intracellular recording
We obtained whole cell recordings from torus neurons following the method of Rose and Fortune (1996). Electrodes were pulled in three stages to a tip diameter of about 1.2 µm and filled with a tip solution containing (in mM): potassium acetate (100), KCl (2), MgCl2 (1), EGTA (5), HEPES (10), KOH (20), and biocytin (43). The shank was filled with an identical solution except that the biocytin was replaced with mannitol. This yielded pipette resistances of 20–30 M
and initial seal resistances >1 G. After gaining intracellular access, we estimated the series resistance and input resistance as the first and second components, respectively, of a double-exponential fit to the voltage response to square-wave current injection of –0.1 nA. The estimated median series resistance was 76 M and the estimated median input resistance was 195 M.
We obtained recordings from a total of 67 neurons in the torus semicircularis that responded to stimulus modulation and met the following criteria for inclusion: stable resting potentials of at least –30 mV after subtracting a calculated liquid junction potential of 5.6 mV (Barry 1994) and spikes with a height of 
10 mV. A small number of neurons (11 of 67) did not produce any spikes at rest or in response to stimulus modulation. However, these neurons had stable resting potentials, responded with robust PSPs to sensory stimulation, and generated large spikes in response to depolarizing current injection. We therefore included these neurons in our analyses of PSP responses. The mean ± SD of the resting potentials was –55.02 ± 8.75 mV, and spike heights typically ranged from 20 to 30 mV.
Intracellular activity was amplified tenfold on an AxoClamp 2B amplifier (Molecular Devices, Palo Alto, CA) then sent to an A/D converter with a sampling rate of 20 kHz and to a Schmitt Trigger with an output to an event timer that recorded spike times at a clock rate of 1 MHz (models DA3-4 and ET1, respectively; Tucker-Davis Technologies [TDT], Gainesville, FL). Intracellular potentials and spike times were saved using custom-made software for Matlab 7.0.1 (The MathWorks, Natick, MA).
Sensory stimulation
Information about PM is extracted centrally by comparing differences in phase between different portions of the body surface (differential PM). To independently stimulate fish with AM and differential PM, we used a phase chamber to electrically isolate the head and trunk of each fish (Fig. 1A). Sinusoidal electric stimuli at a frequency within 20 Hz of the fish's EOD frequency before the experiment (ranging from 350 to 460 Hz) were delivered to both chambers using homemade isolators with field effect transistors. Both chambers received a single sinusoidal signal, in which the carrier signal and any modulations were numerically generated using custom-made software for Matlab 7.0.1, which controlled a D/A board using a sampling rate of 20 kHz (TDT model DA3-4). Two programmable attenuators (TDT model PA4) were used to set the carrier amplitude to values of 1–2 mV/cm as measured near the skin surface. Four different stimuli were used (Fig. 1B): sinusoidal AM presented alone, sinusoidal PM presented alone, Df >0 (sinusoidal AM and PM, with PM advanced by 90° relative to AM), and Df <0 (sinusoidal AM and PM, with PM delayed by 90° relative to AM). In each case, one chamber (head or trunk) received the modulated signal, whereas the other chamber received an unmodulated carrier signal (Fig. 1B). The depth of AM was set at 20–25% of the carrier amplitude, and the depth of PM was set at 15–20° of the carrier cycle.
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Data analysis
We ignored responses to the first modulation cycle to avoid any edge effects. Spiking responses to all four stimuli were assessed by determining mean spike rates and constructing histograms of spike times relative to the modulation cycle, in units of spikes per cycle (Carlson and Kawasaki 2004). To analyze the underlying membrane potentials, we removed spikes using a median filter with a width of 15 ms (Jagadeesh et al. 1993) and defined the resting potential as the mean membrane potential during the 1-s period preceding each stimulus modulation. We estimated the membrane potential derivatives by low-pass filtering the membrane potential using a cutoff frequency of 10 Hz and then differentiating the resulting waveform. To analyze PSP responses to all four stimuli, we calculated the average membrane potential and average derivative with respect to the stimulus modulation cycle and then analyzed a total of 11 different variables from these average responses, including the peak-to-peak PSP amplitude, the maximum and minimum PSP amplitudes relative to rest, the integral of the positive and negative portions of the PSP relative to rest, the maximum and minimum derivative, and the durations of the positive and negative portions of both the average PSP relative to rest and its derivative (rising and falling portions). We measured the degree of sign selectivity (SS) as
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; Jagadeesh et al. 1993).
For both the response histograms and average PSP responses, we compared the observed responses to Df >0 and Df <0 with a linear sum of the separate responses to AM and PM presented alone. Linear summations of the AM and PM responses were obtained in the following way. First, we subtracted either the resting spike rate (for the response histograms) or the resting potential (for the average PSP responses) from the AM and PM responses. Then, we advanced the average PM response by 90° for Df >0 or delayed the average PM response by 90° for Df <0 so that the response was aligned with the combination stimulus. Finally, we added the resulting responses to AM and PM. In the case of the response histograms, negative values were then changed to 0 because spike rates cannot be negative. To determine whether observed spiking responses to Df >0 and Df <0 deviated significantly from a linear sum, the observed spike rates from each modulation cycle were tested against the spike rate derived from the linear summation histogram using a single sample t-test. Observed spike rates that were significantly lower than a linear sum were classified as "suppressed" spike-rate responses, observed spike rates that were significantly greater than a linear sum were classified as "facilitated" spike-rate responses, and observed spike rates that were not significantly different from a linear sum were classified as "linear" spike-rate responses (Carlson and Kawasaki 2004). For the predicted linear PSP responses to Df >0 and Df <0, we measured the same 11 variables as we measured from the actual PSP responses (see above).
We used circular cross-correlation to examine the temporal relationship between the average PSP responses to AM and PM using custom-made software for Matlab 7.0.1 (Oppenheim et al. 1999). The circular cross-covariance (
AM · PM) between the average AM and PM responses is defined as
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is defined with respect to the stimulus modulation cycle (ranging from 0° at the start of the cycle to 360° at the end of the cycle), 
is the delay of the average PM response relative to the average AM response, and µAM and µPM are the means of the average AM and PM responses, respectively. The circular cross-correlation function (
AM · PM), which ranges from –1 (perfect negative correlation) to 1 (perfect positive correlation), is obtained by normalizing the cross-covariance by the autocovariance of the average AM and PM responses at = 0
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All statistical analyses were done using Statistica 6.1 (StatSoft, Tulsa, OK) with a two-tailed 
= 0.05. Unless otherwise stated, all reported values are the mean ± SD. To avoid the inclusion of multiple responses from individual neurons in statistical analyses, we included data obtained only from the modulation rate (1, 2, or 4 Hz) and chamber (head or trunk) that elicited the largest peak-to-peak PSP amplitude in response to either Df >0 or Df <0.
Modeling
We generated simplified, single-compartment, conductance-based models of synaptic integration for qualitative comparison with our intracellular recording data using the following equation for a leaky integrator with a sampling period of 1 ms
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), m is the membrane time constant, equal to the product of Rm and the total membrane capacitance (0.15 nF), Ee and Ei are the excitatory and inhibitory reversal potentials (0 and –75 mV, respectively), Ie is extrinsic current (in nA), rm is the specific membrane resistance (1 M · mm2), ge and gi are the excitatory and inhibitory specific conductances (in nS/mm2), and Pe and Pi describe the probability (ranging from 0 to 1) that excitatory and inhibitory channels are open (Dayan and Abbott 2001). Excitatory and inhibitory responses to sinusoidal stimulus modulations were simulated by specifying the values of ge and gi and varying the open probabilities (Pe and Pi) according to half-wave–rectified sine waves (the rectification prevents negative values) with an amplitude of 1 and a period of 1 s (corresponds to a modulation rate of 1 Hz). Pe had a start angle of 0°, whereas Pi had a start angle of 180°, so that increases in excitatory and inhibitory conductances were offset. To avoid edge effects, we simulated three cycles of stimulation and used the data from the second cycle. To simulate the effect of current injection on responses to a single feature (either AM or PM), we modeled responses in the presence of various values of Ie, which ranged from –0.4 to +0.4 nA. To simulate the integration of responses to two different features (AM and PM), we modeled separate responses to each feature individually and then summed the weighted conductances from the two inputs and modeled the resulting response to both features. To simulate responses to both signs of Df, the conductances from the two inputs were summed in phase (neither response is shifted, simulating the preferred sign of Df) and out of phase (one response is shifted by 180°, simulating the nonpreferred sign of Df). The resulting responses were compared with a linear sum of the two voltage responses, in the same way that the responses of actual neurons to Df >0 and Df <0 were compared with a linear sum of the responses to AM and PM (see above).
To study the effects of a voltage-dependent excitatory conductance, we used the same model, except that the value of ge at any given time was scaled as a sigmoidal function of the voltage at the previous time step (t – 1)
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RESULTS |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSREFERENCES |
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). Of these 67 neurons, 56 (83.58%) generated spikes during stimulus modulation and 11 (16.42%) did not. To investigate the basis of sign selectivity (SS), as measured from spike rate, we analyzed the PSP responses to Df >0 and Df <0 using 11 different measures (Table 1, METHODS). Among those neurons that generated spikes, there was a significant correlation between spike-rate SS and only two of these measures of PSP SS, i.e., the peak-to-peak PSP amplitude and maximum derivative (Table 1). Using peak-to-peak PSP amplitude as a measure of response, neurons with a SS >0.05 were categorized as Df >0 selective and neurons with a SS < –0.05 were categorized as Df <0 selective, resulting in a total of 28 Df >0-selective neurons, 23 Df <0-selective neurons, and 16 nonselective neurons. Unless otherwise stated, all reported SS values are based on peak-to-peak PSP amplitude.
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We tested the hypothesis that the observed sign selectivity resulted from a simple linear addition of the responses to AM and PM. After advancing the average PM response by 90° for Df >0 and delaying the average PM response by 90° for Df <0, we generated these predicted linear responses by simply summing the average responses to AM and PM, as illustrated in Fig. 3 (see METHODS). Responses to the preferred sign of Df were typically equal to or slightly weaker than the responses predicted by a linear sum (Fig. 3). By contrast, responses to the nonpreferred sign of Df were generally much weaker than the predicted responses (Fig. 3). In some cases, the response to the nonpreferred sign of Df was characterized by a reduction in peak-to-peak PSP amplitude compared with a linear sum (Fig. 3, A–C). In other cases, the peak-to-peak PSP amplitude was not substantially different from a linear sum, but the entire response was shifted in a hyperpolarizing direction (Fig. 3D).
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The maximum and minimum derivatives also deviated from the values predicted by a linear sum of the responses to AM and PM (Fig. 4B). The maximum derivative was slightly larger than predicted for the preferred sign of Df, but substantially smaller than predicted for the nonpreferred sign of Df (Fig. 4B), resulting in a significant difference between the preferred and nonpreferred sign of Df [z(51) = 2.859, P = 0.004]. The minimum derivative was slightly less negative than predicted for the preferred sign of Df and was substantially less negative than predicted for the nonpreferred sign of Df (Fig. 4B), also resulting in a significant difference [z(51) = 2.943, P = 0.003]. Therefore responses to the preferred sign of Df were characterized by much more rapid increases and decreases in membrane potential. No significant differences were found for the durations of the positive and negative portions of the responses [z(51) = 1.096, P = 0.27] or for the durations of the rising and falling portions of the responses [z(51) = 0.942, P = 0.35].
Relationship between spike-rate nonlinearities and PSP nonlinearities
For Df >0-selective neurons, the sign selectivity of spike rates (0.1689 ± 0.3516) was slightly larger than the sign selectivity of peak-to-peak PSP amplitudes (0.1127 ± 0.0399), although this difference was not significant [z(25) = 0.0942, P = 0.92]. The sign selectivity of spike rates for Df <0-selective neurons (–0.1889 ± 0.4130) was almost identical to that of peak-to-peak PSP amplitudes (–0.1911 ± 0.1155), also a nonsignificant difference [z(25) = 0.44802, P = 0.65]. This finding indicates that the spike-generating mechanism does not confer additional selectivity to these neurons.
Previous extracellular single-unit recordings from sign-selective toral neurons revealed that spike-rate responses to AM and PM frequently sum nonlinearly (Carlson and Kawasaki 2004). For example, the Df <0-selective neuron shown in Fig. 5A responded to Df >0 with a spike rate of 32.55 spikes/s, significantly lower than the spike rate of 42.17 spikes/s that was predicted by a linear sum of the responses to AM and PM [t(21) = 4.822, P = 0.00009]. By contrast, the spike rate of this neuron in response to Df <0 was 42.67 spikes/s, not significantly different from the predicted spike rate of 42.61 spikes/s [t(20) = 0.057, P = 0.95]. We recorded from 56 neurons that generated spikes in response to stimulus modulation, resulting in a total of 112 responses to Df >0 and Df <0. Of these 112 responses, 12 (10.71%) were characterized as facilitated spike-rate responses (observed spike rate significantly greater than a linear sum), 51 (45.54%) were characterized as suppressed spike-rate responses (observed spike rate significantly lower than a linear sum), and 49 (43.75%) were characterized as linear spike-rate responses (no significant difference between observed spike rate and linear sum).
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Postsynaptic potential interactions depend on the relative timing of the depolarizing and hyperpolarizing responses to AM and PM
The responses to AM and PM were typically aligned for the preferred sign of Df, whereas they were offset for the nonpreferred sign of Df (Fig. 3). We used circular cross-correlation to quantify the relative timing of the depolarizing and hyperpolarizing responses to AM and PM for the preferred and nonpreferred signs of Df (see METHODS). To do so, we first defined the average PSP responses to AM and PM as periodic functions of the angle , which ranges from 0 to 360° (Fig. 6, A and B), and then calculated the correlation between these two responses as a function of their relative delay, (Fig. 6C), which was arbitrarily set as the delay of the average PM response relative to the average AM response. The cross-correlation coefficients at = 90 and 270° give estimates of the degree of AM and PM response alignment for Df >0 and Df <0, respectively, because PM is advanced by 90° relative to AM for Df >0, whereas PM is delayed by 90° relative to AM for Df <0 (see Fig. 3).
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Conductance-based models of postsynaptic potential responses to AM and PM
We constructed simplified models of neuronal responses to changes in excitatory and inhibitory conductances and compared their behavior to the responses of sign-selective neurons to AM, PM, Df >0, and Df <0. These models are not meant to reproduce the actual responses of particular neurons, but simply to serve as conceptual models to help interpret the data from our intracellular recordings and better understand the interaction between synaptic responses to two stimulus attributes.
Figure 7A shows an example of two different inputs that give rise to exclusively excitatory responses. When both inputs occur in phase (corresponding to the preferred sign of Df), the response is weaker than a linear sum of the separate responses to each input, because of a mutual reduction in driving force (Johnston and Wu 1996). When both inputs occur out of phase (corresponding to the nonpreferred sign of Df), however, the response does not deviate from a linear sum because the depolarizations induced by both inputs are offset in time and the response to one input does not affect the driving force of the other. As seen in the graph to the right, this finding holds true regardless of the actual magnitude of the excitatory conductances. The same general result occurs when the two inputs give rise to exclusively inhibitory responses (Fig. 7B), also because of driving-force effects. These results are in stark contrast to the responses of actual sign-selective neurons, for which the deviation from a linear sum was greater when the AM and PM responses were out of phase. This indicates that the suppression of responses to the nonpreferred sign of Df cannot be accounted for by solely excitatory or solely inhibitory inputs.
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; Torre and Poggio 1978).
Voltage-dependent conductances provide another possible mechanism for the suppression of responses to the nonpreferred sign of Df (Magee 1999; Mel 1993). Figure 7D shows an example where the two inputs both consist of a combination of excitation and inhibition. The two panels show results from the same combination of excitatory and inhibitory conductances, except that the excitatory conductance of the example to the right is adjusted as a sigmoidal function of voltage (see METHODS). In the absence of this voltage dependency, there is a suppression of the combination response when the two inputs are either in phase or out of phase, resulting from driving-force reduction and inhibitory shunting, respectively. The addition of voltage dependency to the excitatory conductance, however, serves to linearize the combination response when the two inputs are in phase because the mutual reduction in driving force is somewhat mitigated by a voltage-dependent increase in excitatory conductance. On the other hand, when the two inputs are out of phase, the subtractive voltage effect is enhanced by a voltage-dependent reduction in excitatory conductance.
These modeling results suggest that both shunting inhibition and voltage-dependent conductances are potential mechanisms that could give rise to the observed responses of sign-selective midbrain neurons. To distinguish between these two possibilities, we modeled the effect of injecting various levels of holding current on the membrane potential responses to a single input. Figure 8 illustrates PSP responses in the presence of several holding currents for models consisting solely of excitation (Fig. 8A), solely of inhibition (Fig. 8B), a combination of inhibition and excitation (Fig. 8C), and a combination of inhibition and voltage-dependent excitation (Fig. 8D). To quantify the changes in model PSP responses caused by applying various holding currents, we determined the timing of the maximum and minimum values of the average PSP responses during no current injection (tmax and tmin, respectively, as illustrated in the left panels of Fig. 8, A–D), and then determined the difference in membrane potential measured between these two time points at each holding current [V(tmax) – V(tmin)]. For all possible combinations of excitatory and inhibitory conductances without any voltage dependency, the relationship between V(tmax) – V(tmin) and holding current is linear, with the direction and slope of the relationship depending on the relative balance of excitation and inhibition (Fig. 8, A–C). The addition of voltage dependency to the excitatory conductance, however, makes the relationship between V(tmax) – V(tmin) and holding current nonlinear, with V(tmax) – V(tmin) peaking at a value that depends on the quantitative characteristics of the voltage dependency and the magnitudes of the excitatory and inhibitory conductance changes (Fig. 8D).
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We stimulated several neurons (n = 28) with sinusoidal AM and PM while subjecting the neurons to various holding currents ranging from –0.4 to +0.2 nA and obtained the values of V(tmax) – V(tmin) for each level of holding current. Figure 9A shows examples of the average PSP responses of three neurons to sinusoidal AM at several holding currents and Fig. 9B shows plots of V(tmax) – V(tmin) as a function of holding current for 10 additional neurons, along with the spike rates of the same ten neurons during sinusoidal AM stimulation. In each case, the relationship between V(tmax) – V(tmin) and holding current is nonlinear, with maximum values of V(tmax) – V(tmin) occurring between –0.1 and 0 nA (Fig. 9B). We recorded similar responses to sinusoidal PM under different holding currents (Fig. 9, C and D), indicating that the PSP responses to both AM and PM are shaped by voltage-dependent conductances.
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The evidence for voltage-dependent conductances shaping the responses to AM and PM, combined with the model results illustrating the effects that voltage-dependent conductances can have on the synaptic integration of two inputs, suggest the following hypothesis for the nonlinear enhancement of sign selectivity: when the depolarizing response to AM coincides with the hyperpolarizing response to PM, and vice versa, the subtractive effect of the hyperpolarization is enhanced because of a reduction in voltage-dependent excitatory conductance. To test this hypothesis, we compared the responses of sign-selective neurons to Df >0 and Df <0 during no current injection with the responses obtained while the neurons were subjected to hyperpolarizing and depolarizing holding currents.
Figure 10, A and B, shows the responses of two Df <0-selective neurons to Df >0 and Df <0 in the absence of current injection and in the presence of various holding currents. In both cases, the responses at rest consist of the typical alternation between hyperpolarization and depolarization and the response to Df <0, but not Df >0, is characterized by a sharp depolarization that appears to ride on top of the underlying smooth depolarization. In response to hyperpolarizing current injection, this enhanced response to Df <0 is reduced in magnitude, thereby decreasing sign selectivity. By contrast, injecting moderate levels of depolarizing current appears to boost the response to Df >0 by recruiting the enhanced depolarization, again reducing sign selectivity. Injecting a greater amount of depolarizing current (in Fig. 10A) eliminates this enhanced depolarization from the responses to both Df >0 and Df <0.
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DISCUSSION |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSREFERENCES |
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). Our earlier extracellular recordings from sign-selective neurons revealed that the integration of responses to AM and PM is often nonlinear and, furthermore, that this nonlinearity depends on the relative timing of responses to the two features (Carlson and Kawasaki 2004). By combining experimental results from intracellular recordings with simplified models of synaptic integration, we show that this timing-dependent, nonlinear integration results from a combination of voltage-dependent excitatory postsynaptic potentials (EPSPs) and inhibitory postsynaptic potentials (IPSPs). The responses to both AM and PM presented alone are characterized by alternating EPSPs and IPSPs. For the preferred sign of Df, these alternating responses to AM and PM are in phase and the additive effect of simultaneous EPSPs causes a voltage-dependent increase in excitatory conductance, which somewhat mitigates the effects of reduced driving force. For the nonpreferred sign of Df, these alternating responses are offset and the subtractive effect of IPSPs coinciding with EPSPs is enhanced because of a voltage-dependent decrease in excitatory conductance. The net result is that the voltage dependency causes an increase in sign selectivity, revealing that a voltage-dependent excitatory conductance can act as a nonlinear decoder for enhancing combination sensitivity. The evidence that voltage-dependent conductances are responsible for the nonlinear integration of responses to AM and PM comes from two primary pieces of evidence. First we found a nonlinear relationship between holding current and our measure of V(tmax) – V(tmin) for the responses to both AM and PM presented alone (Fig. 9); our modeling results reveal that this relationship is linear in the absence of voltage dependency (Fig. 8). Second, the degree of sign selectivity and the linearity of AM and PM response summation were significantly affected by current injection (Fig. 10), which would not be the case if nonlinear integration resulted solely from driving-force effects, inhibitory shunting, or extrinsic processes such as presynaptic inhibition.
The spike-rate data indicate that neurons were still operating within a physiologically relevant voltage range at holding currents for which V(tmax) – V(tmin) was maximal (Fig. 9, B and D), which is supported by the fact that 0.05 nA injected into a neuron with an input resistance of 200 M corresponds to a voltage shift of only 10 mV. Therefore although it is not possible to exclude a role for additional mechanisms, our results clearly implicate voltage-dependent conductances in the enhancement of sign selectivity. Future studies will seek to determine whether these conductances arise from synaptically driven, ligand-gated channels, such as NMDA-type glutamate receptors, or from channels sensitive only to voltage, such as Na+ channels (Fortune and Rose 2003). The relatively long time course of PSPs that we observed (on the order of hundreds of milliseconds) would seem to implicate NMDA receptors, because voltage-gated ion channels typically have much more rapid activation and inactivation kinetics (on the order of milliseconds; Johnston and Wu 1996). NMDA receptors play an important role in sensory processing for both visual and auditory systems (Daw et al. 1993; Feldman and Knudsen 1994; Zhang and Kelly 2001) and their unique pharmacological characteristics make them ideally suited for nonlinear processing and for fine-tuning the temporal dynamics of synaptic responses (Gasic and Hollman 1992; Mel 1992, 1993).
We have not directly demonstrated the presence of inhibitory synapses on sign-selective neurons. By injecting sufficient levels of hyperpolarizing current, however, it was possible to change responses that consisted of alternating depolarizations and hyperpolarizations into purely depolarized responses (Fig. 9, A and C), strongly indicating that inhibition is responsible for these hyperpolarizations. Preliminary results using anti–-aminobutyric acid (GABA) and anti–glutamic acid decarboxylase (GAD) immunocytochemistry reveal substantial numbers of GABAergic neurons, fibers, and terminals within the electrosensory torus (Y. Zhang, B. A. Carlson, and M. Kawasaki, unpublished observation), providing further support for this hypothesis. In the auditory forebrain of songbirds, the strong selectivity of combination-sensitive neurons for the bird's own song is also dependent on inhibitory processing (Lewicki 1996; Mooney and Prather 2005; Rosen and Mooney 2006).
Although early models of dendritic integration based purely on the passive cable properties of dendrites have proven quite powerful in understanding many features of synaptic integration (Rall 1964), it is becoming increasingly clear that these passive properties are insufficient to account for the impressive computational power of single neurons (Koch and Poggio 1992; Magee 1999, 2000; Rall 1999). Voltage-gated ion channels are now known to occur in the dendrites of many different types of neurons in the CNS of vertebrates (Llinás 1988; Magee 1999; Reyes 2001). The effects of these voltage-dependent conductances on the electrical properties of neurons and the resulting implications for their input–output functions have primarily been studied in vitro (Häusser et al. 2000; Magee 2000; Reyes 2001). The role of voltage-dependent conductances in the processing of natural, behaviorally relevant sensory stimuli in vivo has not received a great deal of attention, largely as a result of the difficulty of manipulating ion channel conductance in intact preparations. However, studies on electrosensory neurons of the weakly electric fish Eigenmannia (Fortune and Rose 1997) and visual interneurons of the blowfly Calliphora (Haag and Borst 1996) showed that voltage-dependent membrane conductances can play an important role in shaping the frequency filtering of sensory neurons by either enhancing or counteracting the underlying passive filtering properties. In Calliphora, a fast, inward, voltage-dependent sodium current gives rise to a frequency-dependent amplification of visual synaptic inputs that allows neurons with these currents to respond to much higher frequencies of stimulation than neurons that lack these currents (Haag and Borst 1996). By contrast, voltage-dependent conductances in Eigenmannia serve to boost the underlying passive filtering properties of electrosensory neurons and thereby sharpen frequency tuning (Fortune and Rose 1997). There appear to be two distinct voltage-dependent conductances in these electrosensory neurons, one arising from voltage-gated Na+ channels that give rise to a constant duration potential and the other possibly resulting from NMDA-type glutamate receptors that give rise to variable-duration potentials (Fortune and Rose 1997, 2003).
Our findings in the electrosensory system of Gymnarchus add another function for voltage-dependent conductances in the processing of natural, behaviorally relevant stimuli, that is, enhancing selectivity for particular temporal combinations of stimulus attributes. Our modeling results reveal that voltage-dependent conductances can serve to linearize the summation of two inputs occurring in phase with each other by partially mitigating the effects of reduced driving force. A linearizing effect of voltage-dependent conductances on simultaneous synaptic inputs was previously shown using more formal, biophysically detailed compartmental models (Bernander et al. 1994) and was also explicitly demonstrated in vitro (Cash and Yuste 1999). On the other hand, our modeling results also reveal that voltage-dependent conductances can act to suppress the summation of two inputs occurring out of phase with each other by enhancing the subtractive effect of hyperpolarizations on depolarizations. Along these same lines, intracellular recordings in vitro and from cultured neurons showed that voltage-dependent conductances can enhance sensitivity to differences in the relative timing of multiple synaptic inputs (Margulis and Tang 1998; Nettleton and Spain 2000). The current study provides evidence that these characteristics of voltage-dependent conductances play an important role in the processing of behaviorally relevant sensory information in vivo.
Previously, we demonstrated that the spiking responses of sign-selective toral neurons in Gymnarchus are often nonlinear (Carlson and Kawasaki 2004). Although nonlinear spiking responses can arise from a linear summation of the underlying PSPs (Ferster 1994; Jagadeesh et al. 1993), the current study reveals that the spiking nonlinearities of sign-selective neurons in Gymnarchus are associated with nonlinear interactions between the PSP responses to AM and PM. Indeed, we did not find any significant difference between spike-rate sign selectivity and peak-to-peak PSP amplitude sign selectivity. However, facilitated spike rates were not associated with peak-to-peak PSP amplitudes that were greater than a linear sum of the responses to AM and PM; instead, the peak-to-peak PSP amplitudes were approximately equal to a linear sum (Fig. 5B). Linear spike-rate responses were characterized by peak-to-peak PSP amplitudes that were smaller than a linear sum and suppressed spike-rate responses were characterized by even greater sublinear deviations (Fig. 5B). This finding is not surprising, given the nonlinear relationship between membrane potential and spike rate. By contrast, spiking nonlinearities were directly related to deviations of the maximum PSP derivatives (Fig. 5C). Thus facilitated spike rates may be caused by faster increases in membrane potential, which may in turn arise from activation of voltage-dependent conductances in response to the preferred sign of Df. By contrast, suppressed spike rates may be caused by slower increases in membrane potential associated with the reduced activation of voltage-dependent conductances.
The weakly electric fish Eigenmannia is only distantly related to Gymnarchus and the available evidence indicates that they share no common electrogenic or electroreceptive ancestors (Bullock et al. 1983). However, both species perform a JAR that is based on the same computational algorithm of comparing the temporal relationship between AM and PM to determine the sign of Df (Bullock et al. 1975; Fortune et al. 2006; Heiligenberg 1991; Kawasaki 1993). Like Gymnarchus, Eigenmannia has separate electrosensory pathways devoted to encoding these two stimulus features that converge onto sign-selective neurons in the midbrain torus semicircularis (Fortune et al. 2006; Heiligenberg and Rose 1986; Rose and Heiligenberg 1986). Sign-selective neurons in Eigenmannia also show a nonlinear summation of the spike-rate responses to AM and PM and the preferred sign of Df is likewise the one in which these two responses are aligned. Although the underlying postsynaptic potentials have not been explored, the demonstrated existence of voltage-dependent conductances in electrosensory midbrain neurons in Eigenmannia (Fortune and Rose 1997, 2003) suggests that they may also play a role in enhancing the sign selectivity of combination-sensitive neurons in Eigenmannia.
Combination-sensitive neurons are widespread in the auditory and visual systems as well and they exhibit similar nonlinear summations of spike-rate responses to multiple stimulus features (Fuzessery and Feng 1983; Margoliash 1983; Misawa and Suga 2001; Peña and Konishi 2001; Quiroga et al. 2005; Tsao et al. 2006). The widespread occurrence of voltage-dependent conductances in the dendrites of vertebrate neurons and the straightforward mechanism by which these conductances can enhance stimulus selectivity indicate that our findings are likely to prove broadly relevant as a mechanism for extracting information about behaviorally relevant combinations of different stimulus features. Nonlinear decoders, in the form of voltage-dependent conductances, are important candidates for the dynamic enhancement of responses to particular temporal patterns of multiple synaptic inputs.
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