Frequency tuning of synaptic inhibition underlying duration-tuned neurons in the mammalian inferior colliculus

Duration-tuned neurons (DTNs) arise from temporally offset excitatory and inhibitory synaptic inputs. We used single-unit recording and paired-tone stimulation to measure the spectral tuning of the inhibitory inputs to DTNs. The onset of inhibition was independent of stimulus frequency; the offset and duration of inhibition systematically decreased as the stimulus departed from the cell’s best excitatory frequency. Best inhibitory frequencies matched best excitatory frequencies; however, inhibitory bandwidths were more broadly tuned than excitatory bandwidths.

Abstract

Inhibition plays an important role in creating the temporal response properties of duration-tuned neurons (DTNs) in the mammalian inferior colliculus (IC). Neurophysiological and computational studies indicate that duration selectivity in the IC is created through the convergence of excitatory and inhibitory synaptic inputs offset in time. We used paired-tone stimulation and extracellular recording to measure the frequency tuning of the inhibition acting on DTNs in the IC of the big brown bat (Eptesicus fuscus). We stimulated DTNs with pairs of tones differing in duration, onset time, and frequency. The onset time of a short, best-duration (BD), probe tone set to the best excitatory frequency (BEF) was varied relative to the onset of a longer-duration, nonexcitatory (NE) tone whose frequency was varied. When the NE tone frequency was near or within the cell’s excitatory bandwidth (eBW), BD tone-evoked spikes were suppressed by an onset-evoked inhibition. The onset of the spike suppression was independent of stimulus frequency, but both the offset and duration of the suppression decreased as the NE tone frequency departed from the BEF. We measured the inhibitory frequency response area, best inhibitory frequency (BIF), and inhibitory bandwidth (iBW) of each cell. We found that the BIF closely matched the BEF, but the iBW was broader and usually overlapped the eBW measured from the same cell. These data suggest that temporal selectivity of midbrain DTNs is created and preserved by having cells receive an onset-evoked, constant-latency, broadband inhibition that largely overlaps the cell’s excitatory receptive field. We conclude by discussing possible neural sources of the inhibition.

NEW & NOTEWORTHY Duration-tuned neurons (DTNs) arise from temporally offset excitatory and inhibitory synaptic inputs. We used single-unit recording and paired-tone stimulation to measure the spectral tuning of the inhibitory inputs to DTNs. The onset of inhibition was independent of stimulus frequency; the offset and duration of inhibition systematically decreased as the stimulus departed from the cell’s best excitatory frequency. Best inhibitory frequencies matched best excitatory frequencies; however, inhibitory bandwidths were more broadly tuned than excitatory bandwidths.

temporal features of bioacoustic stimuli are critical for conveying information regarding signal meaning. Examples of temporal features include the rate and direction of frequency modulation, the rate and depth of amplitude modulation, the sequence of acoustic elements in a complex signal, and signal duration. Within the central nervous system there exists a class of auditory cells with spiking responses selective for signal duration called duration-tuned neurons (DTNs). These cells provide a potential neural mechanism for duration discrimination on the order of milliseconds such as observed in human speech (Shannon et al. 1995), amphibian mating calls (Narins and Capranica 1980), and the vocalizations of echolocating bats (Schnitzler and Kalko 2001). Moreover, DTNs have been reported from multiple sensory modalities (Duysens et al. 1996) and vertebrate species (Brand et al. 2000; He et al. 1997; Leary et al. 2008; Pérez-González et al. 2006; Wang et al. 2006), and in each case neuronal best durations correlate with species-specific stimulus durations. Thus duration selectivity is hypothesized to be a general feature of sensory processing that has been adapted to the biological constraints of an organism (Sayegh et al. 2011).

The spectral tuning of auditory DTNs is of particular interest given that spectral and temporal features of biological sounds are often comodulated (Heil et al. 1992; Suga 1984). Recent studies have shown that DTNs in the mammalian inferior colliculus (IC) show a trade-off in their spectro-temporal response resolutions in a manner analogous to resonant electrical filters (Morrison et al. 2014). Moreover, the frequency selectivity of a DTN can change when it is stimulated with sound pulses that are varied in duration (Wu and Jen 2008a). These findings demonstrate that the temporal features of an acoustic stimulus can modify the frequency tuning of the inputs to DTNs; however, it is unknown how the inhibitory inputs underlying the temporally selective responses of DTNs are modified by stimulus frequency. These data are important because they may provide information about the anatomical origin and function(s) of the inhibitory synaptic inputs to midbrain DTNs.

The present study used a modified version of paired-tone stimulation (Faure et al. 2003) to characterize the spectral tuning of the inhibitory inputs acting on DTNs in the IC. The paradigm involves stimulating a DTN with a pair of pure tone pulses: a short-duration, excitatory probe tone set to the cell’s best duration (BD) and best excitatory frequency (BEF) and a longer-duration, nonexcitatory (NE) tone that was varied in frequency. The strength and time course of the inhibition evoked by the NE tone were quantified by varying the interstimulus interval (ISI) of the tone pair and measuring the range of ISIs over which BD tone-evoked responses were suppressed by the NE tone. We found that the onset of inhibition acting on DTNs had a constant latency when the NE tone frequency was near or within the cell’s excitatory bandwidth (eBW); however, the duration of the spike suppression systematically decreased as the frequency of the NE tone moved away from its BEF. We used this response feature to measure the best inhibitory frequency (BIF) and inhibitory bandwidth (iBW) of each cell. Our results show that BIFs of DTNs matched their BEFs; however, the iBW was more broadly tuned and largely overlapped the eBW of the same cell. We conclude that this wideband inhibition, which is responsible for creating the physiological property of duration selectivity, helps to preserve the temporal specificity of auditory DTNs in the mammalian IC.

MATERIALS AND METHODS

Surgical preparation.

Electrophysiological recordings were obtained from the IC of 19 big brown bats (Eptesicus fuscus) of both sexes (5 male, 14 female). Before recording, each bat underwent a preparatory surgery in which a small stainless steel post was glued to the dorsal surface of the skull. The head post prevented movement of the bat’s head during recording and precisely replicated the head position between sessions in the stereotaxic apparatus (David Kopf Instruments model 1900). Before surgery, bats were administered buprenorphine (Temgesic) (~0.03 ml sc; 0.025 mg/kg) and placed in an anesthesia induction chamber (12 × 10 × 10 cm, length × width × height), where they inhaled a 1–5% isoflurane-oxygen mixture (flow rate = 1 l/min). The anesthetized bat was then placed in a foam-lined body restraint, which held the bat firmly but comfortably while still allowing access to the bat’s head. The bat’s mouth was placed in a custom bite bar designed to keep the head stable during surgery and fitted with a custom gas mask for continuous anesthetic inhalation. The hair overlying the skull was shaved, and the skin was disinfected with a povidone-iodine surgical scrub (Betadine). A local anesthetic (~0.2 ml bupivacaine sc; 5 mg/ml) was administered before a midline incision was made in the scalp. The temporal muscles were reflected to reveal the dorsal surface of the skull, which was then scraped clean and swabbed with 70–100% ethanol. After drying, a metal head post was glued to the skull overlying the cortex with cyanoacrylate superglue cured with liquid hardener (Pacer Zip Kicker). One end of a chlorided silver wire attached to the head post was placed under the temporal musculature and served as the reference electrode. The wound was then covered with a piece of Gelfoam coated with Polysporin to prevent infection. After surgery, bats were allowed to recover individually in a stainless steel holding cage (¼-in. mesh) located in a temperature- and humidity-controlled room and were provided food and water ad libitum. All procedures were approved by the McMaster University Animal Research Ethics Board and were in accordance with guidelines for the care and use of experimental animals published by the Canadian Council on Animal Care.

Electrophysiological recordings.

Recordings began 1–2 days after surgery. Each bat was used in one to eight recording sessions lasting 4–8 h each and conducted on separate days. Neural recordings were terminated if the bat showed any signs of discomfort. Between sessions, the electrode penetration site was covered with a piece of contact lens and Gelfoam coated in Polysporin. Recordings were conducted inside a double-walled sound attenuation booth with electrical shielding (Industrial Acoustics). Before recording, bats were administered a neuroleptic [0.3 ml; 1:1 (vol/vol) mixture of 0.025 mg/ml fentanyl citrate and 1.25 mg/ml Inapsine (droperidol); 19.1 mg/kg]. Once this took effect, bats were placed in a foam-lined body restraint that was suspended by springs within a small-animal stereotaxic frame customized for bats (ASI Instruments). The entire apparatus was set atop an air vibration table (TMC Micro-G). The bat’s head was immobilized by securing the head post to a stainless steel rod attached to a manual micromanipulator (ASI Instruments) mounted on the stereotaxic frame (David Kopf Instruments). A craniotomy was performed with a scalpel blade, and the dura mater over the dorsal portion of the IC was removed with a sharp pin for the insertion of recording electrodes. The IC can be visually identified as two white ellipses below the translucent skull. Single-unit extracellular recordings were obtained with thin-walled borosilicate glass microelectrodes (outside diameter = 1.2 mm; A-M Systems) filled with 1.5 M NaCl. Typical electrode resistances ranged between 15 and 30 MΩ. Electrodes were positioned over the exposed IC with manual micromanipulators (ASI Instruments) and advanced into the brain with a stepping hydraulic micropositioner (Kopf model 2650). Extracellular action potentials were recorded with a neuroprobe amplifier (A-M Systems model 1600) whose 10× output was band-pass filtered and further amplified (500–1,000×) by a Tucker Davis Technologies spike preconditioner (TDT PC1; low-pass f_c = 7 kHz, high-pass f_c = 300 Hz). Spike times were logged onto a computer by passing the TDT PC1 output to a spike discriminator (TDT SD1) and then an event timer (TDT ET1) synchronized to a timing generator (TDT TG6).

Stimulus generation and data collection.

Stimulus generation and online data collection were controlled with custom software that shows spike times as dot raster displays ordered by the acoustic parameter that was varied. Sound stimuli were digitally generated with a two-channel array processor (TDT Apos II; 357 kHz sampling rate) optically interfaced to two digital-to-analog converters (TDT DA3-2) whose individual outputs were fed to a low-pass antialiasing filter (TDT FT6-2; f_c = 120 kHz), a programmable attenuator (TDT PA5), and two signal mixers (TDT SM5) with equal weighting. The output of each mixer was then fed to a manual attenuator (Leader LAT-45) before final amplification (Krohn-Hite model 7500). Stimuli were presented monaurally with a Brüel & Kjær (B&K) ¼-in. condenser microphone (type 4939; protective grid on), modified for use as a loudspeaker with a transmitting adaptor (B&K type UA-9020) to correct for nonlinearities in the transfer function. The loudspeaker was positioned ∼1 mm in front of the external auditory meatus. The output of the speaker, measured with a B&K type 4138 ⅛-in. condenser microphone (90° incidence; grid off) connected to a measuring amplifier (B&K type 2606) and a band-pass filter (Krone-Hite model 3500), was quantified with a sound calibrator (B&K type 4231) and is expressed in decibels sound pressure level (dB SPL re 20 µPa) equivalent to the peak amplitude of continuous tones of the same frequency. The loudspeaker transfer function was flat ± 6 dB from 28 to 118 kHz, and there was at least 30-dB attenuation at the ear opposite the source (Ehrlich et al. 1997). At sound frequencies <15 kHz the transducers generate harmonic distortions. To compensate for the distortions, we excluded data points collected with frequencies <15 kHz. All stimuli had rise/fall times of 0.4 ms, shaped with a square cosine function, and were presented at a rate of 3 Hz.

Search stimuli consisted of two pure tones that differed in duration (typically 1 and 4 ms, ISI ≥ 110 ms) and were presented monaurally to the ear contralateral to the IC recorded. Upon isolating a unit we determined its BEF (0.1- to 1-kHz resolution), BD (1-ms resolution), and duration filter response class at the BEF (Sayegh et al. 2011). Our study focused specifically on DTNs, so we did not record responses from other types of IC neurons.

Previous studies have categorized DTNs into three duration filter response classes depending on the relative number of spikes evoked across all stimulus durations tested. Our study focused exclusively on band-pass and short-pass DTNs. Band-pass DTNs respond maximally at the BD and drop to ≤50% of the peak spike count in response to stimulus durations both shorter and longer than the BD. Short-pass DTNs also respond maximally at the BD and drop to ≤50% of the peak spike count in response to stimulus durations that are longer, but not shorter, than the BD. Example duration raster plots and duration filter functions for a band-pass and a short-pass DTN are shown in Fig. 1.

Fig. 1.

Duration-tuned neurons (DTNs) from the inferior colliculus (IC) of the big brown bat. A: band-pass DTN with a best duration of 2 ms. B: short-pass DTN with a best duration of 1 ms. Top: dot raster displays showing the timing of action potentials in response to suprathreshold best excitatory frequency (BEF) tone pulses that were randomly varied in duration. Bottom: mean ± SE spikes per stimulus as a function of stimulus duration for suprathreshold BEF tones. Stimulus level was +20 dB (A) and +10 dB (B) re threshold. n = 10 trials per stimulus.

Using BEF and BD stimuli, we then measured the cell’s rate-level function and minimum acoustic response threshold (5-dB resolution). With this information, a cell’s excitatory frequency response area (eFRA) was measured at +10 dB re threshold to determine its excitatory spectral bandwidth (eBW), defined as the lowest and highest frequencies where the spike count was ≥50% of the maximum. We used the eBW of each cell to calculate a quality (Q) factor that describes the sharpness of frequency tuning, defined as Q_{10 dB} = BEF/eBW.

Paired-tone stimulation with BEF and non-BEF NE tones.

We used paired-tone stimulation to measure the strength and time course of the inhibition evoked by a longer-duration NE tone that was varied in frequency. The paradigm consisted of stimulating a cell with a pair of pure tone pulses that differed in duration and ISI (Faure et al. 2003). The BD tone was set to the cell’s BD and BEF to evoke maximal excitation. The NE tone was set to a nonexcitatory duration that was typically 10 times the duration of the BD tone. We did this to ensure that the NE tone would be nonexcitatory and so that there would be a constant energy relationship between the two signals, regardless of each cell’s actual BD. The onset time of the NE tone was fixed between stimulus presentations, while the onset time of the BD tone was randomly varied in 2- to 4-ms steps so that it preceded, overlapped with, and followed the NE tone. The two tones were electronically mixed and presented to the contralateral ear at an amplitude of +10 dB re BD tone threshold. The BD and NE tones were matched in starting phase and could constructively or destructively interfere when they overlapped. When the BD and NE tones were matched in frequency the two signals always constructively interfered, resulting in a composite signal with an amplitude pedestal of +6 dB for the duration of overlap. When the BD and NE tone frequencies were not matched, the resultant signal contained an amplitude pedestal that was sinusoidally amplitude modulated with a modulation index = 1.

To quantify the spectral properties of the inhibition acting on DTNs, we first collected responses with the BD and NE tones matched to the cell’s BEF. We then collected responses from the same cell with the BD tone set to the BEF and the NE tone mismatched in frequency. We tested all DTNs with five NE tone frequencies standardized to the eBW of each cell (Fig. 2). To obtain these frequencies, the eBW was first divided into lower (L_eBW) and higher (H_eBW) spectral partitions (re BEF). The five standardized NE tone frequencies were selected as 1) 1.5 times the span of the L_eBW below the BEF (1.5L_eBW), 2) the midpoint of the L_eBW (0.5L_eBW), 3) the BEF, 4) the midpoint of the H_eBW (0.5H_eBW), and 5) 1.5 times the span of the H_eBW above the BEF (1.5H_eBW). Thus each cell was tested with at least three NE tone frequencies within its 50% eBW (BEF, 0.5L_eBW, 0.5H_eBW) and two NE tone frequencies outside its 50% eBW (1.5L_eBW, 1.5H_eBW). Whenever possible, additional NE tone frequencies were also tested.

Fig. 2.

Determining the 5 standardized NE tone frequencies. Duration-selective neurons were tested with paired-tone stimulation using 5 NE tone frequencies that were standardized relative to the eBW (gray box) of each cell. Figure illustrates a hypothetical isolevel eFRA of a DTN, obtained by recording the number of spikes in response to single BD tones varied in frequency and presented at +10 dB above threshold. The cutoff frequencies (edges of gray box) of the eBW were defined as the lowest and highest stimuli evoking ≥50% (horizontal dashed line) of the maximum spike count measured at the BEF. The eBW was divided into lower (L_eBW) and higher (H_eBW) spectral partitions re BEF (white arrows), and 5 standardized NE tone frequencies (black dots) were selected as 1) 1.5 times the L_eBW below the BEF (1.5L_eBW), 2) the midpoint of the L_eBW (0.5L_eBW), 3) the BEF, 4) the midpoint of the H_eBW (0.5H_eBW), and 5) 1.5 times the H_eBW above the BEF (1.5H_eBW). Thus each cell was tested with at least 3 NE tone frequencies within its 50% eBW (BEF, 0.5L_eBW, 0.5H_eBW) and 2 NE tone frequencies outside its 50% eBW (1.5L_eBW, 1.5H_eBW). Whenever possible, additional NE tone frequencies (not shown) were also tested.

This version of the paired-tone stimulation paradigm is analogous to the classic two-tone stimulation paradigm used for measuring the inhibitory frequency tuning properties of auditory neurons (Fuzessery and Feng 1982; Sutter et al. 1999). In two-tone stimulation cells are presented with a pair of pure tones, with the probe tone fixed to the cell’s BEF (analogous to our BD tone) and a test tone that is varied in frequency (analogous to our NE tone). Unlike classic two-tone stimulation, our paired-tone stimulation paradigm used two signals of unequal duration. The NE tone was 10 times the duration of the BD tone and, critically, was varied in ISI to measure the time course of the inhibition evoked by the NE tone.

Measuring onset and offset of inhibition with spike counts and latencies.

We measured the duration and latency of the inhibition evoked by the NE tone by observing the time points when the BD tone-evoked spike count became suppressed and/or altered in latency, using the same criteria as Sayegh et al. (2014). To measure the time course of the inhibition evoked by the NE tone, we first quantified the cell’s baseline responses evoked by the BD tone at the 10 longest ISIs when the BD tone preceded the NE tone (see baseline data points in Fig. 3). This baseline reflects responses evoked by the BD tone in the absence of inhibition evoked by the NE tone. For each cell, we calculated the mean ± SD baseline spike count, first spike latency (FSL), and last spike latency (LSL). For the example short-pass DTN in Fig. 3A, baseline spiking was measured from responses falling within the parallelogram. The baseline spike count was 1.76 ± 0.80 spikes per stimulus, whereas the baseline FSL was 21.66 ± 2.06 ms and the baseline LSL was 25.25 ± 2.93 ms. Using three criteria, we compared baseline responses with those obtained at each ISI to determine when spike counts or latencies were altered by NE tone-evoked inhibition.

Fig. 3.

Measuring the time course of inhibition with paired-tone stimulation. A: dot raster display showing how changes in a cell’s spike count and/or latencies in response to a roving BD tone were used to infer the time course of the synaptic inhibition evoked by the NE tone with the equations displayed at bottom. The onset time of the BD tone (3-ms black bars) was randomly varied relative to the onset of the NE Tone (30-ms black bar; drawn once for clarity). Bottom x-axis shows time relative to the onset of the NE tone; top x-axis shows the ISI or gap between BD and NE tones. y-Axis shows the offset time of the BD tone relative to the onset time of the NE tone. The 2 tones were electronically mixed and presented monaurally to the ear contralateral to the IC recorded. When the 2 tones were temporally contiguous or overlapping (gray box), a single compound stimulus with an amplitude pedestal resulted. A BD tone bar with a white fill indicates when the BD and NE tones were contiguous. Responses from the first 10 trials with the longest ISIs (spikes in parallelogram) were used to calculate a mean ± SD baseline spike count (1.76 ± 0.80 spikes/stimulus), FSL (L_first = 21.66 ± 2.06 ms), and LSL (25.25 ± 2.93 ms); data points averaged in the baseline calculation are shown as white circles with an X. During paired-tone stimulation BD tone-evoked responses were suppressed by inhibition evoked by the NE tone. Three criteria were used to determine the effective onset (T₁) and offset (T₂) of the inhibition evoked by the NE tone using changes in spike count, FSL, and/or LSL. The first ISI with a significant deviation from the baseline spike count and/or latency was T₁ = −3 ms and was measured with a LSL criterion. The largest ISI with a significant deviation from the baseline spike count or latency was T₂ = 39 ms and was measured with either a spike count or FSL criterion. With the equations shown, T_start = 19.25 ms and T_end = 57.66 ms, resulting in an effective duration of inhibition of 38.41 ms. B: mean ± SE spikes per stimulus plotted as a function of the ISI between the BD and NE tones. Dashed line represents 50% of the baseline spike count. Leftmost open circle is the first ISI with an evoked spike count ≤50% of baseline spike count (T₁ = −1 ms). Rightmost open circle shows the last ISI with an evoked spike count ≤50% of baseline (T₂ = 39 ms). C: mean ± SE FSL as a function of the ISI between the BD and NE tones. Dashed lines represent ±1 SD from the baseline FSL. Leftmost open circle shows the first ISI when the FSL deviated by >1 SD from baseline (T₁ = 1 ms). Rightmost open circle shows the last ISI when the FSL remained deviated by >1 SD from baseline (T₂ = 39 ms). D: mean ± SE LSL as a function of the ISI between the BD and NE tones. Dashed lines represent ±1 SD from the baseline LSL. Leftmost open circle shows the first ISI when the LSL deviated by >1 SD from baseline (T₁ = −3 ms). Rightmost open circle shows the last ISI when the LSL remained deviated by >1 SD from baseline (T₂ = 1 ms). The final values of T₁ (−3 ms) and T₂ (39 ms) were those that most sensitively reflected the time course of the NE tone-evoked inhibition. n = 10 trials per stimulus.

As in our previous studies with paired-tone stimulation, we used a combination of detection criteria to measure the time course of inhibition evoked by the NE tone (Faure et al. 2003; Sayegh et al. 2012, 2014). We used a 50% change in the evoked spike count as the initial criterion to delineate the time points for the onset and offset of spike suppression. Whenever possible, we also used a 1 SD change in spike latency to further refine and extend those estimates because we have found spike latency changes to be a more sensitive indicator for the presence of inhibition than changes in spike counts.

With a spike count criterion, spiking was said to be suppressed when the mean spikes per stimulus decreased to ≤50% of baseline. The use of this criterion is depicted in Fig. 3B; data points below the dashed line, which represents 50% of the baseline spike count, were defined as suppressed. With a FSL criterion, spiking was said to be altered when the mean FSL deviated by >1 SD from baseline. The use of this criterion is depicted in Fig. 3C; data points falling above or below the two dashed lines, which represent ±1 SD of the baseline FSL, were defined as altered. Finally, with a LSL criterion, spiking was said to be altered when the mean LSL deviated by >1 SD from baseline. The use of this criterion is depicted in Fig. 3D; data points falling above or below the dashed lines representing ±1 SD of the baseline LSL were defined as altered.

Each criterion yielded a set of ISIs when the BD tone-evoked spikes were suppressed and/or altered in latency. Two time points were obtained from the three sets of ISIs recorded: the onset of spike suppression (T₁) and the offset of spike suppression (T₂). The value of T₁ was defined as the shortest ISI, starting from when the BD tone preceded the NE tone and moving toward larger positive ISIs, when the spike count and/or latency became altered and the next two consecutive ISIs also deviated for a given criterion. The value of T₂ was defined as the shortest ISI, following T₁, when the spike count and/or latency remained altered and the next two consecutive ISIs had returned to within baseline values for a given criterion. Ideally, three values of T₁ and T₂ were obtained from the changes in spike count, FSL, and LSL for each cell. For the example cell in Fig. 3, the values of T₁ and T₂ were −1 ms and 39 ms with only a spike count criterion, 1 ms and 39 ms with only a FSL criterion, and −3 ms and 1 ms with only a LSL criterion.

The final values of T₁ and T₂ were chosen to be those that were most sensitive in capturing the time course of the suppressed response evoked by the NE tone with a spike count and/or spike latency criterion. The use of spike counts or spike latencies (or both) to quantify changes in a neuron’s responsiveness has previously been validated (Faure et al. 2003; Sayegh et al. 2012, 2014). In cases in which cells responded with only a single spike per stimulus [i.e., baseline first spike latency (L_first) = baseline last spike latency (L_last)], a change in spike count was typically used for selecting T₁ and T₂ because this criterion was more accurate in reflecting the time course of the evoked inhibition. For cells that responded with more than one spike per stimulus (i.e., L_first < L_last) or in cases where the spike count of the cell had recovered to within 50% of baseline even though L_first or L_last (or both) was still clearly deviated by >1 SD from baseline, a change in spike latency was typically used for selecting T₁ and T₂ because this criterion was more sensitive in reflecting the time course of the evoked inhibition. In cases in which the mean spike count or latency had not returned to within 50% or 1 SD of baseline, respectively, over the range of ISIs presented, T₂ was conservatively estimated as the longest ISI tested. For the example cell shown in Fig. 3, the final value of T₁ was −3 ms and was obtained with a LSL criterion, whereas the final value of T₂ was 39 ms and could be obtained with either a spike count or FSL criterion.

We conducted a separate analysis to determine whether the choice of criterion to detect a response change (i.e., a 50% change or 1 SD change) interacted with the measured neural parameter (spike count or latency). For the 38 cells tested with five standardized frequency conditions (38 × 5 = 190 observations), we compared the final values of T₁ and T₂ that were selected with a 1) 50% spike count criterion, 2) 50% spike latency criterion, 3) 1 SD spike count criterion, and 4) 1 SD spike latency criterion. The results of this analysis (not shown) revealed that a 50% criterion worked best for detecting deviations in spike count (but not spike latency) data and a 1 SD criterion worked best for detecting deviations in spike latency (but not spike count) data. There were two reasons for this conclusion. 1) The use of a single criterion did not perform well and was too conservative. For example, there were cases where the spike count of a cell had returned to within 50% of baseline even though its FSL and/or LSL were still clearly deviated by >1 SD from baseline (see, e.g., Fig. 7). There were also cases in which spike counts had decreased by 50% (but not by 1 SD) from baseline even though spike latencies from the same cell were deviated by 1 SD (but not by 50%) from baseline. In these instances, we used the criterion that most sensitively and accurately captured the time course of the cell’s altered response. 2) It was impossible to apply the same numerical criterion—a 50% change or 1 SD deviation—to both spike count and latency data. For example, a 50% change in spike count was able to detect the onset/offset of inhibition in 188 of 190 observations (98.9%), whereas a 50% change in spike latency was able to detect the onset/offset of inhibition in only 52 of 190 observations (27.4%). This demonstrates that a 50% spike latency change was less useful as a detection criterion, likely because most cells were incapable of exhibiting large latency deviations. Similarly, a 1 SD change in spike count detected the onset/offset of inhibition in 146 of 190 observations (76.8%), whereas a 1 SD change in spike latency detected the onset/offset of inhibition in 164 of 190 observations (86.3%). This demonstrates that a 1 SD latency criterion more frequently detected altered responses compared with a 50% latency criterion. Finally, 41 of 190 observations (21.6%) had spike counts with a SD that was larger than the mean, and in these cases inhibition could never be detected with a 1 SD change in spike count because a cell cannot have a spike count below 0. This demonstrates the limitation of this measure with respect to spike counts.

Fig. 7.

Inhibition evoked at the BEF and at a non-BEF outside the 50% eBW: dot raster displays illustrating responses from a short-pass DTN with the NE tone presented at the cell’s BEF (42 kHz; A) and at a non-BEF that was outside of the cell’s eBW (38 kHz; E). A: when the BD and NE tones were matched in frequency, strong suppression was observed when the 1-ms BD tone and the 10-ms NE tone were sufficiently close in time. B: mean ± SE spikes per stimulus as a function of the ISI between the BD and NE tones. The shortest ISI in which the spike count first dropped to ≤50% of baseline was T₁ = −7 ms (leftmost open circle). The longest ISI, starting from T₁, in which the spike count remained ≤50% of baseline, was T₂ = 39 ms (rightmost open circle). C: mean ± SE FSL as a function of the ISI between the BD and NE tones. The shortest ISI in which the FSL deviated by >1 SD from baseline was T₁ = 31 ms (leftmost open circle), and the longest ISI in which the FSL deviated by >1 SD from baseline was T₂ = 57 ms (rightmost open circle). D: mean ± SE LSL as a function of the ISI between the BD and NE tones. The shortest ISI in which the LSL deviated by >1 SD from baseline was T₁ = 31 ms (leftmost open circle), and the longest ISI in which the FSL deviated by >1 SD from baseline was T₂ = 57 ms (rightmost open circle). In the BEF condition, the final value of T₁ (−7 ms) was determined with a spike count criterion and the final value of T₂ (57 ms) was determined with either a FSL or LSL criterion. In the matched condition, the onset of the NE tone evoked inhibition led the excitatory FSL by 5.57 ms, and the inhibition persisted 51.57 ms longer than the NE tone. E: dot raster display illustrating responses from the same DTN when the BD and NE tones were not matched in frequency. F: inhibition evoked by the NE tone again caused a reduction in the cell’s spike count and deviations in the FSL (G) and LSL (H), although the effective duration of the altered response was shorter. The final value of T₁ (−7 ms) was determined with a spike count criterion, and the final value of T₂ (45 ms) was determined with either a FSL or LSL criterion. In the non-BEF condition, the latency of inhibition led the excitatory FSL by 6.30 ms, and the duration of the inhibition was 40.30 ms longer than the NE tone. The 10 data points that were averaged in the calculation of baseline spike counts and latencies are shown as white circles with an X. n = 10 trials per stimulus.

In summary, and as in previous studies (Faure et al. 2003; Sayegh et al. 2012, 2014), we used a mixture of criteria—either a 50% change in spike count or a 1 SD change in spike latency—to detect deviations and demark the onset/offset of altered responses in midbrain DTNs because this was the most sensitive and accurate method for measuring the time course of NE tone-evoked inhibition during paired-tone stimulation. In all instances, the final choice of criterion was confirmed by visual inspection.

Determining latency and duration of NE tone-evoked inhibition.

The final values T₁ and T₂ were used to calculate the effective (observable) start time (T_start), end time (T_end), and duration of inhibition (D_IHB) evoked by the NE tone as

$$T_{\text{start}}=T_1+L_{\text{last}}-D_{\text{BD}},$$ (1)

$$T_{\text{end}}=T_2+L_{\text{first}}-D_{\text{BD}},\; \hspace{0.17em}\; \hspace{0.17em}\text{and}$$ (2)

$$D_{\text{IHB}}=T_{\text{start}}-T_{\text{end}}$$ (3)

where L_first was the baseline FSL, L_last was the baseline LSL, and D_BD was the duration of the BD tone. The onset (T₁) and offset (T₂) of changes in a cell’s evoked responses were detected at ISIs where the BD tone-evoked spike count and/or latency deviated (see Measuring onset and offset of inhibition with spike counts and latencies). Because the paired-tone stimulation paradigm uses a roving BD tone and a stationary NE tone, changes to a cell’s evoked response will depend on the relative timing of the two signals. When the BD tone leads (follows) the NE tone, it is the last (first) spikes in the BD tone-evoked response that initially (finally) become altered (recovered) in number and/or latency owing to the onset (offset) of inhibition evoked by the NE tone. Thus, in the equation for T_start (T_end), the baseline LSL (FSL) is added to T₁ (T₂) because spikes would have occurred at this location in time were they not suppressed by inhibition evoked by the NE tone. Because T₁ (T₂) was measured with respect to BD tone offset whereas the baseline LSL (FSL) was measured with respect to BD tone onset, subtracting the duration of the BD tone from T₁ + LSL (T₂ + FSL) aligns both time axes with respect to NE tone onset.

A DTN was said to have leading inhibition when the onset of inhibition evoked by the NE tone occurred before the FSL (i.e., T_start < L_first) but was said to have lagging inhibition when the onset of NE tone-evoked inhibition occurred after the FSL (i.e., T_start > L_first). A DTN was said to have persistent inhibition when D_IHB was longer than the NE tone duration (D_NE) evoking the suppression (i.e., D_IHB > D_NE).

For the example cell shown in Fig. 3, T_start = 19.25 ms, T_end = 57.66 ms, and D_IHB = 38.41 ms. The cell showed leading inhibition because the latency of inhibition evoked by the NE tone occurred 2.41 ms before the 21.66-ms FSL (L_first − T_start = 2.41 ms). The cell also showed persistent inhibition because the duration of inhibition evoked by the NE tone was 8.41 ms longer than the duration of the 30-ms NE tone (D_IHB − D_NE = 8.41 ms). After stimulation, the cell’s FSL and LSL returned to baseline; however, the mean spike count over the 10 longest positive ISIs when the BD tone followed the NE tone (1.16 ± 0.83 spikes/stimulus) was still significantly lower [t(15.7) = 5.6, P ≪ 0.001] than the cell’s baseline spike count (1.76 ± 0.80 spikes/stimulus). This suggests that persistent inhibition may have extended well beyond stimulus offset. Long-lasting persistent inhibition in DTNs has been reported previously (Faure et al. 2003).

Measuring iFRA, BIF, and iBW.

We obtained a normalized isolevel inhibitory frequency response area (iFRA) and used it to measure the BIF and iBW of each DTN at +10 dB above the excitatory threshold (Fig. 4). A normalized iFRA was calculated by dividing the duration of inhibition evoked at each NE tone frequency by the duration of inhibition evoked at the BEF, denoted as D_IHB/D_IHB(BEF) and plotted as a function of NE tone frequency in octaves (re BEF). The frequency with the largest value was defined as the BIF. To estimate the iBW, we calculated separate linear regressions to measure the low (Slope_Low) and high (Slope_High) slopes of the isolevel iFRA tuning (re BIF) and defined the two cutoff frequencies by interpolating the regression to 50% of the value at the BIF (e.g., Fig. 4). Not every NE tone frequency was included in the linear regression calculations; the highest (or lowest) frequency included was the first normalized data point ≤ 0.1, starting from the BIF and moving higher (or lower) in frequency. A cell was said to have a multipeaked iFRA if data points outside of the iBW returned to ≥50% of the normalized value at the BEF. Cells with fewer than three data points to measure an iFRA slope were excluded from statistical analyses (n = 4).

Fig. 4.

Determining the inhibitory FRA, BIF, and iBW. A: hypothetical isolevel eFRA of a DTN showing mean ± SD spikes per stimulus in response to single BD tones that were varied in frequency and presented at +10 dB above threshold (filled circles). The eBW (gray box) was determined with a 50% spike count criterion re BEF (horizontal dashed line). See Fig. 2 for additional details. B: hypothetical isolevel iFRA of the same cell, measured as the duration of inhibition (D_IHB) evoked at each NE tone frequency at +10 dB re threshold (relative to the BEF) and normalized by the duration of inhibition evoked at the BEF at +10 dB re threshold [i.e., D_IHB/D_IHB(BEF)]. All cells were tested with at least 5 standardized NE tone frequencies described in Fig. 2 (open circles A–E), and whenever possible additional NE tone frequencies were presented (filled circles). Except for the BEF, the number of NE tone frequencies tested was independent of the number of BD tone frequencies in the eFRA. The BIF was defined as the frequency evoking the largest normalized duration of inhibition (open circle C). Separate linear regressions (solid lines) were computed for the low (Slope_Low)- and high (Slope_High)-frequency tuning slopes of the iFRA. Each regression was interpolated to 50% of its maximum normalized duration of inhibition at BIF, and this resulted in slightly different 50% criteria (horizontal dashed lines) to define the lowest and highest cutoff frequencies (edges of gray box) of the Slope_Low and Slope_High tuning slopes. For the hypothetical cell illustrated, the eBW ranged from −0.10 to 0.08 octaves (re BEF) and the iBW ranged from −0.35 to 0.19 octaves (re BEF).

The sharpness of inhibitory tuning, measured with paired-tone stimulation at +10 dB (re BD, BEF threshold), was calculated as a Q factor defined as Q = BIF/iBW. Paired-tone stimulation allowed us to measure an inhibitory Q factor, but unlike our excitatory Q_{10 dB} the level above the inhibitory threshold at which the inhibitory Q was measured was unknown.

Data analysis.

Spike count data are displayed as means ± SD, except in Fig. 1, Fig. 3, Fig. 6, and Fig. 7, where these data are plotted as means ± SE to assist in visual interpretation. All data were tested for normality and homogeneity of variances with Shapiro-Wilk and Bartlett tests, respectively. We used parametric statistics when data were normally distributed with equal variances; otherwise, equivalent nonparametric statistical tests were used and data are reported as medians and interquartile ranges (IQRs).

Fig. 6.

Inhibition evoked at the BEF and at a non-BEF within the 50% eBW. Dot raster displays illustrate responses from a band-pass DTN with the NE tone presented at the cell’s BEF (17.5 kHz; left) and at a non-BEF that was within the cell’s eBW (18.8 kHz; right). A: when the BD and NE tones were matched in frequency, strong suppression was observed when the 1-ms BD tone and the 10-ms NE tone were sufficiently close in time. B: mean ± SE spikes per stimulus as a function of the ISI between the BD and NE tones. The shortest ISI in which the spike count first dropped to ≤50% of baseline was T₁ = −2 ms (leftmost open circle). The longest ISI, starting from T₁, in which the spike count remained at ≤50% of baseline, was T₂ = 38 ms (rightmost open circle). C: mean ± SE FSL as a function of the ISI between the BD and NE tones. The shortest ISI in which the FSL deviated by >1 SD from baseline was T₁ = −2 ms (leftmost open circle), and the longest ISI in which the FSL deviated by >1 SD from baseline was T₂ = 42 ms (rightmost open circle). D: mean ± SE LSL as a function of the ISI between the BD and NE tones. The shortest ISI in which the LSL deviated by >1 SD from baseline was T₁ = −2 ms (leftmost open circle), and the longest ISI in which the FSL deviated by >1 SD from baseline was T₂ = 30 ms (rightmost open circle). In the BEF condition, the final value of T₁ (−2 ms) was determined with all 3 criteria and the final value of T₂ (42 ms) was determined with a FSL criterion. In the matched condition, the onset of the NE tone-evoked inhibition led the excitatory FSL by 1.63 ms, and the inhibition persisted 21.63 ms longer than the NE tone. E: dot raster display illustrating responses from the same DTN when the BD and NE tones were not matched in frequency. F: inhibition evoked by the NE tone also led to a reduction in the cell’s spike count, although the effective duration of spike suppression was shorter, but almost no deviations in either the FSL (G) or LSL (H). The final value of T₁ (−2 ms) was determined with either a spike count or LSL criterion, and the final value of T₂ (18 ms) was determined with a spike count criterion. In the non-BEF condition, the latency of inhibition led the excitatory FSL by 2.14 ms, and the duration of inhibition was −1.86 ms shorter than the NE tone. The 10 data points that were averaged in the calculation of baseline spike counts and latencies are shown as white circles with an X. n = 10 trials per stimulus.

We obtained neural recordings and measured basic response properties from 43 DTNs in the IC of E. fuscus. In some experiments it was not possible to obtain data from the same cell under all conditions (e.g., the cell was lost), and when this occurred our sample size decreased. Not every DTN showed evidence of inhibition during paired-tone stimulation at each of the five standardized NE tone frequencies, and when this occurred data from these cells were excluded from repeated-measures statistical analyses (n = 5); otherwise, the data were included in summary statistics, figures, and/or tables.

Linear regression was used to evaluate the relationship between electrode depth and a cell’s BEF. A Kruskal-Wallis test was used to compare excitatory FSLs as a function of SPL re threshold. Cochran’s Q-test was used to compare the proportion of cells showing leading/lagging or persistent inhibition at the five standardized NE tone frequencies. Welch’s t-test (unequal variances) was used to detect elevated/depressed spike counts (re baseline) in the 10 longest positive ISIs when the BD tone followed the NE tone. The duration of leading/lagging or persistent inhibition measured at the five standardized NE tone frequencies was compared with a Friedman test followed by Nemenyi post hoc tests for all pairwise comparisons; cells for which inhibition could not be measured (n = 5) were not included in this repeated-measures analysis. A Mann-Whitney U-test was used to compare the duration of leading/lagging inhibition in band-pass cells and short-pass DTNs and the difference between the BEF and BIF. Linear regressions were used to evaluate the relationship between the duration of leading/lagging inhibition and BD or FSL at the five standardized NE tone frequencies and to measure the low (Slope_Low)- and high (Slope_High)-frequency tuning slopes of the iFRA for each cell. A Wilcoxon signed-rank test was used to compare the eBW and iBW sizes, excitatory Q_{10 dB} and inhibitory Q factors, and the Slope_Low and Slope_High values measured from each cell’s iFRA. All statistical tests were performed in SPSS or R and used an experiment-wise error rate of α = 0.05.

RESULTS

Tonotopic organization of DTNs in IC.

Tonotopic organization is a general property that is created at the basilar membrane and maintained throughout the nuclei of the central auditory nervous system. In E. fuscus, tonotopic organization has also been well documented (Covey and Casseday 1991; Grothe et al. 2001; Haplea et al. 1994). We examined the spatial distribution of neural BEFs in our population of 43 DTNs and found a strong positive correlation between recording electrode depth and BEF (Fig. 5A; R² = 0.639, P ≪ 0.001). This finding demonstrates that DTNs are also tonotopically organized, thus replicating previous findings about duration tuning in the IC (Haplea et al. 1994; Jen and Wu 2006; Morrison et al. 2014; Pinheiro et al. 1991; Sayegh et al. 2012). Most of the DTNs in our sample (97.6%) had BEFs that fell between 20 and 70 kHz. This frequency range encompasses most of the bandwidth of echolocation calls emitted by E. fuscus (Casseday and Covey 1992) and also matches its most sensitive hearing range (Koay et al. 1997).

Fig. 5.

Tonotopic organization and response latency of DTNs in the IC. A: topographical organization of DTN BEFs. Left: there was a strong positive correlation (R = 0.80) between recording electrode depth and neural BEF (measured at +10 dB re threshold), demonstrating that DTNs were tonotopically organized within the IC. Right: histogram of BEFs (n = 43 cells; bin width = 10 kHz). B: first spike latency of DTNs as a function of sound level above threshold. Box plots illustrate the median (bold line), 25th and 75th percentiles (horizontal edges of box), interquartile range (height of box), 10th percentile (bottom whisker), 90th percentile (top whisker), and data values falling outside of these ranges (black circles). The interquartile range is defined as the 3rd quartile (75th percentile) minus the 1st quartile (25th percentile). Sample sizes decrease with increasing SPL because cells with high thresholds and/or nonmonotonic rate-level functions could not be tested at all SPLs.

Effect of SPL on FSL.

Across the population of DTNs we examined how FSL changed as a function of stimulus level and found that excitatory response latencies remained more or less constant and were independent of the SPL above threshold [Fig. 5B; χ²(4) = 2.67, P = 0.614]. These data demonstrate that the excitatory FSLs of DTNs are time locked to stimulus onset and do not vary with changes in stimulus amplitude. This result contrasts with most other types of auditory neurons, where the FSL systematically decreases with increasing stimulus level (e.g., Heil 2004; Mörchen et al. 1978; Rose et al. 1963; Tan et al. 2008).

Some auditory neurons show paradoxical latency shift (PLS), in which the cell’s FSL increases with increasing stimulus amplitude. Neurons with PLS have been described from both the auditory cortex (Hechavarría and Kössl 2014; Sullivan 1982a, 1982b) and IC (Covey et al. 1996; Galazyuk et al. 2005; Galazyuk and Feng 2001; Hechavarría et al. 2011; Klug et al. 2000; Macías et al. 2016). We did not find evidence of PLS in the population of DTNs in our sample. Mechanistically, two conditions must be satisfied for a cell to exhibit PLS: 1) the onset of inhibition must lead or begin simultaneously with the onset of excitation, and 2) the strength of inhibition must increase more quickly than the strength of excitation with increasing stimulus level. The leading inhibition that is important for creating duration selectivity satisfies the first condition (Casseday et al. 1994, 2000; Covey et al. 1996; Faure et al. 2003; Sayegh et al. 2014), but the amplitude tolerance of the spiking responses of auditory DTNs does not satisfy the second condition (Fremouw et al. 2005; Zhou and Jen 2001).

Inhibition evoked at the BEF and at non-BEFs.

Responses evoked from a band-pass DTN during paired-tone stimulation with the NE tone set to the cell’s BEF and to a non-BEF within the cell’s 50% eBW are shown in Fig. 6. The dot raster display and duration filter function for this cell are shown in Fig. 1A. When stimulated at +10 dB re threshold, the BEF of the cell was 17.5 kHz and its eBW ranged from 16.3 to 20.0 kHz (note: the BEF was 17.0 kHz when stimulated at +20 dB re threshold; Fig. 1A). When the BD and NE tones were matched and set to the cell’s BEF (Fig. 6A), a large reduction in the spike count (Fig. 6B) and significant deviations in both the FSL and LSL were observed when the 2-ms BD tone and 20-ms NE tone were sufficiently close in time (Fig. 6, C and D). This included ISIs when the BD tone immediately preceded, was simultaneous with, and immediately followed the NE tone. The final value for T₁ was −2 ms, and this value concurred across all three criteria. The final value for T₂ was 42 ms and was derived from changes to the cell’s FSL. The effective duration of spike suppression was 41.63 ms. This neuron showed leading inhibition because L_first = 11.59 ms and T_start = 9.96 ms; hence the onset of inhibition preceded the cell’s FSL by 1.63 ms. The cell also showed evidence of persistent inhibition because the effective duration of the altered response lasted 21.63 ms beyond the offset of the 20-ms NE tone. After the offset of inhibition, there was no difference between the baseline spike count (1.78 ± 1.51 spikes/stimulus) and the spike count evoked at the 10 longest positive ISIs when the BD tone followed the NE [1.53 ± 1.35 spikes/stimulus; t(17.47) = 1.1, P = 0.287]. Note the transient increase in the evoked spike count (and latencies) near the offset of the NE tone at ISIs between 18 and 20 ms (Fig. 6, A and B). This offset facilitation has been reported in previous in vivo studies of DTNs that have used paired-tone stimulation (Faure et al. 2003) and may reflect an offset-evoked excitatory event that is a component of conceptual and computational models of duration tuning (Aubie et al. 2009).

Response suppression was also observed when the roving BD tone was presented at the BEF (17.5 kHz) and the stationary NE tone was presented at a non-BEF (18.75 kHz) within the cell’s 50% eBW (Fig. 6E). When the NE tone was set to a non-BEF the onset of spike suppression occurred at the same time as when the NE tone was set to the cell’s BEF (compare Fig. 6, B and F); however, the duration of spike suppression was noticeably shorter, as evidenced by changes in the cell’s evoked spike count (Fig. 6F) but not by deviations in the evoked FSL (Fig. 6G) or LSL (Fig. 6H). The final value for T₁ was −2 ms and was derived from changes in spike count and/or LSL. The final value for T₂ decreased to 18 ms and was derived from changes in the evoked spike count. The effective duration of inhibition was 18.14 ms, which was shorter than the duration of inhibition when the NE tone was set to the BEF. Leading inhibition was observed in the non-BEF condition because L_first = 11.33 ms and T_start = 9.19 ms; hence the onset of inhibition preceded the cell’s FSL by 2.14 ms. The cell did not show persistent inhibition because the effective duration of inhibition was −1.86 ms shorter than the duration of the 20-ms NE tone. After the offset of inhibition, there was no difference between the baseline spike count (1.46 ± 1.28 spikes/stimulus) and the counts evoked at the 10 longest positive ISIs when the BD tone followed the NE tone [1.52 ± 1.21 spikes/stimulus; t(18.00) = 0.3, P = 0.736].

Comparing across the two conditions, the onset of inhibition was similar regardless of whether the NE tone was set to the cell’s BEF or to a non-BEF within its eBW. A sustained inhibition was evoked when the NE tone was set to the BEF, but its duration was shorter when the NE tone was set to a non-BEF within the cell’s eBW. Persistent inhibition was only observed when the NE tone was set to the BEF, indicating that the inhibition evoked at non-BEFs was weaker in strength and/or shorter in duration compared with the BEF condition.

Responses evoked from a short-pass DTN during paired-tone stimulation with the NE tone set to the cell’s BEF and to a non-BEF outside of the cell’s 50% eBW are shown in Fig. 7. The dot raster display and duration filter function for this cell are shown in Fig. 1B. The BEF of the cell was 42.0 kHz, and its eBW ranged from 41.0 to 44.0 kHz at +10 dB above threshold. When the BD and NE tones were matched and set to the cell’s BEF (Fig. 7A), there was a large reduction in the spike count (Fig. 7B) and significant deviations in both the FSL and LSL (Fig. 7, C and D) when the 1-ms BD tone and 10-ms NE tone were sufficiently close in time. This included ISIs when the BD tone immediately preceded, was simultaneous with, and immediately followed the NE tone. The final value for T₁ was −7 ms and was derived from a change in spike count. The final value for T₂ was 57 ms and could be derived from a change in either FSL or LSL. The effective duration of spike suppression was 61.57 ms. This neuron showed leading inhibition because L_first = 22.95 ms and T_start = 17.38 ms; hence the onset of inhibition preceded the cell’s FSL by 5.57 ms. The cell also had persistent inhibition because the effective duration of spike suppression lasted 51.57 ms beyond the offset of the 10-ms NE tone. Compared with the baseline value (1.41 ± 0.65 spikes/stimulus), spike counts evoked at the 10 longest positive ISIs when the BD tone followed the NE tone were slightly higher [1.84 ± 0.64 spikes/stimulus; t(16.2) = 5.5, P < 0.001]. The 10 data points averaged to calculate the baseline response are shown as white circles with an X in Fig. 7. In this cell two or three data points included in the baseline spike count appear to be decreasing owing to inhibition evoked by the NE tone. The net effect of including these values in the cell’s baseline response calculation was a slightly more stringent (conservative) criterion for detecting changes in the evoked spike count, with the overall effect resulting in an underestimation of the time course of inhibition evoked by the NE tone.

Response suppression was again observed when the roving BD tone was presented at the cell’s BEF (42.0 kHz) and the stationary NE tone was presented at a non-BEF (38.0 kHz) located outside of the cell’s 50% eBW; however, the duration of suppression was noticeably smaller (Fig. 7E). Further analyses showed a reduction in the spike count (Fig. 7F) and deviations in both the FSL (Fig. 7G) and LSL (Fig. 7H) of the cell. As in the BEF condition, the final value for T₁ was −7 ms and was derived from a change in spike count. The final value for T₂ decreased to 45 ms and was derived from a change in LSL. This resulted in an effective duration of inhibition of 50.30 ms, which was shorter than the duration of inhibition in the BEF condition. The cell showed leading inhibition in the non-BEF condition because L_first = 23.38 ms and T_start = 17.08 ms; hence the onset of inhibition preceded the cell’s FSL by 6.30 ms. The cell also showed persistent inhibition because the effective duration of inhibition was 40.30 ms longer than the duration of the 10-ms NE tone. Compared with the baseline count (1.16 ± 0.56 spikes/stimulus), spike counts evoked at the 10 longest positive ISIs when the BD tone followed the NE tone (1.66 ± 0.70 spikes/stimulus) were higher [t(17.2) = 4.7, P < 0.001].

Across the two frequency conditions, the onset of inhibition was similar regardless of whether the NE tone was set to the cell’s BEF (17.38 ms) or to a non-BEF (17.08 ms). A long-lasting, sustained inhibition was also evoked when the NE tone was either matched or unmatched to the BEF. Because persistent inhibition was longer when the NE tone was set to the cell’s BEF, this suggests that the inhibition evoked at non-BEFs was either weaker and/or shorter lasting. Another feature apparent in this cell was increased spike counts (compared with baseline) following the presentation of the NE tone in both the matched and unmatched frequency conditions (Fig. 7, B and F). Because the increase in spiking was long lasting and not time locked to the stimulus, it is difficult to attribute the elevated response to a specific mechanism—such as postinhibitory rebound excitation or a separate offset-evoked excitatory synaptic input—that is responsible for creating the short-pass duration selectivity of the cell. We know that postinhibitory rebound excitations can last from a few milliseconds to several seconds (Barrio et al. 1994; Chandler et al. 1994; Hodgkin and Huxley 1952; Koch and Grothe 2003; Owen et al. 1984; Tell and Bradley 1994). Given the cell’s long FSL (~23.0 ms) and strong leading inhibition (5.6 ms), we speculate that there would have been no difference between baseline and recovery spike counts if the cell’s baseline responses had been estimated with a slightly longer gap between the leading BD tone and lagging NE tone. In the last part of this section we report on the consistency of depressed/elevated spike counts (re baseline) in DTNs following the presentation of the NE tone during paired-tone stimulation.

We tested 43 DTNs using paired-tone stimulation with the NE tone set to five standardized frequencies relative to each cell’s eBW (Fig. 2): three frequencies within the 50% eBW (BEF, 0.5L_eBW, 0.5H_eBW) and two frequencies outside the 50% eBW (1.5L_eBW, 1.5H_eBW). Spiking was suppressed in all 43 cells (100%) when the NE tone was presented in the 1.5L_eBW, 0.5L_eBW, BEF, and 0.5H_eBW frequency conditions; however, only 38 cells (88.4%) showed measurable inhibition when the NE tone was set to the 1.5H_eBW high-frequency condition. These data indicate that the strength of the NE tone-evoked inhibition varies with sound frequency.

Leading inhibition was observed in 55% (104/190) of the observations on 38 DTNs that were tested with the five standardized NE tone frequencies, and the proportion of cells with leading inhibition did not differ across the frequencies [χ²(4) = 1.70, P = 0.79, n = 38]. Additionally, the duration of the leading/lagging inhibition did not differ across the five NE tone frequencies [χ²(4) = 4.82, P = 0.31, n = 38], with the mean value remaining relatively constant between 0 and 2 ms (Fig. 8A, black boxes). These results demonstrate that the latency of the inhibition evoked during paired-tone stimulation was more or less constant across NE tone frequencies within or near the cell’s 50% eBW.

Fig. 8.

Distribution of duration of leading/lagging and persistent inhibition across the 5 standardized NE tone frequencies. Two-dimensional histograms show the distributions of leading/lagging inhibition and persistent inhibition in DTNs tested with paired-tone stimulation at 5 standardized NE tone frequencies (re eBW). Mean duration at each NE tone frequency condition is indicated by a black box, with the color scale showing the number of DTNs per bin. A: distribution of the difference between the excitatory FSL and latency of inhibition (FSL − T_start) evoked by the NE tone. Cells with a positive difference have leading inhibition; cells with a negative difference have lagging inhibition. There was no difference in the distribution of FSL − T_start across NE tone frequencies, demonstrating a relatively constant latency of inhibition. B: distribution of the difference between the duration of inhibition evoked by the NE tone and the duration of the NE tone stimulus (D_IHB − D_NE). Cells with a positive difference have persistent inhibition; cells with a negative difference have inhibition lasting less than the duration of the NE tone evoking the inhibition. The distribution of D_IHB − D_NE differed across NE tone frequencies, with cells showing less persistent inhibition as the NE tone frequency moved away from the BEF (see Table 1). n = 38 cells.

In contrast, the proportion of cells with persistent inhibition differed across the five NE tone frequencies. Additionally, the duration of this persistent inhibition differed across the five standardized NE tone frequencies (Table 1). The longest average duration of persistent inhibition occurred when the NE tone was set to the cell’s BEF but decreased as the NE tone frequency was increased or decreased, forming an inverted V shape centered at the BEF (Fig. 8B, black boxes). The shape of this inverted V was asymmetric, with higher NE tone frequencies evoking shorter effective durations of persistent inhibition compared with lower NE tone frequencies. In contrast to the results for the onset of inhibition, these results demonstrate that the offset of NE tone-evoked inhibition systematically decreased as the NE frequency moved away from the BEF.

Table 1.

Comparison of proportion of DTNs showing persistent inhibition at 5 standardized NE tone frequencies and Nemenyi post hoc pairwise comparisons on duration of persistent inhibition at each standardized NE tone frequency

		Pairwise Comparisons of Duration of Persistent Inhibition†
	% DTNs with Persistent Inhibition*	1.5LeBW	0.5LeBW	BEF	0.5HeBW	1.5HeBW
1.5LeBW	73.7
0.5LeBW	92.1	<0.001
BEF	97.4	<0.001	0.977
0.5HeBW	78.9	0.366	0.218	0.056
1.5HeBW	47.4	0.162	<0.001	<0.001	<0.001

Comparison of proportion of DTNs showing persistent inhibition at 5 standardized NE tone frequencies relative to each cell's 50% eBW. Also shown are the results of Nemenyi post hoc pairwise comparisons on the duration of persistent inhibition at each standardized NE tone frequency. Statistically significant correlations are indicated in boldface.

^*Cochran Q-test, χ²(4) = 36.87, P ≪ 0.001, n = 38.

^†Friedman test, χ²(4) = 62.38, P ≪ 0.001, n = 38.

With regard to the consistency of poststimulatory effects (i.e., elevated or depressed spike counts compared with baseline), we reanalyzed our entire data set of 38 cells tested with five standardized NE tone frequencies (190 observations) and compared baseline spikes counts to those measured in the 10 longest positive ISIs when the BD tone followed the NE tone. There were 38 observations when the BD and NE tones were matched in frequency; 15 (39.5%) showed no difference, and 8 (21%) had elevated and 15 (39.5%) depressed spike counts (re baseline) following the presentation of the NE tone. For the remaining 152 observations when the BD and NE tone were mismatched in frequency, 82 (53.9%) showed no difference and 14 (9.2%) had elevated and 56 (36.8%) depressed spike counts (re baseline) following the presentation of the NE tone. With regard to the number of neurons, there were 12 cells with elevated spike counts: 6 at one frequency condition, 3 at two conditions, 2 at three conditions, 1 at four conditions, and 0 in all five frequency conditions. The number of cells with elevated spike counts was smallest at the most extreme NE tone frequencies, with the distribution being 1.5L_eBW = 6 cells, 0.5L_eBW = 3 cells, BEF = 8 cells, 0.5H_eBW = 1 cell, and 1.5H_eBW = 4 cells. There were 29 cells with depressed spike counts: 11 at one frequency condition, 6 at two conditions, 4 at three conditions, 6 at four conditions, and 2 in all five frequency conditions. The number of cells with depressed spike counts was also smallest at the most extreme NE tone frequencies, with the distribution being 1.5L_eBW = 13 cells, 0.5L_eBW = 16 cells, BEF = 15 cells, 0.5H_eBW = 16 cells, and 1.5H_eBW = 11 cells. This latter result is consistent with the shortening of the offset of inhibition as the frequency of the NE tone was moved further away from the BEF (see Fig. 8B). Overall, these data demonstrate that most DTNs did not show consistent poststimulatory effects (i.e., spike count facilitation or spike count depression) during paired-tone stimulation. When they occurred, poststimulatory effects were most frequent when the NE tone was set to the cell’s BEF. One interesting possibility is that cells with poststimulatory elevated spike counts could be displaying a weak form of delay tuning (Macías et al. 2012; Portfors and Wenstrup 1999, 2001) and/or interval tuning (Leary et al. 2008), and such responses may help E. fuscus process ecologically relevant combinations of long- and short-duration sounds separated in time (e.g., during mother-pup social interactions; Mayberry and Faure 2014; Monroy et al. 2011). Future studies should continue to explore any relationship that exists between duration tuning and delay tuning.

Relation of leading/lagging inhibition to BD, FSL, and duration filter class.

Leading inhibition is an important feature of many auditory neurons and plays a role in binaural hearing (Carney and Yin 1989), temporal processing (Galazyuk et al. 2005), and encoding frequency-modulated sweeps (Fuzessery et al. 2011; Razak and Fuzessery 2006). Because leading inhibition has been observed in several types of IC neurons, regardless of whether or not they are duration tuned (e.g., Covey et al. 1996; Faingold et al. 1991; Faure et al. 2003; Kuwada et al. 1997; Voytenko and Galazyuk 2008), this suggests that it is a general property of central auditory processing. Conceptual and computational models of DTNs combined with evidence from electrophysiological recordings indicate that a cell’s BD and duration filter response class depend, in part, on the amount of leading inhibition (Aubie et al. 2009, 2012; Casseday et al. 1994, 2000; Ehrlich et al. 1997; Faure et al. 2003; Fremouw et al. 2005; Fuzessery and Hall 1999). Previous studies have also reported a positive relation between the duration of leading inhibition and BD and/or FSL (Faure et al. 2003; Sayegh et al. 2014).

We evaluated our data for similar relations at the five standardized NE tone frequencies and found a positive correlation between the duration of leading inhibition and BD in all conditions (Fig. 9A). The correlation was strongest when the NE tone matched the BD tone and both were set to the cell’s BEF but systematically decreased as the NE tone departed from the BEF (Table 2). It is important to note that when we removed the 8-ms BD putative outlier point and reanalyzed our data, the results were nearly identical: four of the five standardized frequency conditions (0.5L_eBW, BEF, 0.5H_eBW, and 1.5H_eBW) maintained a positive correlation between BD and the duration of leading inhibition (Fig. 9A). Many studies in E. fuscus have reported DTNs with BDs ≥ 8 ms (e.g., Faure et al. 2003; Ma and Suga 2001; Morrison et al. 2014; Pinheiro et al. 1991), including the original report in bats (Jen and Schlegel 1982). Because the BD and duration of leading inhibition of this cell were not atypical, we conclude that this data point was not an outlier.

Fig. 9.

Relationship of duration of leading/lagging inhibition to BD, FSL, and duration filter class. Duration of inhibition measured with paired-tone stimulation at 5 standardized NE tone frequencies relative to the eBW of short-pass and band-pass DTNs. A: duration of leading inhibition increased in DTNs tuned to longer BDs at all NE tone frequencies. B: duration of leading inhibition also increased in DTNs with longer FSLs at the 4 lowest NE tone frequencies; however, no correlation was observed at the highest NE tone frequency (1.5H_eBW). Regression equations, correlation coefficients (R), and P values for each linear regression are listed in Table 2. n = 38 cells.

Table 2.

Linear relationships on duration of leading inhibition (L_first − T_start) and BD or FSL at 5 standardized NE tone frequencies relative to each cell’s 50% eBW

Comparison	Frequency	Slope	Intercept	R	P Value
Lfirst − Tstart (ms) vs. BD (ms)	1.5LeBW	0.72	−0.41	0.320	0.050
	0.5LeBW	1.25	−0.73	0.531	<0.001
	BEF	1.35	−1.48	0.580	<0.001
	0.5HeBW	1.15	−1.63	0.481	0.002
	1.5HeBW	1.13	−1.90	0.453	0.004
Lfirst − Tstart (ms) vs. FSL (ms)	1.5LeBW	0.30	−2.56	0.437	0.007
	0.5LeBW	0.35	−2.64	0.473	0.003
	BEF	0.37	−3.44	0.497	0.002
	0.5HeBW	0.29	−2.76	0.358	0.027
	1.5HeBW	0.09	−0.96	0.108	0.518

Linear relationships on the duration of leading inhibition (L_first − T_start) and BD or FSL at 5 standardized NE tone frequencies relative to each cell's 50% eBW (n = 38 cells). Statistically significant correlations are indicated in boldface.

There was also a positive correlation between the duration of leading inhibition and FSL for the standardized NE tone frequencies except the 1.5H_eBW condition (Fig. 9B). The relationship was strongest when the NE tone matched the BD tone and was set to the cell’s BEF and decreased as the NE tone frequency moved away from the BEF (Table 2). The strength of the relationship decreased more quickly for NE tone frequencies higher than the BEF, revealing an asymmetry in the correlation with changes in sound frequency. Altogether, these results demonstrate that DTNs with short BDs and FSLs have shorter durations of leading inhibition than cells with longer BDs and FSLs regardless of the frequency used to evoked the inhibition.

Previous paired-tone stimulation studies have also found that the duration of leading inhibition relates to the duration filter class of a DTN, with short-pass cells having shorter durations of leading inhibition than band-pass DTNs when the BD and NE tones were matched in frequency (Faure et al. 2003; Sayegh et al. 2014). We compared the duration of leading inhibition evoked in short-pass and band-pass DTNs in each NE tone frequency condition (Table 3). The duration of leading inhibition differed between short-pass and band-pass DTNs when the BD and NE tones were matched at the cell’s BEF and when the NE tone was unmatched and higher in frequency than the BD tone in the 0.5 H_eBW condition. Although there was a trend, the duration of leading inhibition between short-pass and band-pass DTNs was not significant in the 1.5L_eBW, 0.5L_eBW, and 1.5H_eBW NE tone frequency conditions. In addition to replicating previous in vivo observations, our results expand the findings to other NE tone frequencies by demonstrating that the onset of inhibition to DTNs is broadly tuned and largely frequency invariant.

Table 3.

Mann-Whitney U-tests comparing the duration of leading inhibition (L_first − T_start) in short-pass and band-pass DTNs at 5 standardized NE tone frequencies

Frequency	Duration Filter Class: Median, [IQR], ms	U	P Value
1.5LeBW	Short-pass: 0.039, [−1.23 to 3.08] Band-pass: 2.407, [1.54 to 4.00]	58.0	0.059
0.5LeBW	Short-pass: 0.002, [−0.93 to 4.09] Band-pass: 4.000, [1.90 to 6.41]	62.0	0.083
BEF	Short-pass: 0.000, [−1.01 to 3.62] Band-pass: 3.701, [2.42 to 5.53]	37.0	0.005
0.5HeBW	Short-pass: −0.606, [−1.50 to 3.11] Band-pass: 2.140, [1.94 to 4.57]	36.0	0.005
1.5HeBW	Short-pass: −0.312, [−1.89 to 2.76] Band-pass: 2.608, [−1.85 to 4.91]	63.0	0.091

Results of Mann-Whitney U-tests comparing the duration of leading inhibition (L_first − T_start) in short-pass (n = 31) and band-pass (n = 7) DTNs at 5 standardized NE tone frequencies relative to each cell’s 50% excitatory bandwidth. Statistically significant differences are indicated in boldface.

Comparing excitatory and inhibitory best frequencies, FRAs, BWs, and Q factors.

We used single BD tone pulses at different frequencies to construct each cell’s eFRA and measure its BEF and eBW. We then collected paired-tone stimulation responses from the same DTN at different NE tone frequencies to construct each cell’s iFRA and measure its BIF and iBW. Figure 10A shows an example eFRA measured from a DTN with a BEF of 51.0 kHz and an eBW of 4 kHz (ranging between 49.0 and 53.0 kHz). Excitation in the cell was narrowly tuned, and its excitatory Q_{10 dB} was 12.75. Figure 10B shows the cell’s iFRA with a BIF of 51.0 kHz. In this cell, the BEF exactly matched the BIF. For reference, the five standardized NE tone frequencies used to the test the cell are also illustrated (Fig. 10B; open circles). In contrast, the cell’s iBW was 16.12 kHz (ranging between 40.07 and 56.19 kHz) and its inhibitory Q was 3.16. The data demonstrate that inhibition was more broadly tuned than excitation in this DTN. Because the cell’s eBW was completely (100%) overlapped by the iBW (compare overlap of gray boxes in Fig. 10, A and B), this suggests that the strength of inhibition was maintained over a broad range of frequencies. The low- and high-frequency slopes of the normalized iFRA were Slope_Low = 1.27 and Slope_High = −3.06, respectively. This asymmetry in the normalized duration of inhibition indicates that the strength of inhibition decreased more quickly at high vs. low frequencies.

Fig. 10.

Excitatory and inhibitory best frequencies, FRAs, and BWs of DTNs. Each column shows the excitatory FRA of a DTN, plotted as the mean ± SD spike count as a function of different BD tone frequencies (top), and the inhibitory FRA of the same DTN measured during paired tone stimulation, plotted as the normalized duration of inhibition in octaves (re BEF) as a function of NE tone frequency (bottom). A: the eFRA of a short-pass DTN with a 1-ms BD, BEF of 51.0 kHz, and an eBW ranging from 49.0 to 53.0 kHz illustrated as a gray box between −0.06 and 0.06 octaves (re BEF). B: normalized iFRA of the same cell plotted as the duration of inhibition evoked by NE tones of different frequencies (re duration of inhibition evoked at BEF), including the 5 standardized NE tone frequencies (open circles). The 5 standardized NE tone frequencies are as described in Fig. 2 and used in Figs. 8 and 9. The BIF was defined as the frequency evoking the longest duration of inhibition. We computed separate linear regressions, calculated for the low- and high-frequency slopes of the iFRA, to measure each cell’s inhibitory bandwidth (iBW), with the cutoffs defined as the 2 frequencies where the regression line dropped to 50% of the regressed maximum. It is important to note that not every NE tone frequency was included in the linear regression calculations; in all cases, the lowest (or highest) frequency included was the first data point to reach ≤0.1 (dashed line), starting from the BIF and moving lower (or higher) in frequency. Data points not included in linear regression calculations are shown as gray circles. The BIF of this cell was 51.0 kHz and was matched to its BEF. The iBW ranged from 40.07 to 56.19 kHz or −0.31 to 0.14 octaves (re BEF). C: the eFRA of a short-pass DTN with a 1-ms BD, BEF of 28.6 kHz, and an eBW ranging from 27.8 to 29.8 kHz or −0.04 to 0.06 octaves (re BEF). D: normalized iFRA of the same cell with a BIF of 27.8 kHz or −0.04 octaves below its BEF and an iBW ranging from 23.15 to 29.35 kHz or −0.31 to 0.04 octaves (re BEF). E: the eFRA of a band-pass DTN with a 3-ms BD, BEF of 32.0 kHz, and a multipeaked eFRA. The main peak ranged from 27.0 to 35.0 kHz or −0.25 to 0.13 octaves (re BEF). F: normalized iFRA of the same cell showing a multipeaked iFRA with a BIF of 33.5 kHz or 0.07 octaves re BEF. This cell had 2 secondary inhibitory tuning peaks between 41.0 and 45.0 kHz (0.36–0.49 octaves re BEF) and between 51.0 and 56.0 kHz (0.67–0.81 octaves re BEF) not included in the calculation of the iBW. The iBW ranged from 18.53 to 34.91 kHz or −0.79 to 0.13 octaves (re BEF), and there was 98.9% spectral overlap with the eBW. The rightmost open circle in F (at +0.21 octaves) was included in the regression of the low-frequency tuning slope of the iFRA. Stimuli presented at +10 dB (re BEF, BD threshold); 10 trials per stimulus.

An example DTN where the BEF did not match the BIF is shown in Fig. 10, C and D. The BEF of the cell was 28.6 kHz and its eBW was 2 kHz (ranging from 27.8 to 29.8 kHz), resulting in an excitatory Q_{10 dB} of 14.3 (Fig. 10C). The cell’s iFRA revealed a BIF of 27.8 kHz, which was slightly mismatched (−0.04 octaves below) to the BEF. The iBW of the cell was 6.20 kHz (ranging between 23.15 and 29.35 kHz), and its inhibitory Q was 4.48 (Fig. 10D). Again, excitation in this DTN was more narrowly tuned than inhibition. The cell’s eBW was nearly encapsulated by the iBW, resulting in 77.3% spectral overlap. The low- and high-frequency slopes of the normalized iFRA were Slope_Low = 1.94 and Slope_High = −7.95, respectively.

An example of a DTN with a multipeaked isolevel eFRA and iFRA is shown in Fig. 10, E and F. The BEF of the cell was 32.0 kHz and its eBW was 8.0 kHz (ranging from 27.0 to 35.0 kHz), resulting in an excitatory Q_{10 dB} of 4.0 (Fig. 10E). The cell also had a narrowband secondary peak of excitation (ranging from ~38.0 to 41.0 kHz; 0.25–0.36 octaves re BEF). The iFRA had a BIF of 33.5 kHz, which was 0.07 octaves higher than the BEF, and its iBW was 16.38 kHz (ranging between 18.53 and 34.91 kHz) (Fig. 10F), resulting in an inhibitory Q of 2.05. Inhibitory spectral tuning in this cell was again much broader than excitatory spectral tuning, and there was 98.9% overlap between the eBW and iBW. The slopes of the normalized iFRA were Slope_Low = 0.63 and Slope_High = −8.32, demonstrating that the cell had extremely asymmetric tuning flanks. The cell also had two small secondary inhibitory tuning peaks between 41.0 and 45.0 kHz (0.36–0.49 octaves re BEF) and between 51.0 and 56.0 kHz (0.67–0.81 octaves re BEF).

Across the population of DTNs tested we computed log₂(BIF) − log₂(BEF) and found that the difference did not differ from zero (median difference = 0.00 octaves, IQR = −0.04 to 0.00 octaves, V = 85.0, P = 0.06, n = 39). There were 15 cells (38.5%) where the BIF exactly matched the BEF and another 14 cells (35.9%) where BIF differed by only ±0.05 octaves from the BEF (Fig. 11A). This demonstrates that there was a close correspondence in the sound frequencies evoking maximal synaptic excitation and inhibition in DTNs. Cells with multipeaked iFRAs were observed in only 5 of 39 DTNs (12.8%).

Fig. 11.

Relation of BEF to BIF and correspondence in spectral tuning between excitation and inhibition in midbrain DTNs. A: distribution of the difference in octaves between the BEF and BIF. Cells with a positive difference had a higher BIF relative to their BEF, while cells with a negative difference had a lower BIF compared with their BEF. In most DTNs, the BIF closely corresponded to the BEF. Bin width = 0.05 octaves. B: distribution of % spectral overlap between the eBW and iBW. In the majority of DTNs, neural inhibition completely or nearly overlapped the entire bandwidth of neural excitation. Bin width = 10.0%; n = 39 cells.

To further examine the correspondence in spectral tuning between neural excitation and inhibition, we compared the size and amount of spectral overlap between the eBW and iBW in the same cell. The absolute size of the eBW (median = 4.0 kHz, IQR = 3.0–8.0 kHz) was smaller than the absolute size of the iBW (median = 11.76 kHz; IQR = 6.6–18.0 kHz), and the difference was highly significant (Z = −4.91, P < 0.001, n = 39). In 35 of 39 cells (89.7%), the lowest cutoff frequency of the eBW was higher than the lowest cutoff frequency of the iBW. In 25 of 39 cells (64.1%), the highest cutoff frequency of the eBW was lower than the highest cutoff frequency of the iBW. In 23 of 39 cells (58.9%), the iBW completely overlapped the eBW. Across the population of DTNs tested, spectral overlap between the eBW and iBW averaged 91.7% (Fig. 11B).

To examine the sharpness of excitatory and inhibitory tuning, we compared excitatory Q_{10 dB} and inhibitory Q factors from the same neuron. There was a highly significant difference in the distribution of excitatory Q_{10 dB} (median = 9.25) and inhibitory Q factors (median = 4.16) across the population of DTNs tested (Fig. 12; Z = −5.01, P < 0.001, n = 39). Only 4 cells (10.3%) had excitatory Q_{10 dB} factors smaller than their inhibitory Q factors. This demonstrates that inhibitory inputs to DTNs were more broadly tuned in frequency than excitatory inputs. Broad inhibitory tuning has also been seen in whole cell patch-clamp recordings of awake bats, where the frequency tuning curves of most IC neurons were dominated by inhibition (Xie et al. 2007). The inhibitory Q factors of the DTNs we studied fell into a very narrow range (IQR = 2.85–5.10), whereas excitatory Q_{10 dB} factors were widely distributed (IQR = 4.86–14.30) and were similar to excitatory Q_{10 dB} factors of DTNs from a previous study (Morrison et al. 2014).

Fig. 12.

Sharpness of excitatory and inhibitory tuning in DTNs. Excitatory and inhibitory tuning sharpness plotted as quality (Q) factors measured at +10 dB (re excitatory threshold). Excitatory tuning sharpness measured as Q_{10 dB} = BEF/eBW; inhibitory tuning sharpness measured as Q = BIF/iBW. Most inhibitory Q factors were smaller than their corresponding excitatory Q_{10 dB} factors measured from the same cell, as demonstrated by the majority of points falling below the y = x identity line. n = 39 cells.

Finally, we examined the symmetry of the low- and high-frequency flanks of the isolevel iFRA by comparing the slope of the low-frequency slope (Slope_Low) to the absolute value of the slope of the high-frequency slope (|Slope_High|). Differences between the slope values reflect changes in the normalized duration of inhibition as a function of NE tone frequency. Across the population of DTNs tested, Slope_Low values (median = 2.11, IQR = 1.27–3.69) were smaller than |Slope_High| values (median = 4.46, IQR = 2.53–5.98; Z = −4.36, P < 0.001, n = 39). Only 6 cells (15.4%) had a Slope_Low steeper than |Slope_High| (Fig. 13). These results demonstrate that inhibition was strongest for sound frequencies at and below the BIF.

Fig. 13.

Steepness of the low- and high-frequency tuning slopes of the normalized iFRA. |Slope_High| vs. Slope_Low are plotted as well as the identity line (y = x). Points above the identity line indicate cells with an iFRA with high-frequency slope steeper than low-frequency slope, whereas points below the line indicate cells with an iFRA with low-frequency slope steeper than high-frequency slope. Most DTNs had asymmetric iFRAs, with normalized durations of inhibition falling off more quickly at higher compared with lower frequencies. n = 39 cells.

DISCUSSION

Inhibitory inputs to DTNs are onset evoked and broadly tuned in frequency.

Duration tuning is an emergent electrophysiological response property that appears to be created de novo in the auditory midbrain (Ehrlich et al. 1997; Sayegh et al. 2011). Previous work has shown that duration tuning arises through the interaction of sound-evoked excitatory and inhibitory synaptic inputs that are offset in time (Casseday et al. 2000; Covey et al. 1996; Faure et al. 2003; Fuzessery and Hall 1999; Leary et al. 2008). It should be noted that, technically, neural inhibition is not required to create a duration-selective neural circuit. For example, in the coincidence mechanism of duration tuning two subthreshold excitatory components must coincide in time to cause the membrane potential of the DTN to become suprathreshold: 1) an onset-evoked subthreshold excitatory input and 2) an offset-evoked subthreshold excitatory input (see Aubie et al. 2009; Sayegh et al. 2011). However, application of pharmacological antagonists that block inhibitory neurotransmitters has shown that duration selectivity broadens or is eliminated when inhibition is absent (Casseday et al. 1994, 2000; Fuzessery and Hall 1999; Jen and Feng 1999; Jen and Wu 2005; Yin et al. 2008). Furthermore, evidence from extracellular single-unit and intracellular whole cell patch-clamp recordings has shown that short-pass and/or band-pass DTNs receive an onset-evoked inhibitory input that precedes its onset-evoked excitatory input and that inhibition is sustained for as long or longer than the duration of the stimulus (Casseday et al. 1994, 2000; Covey et al. 1996; Ehrlich et al. 1997; Faure et al. 2003; Leary et al. 2008). These data demonstrate that duration selectivity is created, in part, by the inhibitory control of excitatory responses.

In this study we found that neural inhibition to DTNs was broadly tuned, with an onset latency that remained constant across a wide range of sound frequencies both within and outside the 50% eBW of the cell (Fig. 8A and Fig. 12). In contrast, many auditory neurons show substantial changes in FSL with changes in stimulus amplitude and/or frequency (Heil 2004; Tan et al. 2008). We propose the columnar division of the ventral nucleus of the lateral lemniscus (VNLLc) as a potential location where inhibitory inputs to midbrain DTNs may originate. The VNLLc consists of a three-dimensional matrix of neurons in which projections from the anteroventral cochlear nucleus converge onto sheets of cells innervated by calyceal endings (Covey and Casseday 1986). This anatomical arrangement makes the VNLLc ideally suited for temporal processing because a large number of anteroventral cochlear nucleus inputs, all tuned to different frequencies, converge onto a small network of VNLLc neurons. This arrangement would result in VNLLc having low spectral selectivity but high temporal precision.

Several lines of evidence support the hypothesis that the VNLLc is a suitable candidate nucleus to provide inhibition to DTNs in the IC. First, the VNLLc projects primarily to the IC (Covey and Casseday 1986). Second, cells in the VNLLc have a short response latency (Covey and Casseday 1991), which is a feature of the leading inhibition to DTNs (Fig. 8A and Fig. 9). Third, VNLLc neurons are broadly tuned in frequency and their threshold tuning curves are asymmetric, with high-frequency flanks steeper than low-frequency flanks (Covey and Casseday 1991). The former feature matches the spectral tuning of the neural inhibition acting on DTNs (Fig. 10 and Fig. 12), while the latter matches the asymmetric steepness in the slopes of DTN iFRAs (Fig. 13). Third, the responses of VNLLc neurons are primarily monaural (Covey and Casseday 1991), and a recent study using binaural paired-tone stimulation found that the responses of DTNs in the IC of E. fuscus were primarily created with monaural circuits (Sayegh et al. 2014). Finally, VNLL neurons with glycinergic inhibition project directly to the IC. These inputs are known to participate in the spectro-temporal processing of combination-sensitive neurons. Combination-sensitive neurons are cells whose excitatory response to one sound element is facilitated by the presentation of another sound element (Portfors and Wenstrup 1999; Yavuzoglu et al. 2011). Given that some midbrain DTNs also have combination-sensitive response selectivity for the delay between two sounds (Macías et al. 2013), this leaves open the possibility that DTNs and delay-tuned neurons may receive the same (or similar) source(s) of neural inhibition.

Despite these similarities, a majority of VNLLc neurons show phasic spiking responses, whereas the inhibition acting on DTNs is sustained, suggesting some type of tonic input. One possibility is that the small proportion of VNLLc neurons with tonic responses provide inhibitory inputs to DTNs. This seems less likely when one considers that up to a third of cells are reported to be duration selective in the IC of E. fuscus (Ehrlich et al. 1997) yet only 5% of VNLLc neurons had tonic responses (Covey and Casseday 1991). Another possibility is that VNLLc neurons with phasic responses provide the source of the broadly tuned, constant-latency, onset-evoked inhibition to DTNs and that other cells with tonic responses provide sustained inhibition to DTNs. In the present study, we found that the leading inhibition acting on DTNs was more broadly tuned than the later sustained inhibition (Fig. 8). That two components of the neural inhibition acting on DTNs had different spectral tuning suggests they may have arisen from different sources. A previous study found that the inhibition acting on DTNs was strongest at its onset (Faure et al. 2003), suggesting that the early portion of the onset-evoked sustained inhibition had a strength and time course different from the later portion. Other studies have shown that midbrain DTNs have both γ-aminobutyric acid (GABA)ergic and glycinergic inputs (Casseday et al. 1994, 2000), raising the intriguing possibility that phasic and tonic inhibitory inputs to DTNs could be using different neurotransmitters. If true, then this may help to explain why the application of one neuropharmacological antagonist (e.g., GABA or glycine) sometimes broadened duration selectivity, whereas application of two antagonists (e.g., GABA and glycine) completely abolished it (Casseday et al. 2000; Yin et al. 2008).

Mechanism of spike suppression during paired-tone stimulation.

Previous studies using paired-tone stimulation on DTNs have assumed that spike suppression was caused by synaptic inhibition (e.g., Faure et al. 2003; Sayegh et al. 2014). Intracellular recordings have shown that DTNs receive prominent synaptic inhibition (Covey et al. 1996; Leary et al. 2008). Moreover, iontophoretic application of antagonists of inhibitory neurotransmitter has demonstrated that synaptic inhibition is necessary for the electrophysiological response property of duration tuning (Casseday et al. 1994, 2000; Fuzessery and Hall 1999; Jen and Feng 1999; Jen and Wu 2005; Yin et al. 2008). An alternative is that spike suppression was caused by postsynaptic mechanisms, such as intrinsic membrane properties of a cell triggered by synaptically mediated excitation, instead of synaptic inhibition. For example, the biophysical properties of the family of small-conductance calcium-activated potassium (SK_Ca) channels can cause spike suppression after a cell receives a depolarizing (excitatory) event due to an increase in intracellular calcium (Hu and Mooney 2005; Sah 1996; Sah and Faber 2002). Activation of the SK_Ca channel following an action potential causes an afterhyperpolarization that suppresses spiking from milliseconds to seconds. If intrinsic membrane properties caused spike suppression in DTNs during paired-tone stimulation, then the strength and time course of the suppression should correlate to the excitatory response. Our data demonstrate that suppression was unrelated to the presence or strength of suprathreshold excitation. Spike suppression occurred in DTNs stimulated with NE tone frequencies falling both within and outside the eFRA (e.g., Fig. 10). Additionally, the evoked suppression was more broadly tuned than the evoked excitation in the same cell (Figs. 8, 10, and 12), and in most DTNs stimulated with long-duration BEF tones there was no spiking event to activate an intrinsic mechanism. Finally, although intrinsic membrane properties may account for the persistent inhibition of DTNs during paired-tone stimulation (Figs. 3, 6, 7, and 8B), they do not explain leading inhibition.

Response properties of DTNs are stable across the eBW.

The neural inhibition acting on DTNs displays four properties that may help to ensure that a cell’s BD, duration filter class, and basic response properties remain stable with changes in sound frequency: 1) the onset of inhibition was frequency tolerant (Fig. 8A); 2) sustained inhibition lasted nearly as long or longer than the duration of the stimulus evoking the inhibition (Fig. 8B); 3) the BIF matched the BEF (Fig. 11A); and 4) inhibition was as broad as (Fig. 11B) or more broadly tuned than (Fig. 8 and Fig. 10) excitation.

That the latency of inhibition to DTNs was tolerant to changes in stimulus frequency suggests that the onset of inhibition plays an important role in shaping the BD, duration filter class (i.e., short-pass or band-pass), temporal bandwidth of duration tuning, and FSL because these response properties are created, in part, by the difference in latency between inhibition and excitation (Aubie et al. 2009, 2012; Casseday et al. 1994, 2000; Covey et al. 1996; Faure et al. 2003; Fuzessery and Hall 1999; Sayegh et al. 2014). Our study replicated and extended this finding by demonstrating that the duration of leading inhibition remained constant across a broad range of NE tone frequencies (Fig. 8A). Moreover, the correlation between leading inhibition and BD (or FSL or duration filter class) was also roughly maintained across the cell’s eFRA (Fig. 9; Table 2 and Table 3).

That sustained inhibition was evoked across a broad range of frequencies within a cell’s eBW could help to ensure that inhibition lasts sufficiently long to coincide with an offset-evoked excitatory input that plays a critical role in the coincidence detection mechanism of duration selectivity; the sustained inhibition would suppress spiking at stimulus durations outside the excitatory temporal bandwidth (Aubie et al. 2009, 2012). Sustained/persistent inhibition was longest at BEF but systematically decreased at non-BEFs. This effect appeared to be strongest for stimulus frequencies higher than BEF (Fig. 8B and Fig. 13). It seems possible that spectral tuning of the inhibitory inputs to a DTN simply reflects the asymmetric frequency tuning curves that primary auditory afferents (and other cells) inherit as a result of the asymmetric mechanical band-pass displacement tuning curves of the cochlea. In theory, if the duration of sustained inhibition in a DTN changes with sound frequency then this may alter the cell’s response to echolocation calls and echoes. Although some cells may lose their duration selectivity with increases in stimulus frequency above the BEF, the temporal selectivity of cells with higher BEFs could improve. Therefore, across the overall population of DTNs within the IC, duration selectivity will be reduced in some cells and enhanced in others, with the exact effect depending on the relative difference between stimulus frequency and each cell’s BEF. Within bats, these effects may also differ between high-duty-cycle species that employ Doppler shift compensation and low-duty-cycle bats that do not (Macías et al. 2016).

The iFRA of a DTN is broadly tuned with the BIF centered on the BEF, ensuring the cell receives inhibition throughout its eFRA. Several studies have shown that inhibition is necessary for creating duration selectivity in the IC (Casseday et al. 1994, 2000; Fuzessery and Hall 1999; Jen and Feng 1999; Jen and Wu 2005; Yin et al. 2008). Broadband inhibition would also help to preserve duration tuning at non-BEFs. It is important to note that excitatory spectral tuning could be broader than what is measured from a cell’s spiking discharge pattern (e.g., subthreshold excitation or suprathreshold excitation that is sculpted by inhibition; Xie et al. 2007). For temporal selectivity to be preserved across a wide range of frequencies, a DTN should receive an inhibitory input whose spectral tuning is as broad as or broader than the tuning of its excitatory input. This is exactly what we found: the iBWs of DTNs were significantly larger than their eBWs (Fig. 12).

Two previous studies found that the temporal response properties of some DTNs changed when cells were stimulated at non-BEFs (Brand et al. 2000; Macías et al. 2016). In our study, 5 of 43 DTNs showed no evidence of inhibition when stimulated with NE tones set to the 1.5 H_eBW condition, and in the remaining 38 cells the average duration of the evoked inhibition was shorter than the duration of the NE tone stimulus (Fig. 8B). Computational circuit models and in vivo neuropharmacological experiments have both shown that when the sustained/persistent inhibition of a DTN is lost/blocked, duration selectivity becomes reduced or abolished (see Aubie et al. 2009; Casseday et al. 2000). Given the modulatory role of inhibition in temporal processing, it seems possible that the temporal selectivity of a DTN could change when stimulated at non-BEFs, and particularly at frequencies higher than BEF. In the mustached bat (Pteronotus parnellii) spike discharge patterns of resting-frequency DTNs changed for stimulation at different frequencies (Macías et al. 2016). This result differs somewhat from the temporal properties of inhibition observed in DTNs of E. fuscus, where the onset of leading inhibition was frequency independent but the duration of the sustained persistent inhibition was not. Alternatively, the properties (e.g., latency, discharge pattern) of excitation may also change when DTNs are stimulated with non-BEFs. Future studies should measure the temporal tuning profiles of DTNs at different sound frequencies.

Persistent inhibition and recovery cycles.

Persistent inhibition is a property of many IC neurons regardless of whether or not they are duration tuned (Covey et al. 1996; Faingold et al. 1991; Faure et al. 2003; Klug et al. 1999; Kuwada et al. 1997; Pollak and Park 1993; Sayegh et al. 2014; Yin 1994). Two previous studies have discussed the role of persistent inhibition in determining the recovery cycle time for a DTN (Sayegh et al. 2012; Wu and Jen 2006). The recovery time of a neuron is typically determined with paired-pulse stimulation and is measured as the minimum ISI required for the response (i.e., spike count or latency) evoked by a second stimulus to recover within a specified level of the response evoked by the first stimulus (Grinnell 1963). Paired-pulse stimulation is similar to the paired-tone stimulation paradigm that we employed, the difference being that in the latter the BD and NE tones differed in duration.

In our study, the duration of the sustained inhibition occurred on a timescale similar to the recovery cycle times of DTNs when the BD and NE tones were matched in frequency (Sayegh et al. 2012). The present results also show that the duration of the sustained inhibition evoked by the NE tone systematically decreased as the NE tone frequency moved away from the BEF. This finding predicts that a DTN stimulated at a non-BEF will have a shorter recovery cycle time compared with stimulation at the BEF. Other studies found that the frequency selectivity of DTNs sharpened during paired-pulse stimulation when the second tone was presented at short ISIs compared with longer ISIs (Wu and Jen 2008b, 2008c). These results are generally consistent with our findings (Fig. 8B). For a more direct comparison, future studies on DTNs should test the effect of varying the BD tone frequency during paired-tone stimulation. We acknowledge that the duration of the NE tone could also influence the strength of the inhibition evoked by it, as shown in computational (Aubie et al. 2009, 2012) and neurophysiological (Faure et al. 2003) studies.

Frequency tuning of temporal masking.

Psychophysical auditory temporal masking experiments are analogous to the paired-tone stimulation paradigm that we used to test DTNs from the IC of E. fuscus. The BD tone is analogous to the probe (or signal) tone, while the NE tone is analogous to the masker (or suppressor) tone. Neural correlates of auditory temporal masking patterns have been identified in DTNs with paired-tone stimulation (Faure et al. 2003; Sayegh et al. 2014). Spike suppression when the BD tone preceded the NE tone is the neural equivalent of backward masking and occurred as a result of the leading inhibition evoked by the NE tone. Similarly, spike suppression when the BD tone overlapped with the NE tone to produce a composite stimulus is the neural equivalent of simultaneous masking and occurred as a result of the sustained inhibition evoked by the NE tone. Finally, spike suppression when the BD tone followed the NE tone is the neural equivalent of forward masking and occurred as a result of the persistent inhibition evoked by the NE tone.

We found that the onset-evoked, leading and sustained inhibition were stronger and more broadly tuned than the persistent inhibition evoked in the same cells (Fig. 8). Moreover, the low-frequency slope of a DTN’s iFRA was shallower than its high-frequency slope (Fig. 13). Interestingly, psychophysical masking data show similar relationships in frequency selectivity to DTNs in paired-tone stimulation. Psychophysical tuning curves measured during simultaneous masking were broader than those of forward masking, with forward masking thresholds increasing more steeply at higher frequencies (Bacon and Moore 1986; Moore 1978; Soderquist et al. 1981). In contrast, psychophysical tuning curves measured in backward masking were more variable. Some human studies suggest that backward masking is more broadly tuned than forward masking (Dye and Yost 1981; Miyazaki and Takayuki 1984). One study found that human psychophysical tuning curves were equally broad in forward and backward masking, whereas in birds forward masking psychophysical tuning curves were broader than their backward masking counterparts (Dooling and Searcy 1985).

GRANTS

This research was supported by an Operating Grant to P. A. Faure from the Institute of Neuroscience, Mental Health and Addiction of the Canadian Institutes of Health Research (CIHR) and the Natural Sciences and Engineering Research Council (NSERC) of Canada. The McMaster Bat Laboratory is also supported by infrastructure grants from the Canada Foundation for Innovation and the Ontario Innovation Trust.

DISCLOSURES

No conflicts of interest, financial or otherwise, are declared by the author(s).

AUTHOR CONTRIBUTIONS

R.V.-R. performed experiments; R.V.-R. and P.A.F. analyzed data; R.V.-R. and P.A.F. interpreted results of experiments; R.V.-R. and P.A.F. prepared figures; R.V.-R. and P.A.F. drafted manuscript; R.V.-R. and P.A.F. edited and revised manuscript; R.V.-R. and P.A.F. approved final version of manuscript; P.A.F. conceived and designed research.