INTRODUCTION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

Sinusoidally amplitude-modulated (SAM) tones induce in human listeners, over different modulation frequency ranges, a variety of percepts such as fluctuation, roughness, and pitch. SAM signals have also been used in psychophysical experiments within a linear systems framework to study the temporal filtering properties of the auditory system, as distinguished (but not separate) from its spectral filtering properties (e.g., Dau et al. 1997; Salvi et al. 1982; Viemeister 1979). It is known that human speech and animal communication sounds contain many amplitude-modulated features (e.g., Rosen 1992). In particular, the envelopes found in natural speech have been shown to contain sufficient information below 50 Hz to allow a high degree of speech recognition performance, even in the relative absence of spectral cues (Shannon et al. 1995). Further, it has been reported that training language-learning impaired children with modified speech that included enhancement of envelope components in a similar frequency range (3-30 Hz) led to significant improvements in performance on various speech and language tests (Tallal et al. 1996). Understanding the processing of modulated signals is also of relevance to the design of stimulation strategies for cochlear implants, where one attempts to convey information about speech signals with a temporally varying stimulation strength at a limited number of points on the cochlea.

There now exist considerable data on physiological responses to SAM tones in the auditory nerve (e.g., Joris and Yin 1992) and cochlear nucleus (e.g., Frisina et al. 1990; Moller 1974; Rhode 1994; Rhode and Greenberg 1994). Neurons in these lower levels of the ascending auditory pathway convey information about the envelope by "phase locking" to the modulation frequency of the SAM tone. Spike rate variations with modulation frequency are generally poorly tuned or nonexistent in the auditory nerve and for most neuronal types in the cochlear nucleus. In contrast, neurons at higher levels of the auditory system, including the inferior colliculus (IC), have been shown to exhibit large variations in average spike rate as the modulation frequency of the SAM tone is varied (e.g., Langner and Schreiner 1988; Rees and Moller 1983; Schreiner and Urbas 1988). It has been suggested that this represents a transformation from a "temporal code" for modulation frequency in the auditory nerve and cochlear nucleus to a "rate code" at higher levels, and that this transformation is essentially complete at the level of the IC (Langner and Schreiner 1988). However, many details of the parametric dependence of the responses to SAM tones of single neurons at locations other than the auditory nerve and cochlear nucleus remain unclear. As a result, existing models of the processing of amplitude-modulation (AM) at higher levels of the auditory system are poorly constrained by experimental data and hence difficult to evaluate.

The IC is an obligatory relay in the primary lemniscal pathway from the extensively interconnected auditory midbrain network to the cortex. It receives ascending projections from various ipsilateral and contralateral sites in the auditory periphery and descending projections from the cortex (Oliver and Huerta 1991). As a result of this extensive set of excitatory and inhibitory inputs and because it is the primary source of projections to the thalamus and cortex, it is often considered to perform an "integrative" role in auditory processing. In particular, in contrast to auditory nerve fibers and most neurons in the cochlear nucleus, prior studies (e.g., Heil et al. 1995; Langner and Schreiner 1988) of the responses of IC neurons to SAM tones with different modulation frequencies (and all other parameters fixed) have reported that most neurons in the IC show systematic variations of average spike rate with modulation frequency, with neurons often showing a clear maximum response at a best modulation frequency (BMF). However, studies (e.g., Rees and Moller 1983; Rees and Palmer 1989) that have varied other parameters of the stimulus have indicated that response patterns to SAM tones can be strongly dependent on stimulus parameters other than modulation frequency, like the sound pressure level (SPL) of stimulation. Nonetheless, a systematic description of the spike rate and synchronization properties of single IC neurons to SAM tones with a wide range of parameters is still lacking. Such a description would help clarify the implications of the emergent rate tuning in the auditory midbrain, both for neural processing mechanisms and for the representation of modulation frequency in the auditory system.

With this in mind, we present here the results of a detailed characterization of extracellularly recorded responses from single neurons in the physiologically defined central nucleus of the IC of the Mongolian gerbil (Meriones unguiculatus) to SAM tones with a range of modulation frequencies presented via a closed system to the contralateral ear at multiple modulation depths, SPLs, and carrier frequencies (F_cs).

	METHODS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

Surgical and recording procedures

Adult Mongolian gerbils with clean external ears and no sign of middle ear infections were initially anesthetized with an intraperitoneal injection of pentobarbital sodium (60 mg/kg) and subsequently maintained in an areflexive state with supplemental intramuscular injections of ketamine hydrochloride (approximately 30 mg · kg¹ · h¹). A heating pad was used to maintain a constant rectal temperature of 37°C. The pinnae were removed, and craniotomy of the interparietal bone was performed to expose the cerebellum. The animal was then transferred to a double-walled sound-attenuated room (IAC), where sound delivery speculae were sealed to the temporal bone and muscle around the opening of the external auditory meatus bilaterally.

Activity of single units was recorded with platinum-plated, glass-insulated tungsten microelectrodes advanced into the IC through the intact cerebellum with a stepping motor microdrive (CalTech). Electrodes typically had exposed tip lengths of 5-10 µm and an impedance of 2-5 M at 1 kHz. Electrical signals recorded from the brain were amplified (variable gain) and filtered (typically 0.25-10 kHz). Neural signals were displayed on an oscilloscope and fed to an audio monitor. Single units were identified and isolated using the criteria of waveform similarity and separation of successive spikes by an absolute refractory period; only very well isolated single units were studied. An event timer (MALab, Kaiser Instruments) logged the occurrence of discriminated action potentials together with stimulus zero-crossings to a resolution of 1 µs. Event times were stored in a FIFO buffer from which they were retrieved by the host computer. Acoustic stimuli were presented as the electrode was advanced to isolate responsive units. As the electrode passed through the dorsal mantle of the IC, responses that were broadly tuned, driven better by broadband noise than tones, and often habituating to repeated tonal stimulation were found. Occasionally, a coarse descending tonotopic sequence was encountered. Entry into the physiologically defined central nucleus was always marked by an increase in spontaneous background activity and the beginning of a clear ascending tonotopic progression, with narrowly tuned tone response areas that showed no signs of habituation to repeated stimulation. Within the central nucleus, both modulated and unmodulated tonal stimuli were effective in revealing responsive units.

Stimulus generation and data acquisition

Stimulus waveforms were generated by two digital synthesizers controlled by a microprocessor and custom hardware for timing, data logging, and waveform control (MALab, Kaiser Instruments). The dedicated microprocessor communicated with a host computer via an IEEE-488 interface. Stimuli were digitally attenuated and transduced by electrostatic earphones (Stax Lambda, housing designed by G. Sokolich) coupled to the ear pieces. For each individual animal, SPL (expressed in dB re 20 µPa) near the tympanic membrane was calibrated for both ears from 40 Hz to 40 kHz under computer control using a previously calibrated probe tube and a condenser microphone (Bruel and Kjaer, type 4134). Phase was calibrated for both ears from 40 Hz to 5 kHz by measuring the disparity in phase between a reference sinusoid generated electrically and the recorded acoustic signal. Note that all the data in this paper result from monaural contralateral presentation of sound. The magnitude transfer function of the speaker was usually smooth, with a slow rolloff until 25 kHz, the maximum frequency used; two or three local resonances, never deviating by more than 10 dB from the baseline, were also present. Deviations of the phase response from linearity were small, and not usually present. Appropriate compensations were made to the carrier prior to modulation. All acoustic stimuli were shaped digitally with a cosine-squared ramp of 5-50 ms rise time to reduce spectral splatter at onset and offset. The SAM tone is represented by the formula A sin(_ct)[1 + m sin(_mt)], where _c is the angular frequency of the carrier, _m that of the modulator, A the amplitude of the carrier, t the time after signal onset, and m the modulation depth (0-100%). Such a stimulus, if sufficiently long, has a simple three component spectrum centered at F_c, as shown in Fig. 1. The SPL of the SAM tone is defined as the SPL of the carrier that is being modulated. The modulation frequency is the frequency corresponding to _m.

View larger version (31K): [in this window] [in a new window]   Fig. 1. Summary of stimulus characteristics and response measures. A: amplitude vs. time plot of a sinusoidally amplitude-modulated (SAM) tone. Carrier frequency, 10 Hz; modulation frequency, 1 Hz; modulation depth, 100%. Carrier amplitude is arbitrarily set to 1. Actual stimuli used had Fcs from 40 Hz to 25 kHz. B: the spectrum of an infinitely long SAM tone has 3 components. Fc, carrier frequency; Fm, modulation frequency; A, amplitude; m, modulation depth. C: raster plot showing cartoons of spike responses demonstrates locking to the envelope of the stimulus depicted in A. D: modulation period histogram generated from the spike trains in C (binwidth = 1 ms) demonstrates that spikes tend to occur only over a certain phase-range ("phase-locking"). Vector strength is 0.76 and the response shows a small negative phase-lead of 0.6° relative to the stimulus envelope. E: the 1st peak in the rate modulation transfer function (rMTF) was chosen as the best modulation frequency (BMF; see METHODS and Fig. 18 legend). WMF, worst modulation frequency. F: examples of period histograms at different modulation frequencies (MF) and their associated vector strengths (VS) and phase leads (PL). Narrow histograms give vector strengths closer to 1.

Frequency response areas, either at a single SPL or at multiple SPLs, were recorded using pure tones (usually 100 ms, with a rise time of 10 ms, and a repetition rate <2.5 Hz) and the best frequency (BF) was noted. Following this, a complete spike rate versus SPL function [rate-level function (RLF)] was usually measured (at BF). Neurons were then studied using pure tones (at multiple SPLs) and SAM tones while monitoring the responses (spike rate and vector strength) on-line to gain an initial qualitative characterization of the neuron's response properties. This initial exploration helped confine the formal presentation to the ranges of levels, depths, carrier frequencies, durations, and modulation frequencies where clear variations in response were present, thus maximizing the use of the limited recording time available. Modulation frequencies were varied within the range of 0.1 Hz to a value just less than the F_c used. Stimulus durations varied from 1 to 10 s (this was determined partly by the period of the lowest modulation frequency used, so that at least 1 period was presented), while rise times varied from 5 to 50 ms. Unless it was itself the parameter being varied, F_c was set to the BF of the neuron (as measured using pure tones) at the SPL being tested. If responses were being recorded at multiple SPLs, F_c was kept constant and usually equal to the BF at an SPL in the middle of the spanned SPL range. Because it was not uncommon for the BF to vary with SPL (e.g., Kuwada et al. 1984), F_c sometimes differed slightly from the BF at some SPLs. In any case, the BF can also depend on the kind of stimulation (SAM tone vs. pure tone), the duration of stimulation (100 ms vs. 1-10 s) and the modulation frequency of stimulation (see RESULTS).

Data analysis

Three descriptive measures of the pure-tone response are used in this paper. The first is the mean spike rate averaged over the duration of stimulation. The second is the minimum (across all SPLs tested) mean (averaged across stimulus presentations) latency at the BF of the neuron or close to it (if the BF varied with SPL). Finally, neurons were classified into one of four classes (onset, onset-sustained, pauser, and sustained) on the basis of their peri-stimulus time histograms (PSTHs) (as in Le Beau et al. 1996). However, because PSTHs can change with SPL, we also used some additional criteria: neurons were classified as pausers if they showed a pauser pattern at any SPL, and neurons were classified as sustained or onset types only if they showed this pattern at all SPLs. The few broad onset neurons found were included in the onset-sustained category, and since the identification of choppers requires more tone presentations than we used, these were not separately identified.

The response to AM is also characterized by three measures: mean spike rate (averaged over the duration of stimulation), vector strength at the modulation frequency¹ (Goldberg and Brown 1969) and the mean phase-lead of the response relative to the modulating sinusoid. The functions describing the variation of each of these measures with modulation frequency will be referred to as modulation transfer functions (MTFs). MTFs plotted using the spike rate, vector strength, and mean phase-leads are called rate modulation transfer functions (rMTFs), temporal modulation transfer functions (tMTFs), and phase modulation transfer functions (pMTFs), respectively.

The vector strength is a measure of the synchrony to the modulating waveform and is equal to F₁/F₀, where F₁ is the spectral magnitude of the response at _m and F₀ the average spike rate. It varies from a minimum of zero to a maximum of one, and as a reference, the vector strength of the sinusoidal modulating waveform of a 100% depth SAM tone is 0.5, while that of a half-wave rectified sinusoid is 0.784. A response with all spikes at precisely the same unique phase has a vector strength of 1 ("perfect" phase locking). The significance of the vector strength was assessed using the Rayleigh statistic (Stephens 1969) at the 1% significance level. Additionally, to minimize the contribution of onset spikes, at least six spikes per stimulus presentation were required for significance. The mean phase-lead was computed as (90  ), where  is the direction of the mean vector in the vector strength calculation. The mean phase-lead is equal to the phase of the spectral component of the response at _m, relative to that of the modulating waveform. (The direction of the mean vector of the modulating waveform is 90°, since it produces a unimodal nonnegative period histogram symmetric about its peak at 90°.) The mean phase-lead was decremented by an appropriate multiple of 360°, i.e., unwrapped, whenever it went from a response close to 360° to one closer to 0°. pMTFs were truncated when the sampling resolution became poor enough that the phase might have skipped more than one cycle; this was not usually required, and usually only affected values above 300 Hz. Only significant vector strengths and their associated mean phase-leads are shown in the plots in this paper. Consistent with the fact that phase locking to pure tones is common only below 600 Hz (Kuwada et al. 1984), we observed significant vector strength at the carrier frequency only in the few neurons in our sample with BFs in that frequency range. Synchrony to the carrier will not be discussed further in this report.

Most MTFs did not vary much when different 1-s time windows after the beginning of the stimulus were chosen for analysis, even though most neurons showed an adaptation of their mean firing rate during the stimulation period. All measures were therefore calculated over the entire stimulation period.

A BMF was defined for each rMTF as follows: first, the modulation frequency that elicited the maximum spike rate was identified. If there were two distinct maxima (e.g., Fig. 3A), the one at the lower modulation frequency (primary peak) was taken. Following this, a range of modulation frequencies (b₁ to b₂, Fig. 1E) where the response was >90% of this response maximum was extracted. The BMF was chosen as the mean of b₁ and b₂. This procedure essentially corrected for skewed or irregular peaks and was almost always close to the BMF as chosen by eye. BMFs were only measured if the spike rate dropped by at least 70% on both sides of the BMF. If a 70% drop was only present on the high-frequency side, then the modulation frequency (higher than the BMF) that elicited 90% of the maximum response was chosen as the corner frequency of the rMTF. A cutoff frequency was also measured; this was the frequency at which the response fell to the minimum spike rate plus 10% of the difference between the maximum and minimum spike rates, on the high-frequency side of the primary peak (w₁ in Fig. 1E). Finally, a worst modulation frequency (WMF) was extracted in rMTFs with a clear suppressive region, as evidenced by a lower spike rate in comparison with that to one or more lower depth stimuli. The method was similar to that used for the BMF: the mean of a 10% range (w₁ to w₂, Fig. 1E) was taken as the WMF. In all cases, linear interpolation was used if required.

Kendall's  (Press et al. 1993) is used often in this paper as a nonparametric measure of correlation between two or three variables.

	RESULTS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

We measured responses from 109 single neurons in the physiologically characterized central nucleus of the IC in 34 Mongolian gerbils. Three onset neurons were unresponsive to AM across the entire parameter space, a proportion similar to that reported earlier (Rees and Palmer 1989).

Varying modulation depth

Varying SAM tone modulation depth revealed that IC rMTFs were composed of 1 or 2 regions of enhancement (modulation frequency ranges where the spike rate increases with increase in stimulus modulation depth) and/or 1 region of suppression (a range of modulation frequencies where the spike rate decreases as stimulus modulation depth increases). Figures 2 and 3 show illustrative examples of rMTFs and tMTFs measured from individual neurons (with a range of BFs) using SAM tones with varying modulation depths and constant SPL. In all cases (except Fig. 2D, see legend), the F_c was equal to the BF of the neuron at that SPL. The rMTFs in Fig. 2 show examples of neurons with rMTFs that predominantly show either an increase (A-C) or decrease (D) in spike rate with increasing modulation depth at all modulation frequencies. The magnitude of change depends on the modulation frequency. These changes create band-pass (A-C) or bandsuppressive (D) rMTFs that are characterized by their single prominent region of enhancement and suppression, respectively. In contrast, Fig. 3 illustrates examples of neurons whose rMTFs show both regions of enhancement and suppression. In other words, both the direction (increase or decrease) and magnitude of change (in spike rate with modulation depth) depends on the modulation frequency. The rMTFs in Fig. 3, A, C, and D, show secondary peaks at higher modulation frequencies; these were only found in eight neurons (see DISCUSSION). However, in contrast to responses at the primary peak (BMF), responses at the secondary peak possessed low vector strength; i.e., they were not synchronized to the modulation frequency. We formally recorded the effects of systematic variation of modulation depth from 31 neurons; in most cases, the spike rate at any given modulation frequency increased or decreased almost monotonically with increasing modulation depth.

View larger version (39K): [in this window] [in a new window]   Fig. 2. Effects of varying modulation depth. Spike rate can be either enhanced (A-C) or suppressed (D) as stimulus modulation depth increases. Each row (Fig. 2, A-D) depicts responses from 1 neuron. The 1st column shows rMTFs, and the 2nd column temporal MTFs (tMTFs) for 4 neurons (A-D) studied with SAM tones of different modulation depths (identified by different symbols) and Fc at BF [for the tested sound pressure level (SPL)]; except in D, where Fc was below the BF of 1-5 kHz (see Fig. 4 for this neuron's response at BF). Dashed lines between points in tMTFs indicate that (unplotted) responses at some intervening modulation frequencies did not reach significance. In case of a zero depth stimulus (unmodulated tone), the mean of the responses (points in gray) is shown with a horizontal line (e.g., Fig. 2D). The right column shows the rate-level function (RLF), and the vertical dashed line shows the SPL at which the SAM tone was presented. The text below gives the neuron number, peri-stimulus time histogram (PSTH) class, minimum mean latency, SAM tone duration, and Fc. Tone-pip duration, rise time, number of presentations (per data point in the RLF), SAM tone rise time, and number of presentations (per data point in the MTFs) in each case were as follows, respectively. A: 100 ms, 10 ms, 10, 30 ms, 1. B: 100 ms, 10 ms, 10, 50 ms, 1. C: 100 ms, 10 ms, 10, 30 ms, 1. D: 100 ms, 10 ms, 10, 10 ms, 1.

View larger version (43K): [in this window] [in a new window]   Fig. 3. Effects of varying modulation depth. A single rMTF can show both enhancement and suppression (at different modulation frequencies) as the stimulus modulation depth increases. The format of this figure is identical to that of Fig. 2. Stimulus parameters as in Fig. 2 were as follows. A: 100 ms, 10 ms, 10, 50 ms, 1. B: 300 ms, 10 ms, 10, 50 ms, 1. C: 300 ms, 10 ms, 10, 50 ms, 1. D: 250 ms, 5 ms, 15, 30 ms, 1.

tMTFs ranged from low-pass to band-pass (more peaked) shapes; this is related to the SPL of stimulation, as will be shown in a subsequent section. Notice that the vector strength remains high (and often reaches its peak) as the spike rate reaches its minimum (Figs. 2D and 3). Also, low modulation depths can elicit responses with high vector strengths, i.e., the dynamic range of the vector strength measure is small as modulation depth is varied. For example, the neuron in Fig. 2C showed a vector strength >0.8 in response to a 10% stimulus modulation (an increase of 0.82 dB and a decrease of 0.91 dB from the mean SPL) at 30 Hz. In contrast to the rapid saturation of the vector strength of the response (VSr), the vector strength of the modulating waveform (VSs; equal to half the modulation depth) increases linearly with depth from 0 to 0.5. As a result, an alternative measure of synchrony, modulation gain [20 log(VSr/VSs)] (e.g., Frisina et al. 1990) decreases almost monotonically as the depth increases. No consistent trend was found in the behavior of pMTFs at different modulation depths, and in most cases, the magnitude of variation was small.

Varying sound pressure level

The rMTFs for each of the neurons in Figs. 2 and 3 were recorded at a fixed SPL and F_c. Therefore it is of interest to know whether the observed rMTFs are invariant characteristics of the neuron, independent of the particular parameters (SPL and F_c) chosen for stimulation. Figure 4 partially answers this question by demonstrating that it is possible for a region of enhancement in the rMTF from a single neuron to be transformed systematically into a region of suppression as the SPL is increased. Note that these rMTFs were measured with the carrier at 1,500 Hz, while the effects of using a 1,200-Hz carrier are shown in Fig. 2D for the same neuron. The position of the rate minimum is not affected by this change in F_c, suggesting that spectral effects (like the positioning of the AM sidebands in putatively inhibitory regions of the frequency response area) are not important in its generation (see subsequent section on effects of varying carrier frequency). The tMTFs at multiple SPLs and 100% depth show a systematic "low-pass to band-pass shift," as a result of the decrease in vector strength at low modulation frequencies with increasing SPL (Fig. 4F).

View larger version (25K): [in this window] [in a new window]   Fig. 4. The region of enhancement may become a region of suppression with increasing SPL. A-E: rMTFs measured at different SPLs (increasing from A to E) and multiple modulation depths (see key in A). The common Fc and duration of stimulation for A-F are given in A. rMTFs measured at 50, 70, and 100 dB (not shown) behaved intermediate to the rMTFs at the flanking SPLs. Note that the ordinate scale varies while the abscissa is identical in A-F. F: tMTFs at 100% depth and multiple SPLs (see key in F) are plotted for the same neuron (also see Fig. 2D). Each data point in A-F resulted from a single presentation of the SAM tone (10-ms rise time).

To explore the emergence of suppression at higher SPLs further, we systematically varied the SPL while keeping the depth at 100% and the carrier at or close to the BF in 56 neurons. Illustrative examples spanning the range of behaviors seen are shown in Figs. 5 and 6. Figure 5 shows examples of MTFs at multiple SPLs from four neurons with a range of best frequencies and with rMTFs that remain band pass (but with varying bandwidths) at all tested SPLs. The neurons depicted in A and B responded at all modulation frequencies tested, but suffered a loss of tuning at higher SPLs (possibly due to saturation of the spike rate). A qualitatively similar pattern has been reported previously (Rees and Palmer 1989). The neurons in C and D were "transient responders," with a poor or absent response to long-duration unmodulated tones. Neurons of this kind maintain their tuning over a broad range of SPLs. The spike rate at a given modulation frequency varied with SPL in either a monotonic or a nonmonotonic fashion, in a manner that could depend on modulation frequency (A and D). The BMF showed shifts of variable direction and magnitude as the SPL increased. As in Fig. 4, the tMTFs show variable degrees of a "low-pass to band-pass shift," similar to that seen in the cochlear nucleus (Frisina et al. 1990; Rhode 1994; Rhode and Greenberg 1994).

View larger version (38K): [in this window] [in a new window]   Fig. 5. Effects of varying SPL. Some rMTFs are dominated by a region of enhancement at all tested SPLs. The 1st column shows rMTFs and the 2nd column tMTFs for 4 neurons (A-D) studied with SAM tones at 100% depth, varying SPL (identified by different symbols) and fixed Fc (at or close to BF). Dashed lines in tMTFs indicate intervening responses (not plotted) with insignificant vector strength. The column at extreme right shows the RLF measured using brief tone pips, and in the text below, the neuron number, its PSTH class and minimum mean latency, and the SAM tone duration and Fc are identified. The vertical dashed lines show the different SPLs at which the SAM tone was presented. Stimulus parameters as in Fig. 2 were as follows. A: 100 ms, 10 ms, 10, 10 ms, 1. B: 200 ms, 5 ms, 10, 10 ms, 1. C: 100 ms, 10 ms, 10, 30 ms, 1. D: 100 ms, 5 ms, 20, 10 ms, 1.

View larger version (48K): [in this window] [in a new window]   Fig. 6. Effects of varying SPL. Some rMTFs contain a region of suppression, emerging at higher SPLs or present at all tested SPLs. The format of this figure is identical to that of Fig. 5. Stimulus parameters as in Fig. 2 were as follows. A: 100 ms, 10 ms, 20, 10 ms, 1. B: 300 ms, 10 ms, 5, 50 ms, 1. C: 200 ms, 10 ms, 10, 10 ms, 1. D: 300 ms, 10 ms, 10, 10 ms, 1.

Four examples of neurons with a suppressive region in their rMTFs are shown in Fig. 6. The suppressive region either emerges at higher SPLs (Fig. 6, A-C) as in the example of Fig. 4 or is present at all tested SPLs (Fig. 6D). The tMTFs show the same low-pass to band-pass shift seen in Fig. 5. Again, responses at modulation frequencies within the suppressive region retain considerable synchrony (i.e., show high vector strengths).

A correlation with some other neuronal response property would clearly be useful in delineating the possible mechanisms underlying the variety of rMTF changes seen with increases in SPL. No systematic relationship seems to exist between the presence of a suppressive region and the shape of the RLF (i.e., whether it is monotonic or nonmonotonic). However, it was found that the presence of a suppressive region in the rMTF at 1 or more SPLs was significantly correlated with the PSTH pattern in response to pure tones (Table 1). An rMTF region was defined as suppressive if the spike rate at modulation frequencies within that region showed a clear decrease as the modulation depth was increased (see METHODS). Neurons classified as pausers or sustained types on the basis of their PSTHs were more likely to possess rMTFs with a suppressive region, while rMTFs from neurons with onset or onset-sustained PSTHs usually only had a single region of enhancement (Fig. 5). However, it should be noted that using our aforementioned criterion, suppression can only be demonstrated clearly for neurons that respond well to unmodulated tones; for example, the rMTFs in Fig. 2B probably possess a suppressive region of very small magnitude between 20 and 100 Hz. Eleven of the 18 onset or onset-sustained neurons, and 2 of the 5 pauser neurons without a suppressive region in their rMTFs did not respond well to long-duration unmodulated tones. It therefore remains possible that a putative suppressive mechanism (possibly inhibition: see DISCUSSION) sharpens the high-frequency slope in rMTFs like those in Fig. 5, C and D, without actually resulting in a visible suppressive region. This is consistent with the fact that spike rates are often nonmonotonic with SPL over broad ranges of modulation frequency, even in rMTFs without suppression (e.g., Fig. 5D).

The final measure used to characterize MTFs was the mean phase of the response. Figure 7 shows the pMTFs for three neurons, whose rMTFs and tMTFs have been shown in earlier figures (Figs. 5, A and D, and 6D). A systematic increase in the phase lead (phase-advance) with increasing SPL, as illustrated in Fig. 7, A and B, was observed in the pMTFs from 30 of 56 neurons. Other neurons showed both increasing and decreasing leads over different modulation frequency ranges in their pMTFs. A decreasing phase lead (phase-delay) was sometimes seen in the pMTF in frequency regions corresponding to the decreasing high-frequency slope of the associated rMTF (especially in neurons with sustained PSTHs). This behavior was usually less systematic, but a fairly clear example is shown in Fig. 7C. The phase-advance is not always accompanied by an increase in spike rate; for example, the neuron in Fig. 7A shows a phase-advance even though its rMTFs are nonmonotonic with SPL (Fig. 5D). The phase-advance in Fig. 7B seems to be at least partly due to the marked adaptation seen in the response that shifts the peak of the response toward the beginning of the cycle (see the period histograms). The phase advance in Fig. 7A could be due to a phasic response that occurs earlier in the cycle as the SPL increases; this could possibly also be viewed as a very rapid adaptation. There was a consistent tendency for the phase-advance to be maximum at intermediate modulation frequencies, as exemplified by the data in Fig. 7B. This implies that it is inaccurate to view the phase-advance as simply reflecting a decreased time delay at higher SPLs that mirrors the known decrease in latency with SPL for pure tones; because that explanation predicts, at least in its simplest form, a linear relationship between phase-advance and modulation frequency (i.e., the phase-advance ought then to be maximum at the highest modulation frequency). On the contrary, the phase-advance is often minimal at the highest modulation frequencies. Finally, the modulation frequency at which the maximum phase-advance in a given neuron was found was not necessarily identical to that at which its rMTF peaked.

View larger version (36K): [in this window] [in a new window]   Fig. 7. Phase MTFs (pMTFs) of inferior colliculus (IC) neurons show systematic increases in lead (A and B) and lag (C) with increasing SPL. Phase-lead of the response is plotted vs. modulation frequency at multiple SPLs for 3 neurons (A-C). SPLs are identified by different symbols (symbol key in Fig. 7B). Dashed lines between points in pMTFs indicate intervening insignificant responses (not plotted). Also shown are modulation period histograms at selected modulation frequencies and SPLs for each of the 3 neurons. The text inside each period histogram gives the corresponding phase lead and vector strength. Histograms contain 100 (A and B) or 91 bins (C). See Figs. 5, A and D, and 6D for the rMTFs and tMTFs corresponding to these pMTFs. Note that phase values at very low modulation frequencies (e.g., 0.1 Hz in Fig. 7B) where only a few stimulus cycles are present, are biased (toward positive phase values) as a result of adaptation at stimulus onset.

The properties of the only offset neuron observed in this study are shown in Fig. 8. The rMTF showed a band-pass shape, while the vector strength remained high throughout the range of modulation frequencies that elicited a response. The pMTF showed a systematic phase-delay with SPL at low modulation frequencies. The period histogram suggests that this is the result of a phasic response occurring later in the cycle as SPL increases. Consistent with its "offset" nature, the neuron fires during the falling phase of the amplitude envelope (as indicated by the negative value of the low modulation frequency asymptote). These properties are similar to the recently described properties of offset neurons from periolivary regions (Kuwada and Batra 1999).

View larger version (20K): [in this window] [in a new window]   Fig. 8. One offset neuron encountered showed a peaked rMTF, excellent phase locking over a range of modulation frequencies, and a tendency to fire later during the falling phase of the amplitude envelope as the SPL increased. The rMTF (A), tMTF (B), and pMTF (C) are shown. The format for the phase plot is similar to that in Fig. 7. Cell number, PSTH class, mean minimum latency, SAM tone duration and Fc are shown in A. Each data point resulted from a single presentation of the SAM tone (10-ms rise time).

MTF characteristics across the population

Of the 106 neurons responsive to SAM tones, 96 were studied by stimulating at 100% depth and with a F_c that was at or close to the BF of the neuron at all the SPLs studied. Figure 9 is a representation of the BMFs at 100% depth and different SPLs for all 96 neurons. The mean BMF (averaged across the different SPLs tested and including corner frequencies; see METHODS) did not show a significant correlation (Kendall's  = 0.0708; P = 0.1533) with the BF. Some interesting properties are evident in the cumulative probability distribution of the mean BMF, shown in Fig. 10A. The maximum mean BMF encountered was 140 Hz, and about 50% of the mean BMFs lay below 25 Hz. The range of variation of the BMF for an individual neuron (both absolute and relative to the mean) observed at different SPLs is also shown on the same graph. Fifty percent of the 49 neurons tested over at least a 20-dB range of SPLs showed a BMF variation larger than 66% of their mean BMF; in absolute terms, 50% of the neurons showed a range larger than 10.9 Hz. No systematic pattern was found in the variation of BMFs with SPL for individual neurons (Fig. 10B).

View larger version (23K): [in this window] [in a new window]   Fig. 9. Population characteristics of the BMF. BMFs from rMTFs at 100% depth and Fc at or close to BF are plotted for 96 neurons. Each vertical line joins BMFs recorded at multiple SPLs from an individual neuron; symbol size increases with increasing SPL. Neurons are arranged on the abscissa in order of increasing Fc. For rMTFs that did not show a clear primary peak, corner frequency (see METHODS) was plotted (). Neurons studied over at least a 20-dB range of SPLs are marked with a black square above the line connecting their BMFs.

View larger version (16K): [in this window] [in a new window]   Fig. 10. Most mean BMFs and WMFs lie below 100 Hz, and over half the neurons show a BMF range larger than 66% of their mean BMF. A: mean BMF, absolute range (both plotted on the left ordinate) and range as a percentage of the mean BMF (right ordinate) plotted vs. their cumulative probability. B: BMF variation with SPL did not show any systematic pattern. Lines join BMFs recorded from a single neuron at different SPLs; data are shown for neurons that showed peaked MTFs at all (>1) tested SPLs. Dotted lines connect data from neurons whose BMF at the highest SPL is lower than that at the lowest SPL. C: histogram of mean WMFs from neurons with a suppressive region in their rMTFs.

At least one rMTF with a suppressive region was observed in 43 of the 96 neurons. The mean WMF (averaged across SPL; see METHODS) lay between 0 and 200 Hz in most cases, with a mode near 100 Hz (Fig. 10C). No systematic pattern was found in the variation of WMFs with SPL for individual neurons (data not shown).

The minimum mean latency in response to pure tones at BF is significantly correlated (Kendall's  = 0.3276, P = 0.0001) with the mean BMF (averaged across SPL) of the neuron in response to SAM tones at 100% depth and with a carrier at or close to BF (Fig. 11). Neither measure showed a significant correlation with the BF [ (BF-latency) = 0.0288 (P = 0.366) and  (BF-mean BMF) = 0.0329 (P = 0.3479)]. Accordingly, a three-way test resulted in a  of 0.3269, only slightly different from that for the BMF-latency relationship, suggesting that the BF of the neuron was not a confounding variable.

View larger version (17K): [in this window] [in a new window]   Fig. 11. Neurons with shorter minimum latencies have higher mean BMFs. Mean BMFs are plotted vs. minimum mean latency for neurons whose minimum latency was identified using a pure tone RLF. Symbols indicate PSTH type: onset (), sustained or pauser (), and onset-sustained (). Filled symbols have corner frequencies included in the mean BMF calculation (see legend to Fig. 9).

Figure 12A reveals that cutoff frequencies (see METHODS) are markedly lower in rMTFs that possess a suppressive region, when compared with those that do not. This could be interpreted as an effect of the suppressive mechanism sharpening the high-frequency slope of the rMTF, thus leading to a lower rMTF cutoff frequency.

View larger version (19K): [in this window] [in a new window]   Fig. 12. Properties of the cutoffs of rMTFs and tMTFs. A: histograms of mean cutoff frequencies of rMTFs with (n = 43) and without (n = 67) suppression (averaged across SPL, from individual neurons) plotted, respectively, to the left and right of the dark line at 0 Hz; 14 neurons contributed to both sides, and 2 points (1,970.43 and 1,269.4 Hz) are plotted outside the range for clarity. It is unlikely (P < 0.001, Mann-Whitney U = 5.14) that the 2 histograms arose via random sampling from a common distribution. B: tMTF cutoff frequency (maximum modulation frequency at which a significant vector strength was found) vs. Fc (at or close to BF). One data point (125 Hz Fc and 120 Hz cutoff frequency) was omitted for clarity; 5,149 points were tested for significance while creating this plot.

The tMTF cutoff frequency (defined here as the maximum modulation frequency at which neurons retain synchrony to the modulation frequency) can be regarded as an index of the low-pass filtering and internal noise in the system. The measure shows no significant correlation with the F_c used (Kendall's  = 0.003, P = 0.4829). Over 85% of neurons lack significant synchrony above 300 Hz (Fig. 12B). Cutoff frequencies in the IC are thus substantially lower than those found at lower levels like the cochlear nucleus and the lateral superior olive (Joris and Yin 1998; Rhode and Greenberg 1994; both in the cat).

Some other aspects of the vector strength transformation between the cochlear nucleus and the IC are shown in Fig. 13. As shown in Fig. 13A, the maximum synchrony found in responses from almost all IC neurons (0.907 ± 0.009, mean ± SE, n = 96) is clearly more than the means reported for any neuron type in the cochlear nucleus, with the possible exception of O_I units (Rhode 1994; Rhode and Greenberg 1994). Also, responses from neurons that possess BMFs (i.e., the rMTF shows a clear peak, see METHODS) at all SPLs studied are almost maximally synchronized at the BMF; i.e., the mean difference between the vector strength at BMF and the maximum vector strength is close to zero (e.g., MTFs in Figs. 2, A-C, and 5). In contrast, neurons that possess corner frequencies show larger mean differences between the vector strength at their rMTF peak (BMF or corner) and the maximal vector strength in the associated tMTF (for example, see MTFs in Figs. 3, 4, and 6).

View larger version (16K): [in this window] [in a new window]   Fig. 13. IC responses are more synchronized than cochlear nucleus responses. A: the maximum vector strength (), and the mean difference (across different SPLs, at 100% depth) between the vector strength at the rate BMF and the maximum vector strength ( and ) are plotted vs. Fc (at or close to BF). , the 29 neurons that have at least 1 rMTF with a corner frequency (instead of a BMF); , the other 67 neurons. One  (BF of 125 Hz, maximum vector strength of 0.85 and a difference of 0.04) was omitted for clarity. The mean maximum vector strengths are indicated by asterisk a for the IC population (0.907, n = 96) and by range b (0.56-0.78) for the various neuron types in the cochlear nucleus (Rhode and Greenberg 1994, cat). B: minimum depth of stimulation (across all modulation frequencies tested) that elicited a significantly synchronized response plotted vs. the vector strength of the response for neurons studied by varying depth systematically while keeping Fc (at BF) and SPL constant. Note that at 20% modulation depth, stimulus amplitude varies from 1.9 dB below to 1.6 dB above mean SPL; at 40%, the corresponding range is 4.4 to 2.9 dB.

The examples in Figs. 2 and 3 suggest that IC neurons show considerable phase locking (i.e., high vector strength) at relatively low depths of modulation. This is confirmed in Fig. 13B, where the lowest modulation depth at which a significant vector strength was found is plotted against the value of the vector strength for the 31 neurons whose MTFs were recorded at multiple depths. Comparing this to modulation depth-vector strength functions recorded from the cat cochlear nucleus population (Rhode 1994: Fig. 13) confirms that vector strengths of IC neurons at low depths are more than those for almost all cochlear nucleus neuron types (onset-choppers being the exception).

One pMTF each from 95 of the 96 neurons is plotted in Fig. 14A to display the population characteristics of the pMTFs. The positive low modulation frequency asymptotes indicate a tendency for most neurons to fire on the rising portion of the sinusoidal envelope. A straight line was often a good fit to the high-frequency (greater than or equal to 100 Hz; in our observations, responses in this range usually showed small or absent SPL-dependent phase shifts) phase responses; the maximum and minimum values of the slope (see legend) across all neurons were 15.6 and 6.09 ms. These may be interpreted as time delays (e.g., Anderson et al. 1971; but also see Ruggero 1980) that contain possible contributions from the fixed delays and filtering properties of the system.

View larger version (17K): [in this window] [in a new window]   Fig. 14. Population characteristics of the phase response. A: the pMTF at a single SPL (usually the highest of all SPLs tested) plotted vs. modulation frequency for 95 neurons; 1 neuron that exhibited response synchrony at fewer than 4 modulation frequencies was excluded. Thick dashed lines show straight line fits to the pMTFs with maximum and minimum slope above 100 Hz (see text). Slope values (divided by 360° and multiplied by 1) are shown in milliseconds. The curve with asterisks is from the offset neuron in Fig. 8. B: a clear phase advance with rise in SPL was seen in 30 of 56 neurons studied at multiple SPLs (with Fc at or close to BF). Each line joins phase leads measured at different SPLs (at the particular modulation frequency that produced the maximum advance) from a single neuron. C: histogram of the phase advance per 10 dB rise in SPL for the sample in B.

Thirty of the 56 neurons studied at multiple SPLs showed a systematic phase-advance as the SPL increased. This is shown in Fig. 14B, where phase leads (at the modulation frequency at which the largest phase-advance was found) are plotted as a function of SPL for each of the 30 neurons. The distribution of the maximum phase-advance (i.e., the range of each of the 30 functions in Fig. 14B) per 10-dB rise in SPL is shown as a histogram in Fig. 14C. The mean maximum increase was 23.81° per 10 dB (SE, 1.78). This may be larger than similar increases reported from responses at lower levels in the auditory pathway (see DISCUSSION).

Varying carrier frequency

We also investigated in 34 neurons the effects of stimulating different parts of the frequency response area by varying the F_c of the SAM tone. Illustrative examples are shown in Figs. 15 and 16. The examples in Fig. 15 show that band-pass rMTFs derived from an individual neuron can have different shapes; i.e., they are not scaled versions of each other. The BMFs can show shifts of varying magnitude and direction. The spike rate varies with carrier frequency in a manner that is roughly consistent with the frequency response area. Finally, as discussed earlier in the context of Fig. 4, one might imagine that suppressive regions could result from the positioning of the AM sidebands over inhibitory regions of the frequency response area. This explanation might also predict that as F_c is varied, suppressive regions would show shifts of the same magnitude as the shift in F_c. This does not seem to be the case (Fig. 16, A-C).

View larger version (42K): [in this window] [in a new window]   Fig. 15. Illustrative examples of neurons with band-pass rMTFs studied at multiple Fcs. rMTFs (1st column) and tMTFs (2nd column) shown for 4 neurons (A-D) studied with SAM tones at 100% depth, constant SPL and varying Fc (identified by different symbols). Dashed lines indicate intervening responses (not plotted) with insignificant vector strength. The top plot at extreme right in each row shows the spike rate vs. frequency function measured using brief tone pips (thin line) and SAM tones (thick line, modulation frequencies of 60, 100, 30, and 30 Hz in A, B, C, and D respectively), both normalized to their respective peak values and measured at SPLs within 10 dB of each other. The bottom plot shows the dependence of BMF on Fc. The rMTFs in D did not have a clear BMF at many Fcs, and the BMF-Fc plot was omitted. The cell number, PSTH class, mean minimum latency, SAM tone duration and SPL are given inside the tMTF axes. Carrier frequencies shown in A: 5.4, 5.6, 6.0, 6.4, 6.6, and 6.8 kHz. B: 3.5, 4.5, 5.5, 6.5, and 7.0 kHz. C: 12.6, 12.8, 13.0, 13.4, 13.6, 14.0, and 14.3 kHz. D: 40-200 Hz at intervals of 20 Hz. rMTFs and tMTFs at a few intervening Fcs followed the trend shown by those at flanking Fcs and were omitted for clarity; however, points from these omitted MTFs are included in the panels at extreme right. SAM tone rise time and number of presentations in A: 30 ms, 1; B: 30 ms, 2; C: 30 ms, 1; D: 10 ms, 1.

View larger version (45K): [in this window] [in a new window]   Fig. 16. Illustrative examples of rMTFs containing a suppressive region, from 4 neurons studied at multiple Fcs. The format is similar to that of Fig. 15, except for the absence of the BMF-Fc plots. rMTFs and tMTFs at a few intervening Fcs were omitted for clarity. Fcs presented in A: 1, 1.1, 1.25, 1.35, 1.45, 1.6, 1.8, 2, and 2.15 kHz; B: 1.3, 1.6, 1.8, 2, 2.3, and 2.6 kHz; C: 0.5, 0.6, 0.8, 0.9, 1, 1.1, and 1.3 kHz; D: 12, 12.5, 13, 13.5, 14.5, and 15.5 kHz. SAM tone rise time and number of presentations in A: 10 ms, 1; B: 50 ms, 1; C: 10 ms, 1; D: 10 ms, 1. Modulation frequencies used for Fc-spike rate function at extreme right were 10, 0.5, 0.5, and 1 Hz in A, B, C, and D, respectively.

Figure 16D shows data from a neuron whose rMTF seems to lack suppressive regions when stimulated well away from its BF. Because suppressive regions can emerge at higher SPLs (see Fig. 6A for MTFs at multiple SPLs from the same neuron), this raises the issue of whether the effects of F_c variation can be explained in part on the basis of the SPL relative to threshold at each F_c. We do not yet have sufficient data to address this question.

The tMTF variation with F_c is roughly similar to the variation observed in the same neuron when SPL is varied. Thus when F_c is varied at a particular SPL, tMTFs appear to vary over the same range of values seen when stimulated between threshold and that particular SPL at BF. For example, the neuron in Fig. 15C showed almost invariant tMTFs as the SPL was varied (data not shown, but similar in this respect to Fig. 5, C and D); this was mirrored in the tMTF invariance with F_c. Similarly, the neuron in Fig. 16A showed a large drop in vector strength at low modulation frequencies as SPL increased (Fig. 4); the tMTF in Fig. 16A shows the same property as F_c became closer to BF. However, the details of the variation within this range did not show any clear pattern, especially at higher levels; for example, the vector strength did not show a consistent relationship either with F_c or with spike rate. These results are similar to those reported from the cochlear nucleus (Rhode 1994). Finally, no systematic changes in the pMTFs were found when F_c was varied.

One scheme for the generation of spike rate tuning to modulation frequency in the midbrain (Langner 1981) for low carrier frequencies predicts a linear relation between 1/BMF and 1/F_c (and therefore a monotonic relationship between BMF and F_c). Figure 17, A-E, show data from the five cells (in this study) with peaked rMTFs that were studied at multiple low carrier frequencies (<5 kHz) within their frequency response area. No systematic pattern was found for BMF shifts with F_c. Plotting these shifts as functions of 1/BMF versus 1/F_c (Fig. 17F) confirms the lack of any systematic linearity in our data.

View larger version (46K): [in this window] [in a new window]   Fig. 17. BMFs from rMTFs at different Fcs within the frequency response area do not show any consistent pattern. A-E: rMTFs from the 5 low-frequency neurons in the population with clearly defined rMTF peaks are displayed. The format is similar to that in Fig. 15, except for the absence of the tMTFs. The PSTH pattern in D was measured at a single SPL. F: 1/BMF vs. 1/Fc plots are not linear. Each of the 5 lines joins BMFs at different Fcs for a single neuron (extracted from the rMTFs in A-E and identified by the symbols next to the letters A to E). Fcs presented in A: 0.9-1.8 kHz at intervals of 0.1 kHz; B: 2.4-3.6 kHz at intervals of 0.2 kHz; C: 0.6-1.4 kHz at intervals of 0.1 kHz, 0.8 kHz was omitted; D: 0.5, 0.7, 0.9, 1, 1.2, 1.4, 1.5, 1.6 kHz; E: 0.8-1.4 kHz at intervals of 0.1 kHz, 1.6, 1.8, and 2 kHz. SAM tone rise time and number of presentations in A: 10 ms, 1; B: 50 ms, 1; C: 30 ms, 2; D: 50 ms, 1. E: 50 ms, 1. Modulation frequencies used for Fc-spike rate function in extreme right were 60, 50, 40, 20, and 60 Hz in A, B, C, D, and E, respectively.

	DISCUSSION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

The present study provides detailed descriptions of the variations in spike rate, synchrony, and phase of spike discharges of single neurons in the IC in response to variations in modulation depth, SPL, and F_c of SAM tone stimuli at a range of modulation frequencies. The systematic (and often dramatic) changes seen in all these response measures when stimulus parameters are varied have been described in RESULTS. We now discuss the implications of these findings both for the neural mechanisms generating AM responses in the IC and for performance in psychophysical tasks involving auditory temporal processing.

Excitation and inhibition together create the IC rMTF

Most neuron types in the cochlear nucleus predominantly show poorly tuned or nonexistent variations in spike rate (i.e., low-pass or flat rMTFs) with modulation frequency (Frisina et al. 1990; Rhode and Greenberg 1994). Information about the modulation frequency is instead present in the response component locked to the modulation frequency (i.e., a "temporal code" rather than a "rate code"). In contrast, neurons in the IC show large variations of spike rate with modulation frequency. These variations have previously been reported to result in rMTFs of varied complex shapes, with band-pass rMTFs that possess a BMF being the most common variety (Heil et al. 1995; Langner and Schreiner 1988; Rees and Palmer 1989). The data in this paper show that rMTFs are composed of regions of enhancement and suppression, where the spike rate increases or decreases, respectively, with an increase in the modulation depth of the SAM tone stimulus. In particular, almost all IC rMTFs could be described by some combination of a primary and a secondary region of enhancement and an intervening region of suppression (Fig. 18), with these regions present to varying degrees in individual rMTFs. The regions of enhancement have band-pass shapes, with the low-frequency region of enhancement (E1) forming the primary peak (BMF or corner frequency), and the much less commonly found high-frequency region (E2) the secondary peak. The region of suppression creates the band-suppressive shape, with its trough forming the WMF.

View larger version (13K): [in this window] [in a new window]   Fig. 18. IC rMTFs can be described by some combination of a primary (E1) and a secondary (E2) region of enhancement and an intervening region of suppression, with these regions present to varying degrees in individual rMTFs. E1 forms the primary peak (BMF or corner frequency) and E2 the secondary peak. Modulation frequency in S where the spike rate reaches a minimum is the WMF. Horizontal line shows response to an unmodulated tone. E2 is outlined using dashed lines to indicate that it was only occasionally found, and that its properties remain unclear (see text).

In the spirit of most current models (see Mechanisms generating the secondary region of enhancement), we speculate that the primary region of enhancement is primarily the result of a transformation of excitatory inputs to the IC. This seems plausible because at least some rMTFs in the mustache bat IC remain band-pass after iontophoretic application of various inhibitory blockers (Burger and Pollak 1998). A similar result has been reported for onset neurons in the mustache bat dorsal nucleus of the lateral lemniscus (DNLL) (Yang and Pollak 1997), supporting the notion that purely excitatory mechanisms are capable of creating band-pass rMTFs. However, it is possible that both in the IC and the DNLL, the inputs themselves show band-pass spike rate tuning (see next section); this could also account for the minimal effect of inhibitory blockers on the band-pass tuning of IC rMTFs. On the other hand, it seems very likely that inhibitory inputs shape the rMTF by creating the region of suppression. In addition, inhibition may sharpen the high-frequency rolloff of the primary region of enhancement without resulting in a visible region of suppression (as a result of the low firing rate in response to unmodulated tones: see discussion of Table 1 in RESULTS). The properties of the secondary region of enhancement remain unclear; potential mechanisms that could generate it are discussed in a later section.

In the next few sections, various issues related to the observed MTFs are discussed in greater detail. However, it must be emphasized that in the absence of much pertinent data about intrinsic properties and input patterns of IC neurons, as well as the AM response properties of inputs to the IC, much of this discussion must remain speculative.

Is rate tuning created de novo in the IC?

With contralateral sound presentation, the excitatory afferents to the IC that are likely to be active include those from the contralateral cochlear nucleus (in particular, stellate cells in the ventral cochlear nucleus, and fusiform cells in the dorsal cochlear nucleus), contralateral lateral superior olive (LSO), ipsilateral medial superior olive (MSO), and possibly, the contralateral IC (Moore et al. 1998; Oliver and Huerta 1991). Most neurons in the cochlear nucleus do not show much rate tuning. Although little is known about the response properties of MSO neurons to SAM tones, it appears from preliminary data that neurons in the LSO possess, in addition to tuned tMTFs, rMTFs that show systematic changes of spike rate with modulation frequency (Thornton SK and Semple MN, unpublished observations). LSO rMTFs can show peaks (BMFs); the majority of BMFs seem to lie below 400 Hz. Thus rMTFs of IC neurons may at least in part reflect the rate tuning present in their rate-tuned inputs (e.g., from the LSO); low-pass filtering of the inputs (which are also phase locked to the modulation frequency) may potentially account for the lower BMFs in the IC. However, the extent to which different inputs overlap in their projections onto single IC cells is not clear. It therefore remains plausible that at least some of the rate tuning seen in the IC emerges as a result of collicular processing.

Coincidence detection mechanisms may create the primary region of enhancement

Mechanisms clearly exist in the auditory midbrain to create tuned rMTFs from inputs (e.g., from the cochlear nucleus) that show varying amounts of synchrony to the modulation frequency, but little or no spike rate changes with modulation frequency. One candidate scheme suggests that band-pass rMTFs (regions of enhancement) seen in IC neurons result from coincidence detection of synchronized excitatory inputs (Hewitt and Meddis 1994). In this model, the IC neuron is considered to be a coincidence detector that fires maximally when its inputs (from the cochlear nucleus) are maximally synchronized, thus converting the peak in the input tMTFs to a rMTF peak in the IC. Such a model can reproduce some aspects of the previously reported data, including the flattening of some rMTFs at high SPLs (Rees and Palmer 1989) (Fig. 5A in present study: because the coincidences generated by the high input spike rates at high SPLs fire the coincidence detector independent of the synchrony in the inputs). However, in comparison to the tMTF peaks in the inputs from the cochlear nucleus (80-520 Hz: Frisina et al. 1990, gerbil; mean = 330 Hz: Rhode and Greenberg 1994, cat) and the lateral superior olive (200-600 Hz: Joris and Yin 1998, cat), IC BMFs appear to span a much lower range (0-100 Hz: Fig. 10A). In other words, rMTF peaks in the IC do not seem to be equal to tMTF peaks in their inputs, as specified in the model. Other mechanisms (possibly including some combination of a stage of low-pass filtering, inhibitory inputs causing a sharper high-frequency rolloff, or intrinsic cellular properties) may need to be included to account for the data. However, it seems prima facie possible that such a model (with the addition of inhibitory inputs to create the region of suppression: see next section) might serve as a good first attempt to reproduce various other aspects of AM responses reported in this paper. An extensive modeling study would also offer insight into input patterns and cellular properties that could generate the diversity of MTF characteristics seen in the IC.

An alternate scheme that has been proposed to explain peaked rMTFs also treats the IC neuron as a coincidence detector. However, the structure of this model is very different from that above: it is posited that a cross-correlation analysis is performed by neurons that detect coincidences between spike trains synchronized to the modulation frequency and carrier frequency, respectively, and delayed by different small time periods (Langner 1981