INTRODUCTION

Neurons in the inferior colliculus, the major nucleus of the ascending auditory pathway for binaural information, are sensitive to the interaural phase difference (IPD) (e.g., Irvine 1992). The IPD arises from the interaural time difference (ITD) of the sound arrival, which varies with sound source location. Responses of IC neurons to the IPD are sensitive to the stimulus context, where “context” refers to the history of stimulus, or the properties of a sound preceding a sound of interest. Previous studies often used stimuli with a continuously varying IPD, or dynamic IPD to examine the IC sensitivities to the stimulus context (Ingham and McAlpine 2004; McAlpine et al. 2000; Spitzer and Semple 1991, 1993; Yin and Kuwada 1983). A dynamic IPD stimulus would produce the sensation of a moving sound source. Those studies found that the IC neural responses to the IPD of a given instance strongly depend on the pattern of the preceding IPD modulation.

Possible mechanisms underlying the context effect have been proposed by many studies (Borisyuk et al. 2002; Cai et al. 1998a, b; McAlpine et al. 2000, 2002; Spitzer and Semple 1991, 1993). One such mechanism is spike rate adaptation (Borisyuk et al. 2002; Cai et al. 1998a, b; McAlpine et al. 2000, 2002). A stronger response driven by a stimulus with an IPD close to the unit’s preferred IPD would induce a greater degree of adaptation, and thereby reduce the responses to subsequent stimuli by a greater amount. Another possible mechanism is the interaction of binaurally sensitive excitatory and inhibitory synaptic inputs with different time courses, directly from bilateral medial superior olives (MSOs) or indirectly by the dorsal nucleus of the lateral lemniscus (DNLL) (Borisyuk et al. 2002; Cai et al. 1998a, b; Spitzer and Semple 1998). The same type of mechanism has been proposed to explain the IC responses to stimuli simulating echoes, i.e., pairs of successive clicks (Fitzpatrick et al. 1995; Litovsky and Yin 1998b; Yin 1994). However, the specific role played by the IPD-context sensitivity of the IC neurons in the processing of auditory information remains unclear.

This study sought the functional significance of the context dependency of IC neurons in terms of neural information coding. Our working hypothesis was that the context dependent changes in the IC neural population responses would result in changes in the IPD representation in the IC, which in turn would emphasize the perceptual contrast between sounds presented in sequence. The psychophysical localization aftereffect (Carlile et al. 2001; Kashino and Nishida 1998b; Thurlow and Jack 1973) is an example of the context dependency of human sound localization, which could play a positive role in sound localization. In experiments on the localization aftereffect, Kashino and Nishida (1998b) for example, presented an adapter tone at a certain IPD, followed by a test tone, and the listener’s perceived IPD for the test tone tended to shift systematically with the adapter IPD. Consistent with the results of other previous studies on the localization aftereffect, Kashino and Nishida found that the shift was in a direction away from the adapter IPD, which would emphasize the perceptual difference between the IPDs of the adapter and the test tones. Also, consistent with the emphasis hypothesis, Getzmann (2004) and Kashino (1998a) reported that sound location discrimination improved after exposure to an adapter under certain conditions.

In the present study, we used 2-tone sequences (a conditioner and a probe) as stimuli, and we varied their IPDs independently. This stimulus design was inspired by Kashino and Nishida’s psychophysical studies, albeit on a different timescale. The present paper consists of 2 parts. In the first part, we examined how the responses of single neurons to the probe were modulated by the IPD of the conditioner. We predicted, based on the spike rate adaptation, that the strength of the response to the probe would be minimal when the conditioner evoked the maximal response. We tested whether this prediction held in our stimulus configuration of the conditioner-probe sequence. In addition, we examined how the conditioner affected the other properties of the IPD sensitivity of probe-driven responses, such as the unit’s preferred IPD and the IPD tuning, which are key characteristics in terms of neural information processing.

In the second part, based on the results for single neural responses, we estimated the effects of the conditioner on the neural population level representation of IPD. Studies of the ITD sensitivities of mammalian IC neurons suggest that the stimulus ITD is represented by the activities of populations of neurons with a relatively broad ITD tuning, rather than by the activities of small numbers of neurons that are sharply tuned to a specific ITD (Fitzpatrick et al. 1997; McAlpine et al. 2001). In the present analyses, we adopted relatively simple population-based models. One was the population vector model, which is similar to the population vector model initially proposed for coding the direction of arm movement by the motor neuron population (Georgopoulos et al. 1988, 1993), and which was employed by Fitzpatrick et al. (1997) to evaluate ITD coding efficiencies in several auditory nuclei. The other model was that suggested by McAlpine et al. (2001, 2003), which assumed that the stimulus IPD or ITD is represented by the activities of 2 hemispheric channels, each of which is broadly tuned to sound that is contralateral to the IC.

METHODS

The experiments were conducted in the physiological laboratories of Doshisha and Tokai Universities. Animal experimental procedures were performed in accordance with “Guide for Care and Use of Laboratory Animals” (Institute for Laboratory Animal Research, National Research Council) and were approved by the Animal Experimental Committees of Doshisha University and of Tokai University (Isehara Campus).

Animal preparation and recording procedure

The experiments were performed on 35 adult Mongolian gerbils (Meriones unguiculatus) of both sexes, weighing between 45.8 and 85.1 g. The animals were initially sedated with an intramuscular injection (approximately 1.4 ml/kg) of a 2:1 mixture of ketamine hydrochloride (50 mg/ml) and xylazine (25 mg/ml). Additional injections were given as needed to maintain an areflexive state. A heating pad was used to maintain the animal’s body temperature. The scalp and pinnae were removed to expose the skull and the interparietal bone. A head holder was mounted around bregma of the skull.

Unit activity was recorded extracellularly with custom-made enamel-coated Elgiloy electrodes or Epoxilite-insulated tungsten electrodes (FHC, Bowdoinham, ME), with a nominal impedance of 1–2 MΩ at 1 kHz. For 5 animals, electrodes were dorsoventrally inserted into the IC through several holes (about 0.5 mm diameter) made in the posterior region of the skull. For the other 30 animals, a craniotomy of the intraparietal bone was performed, after which the cerebellum was partially removed to expose the caudal poles of the ICs, which allowed an electrode to be inserted caudorostrally into the IC. At Doshisha University, the unit responses were amplified with a preamplifier (DAM80, World Precision Instruments, Sarasota, FL) and digitized at a sampling rate of 44.1 kHz with a sound card (Siena, SEK’D, West Hollywood, CA). At Tokai University, the unit responses were amplified and digitized at a sampling rate of 12,207 Hz with an RA16 system (Tucker-Davis Technologies, Alachua, FL). The digitized data were stored for on- and off-line analyses. On-line, the responses were band-pass filtered (passband 0.3–3 kHz), and the activities of single units or multiunit clusters were monitored. We used this information to determine the best frequencies (BFs) and threshold sound pressure levels (SPLs) of neurons. Off-line, we isolated the responses of single units with a template-matching algorithm for the formal analyses. A spike was adopted as a single-unit response when it belonged to a distinct cluster of spike waveforms with small deviations from the template waveform.

Recording lasted typically for about 12 h. Once the recording had been completed, the animal was killed with an intraperitoneal injection of a lethal dose of sodium pentobarbital. Some animals were perfused transcardially with phosphate buffer (pH 7.4), followed by 4% paraformaldehyde in the phosphate buffer. Brains were removed, postfixed with 4% paraformaldehyde, and then transferred to a 20–30% sucrose solution. Frozen sections were made in the coronal plane at 25–50 μm, and were Nissl or cytochrome-oxidase stained to examine the sites of the electrode tracks.

We infer that the majority of the units were in the central nucleus of the IC because the distribution of the BFs in the IC was generally consistent with the tonotopic organization of the central nucleus reported in previous studies (e.g., Harris et al. 1997). The stained brain slices, however, showed electrode tracks not only in the core region but also in the indefinite margins of the central nucleus of the IC (Morest and Oliver 1984; Nordeen et al. 1983). Thus the units in the present data might include units in noncentral nuclei.

Stimulus presentation

The animal was placed inside a sound-attenuating chamber and stimuli were delivered dichotically through earphones (MDR-EX70SL, Sony, Japan, or ER-4S, Etymotic Research, Elk Grove Village, IL) coupled to plastic tubes with an inner diameter of 3 mm, which were fitted to the openings of the external auditory meatuses. We calibrated the sound-delivery system by creating finite impulse-response filters, based on frequency responses recorded by probe-tube microphones (ER-7C, Etymotic Research), which were placed in both ears at about 3 mm from the tympanic membranes. The frequency responses of the calibrated systems were flat so the SD within the calibrated frequency range was <1 dB. Signals were produced by custom-made software on a Windows-operated personal computer. At Doshisha University, signals were generated through a sound card at a sampling rate of 44.1 kHz and with a 16-bit resolution. At Tokai University, a system fabricated by Tucker-Davis Technologies (RP2.1) was used to generate signals at a sampling rate of 48,828 Hz and with a 24-bit resolution.

Search stimuli were single-tone bursts (duration 50 to 250 ms) that varied in frequency and SPL. The tone bursts were either diotic stimuli (IPD = 0) or “binaural beat” stimuli, in which the frequencies for the 2 ears differed typically by 5 Hz. Once a single unit was detected, we determined the unit’s BF (with 1/6–1/3 octave resolution) and the threshold SPL (with 5-dB resolution), using the same type of stimuli (i.e., diotic or binaural beat stimuli) as the search stimuli.

Subsequently, we used 2-tone sequences to examine the IPD-context effects on the unit responses. Figure 1 shows the 2-tone sequence that we used. A tone sequence consisted of a conditioner followed by a probe. The durations of the conditioner and the probe were 200 and 50 ms, respectively. We chose a 200-ms duration for the conditioner because Finlayson (1999), in his forward-masking experiment on IC units, found that the degree of suppression induced by a masker (comparable to our conditioner) increased with increasing masker duration, but was relatively constant for masker periods of more than about 200 ms. The tones were gated on and off synchronously between the ears with 5-ms raised-cosine ramps. There was a brief silent gap between the conditioner and the probe. We used a common frequency (typically the unit’s BF) and SPL (10 or 20 dB above the unit threshold) for the conditioner and the probe. A frequency lower than the BF was used when the unit showed IPD sensitivities only for a lower frequency. For most units, we tested only one duration of the silent gap between the conditioner and the probe. The gap duration was usually set at the shortest possible value (but ≥5 ms) sufficient to prevent any interaction between the post-conditioner-offset “ringing” and the onset of the probe at the level of the auditory periphery. We estimated the degree of interaction at the auditory periphery by examining the output of a gammatone filter (Slaney 1993) that was centered at the stimulus frequency. The gammatone filter coefficients were chosen so that the equivalent rectangular bandwidth of the filter corresponded to the bandwidth obtained in a behavioral study by Kittel et al. (2002). We used a longer gap duration when the unit failed to respond to the probe because of strong postconditioner suppression. Thus the gap duration varied among units and ranged between 5 and 100 ms (median 10 ms). For some units, we tested multiple gap durations, ranging typically between 5 and 320 ms (maximum 640 ms).

We varied the IPDs for the conditioner and the probe independently. In this study, a positive IPD indicates that the phase for the ear contralateral to the side of the recorded IC was in advance of the phase for the other ear. For the conditioner, we tested several IPD values, the number of IPD values being varied among units (range 2–10 IPDs; typically 8 values). For 52 units, the intervals of the conditioner IPDs were set so that they had equal steps. For the probe, the IPD varied between −180 and +180°, with typically 8 equal angular intervals (maximum 18 intervals). We also used stimuli without a conditioner. The stimuli were presented in pseudorandom order such that all conditioner and probe IPD combinations were tested once before repeating all the stimuli again in a different random order. The number of repetitions for each condition varied among units (10–55 repetitions; median 40 repetitions). The interstimulus interval was 1 to 1.5 s.

Data analysis

Response properties of single neurons.

We used MATLAB (The MathWorks, Natick, MA) for data analysis. In analyzing the results, we focused on the mean spike count (the number of spikes per trial) driven by the conditioner or the probe. We determined the duration of the analysis time window for both conditioner-driven and probe-driven spike counts, individually for each unit, by visually inspecting the postconditioner-onset histograms of the spike times pooled over the stimulus conditions. The window for the conditioner-driven responses spanned the interval from the conditioner onset to the time of the minimum response within the range between the conditioner offset and the onset of the probe-driven responses. The window for the probe-driven responses had a duration of 50 to 80 ms that started at the onset of the probe-driven responses. We found practically no ambiguity when distinguishing between the conditioner-driven and the probe-driven responses.

Each unit’s sensitivity to the probe IPD, termed the IPD function, was determined from the plot of the mean probe-driven spike counts versus the probe IPD. The properties of the IPD function were described in terms of the overall response strength (ORS), the mean IPD, and the vector strength. The ORS was the spike count for the probe averaged across the probe IPDs, and thus indicated the response strength to the probe irrespective of the probe IPD. The mean IPD and the vector strength are the direction and the resultant length, respectively, of the vector average of the spike-count–weighted probe IPD (Batra et al. 1989; Goldberg and Brown 1969), which are indices of the unit’s preferred IPD and the degree of IPD selectivity. The mean IPD without the conditioner was referred to as the unit’s best IPD. High vector strength values indicated that a greater proportion of spikes were elicited by stimuli with a particular IPD, indicating a sharper IPD tuning.

For 29 units, for which multiple gap durations were tested, we examined the recovery of the ORS after the conditioner offset. To examine the recovery from conditioner-induced suppression or facilitation, we averaged the ORSs across conditioner IPDs for each gap duration and each unit (Fig. 8D). As in the forward-masking experiment reported by Finlayson (1999), we fitted the recovery data of the averaged ORS with a single exponential function: y = k₀ + k₁e^−t/τ, where k₀ and k₁ are constants indicating the asymptotic response magnitude and the difference between the final and the initial response levels, respectively. Here, t is the gap duration and τ is the time constant. The recovery time constant for the ORS recovery (τ) was fitted using the MATLAB’s “lsqcurvefit” function. The goodness of fit was evaluated in terms of the coefficient of determination, which was the squared correlation coefficient between the actual ORS and the estimation by the fitted function. The coefficient of determination indicates the fraction of variance accounted for by the fit relative to the total variance of the ORS.

We also examined the recovery from the conditioner IPD effect (i.e., the conditioner IPD–sensitive component of the ORS). The conditioner IPD effect for a gap duration was quantified as the ORS difference, or the difference between the ORSs for the conditioner IPDs nearest to and farthest from the unit’s best IPD (indicated by the arrow in Fig. 8D). A negative value for the ORS difference indicates that the ORS was reduced by a greater amount by a conditioner with an IPD closer to the best IPD. A greater absolute value of the ORS difference indicates a greater effect of the conditioner IPD. The ORS difference was expressed as the fraction of the ORS when the conditioner was absent. We fitted the same single exponential function as above to the recovery data of the ORS difference. The time constant of the fitted function was the recovery time constant for the ORS difference.

Models of ipd representation by neural populations.

We evaluated how the conditioner-induced change in the probe-driven responses for individual units would be reflected in the representation of the probe IPD by the IC unit population. The IPD representation was evaluated using 2 types of neural population based models. One was a version of the population vector model proposed for coding the direction of arm movement by motor neuron population (Georgopoulos et al. 1988, 1993). In the model, the representation of the probe IPD (IPD_pop) by a neural population was essentially the centroid (i.e., response-weighted center of mass) of the response strength distribution along the best IPD axis. This concept is illustrated in Fig. 10A. When computing IPD_pop, the IPD functions (with and without the conditioner) for each unit were normalized by dividing them by the maximum probe-driven spike count of the unit without the conditioner. Let f_i(θ, φ) denote the normalized IPD function for the ith unit in the presence of a conditioner with an IPD of θ, where φ is a probe IPD. Each unit was represented by p_i, which is a vector-form representation of the ith unit’s best IPD (i.e., |p_i| = 1; ∠ p_i = best IPD). We then computed the “population vector” [v(θ, φ)], which is the response-weighted vector average of the best IPDs across units in the presence of a conditioner with an IPD of θ: v(θ, φ) = ∑_i [f_i(θ, φ)p_i]. Finally, the IPD_pop for a given probe IPD was defined as the direction of the population vector: IPD_pop (θ, φ) := ∠ v(θ, φ).

The other model we examined was that suggested by McAlpine et al. (2001, 2003), in which the stimulus IPD or ITD is represented by the activities of 2 hemispheric channels, each of which is broadly tuned to sound that is contralateral to the IC. We realized this model simply by averaging the IPD functions (normalized as in the population vector analysis) across units. We regarded the averaged responses as representing the outputs from the “channel” in one hemisphere of the ICs. Before averaging, each IPD function was interpolated in 1° steps, using MATLAB’s “interpft” function. Then, we simulated the outputs from the channel in the other hemisphere by inverting the sign of the IPDs for the channel. The difference between the outputs of the 2 hemispheric channels was the IPD representation provided by the hemispheric channel model.

RESULTS

In this study, response characteristics were examined, unless otherwise stated, in terms of the average count of spikes driven by a probe with a duration of 50 ms. We restricted our analyses to 74 units that showed significant tuning to the probe IPDs when the conditioner was absent (Rayleigh test, P < 0.01). Figure 2 summarizes the distribution of units’ BFs, stimulus frequencies, and units’ best IPDs for our data set. The units’ BF (figure abscissa; open circles and crosses) ranged between 100 and 3,800 Hz (median 800 Hz). For 12 units with a BF >952 Hz that exhibited IPD sensitivities only for frequencies lower than the BFs, we used stimuli with lower frequencies (filled circles connected to crosses). Thus the stimulus frequency (open and filled circles) ranged between 100 and 1,600 Hz (median 800 Hz). The units’ best IPDs (figure ordinate) had a circular average of 66°, and 55 of the 74 units exhibited positive best IPDs (i.e., contralateral tuning).

In the following sections, we first describe the responses of individual units, mainly with respect to the effects of the conditioner IPD on the probe-driven responses. Then, based on the results for these individual units, we predict the possible consequences of the conditioner IPD effects on the IPD representation by neural populations.

Effects of conditioner on IPD sensitivities of single neurons

Figure 3 shows an example of unit responses in our data set (unit 030417a), demonstrating a typical pattern of responses. Figure 3A shows the IPD functions of the unit (thick gray line: conditioner absent; lines with symbols: conditioner present). It can be seen that the strength of the response to the probe was generally reduced by the presence of a conditioner, whose size of the reduction was sensitive to the conditioner IPD. The overall profile of the IPD function, however, was relatively invariant with conditioner IPD.

The overall response strength (ORS) for the probe (i.e., the average probe-driven spike count across the probe IPDs and trials) was suppressed by the presence of the conditioner and was sensitive to the IPD of the conditioner (Fig. 3B). The ORS was modulated (a modulation depth of 56%) systematically by the variation in the conditioner IPD, being smallest when the conditioner IPD was near the unit’s best IPD (72°; vertical dashed line). This tendency can be more clearly seen when the ORS is plotted as a function of the angular separation of the conditioner IPD from the best IPD (Fig. 3E). Thus ORS increased approximately linearly with increasing angular separation (r = 0.902). The slope of the linear fit for the normalized ORS (percentage with respect to the maximum across the conditioner IPDs) was 0.334. This indicates that, for example, a 90° increase in the separation of the conditioner IPD from the best IPD would increase the ORS by nearly 30 percentage points (0.334 × 90°). When the ORS was plotted as a function of the conditioner-driven response, there was a strong negative correlation (r = −0.973; Fig. 3F). This tendency is as expected from the spike-rate adaptation.

When the generally broad tuning of the IPD functions was taken into account, there was relatively little deviation in the mean IPD in the presence of a conditioner from the best IPD (maximum 11°) and little variation in the mean IPD when the conditioner IPD was varied (maximum 9°) (Fig. 3C).

The vector strength, as an index of the IPD selectivity, varied with the conditioner IPD (Fig. 3D). It was maximum (indicating a narrow IPD tuning) when the conditioner IPD was close to the unit’s best IPD.

Below, we examine the influence of the conditioner IPD effects on the statistics described above for the sample populations of the units in our data set. Then, we examine the extent to which the duration of the gap between the conditioner and the probe influenced the conditioner effects.

Overall response strength.

As found for unit 030417a (Fig. 3A), the conditioner suppressed the responses of the majority of the units, and the ORS was generally modulated by varying the conditioner IPD. This can be seen by the fact that many points fell below the diagonal line of Fig. 4A, which is the plot of the ORS with the conditioner versus that without it. In the figure, the range of ORSs across all the conditioner IPDs tested for a unit is indicated by the range of a line connecting a pair of dots. Sixty-three of the 74 units exhibited a >10% decrease or increase in the ORS for at least one conditioner IPD. For 50 units, the ORS decreased by >10% for all the conditioner IPDs. A small population of units exhibited the facilitative effect of the conditioner (8 units; >10% increase for all conditioner IPDs; open symbols in Fig. 4A). We noted a close association between the facilitative effect and the units’ temporal response pattern (i.e., a “buildup” type response); that is, for the units that exhibited facilitation, there was generally a rather weak response initially after the conditioner onset, but the response increased toward the end of the conditioner. Even once the conditioner has stopped and during the silent gap, the excitability appeared to remain to enhance the responses to the probe (although even for such units, there was virtually no response during the silent gap). By contrast, in the absence of a conditioner, the probe did not last long enough for the excitability to build up. Thus the conditioner had a facilitative effect.

As seen for the example shown in Fig. 3, B and E, the ORS was sensitive to the conditioner IPD for the majority of units (49 of 74 units showed >25% modulation), and the dependency on conditioner IPD was generally well accounted for by the angular separation of the conditioner IPD from the best IPD. We computed the correlation coefficient for the ORS and the absolute angular separation of the conditioner IPD from the unit’s best IPD. As indicated by the histogram of correlation coefficient (Fig. 4B, gray bars), most units showed a high correlation (43 of the 74 units showed r > 0.5). Of the 49 units that exhibited a relatively large ORS modulation (>25%) with the conditioner IPD (Fig. 4B, black bars), 35 units showed r > 0.5. For the 49 units, we fitted a straight line to the plot of the normalized ORS (the ORS divided by the maximum value for all the conditioner-present conditions) versus the separation between the conditioner IPD and the best IPD (cf., Fig. 3E). The mean and the SD of the slope for the 49 units were 0.17 and 0.23 percentage points/degree, respectively. This indicates that when the conditioner IPD was at the unit’s best IPD, the ORS was an average of 15 percentage points (0.17 × 90°) less than when the separation was 90°.

The dependency of the ORS on the conditioner IPD was generally well accounted for by the conditioner-driven response, as demonstrated for unit 030417a (Fig. 3F). Figure 4C is a histogram of the correlation coefficient between the ORS and the conditioner-driven spike count for the 49 units that exhibited a relatively large ORS modulation. Clearly, the majority of the units exhibited a highly negative coefficient (42 of the 49 units showed r < −0.5). A minority of the units (5 of the 49 units) showed positive correlations (r > 0.5). We found that a positive correlation was often (i.e., for 3 of the 5 units) associated with the conditioner-induced facilitation, or with the buildup-type response. As with unit 030417a (Fig. 3F), we fitted a straight line to the plot of the normalized ORS versus the normalized conditioner-driven spike count for each unit. The mean and the SD of the slope were −0.54 and 0.51, respectively. This indicates that on average, an increase of 1.0 percentage point in the conditioner-driven response would result in a decrease of 0.54 percentage point in the probe-driven response.

We found a few cases in which the conditioner elicited virtually no spikes but appreciable conditioner-induced suppression was present. These cases are inconsistent with the explanation of the conditioner IPD effect in terms of the conditioner-driven response. Three of the 74 units exhibited virtually no conditioner-driven response (<0.1 spikes per trial) for at least one conditioner IPD. Of those units, only one showed suppression of >90% at that IPD, and the other 2 units showed relatively weak suppression (26 and 18%).

Mean ipd.

The conditioner had relatively little effect on the mean IPD. This can be seen in Fig. 5, in which the mean IPD range for various conditioner IPDs is plotted versus the mean IPD when there is no conditioner (i.e., the best IPD). The mean IPD for many units clustered around the diagonal line. A small population of units exhibited a statistically significant effect (P < 0.01, Watson’s nonparametric test for common mean direction; Fisher 1993) of the presence of a conditioner (16 of the 74 units) and/or of the conditioner IPD (8 of 74). Unlike for the ORS, across those 8 units that exhibited a significant effect of the conditioner IPD, we failed to find a consistent relationship between the variation of mean IPD and the angular separation of the conditioner IPD from the unit’s best IPD.

Vector strength.

The vector strength generally increased (i.e., tuning narrowed) in the presence of a conditioner (Fig. 6A). The figure, which is a plot of the range of vector strength in the presence of a conditioner against the vector strength without the conditioner, shows that many data points fell above the diagonal line. For 54 of the 74 units, the mean vector strength (across conditioner IPDs) was greater when the conditioner was present than when it was absent.

Unlike for the ORS, however, we failed to find a consistent pattern of conditioner IPD dependency across the units as regards vector strength. Figure 6B is a histogram of the correlation coefficient for the vector strength and the absolute angular separation of the conditioner IPD from the unit’s best IPD (cf. Fig. 4B). Here, a positive coefficient indicates that the vector strength increased (i.e., the IPD tuning sharpened) with increasing separation of the conditioner IPD from the unit’s best IPD. The figure indicates that generally the coefficients distributed broadly between −1 and 1, albeit with a weak bias toward negative values (Fig. 6B, gray bars). When the examination was restricted to the units exhibiting relatively large conditioner IPD dependency (i.e., >25% modulation induced by conditioner IPD; 35 units; black bars in Fig. 6B), nearly equal numbers of units exhibited negative and positive correlation coefficients (19 and 16 units, respectively).

To overview the effects of conditioner IPD on the response properties described above, the units in our data set are sorted in terms of best IPD and are plotted in Fig. 7. Each panel of Fig. 7 shows the responses of 42 units for which we experimentally tested conditioner IPDs of −180, −90, 0, and +90°. The 3 columns from left to right indicate the characteristics of the IPD function, that is, the ORS, the mean IPD, and the vector strength, respectively. In each panel, the abscissa indicates the unit’s best IPD and the ordinate indicates the deviation of the measure of interest from the mean value. For the ORS and the vector strength, we scaled the values for each unit relative to the maximum value across all the conditioner IPDs, before calculating the deviations.

There is a trend that the ORS was relatively small for units with best IPDs near a conditioner IPD (dashed vertical lines). The trend could be easily seen when a cosine function was fitted to the ORS-versus-best-IPD functions (thick lines). The coefficient of determination for the fit (R²) ranged between 0.165 and 0.449, indicating that the 16.5 to 44.9% variability among the units could be accounted for by a cosine function. The minima of the fitted curves corresponded approximately to the conditioner IPD. This indicates that the ORS was reduced rather selectively for units with best IPDs near the conditioner IPD.

We failed to find such systematic trends for the mean IPD and the vector strength: R² range for the cosine fit was as small as 0.005–0.068 for the mean IPD and 0.004–0.028 for the vector strength, which indicates that the effects of the conditioner IPD on the mean IPD and the vector strength were negligible or, if they existed, were inconsistent among units.

Effects of gap duration

In the previous sections, the duration of the silent gap between the conditioner and the probe was fixed for each unit (see methods). In this section, we describe supplementary experiments that we conducted to examine to what extent the conditioner effect would be sensitive to the gap duration, and recovery functions from the conditioner effect. We tested 4 to 7 gap durations (maximum 640 ms) for 29 units.

The results for unit 030218c, which is representative of the units in our data set, are shown in Fig. 8, the top panels of which (Fig. 8, A–C) show IPD functions, each panel representing one conditioner IPD, and each function within a panel representing an IPD function for one gap duration. The basic properties of the IPD functions, that is, ORS, mean IPD, and vector strength, are represented in the bottom panels (Fig. 8, D–F), as a function of gap duration.

Within any given gap duration, the effect of the conditioner was generally consistent with our typical results described in the previous sections (Fig. 8, D–F). The conditioner IPD near the unit’s best IPD had the greatest suppressive effect on the ORS. The mean IPD was relatively insensitive to the conditioner IPD. For this unit, the vector strength tended to be largest for the conditioner IPD near the unit’s best IPD. For all the statistics, the effect of the presence of a conditioner was maximal for the shortest gap duration, and the recovery was monotonic as the gap duration increased.

We focused on the ORS to evaluate the recovery from the conditioner effect. We quantified the recovery of the ORS from the general suppression (i.e., the component of the ORS change that was insensitive to conditioner IPD) by fitting an exponential function to the average ORS across conditioner IPDs (indicated by dots in Fig. 8D) as a function of gap duration (see methods). The fitted exponential curve is shown by the gray line in Fig. 8D. The recovery time constant was 111.8 ms. Similarly, we applied the exponential function to the recovery function for the 29 units for which there were more than 3 gap durations. In general, the exponential function accounted well for the ORS recovery function; the median of the coefficient of determination was 0.91. Figure 9A is a histogram of the recovery time constants, representing 25 of the 29 units for which the coefficient of determination was >0.75. The median time constant was 111.8 ms.

We also examined the recovery from the conditioner IPD effect (i.e., the component of the ORS change that was sensitive to conditioner IPD). The effect of the conditioner IPD for a given gap duration was quantified as the ORS difference, which was the difference between the ORSs for the conditioner IPDs nearest to and farthest from the unit’s best IPD (illustrated by the arrow in Fig. 8D, which is an example for a 5-ms gap). See methods for details. For the unit shown in Fig. 8, the size of the ORS difference decreased monotonically with increasing gap duration. The fitted exponential function had a recovery time constant of 114.8 ms.

An examination of the ORS differences for the population of the 29 units led us to conclude that, in general, varying the gap duration would influence the magnitude but not the direction of the conditioner IPD effects. For each unit, we compared the signs of the ORS differences across gap durations. Altered signs should indicate that the direction of the conditioner IPD effect (i.e., whether a conditioner IPD nearest the best or the worst IPD induced the greatest suppression of the ORS) varied depending on the gap duration. We restricted the examination to the ORS differences with appreciable sizes, that is, those for which the absolute value (expressed as a fraction of the ORS when the conditioner was absent) was >0.1. The criterion value of 0.1 corresponded to the median of the absolute values of the ORS differences across all units and gap durations. As a result, only 3 units exhibited altered signs of the ORS difference, indicating the dependency of the direction of the conditioner IPD effect on the gap duration.

The exponential function was fitted to the plot of the ORS difference versus gap duration. Figure 9B shows the distribution of the time constants for the population of units, representing 14 of the 29 units for which the coefficient of determination was >0.75 (the coefficient of determination for all 29 units had a median of 0.74). The median time constant was 68.6 ms.

Conditioner effects on neural population codes

In this section, we explore the functional significance of the conditioner effects in the IPD representation at the level of neural population in the IC. We adopted 2 types of models: the population-vector model and the hemispheric-channel model (see methods).

The population-vector model assumes that there is an array of IC units, somewhat broadly tuned to various IPDs, and that each unit is represented by its best IPD (Fig. 10A, top). Presenting a probe would evoke responses from the populations of IC units, and the IPD of the probe would determine the pattern of the response distribution along the axis of the unit’s best IPD (Fig. 10A, bottom). We assumed that the population representation of the probe IPD (IPD_pop) is derived as the centroid (i.e., response-weighted center of mass) of the population response distribution along the best IPD axis. Changes in the individual IPD functions arising from the presence of a conditioner should somehow alter the population response distribution, and thus the IPD_pop. Earlier analyses of the individual units indicated a tendency for the ORS to be reduced by the greatest amount for units with their best IPDs close to the conditioner IPD, whereas the mean IPD was generally invariant with conditioner IPD (Fig. 7). An expected consequence of this trend is shown in Fig. 10B. The figure reveals that when a conditioner was present with an IPD of zero, for instance, the response strengths of the units with their best IPDs near zero would be rather selectively reduced (Fig. 10B, top). We expect that this change would shift the centroid of the population response for a given probe IPD in a direction away from the conditioner IPD (Fig. 10B, bottom).

We tested this expectation using a database consisting of 42 units for which we experimentally tested conditioner IPDs of −180, −90, 0, and +90°. We formed a unit array that consisted of the 42 units, plus the same 42 units for which the signs of the conditioner and the probe IPDs were inverted. We combined the units with unaltered and inverted IPD signs, to simulate the population responses in bilateral ICs. In this analysis, we neglected differences among units with respect to unit properties such as best frequency and threshold SPL and with respect to stimulus properties such as frequency, SPL, and gap duration. We computed the IPD representation by neural population, IPD_pop, for each conditioner state. See methods for details.

To illustrate our population-vector analysis, we provide examples of unit-array responses for a probe at +90° IPD in Fig. 10C. In the absence of a conditioner (open circles), units with best IPDs of about +90° were generally most active (compare this with Fig. 10A, bottom). The centroid of the response distribution (i.e., IPD_pop) was +64° (vertical dashed line). The 26° offset of IPD_pop from the probe IPD (+90°) was attributed to the overrepresentation of best IPDs of −90 to +90°. When a 0-IPD conditioner was present (asterisks), the responses decreased particularly for best IPDs of 0 ± 90° (compare this with Fig. 10B, bottom). Thus the profile of the response distribution was altered. We can easily see the change in the distribution profile when we compare the running averages of the responses in the absence (broken gray line) and in the presence (solid gray line) of the conditioner. The IPD_pop when the conditioner was present was +84° (vertical solid line). That is, the IPD_pop for the +90 ° probe shifted by 20° (i.e., 84–64°) toward positive IPDs, in the presence of the 0-IPD conditioner.

The results of the analysis indicated that the IPD_pop in the presence of a conditioner tended to shift from that without a conditioner (Fig. 11, lines connecting dots). In the figure, the shift of the IPD_pop is plotted as a function of the probe IPD, for each conditioner IPD. Except for a conditioner IPD of −180° (Fig. 11A), the maximum shift was as great as about 45°. For each panel, the sign of the shift tended to change at a probe IPD near the conditioner IPD. The IPD_pop for a probe at a positive IPD relative to the conditioner IPD was generally biased toward a positive IPD, and vice versa. This result is consistent with our expectation as illustrated in Fig. 10B.

The analysis with the hemispheric channel model was conducted as follows. We averaged the (normalized) IPD functions of 30 units for which the best IPDs were positive and where we experimentally tested conditioner IPDs of −180, −90, 0, and +90°. We regarded an averaged IPD function as being proportional to the outputs from the single hemispheric “channel.” Each IPD function was interpolated in 1 ° steps, before averaging. Figure 12A shows the averaged IPD functions in the absence (thick gray line) and the presence (thin lines with symbols) of a conditioner. As expected from the results reported in previous sections, the response strength (i.e., the channel output) was reduced when a conditioner was present, and the degree of reduction generally increased as the conditioner IPD changed from negative to positive. Next, by inverting the sign of the IPDs for the channel, we simulated the outputs from the contralateral channel. Then, we regarded the differences between the outputs of the 2 hemispheric channels as the IPD representation provided by the hemispheric channel model. The differences between the channels are shown in Fig. 12B. It can be seen that the model output when the conditioner was present deviated from that when the conditioner was absent. We estimated the conditioner-induced shift of the IPD representation from the difference in the probe IPD that would elicit an equal model output. With the −90° conditioner, for instance, the model output for a probe IPD of, say, 0° was about 0.16 (Fig. 12C). Without the conditioner, the same output would be elicited by a probe at about 15°. We could interpret this result as showing that the IPD representation for the 0-IPD probe had shifted toward a positive IPD by about 15°.

The shifts in the IPD representation estimated as described above (indicated by the circles in Fig. 11) exhibited similar properties to those estimated with the population-vector model, despite differences in the detailed model structure. The shift size of the IPD representation was as much as about 40°. The sign of the shift tended to change at a probe IPD near the conditioner IPD, which indicates that the presence of a conditioner would shift the IPD representation in a direction away from the conditioner IPD.

DISCUSSION

The present study examined the responses of single units in the gerbil IC to sequences of 2 steady tones, the IPDs of which were varied independently. In general, the presence of a conditioner reduced the response strength to the probe and increased the IPD selectivity (i.e., increased the vector strength). The response strength varied systematically with the conditioner IPD, whereas the effects of the conditioner IPD on the neurons’ preferred IPDs and IPD selectivities were slight or inconsistent among units. We evaluated the effects of conditioner IPD on the IPD representation at the level of neural population, based on the results obtained for individual units using 2 types of models. One was a version of the population-vector model (Georgopoulos et al. 1988, 1993) and the other was the hemispheric-channel model (McAlpine et al. 2001). The results provided by the 2 models consistently indicated that the IPD representation by neural population for a given probe IPD would be biased by the presence of a conditioner in a direction away from the conditioner IPD.

Comparison with previous studies

We found that the time course and the type of the present stimuli were particularly comparable to that used in a forward-masking study by Finlayson (1999), in which he examined the responses of IC neurons to a 200-ms-long masker (corresponding to our conditioner) followed by a 30-ms probe, presented monaurally and diotically. Our results for the effects of a conditioner on the ORS were generally in agreement with Finlayson’s findings for monaural stimulation. For the majority of units (>67%), the conditioner (or the masker) had a suppressive effect. The minority of units that exhibited a facilitative effect were associated with a temporal response pattern of the long-latency or the build-up type. Our recovery time constants were slightly longer (a median of 111.8 ms) than Finlayson’s (a median of 72.8 ms). However, we consider the difference between the studies to be small, considering the differences in the analysis procedure, sample numbers, and precision of analysis.

The present study agreed with previous studies on dynamic IPD stimuli (McAlpine et al. 2000; Spitzer and Semple 1991, 1993), in that the IC neurons’ sensitivities depended on the IPD context or the IPD history. It might appear inconsistent that in earlier studies, the shape of the IPD function was substantially modulated by a dynamic IPD, depending on the direction and range of the IPD modulation, whereas for the present stimuli, the mean IPD was relatively invariant with the conditioner IPD. We consider, however, that these 2 observations are not contradictory. As discussed in the next section, our results are generally consistent with the prediction by the spike-rate adaptation mechanism. The spike-rate adaptation mechanism is known to be able to account for, at least partially, the variation of the IPD function for the dynamic IPD stimuli (McAlpine et al. 2000). Thus we expect that even for 2-sequence stimuli such as ours, the IPD function should exhibit some apparent modulation because of the variation of conditioner IPD for certain combinations of conditioner and probe IPDs. Note that in the studies on the dynamic IPD, an IPD function was drawn for a fixed IPD change from the preceding stimulus (i.e., for a given point on an IPD function, the preceding IPD was separated from the IPD at that point by a fixed amount and direction). By contrast, in our study an IPD function was drawn for each fixed conditioner IPD.

The results for the dynamic IPD stimuli, however, were substantially different from ours, in that the spike probability often substantially exceeded that predicted from the responses to a static IPD (McAlpine et al. 2000; Spitzer and Semple 1991, 1993). In contrast, in the present study the conditioner had a predominantly suppressive effect. We speculate that this difference arose from the difference in the timescale of the stimulus and in the analysis time window. The dynamic IPD stimuli typically had a relatively long (>8 s) duration, and the spike-count calculation was based on the sustained portions of the response. In the present study, on the other hand, the mean spike counts were computed for short (50-ms) probe tones, in which transient responses at the probe onset were the major determinant of the mean spike count. It may be that the onset responses were more susceptible to the conditioner-induced suppression than the sustained portions of the responses and thus we rarely observed facilitative effects.

Extensive studies have been conducted on the IC parallels of the precedence effect (PE), that is, the perceptual dominance of the first-arriving sound (or the direct sound from a source) over echoes in sound localization (Fitzpatrick et al. 1995, 1999; Litovsky et al. 1998a, b, 2002; Yin 1994). Stimuli for PE experiments are similar to ours in that they consist of a leading and lagged sounds (typically clicks), varied in terms of spatial location or ITD. Despite differences in stimulus type and temporal structure, the major finding of the present study is comparable to the results of PE studies. Litovsky and colleagues (1998b, 2002) found that IC units of anesthetized cats generally exhibited lead-induced suppression of the lag-driven response, and for the majority (about 80%) of units, the suppression was maximal when the lag location was in the unit’s response area (Litovsky et al. 1998b, 2002). It should be pointed out, however, that the predominance of the units exhibiting the greatest lag suppression by the best stimulus lead was not true for unanesthetized animals, that is, rabbits (Fitzpatrick et al. 1995).

Mechanisms underlying the conditioner effects

The presence of a conditioner generally suppressed the responses to the probe. We infer that this general suppression was largely the result of the accumulated short-term adaptation that took place in non-binaural-specific pathways below the level of the IC (Finlayson 1999).

The conditioner IPD–sensitive component of the response suppression could be well accounted for by the spike-rate adaptation (Borisyuk et al. 2002; Cai et al. 1998a, b; Ingham and McAlpine 2004; McAlpine et al. 2000, 2002). This is because, for the majority of units, the response strength to the probe was highly negatively correlated with the conditioner-driven spike count (Fig. 4C). It should also be noted that the mean IPD for the probe was relatively invariant with the conditioner IPD, indicating that there was little interaction between the conditioner and the probe IPDs in determining the probe-driven response strength. This was as expected from the spike-rate adaptation explanation because it assumes that the effect of the conditioner IPD is mediated by the conditioner-driven responses, and thus the probe-driven response would have no memory of the conditioner IPD, per se.

Arguments against the explanation in terms of the spike-rate adaptation, however, are possible, because of the following 2 observations: One is that there were a few units for which the conditioner elicited virtually no spikes but there was appreciable conditioner-induced suppression; the other is that the recovery time constant for the conditioner IPD effect (a median of 68.6 ms; Fig. 9B) was considerably shorter than the time constants estimated for the spike-rate adaptation (more than a few hundreds of milliseconds; Ingham and McAlpine 2004). One should be cautious, however, when comparing time constants for the 2 studies. Ingham and McAlpine (2004) derived time constants in experiments in which the binaural adaptation components were carefully segregated from those of the monaural adaptation, whereas the present experiment was not specifically designed to segregate the 2 types of components.

It is possible that mechanisms other than the spike-rate adaptation played certain roles in shaping the conditioner IPD effects. For example, the observed effect could be accounted for by the interaction between binaurally sensitive excitatory and inhibitory synaptic inputs with different time courses, directly from bilateral MSOs or indirectly by DNLL (Borisyuk et al. 2002; Cai et al. 1998a, b; Fitzpatrick et al. 1995; Litovsky and Yin 1998b; Spitzer and Semple 1998; Yin 1994).

Validity of neural population analyses

Some might be concerned that in conducting the population analyses, we pooled the IPD functions obtained for units with different BFs. We considered this pooling acceptable because a previous report indicated that the central tendency of the best IPD, rather than the best ITD, was relatively invariant with BF (McAlpine et al. 2001). Thus the pooled population among different BFs reflected, to some degree, a population of IPD functions of units with a given BF, although the best IPDs for the units in the present study were distributed relatively broadly. It should also be noted that the 2 different models examined in the present analyses reached essentially the same conclusion as to the direction of the representation shift. Thus we consider that the predicted direction of the conditioner-dependent shift of the IPD representation by neural populations should be relatively insensitive to the details of differences among units or model structures.

Implications of population sensitivity to IPD context

The present analyses estimated that the IPD of a preceding sound systematically biases the IPD representation by IC-neural populations, even though the effects of the context on individual units were merely seen in changes of response gain, without consistent changes of preferred IPD.

This bias of the population representation might be viewed as a distortion of the auditory space representation, which thus loses the coding accuracy for location-related information. There is another view, however. The context-dependent change of the neural representation enhances the representational contrasts between successive sounds, improving the efficiency of the information processing of environmental sounds. This view is along the same lines as the general notion that neural adaptation plays positive roles in efficient stimulus coding (e.g., Barlow 1990; Brenner et al. 2000; Wainwright 1999). Consistent with this view is the fact that the representation shift induced by the conditioner was in a direction away from the conditioner IPD, which would emphasize the difference between representations of the conditioner and the probe IPDs.

The direction of the IPD-representation shift was the same as that of the perceptual shift found in the psychophysical localization aftereffects (Carlile et al. 2001; Kashino et al. 1998a, b, 1999; Thurlow and Jack 1973). There are also studies reporting that spatial discrimination on the horizontal plane improved after the presentation of an adapter sound, specifically when the target sound was close to the adapter in terms of spectral content and spatial location (Getzmann 2004; Kashino 1998a). These results of adaptation experiments are consistent with the above view that enhancement is provided by a preceding sound. However, it should be noted that the stimuli for the adaptation experiments generally had a timescale that was about an order of magnitude longer (i.e., an adapter tone ≥1 s long followed by a ≥100-ms test tone). It is therefore possible that the neural mechanisms of the localization aftereffect are not directly relevant to the physiological findings in the present study.

Unfortunately, we are unaware of compelling psychophysical evidence for stimuli with a timescale comparable to ours that indicates a shift of perceived IPD. Perhaps the most comparable psychophysical experiment so far is the experiment on the PE (for review see Litovsky et al. 1999), typically using 2 successive clicks presented from separate sources in space with a relatively short interval (a few to a few hundreds of milliseconds). Given the similarities between the results of the previous physiological studies on the PE (Litovsky et al. 1998b, 2002) and the present study (see earlier section), we can expect a perceptual bias with respect to the lagging click’s location if our neural population models are applicable to the stimuli of paired clicks. However, as far as we are aware, there has been no psychophysical report explicitly indicating such a bias, at least for relatively long interclick intervals (more than a few tens of milliseconds). The lack of evidence may simply be because the previous PE experiments were not intended to detect a small perceptual bias or were insufficiently sensitive for this purpose. It is also possible that the neural population models hypothesized in the present study do not properly account for the neural mechanisms underlying human sound localization and/or that the single neuronal responses observed in earlier PE (Litovsky et al. 1998b, 2002) and the present studies could not be appropriately compared with the neural responses of an awake human.

Clearly, behavioral experiments are needed that use stimuli comparable to ours in timescale and in stimulus type to determine the perceptual consequences of the physiological context effects. We expect that, when compared with the results of appropriate behavioral studies in the future, the present results should help us not only to clarify the significance of the physiological context effects but also to gain insights into the coding of binaural information in the IC.

GRANTS

This study was partly supported by special coordination funds from the Science and Technology Agency of the Japanese government, and a grant to Research Center for Advanced Science and Technology at Doshisha University from the Japan Ministry of Education, Culture, Sports, Science and Technology.

FOOTNOTES

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