Frequency-dependent interaural delays in the medial ...

Frequency-dependent interaural delays in the medial superior olive:implications for interaural cochlear delays

Mitchell L. Day and Malcolm N. SempleCenter for Neural Science, New York University, New York, New York

Submitted 15 February 2011; accepted in final form 20 July 2011

Day ML, Semple MN. Frequency-dependent interaural delays inthe medial superior olive: implications for interaural cochlear delays.J Neurophysiol 106: 1985–1999, 2011. First published July 20, 2011;doi:10.1152/jn.00131.2011.—Neurons in the medial superior olive(MSO) are tuned to the interaural time difference (ITD) of soundarriving at the two ears. MSO neurons evoke a strongest response attheir best delay (BD), at which the internal delay between bilateralinputs to MSO matches the external ITD. We performed extracellularrecordings in the superior olivary complex of the anesthetized gerbiland found a majority of single units localized to the MSO to exhibitBDs that shifted with tone frequency. The relation of best inter-aural phase difference to tone frequency revealed nonlinearities insome MSO units and others with linear relations with characteristicphase between 0.4 and 0.6 cycles. The latter is usually associatedwith the interaction of ipsilateral excitation and contralateral inhi-bition, as in the lateral superior olive, yet all MSO units exhibitedevidence of bilateral excitation. Interaural cochlear delays andphase-locked contralateral inhibition are two mechanisms of inter-nal delay that have been suggested to create frequency-dependentdelays. Best interaural phase-frequency relations were comparedwith a cross-correlation model of MSO that incorporated interauralcochlear delays and an additional frequency-independent delaycomponent. The model with interaural cochlear delay fit phase-frequency relations exhibiting frequency-dependent delays withprecision. Another model of MSO incorporating inhibition basedon realistic biophysical parameters could not reproduce observedfrequency-dependent delays.

interaural time delay; interaural time difference; sound localization;gerbil; superior olivary complex

HUMANS AND MANY OTHER ANIMALS localize sound in the hori-zontal plane using interaural sound cues. In humans, theinteraural time difference (ITD)—the difference of arrival timeof sound to the two ears—is the dominant cue to localize soundazimuth whenever low-frequency information is available(Wightman and Kistler 1992). The medial superior olive(MSO) is considered the primary site along the auditory path-way to encode ITDs in its neuron’s firing patterns (Yin 2002),as it receives input bilaterally from monaural brain stem nuclei[the anteroventral cochlear nuclei (AVCN)] and yields spikerate responses that are tuned to the ITD of sound (Goldberg andBrown 1969; Yin and Chan 1990).

As initially proposed by Jeffress (1948), the excitatoryinputs onto the ITD processor phase-lock to pure tones (e.g.,Joris et al. 1994a) and elicit a tuned rate response to ITD in theMSO via coincidence detection (Goldberg and Brown 1969).While the basic construction of ITD sensitivity is clear, therehas been much debate over the mechanisms of internal delay

that determine which ITD elicits the greatest rate response, i.e.,the best delay (BD) (Joris and Yin 2007; McAlpine and Grothe2003). The dependence of BDs across the range of frequenciesused for ITD processing has implications for the neural codingof ITD (e.g., Harper and McAlpine 2004; McAlpine et al.2001).

The traditional candidate mechanism of internal delay isdifferences in axonal conduction time of the bilateral inputsonto MSO. Jeffress (1948) originally proposed systematicdelay lines of axonal conduction differences onto a binauralnucleus (now known to be the MSO); anatomical reconstruc-tion of these axonal projections found the pattern of delays tobe inconsistent with Jeffress’ proposal and, further, could notfully account for the distribution of BDs observed physiolog-ically (Karino et al. 2011). Another mechanism of internaldelay is the contralateral glycinergic inhibition onto MSOfrom the medial nucleus of the trapezoid body, whose phar-macological manipulation was found to shift the BDs ofgerbil MSO neurons (Brand et al. 2002; Pecka et al. 2008).Differences in the synaptic dynamics of ipsilateral and con-tralateral excitation onto MSO have also been proposed as amechanism of internal delay (Jercog et al. 2010). Finally,interaural cochlear delays—the topic of the present study—may be a mechanism of internal delay, as first proposed bySchroeder (1977) and later elaborated on in a computationalmodel by Shamma et al. (1989).

Interaural cochlear delays arise from the mismatching ofbilateral axons onto a target MSO neuron (Fig. 1). Centralauditory nuclei are cochleotopically arranged, with a givenneuron receiving inputs that originate from a common lo-cation along the cochlear basilar membrane. If the conver-gence of inputs from the ipsilateral and contralateral AVCNonto a given MSO neuron is not cochleotopically precise, aninteraural internal delay will be created because of the extratime it takes the cochlear traveling wave to propagate alongthe basilar membrane on one side (Fig. 1A). The frequencytuning of the ipsilateral and contralateral inputs onto anindividual MSO neuron will largely overlap but may differslightly in characteristic frequency (CF)—the frequencywith the lowest threshold (Fig. 1B). Modeling studies haveshown that small CF mismatches can qualitatively accountfor large delays in experimental data (Bonham and Lewis1999; Shamma et al. 1989). Furthermore, a simulation ofMSO response via a cross-correlation of physiologicallyrecorded spike trains of auditory nerve (AN) fibers withslightly different CFs demonstrated that interaural cochleardelays could account for the observed dependence of BDson CF (Joris et al. 2006). CF mismatches have been mea-sured in the barn owl nucleus laminaris (the avian analog of

Address for reprint requests and other correspondence: M. L. Day, Eaton-Peabody Laboratories, Massachusetts Eye and Ear Infirmary, 243 Charles St.,Boston, MA 02114 (e-mail: [email protected]).

J Neurophysiol 106: 1985–1999, 2011.First published July 20, 2011; doi:10.1152/jn.00131.2011.

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MSO) and found to be clustered near zero but could be aslarge as 500 Hz for CFs in the barn owl range of 3– 8 kHz(Fischer and Pena 2009; Pena et al. 2001). These barn owlstudies found that CF mismatches did not correlate with thecharacteristic delay of laminaris neurons. However, thisdoes not rule out the influence of interaural cochlear delaysin conjunction with other mechanisms of internal delay. Inthe mammalian MSO, there are currently no data on mon-aural threshold frequency tuning or other compelling evi-dence for interaural cochlear delays.

In this study, we report data from the gerbil MSO thatimplicate the influence of interaural cochlear delays in additionto other mechanisms of internal delay. We observed a tendencyin many MSO neurons of the BD to shift systematically withtone frequency, i.e., a frequency-dependent internal delay.Frequency-dependent delays have been reported previously indata from the superior olivary complex (SOC) (e.g., Batra et al.1997), although in some cases the anatomical localization ofthese responses to the MSO has been unclear. It has beensuggested that frequency-dependent delays could arise frominteraural cochlear delays (Yin and Kuwada 1983) or phase-locked inhibition (Batra et al. 1997; Leibold 2010). Bonhamand Lewis (1999) found in a MSO model consisting of thecross-correlation of model AN output that CF mismatchescreated frequency-dependent delays. We used a similar modeland show that interaural cochlear delay can both qualitativelyand quantitatively account for the types of frequency-depen-dent delays occurring in our data. We also found that a modelof phase-locked inhibition using realistic biophysical parame-ters could not account for frequency-dependent delays.

METHODS

All experimental procedures were approved by the InstitutionalAnimal Care and Use Committee at New York University.

Surgery. Adult (P58–P105) Mongolian gerbils (Meriones unguicu-latus) of both sexes, weighing between 52 and 90 g, were used.Gerbils were initially anesthetized with pentobarbital sodium (60mg/kg ip). Anesthetic state was monitored every 15 min duringsurgery and every 30 min during recording, with additional doses ofpentobarbital sodium (�12 mg/kg ip) and ketamine hydrochloride(�12 mg/kg im) as needed to maintain slow respiration rate and nowithdrawal to foot pinch. A heating pad was used to maintain aconstant rectal temperature of 38°C. The trachea was cannulated. Theskull was exposed, and two small screws were placed laterally into theparietal bones, followed by the fixing of a metal headpost rostral tothe lambdoid suture with bone cement (Biomet Orthopedics). Acraniotomy was performed immediately caudal to the transverse sinusand centered on the midline. The headpost was inserted into astereotaxic apparatus with the rostrocaudal axis of the head tilted tomake the eyes level with the ear canals. The pinnae were removed,and sound delivery earpieces were sealed around the openings of theear canals. The electrode was lowered vertically into the cerebellumthrough a hole in the dura.

Electrophysiological recording. Extracellular recordings weremade with parylene-coated tungsten microelectrodes (Microprobe)with tips plated with gold and then platinum. Electrical signalsrecorded in the brain stem were amplified and band-pass filtered at0.8–10 kHz. Filtered neural signals were fed to an event processorwith associated data acquisition/analysis software (MALab, KaiserInstruments).

Single unit isolation in the MSO is notoriously difficult, owing tothe small, graded amplitude of the action potential (Scott et al. 2005,2007) in the midst of a large, coherent local field potential (theneurophonic) driven by highly phase-locked inputs. Spontaneousfluctuations of the neurophonic in silence and at low sound levelswere not readily distinguishable from spikes, nor were the sharpfluctuations of the neurophonic in response to noise stimuli. Unlikeother areas of the brain, action potential amplitudes recorded with invitro whole cell recordings at the soma of MSO neurons have beenshown to be highly variable within the same unit (Scott et al. 2007).Furthermore, the action potential amplitude decreases with the risetime of the underlying excitatory postsynaptic potential (EPSP) (Scottet al. 2007), i.e., multiple, coincident synaptic events summate toproduce a short rise time of the EPSP and also a large-amplitudeaction potential. We were able to successfully isolate single units bylimiting our stimulus set to moderate- to high-level pure tones—levelsthat would increase the rate of coincident EPSPs and likely producemore higher-amplitude action potentials to rise above the neuro-phonic. Binaural beats (dichotic pure tones; see Acoustic stimulation)at 70 dB SPL were used to search for units and produced highlystereotyped oscillations in the neurophonic, unlike the erratic neu-rophonic fluctuations in response to noise. Spikes could then beidentified visually as small, sharp deflections riding on top of theoscillating neurophonic (see Figs. 5A and 6F, insets). Spike eventswere recorded with a 1-�s resolution after crossing an adjustablevoltage threshold chosen to capture the small spikes but avoid theneurophonic.

To gain confidence that threshold crossings were spike events andnot simply transient fluctuations in the neurophonic, we performedanalysis of the interspike intervals (ISIs) off-line. Units reported hereall had gaps in the ISI histogram below 1 ms (see Fig. 5A, inset),characteristic of the refractory period of a single unit but not ofmultiunit or neurophonic recordings.

Electrolytic lesions were placed in all electrode tracks containingrecording sites by passing 5 �A of anodal DC current through theelectrode for 15 s. Lesions were placed directly at most recordingsites. In those cases in which two or more sites were relatively near

Fig. 1. Interaural cochlear delay. A: the eventual input to a medial superiorolive (MSO) neuron from each side originates in the cochlea from spiralganglion neurons that are excited by slightly different locations along thebasilar membrane (gray dots). An interaural delay arises from the differ-ence in propagation time of the cochlear traveling wave to each location.B: the frequency tuning of the ipsilateral (dashed) and contralateral (solid)input onto the MSO neuron will largely overlap but have slightly differ-ent characteristic frequencies. C: the interaural cochlear delay shifts thebest delay of the interaural time difference (ITD) tuning function. Here,sound with a positive (contralateral leading) ITD compensates for thelonger propagation time of the cochlear traveling wave on the contralateralside.

1986 FREQUENCY-DEPENDENT DELAYS IN MSO

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each other in the same track (�300 �m), a lesion was placed at onesite and the locations of the other sites were determined relative to it.

Histology. After each experiment a lethal dose of pentobarbitalsodium (180 mg/kg ip) was administered. The gerbil was perfusedintracardially with 0.12 M phosphate-buffered saline (PBS) followedby buffered 3.7% formaldehyde solution. After perfusion, the headwas immersed in fixative for at least 24 h. The brain was thenextracted and immersed in a solution of 30% sucrose in fixative untilsinking (�2 days). Coronal sections (50 �m) of the brain stem weresliced on a freezing microtome and transferred to slides. Becauseelectrolytic lesions were much more visible before staining, unstainedsections with lesions were traced onto transparent paper. Sectionswere then stained with cresyl violet and coverslipped. The MSOcolumn was highly visible after staining; however, the lesions weredifficult to identify unaided and usually looked like a lighter-stainedpatch in the Nissl background (Fig. 2A). Tracings from the unstainedsections were superimposed over the stained sections to aid localiza-tion of recording sites.

Acoustic stimulation. Acoustic stimuli were digitally generated andconverted to analog signals by a synthesizer (Kaiser Instruments)controlled by stimulation software (MALab, Kaiser Instruments). Theanalog signal was attenuated (STAX) and transduced through elec-trostatic earspeakers (STAX Lambda), whose sound output was de-livered through earpieces sealed to the ear canals. Before eachexperiment, the sound delivery system was calibrated under computercontrol for level from 100 Hz to 40 kHz and for phase from 100 Hzto 3 kHz with a previously calibrated probe tube and condensermicrophone (Brüel and Kjaer, 4134). Specifically, a sequence of puretones at different frequencies was presented at a fixed amplitude andphase and compared with the amplitude and phase of the waveformmeasured in the probe tube to determine correction values.

All aspects of sound stimuli were controlled dichotically. Thesearch stimulus was a 1-Hz binaural beat, created by presenting a puretone at fc � 0.5 Hz to the left ear and a pure tone at fc � 0.5 Hz to theright ear, where fc is the center frequency varied under user controlfrom 0.05 to 2.5 kHz. The binaural beat is equivalent to a binauralpure tone of frequency fc undergoing continuous 1 cyc/s interauralphase shift. After a unit was isolated, the response to a binaural beatwas collected at several frequencies at 60 or 70 dB SPL (10-sstimulus, 2-s silence, 4 repetitions, 10-ms on/off cosine ramp). Thebest frequency (BF) was determined as the frequency that producedthe greatest spike count in response to a binaural beat at a sound levelof 60 or 70 dB SPL. Responses to a binaural beat at BF were thencollected for sound levels varied above and below 70 dB SPL. At lowsound levels, the coherent, stereotyped oscillations of the neurophonic(described above) were reduced and became obscured by spontane-ous, erratic fluctuations, preventing the choice of an event voltagethreshold that could adequately segregate neurophonic events fromspike events. Therefore, the CF (frequency at response threshold)could not be measured.

For each unit, responses were also collected to monaural pure tonesat BF presented ipsilaterally and contralaterally at 70, 80, 90, andsometimes 100 dB SPL (100-ms stimulus, 200-ms silence, 100 rep-etitions, 3-ms on/off cosine ramp). Other stimuli were also presentedto each unit, unrelated to the present study.

Data analysis. The 1-Hz interaural phase difference (IPD) modu-lation of the binaural beat is sufficiently slow such that the beat periodhistogram of spikes (the dynamic IPD tuning function) was equivalentto the static IPD tuning function. Best phases (BPs, the mean phase)derived from responses to binaural beats were highly correlated withBPs derived from responses to stimuli with static IPDs (�CC � 1.84,P � 0.001, n � 48, circular-circular correlation, fit line slope � 0.98).The first second of response to binaural beat stimulation was excludedfrom analysis to prevent transient rate adaptation from distorting thesteady-state IPD function, although subsequent inclusion of these dataproduced no significant change in BP. The strength of IPD tuning wasmeasured by the vector strength (Zar 1999). The first 10 ms of

response to monaural stimulation was excluded from analysis becauseof the likely false triggering on large, transient upswings in theneurophonic at onset.

A binaural beat run was included in the analysis if the total spikecount in the analyzed time window over all repetitions was �100 andthe IPD tuning function was unimodal and reasonably symmetric and

Fig. 2. Location of recording sites. A: coronal section of the ventral brain stemshowing 2 electrolytic lesions at recording sites. Arrows point to tissue damagedby electrolytic lesions at the recording sites: one at the dorsal end of the MSOcolumn and one in the medial dendritic field. Triangles mark tissue damage fromthe corresponding electrode tracks. Scale bar, 200 �m. B: composite map of allrecording sites. Left and right recording sites were grouped into right-handcoronal sections along the rostrocaudal extent of the MSO as indicated in theparasagittal section at top right (arrow indicates trajectory of electrode). Siteswithin 200 �m of the center of the MSO column were classified as MSO (�,n � 30) and the rest as non-MSO superior olivary complex (SOC) (Œ, n � 28).LNTB, lateral nucleus of the trapezoid body; LSO, lateral superior olive;MNTB, medial nucleus of the trapezoid body; SPN, superior paraolivarynucleus; VNLL, ventral nucleus of the lateral lemniscus; VNTB, ventralnucleus of the trapezoid body.

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had a vector strength � 0.2. Those runs that met these criteria had IPDtuning functions that failed the Rayleigh test of uniformity (P �0.001) (Zar 1999). IPD tuning functions that were bimodal or asym-metric indicated multiunit contamination. Similarly, a monaural puretone run was included if the spike rate was �3 spikes/s and the periodhistogram was unimodal and reasonably symmetric and failed theRayleigh test of uniformity (P � 0.001). Peak binaural spike rate wasdetermined as the highest spike rate across bins when the beat periodhistogram was computed with 18 bins.

The relation between BP and tone frequency of each unit was fitwith a straight line by the least-squares method after weighting eachdata point by its spike count. Composite ITD tuning functions werecalculated by averaging no less than four ITD tuning functionscollected at equally spaced frequencies. The composite peak waschosen as the ITD of the highest peak of the composite ITD function.If a side peak was within 15% of the amplitude of the highest peak,both peaks were plotted as the composite peaks, as a choice of whichpeak was most “central” was ambiguous.

Correlation of linear variables was assessed by using Kendall’srank correlation �, a nonparametric statistical test with � taking valuesbetween �1 and 1. Correlation of circular variables was assessed withcircular-circular correlation �CC, a parametric statistical test with �CC

taking values between 0 and 2 (Batschelet 1981). Confidence intervalsof BP were calculated assuming a von Mises distribution of circularvalues (Zar 1999). A test comparing the dispersions of two samples ofcircular values was performed with the statistic listed by Mardia andJupp (2000).

Interaural cochlear delay model. The phase-frequency relations ofneurons were compared with the output of an interaural cochlear delaymodel similar to that of Bonham and Lewis (1999) (see Fig. 6A). First,a pure tone sound pressure waveform was synthesized at a given tonefrequency (500-ms stimulus, 10-ms on cosine ramp, 70 dB SPL) anddiscretized at a sampling rate of 50 kHz. The sound pressure wave-form was input into an AN model whose parameters had been fit toexperimentally derived reverse correlation functions of low-frequencycat AN fibers (Tan and Carney 2003) (available online: http://earlab.bu.edu/modeling/downloadable/). The only free parameterof the AN model was its CF. The sound pressure waveform was inputinto ipsilateral and contralateral AN models with separately chosenCFs; the output of each AN model was a time-varying spike rate, r.The output of the MSO model was approximated by a cross-correla-tion of ipsilateral and contralateral rates:

X(�) � �tbegin

tend

rI(t � � � �fixed)rC(t)dt

where �fixed is a frequency-independent interaural delay and � is theITD. The cross-correlation was performed over the ITD values, � �[�2, 2 ms], discretized at the sampling rate, with positive � indicatingcontralateral-leading sound. The integration over time-varying rateswas confined to a 50-ms segment near the end of the response in orderto calculate the correlation at steady state. The ITD that maximizedX(�) was selected as the BD, and this value was transformed into theBP by dividing by the tone period. Altogether, there were threeparameters in the interaural cochlear delay model: the ipsilateral andcontralateral CFs of the AN modules and the frequency-independentinteraural delay, �fixed. The parameters were adjusted to fit the mod-eled phase-frequency relation to measurements from individual MSOunits. Either the ipsilateral or the contralateral CF was initially givena value near the BF of the neuron, �fixed was then adjusted toapproximate the slope of the phase-frequency relation, and then theCF mismatch was adjusted to more precisely fit the relation. Allparameters were then varied in small increments until the meanabsolute residual between modeled and measured phase-frequencyrelations was minimized.

Biophysical MSO model with inhibition. The effect of synapticinhibition on interaural delay was predicted with a Hodgkin-Huxley-

type, point-neuron MSO model as implemented previously (Day et al.2008) and similar to the model in Brand et al. (2002). The ion channelcomposition and dynamics were based on a type II VCN model(Rothman and Manis 2003) with a fast membrane time constant anda low-threshold potassium conductance, similar to MSO (Scott et al.2005). The following excitatory and inhibitory synaptic currents,

IE(t, V) � gE(t)(V � EE)

and

II(t, V) � gI(t)(V � EI),

were added to the current-balance equation, where gE(t) and gI(t) were thetime-varying excitatory and inhibitory conductances, V was the mem-brane potential, and EE � 0 mV and EI � �90 mV were the excitatoryand inhibitory reversal potentials, respectively. Miniature postsynapticconductance events were modeled by an -function:

gmini(t) � gexc,inh

t

�exc,inhexp�1 �

t

�exc,inh�

where gexc and ginh were the excitatory and inhibitory maximumunitary conductances and �exc � 0.1 ms and �inh � 0.1 ms (or 0.4 ms)were the excitatory and inhibitory time constants, respectively. Syn-aptic input was modeled as the convergence of 32 independentexcitatory fibers from each side and 32 contralateral inhibitory fibers,with each fiber firing in a time-varying Poisson-like manner at �160spikes/s for 2 s, and phase-locked to an input frequency f, with avector strength R � 0.9. The number of excitatory and inhibitoryfibers was larger than the estimated minimum number necessary toevoke an action potential in MSO (Couchman et al. 2010); however,a larger number may be necessary to maintain sustained activity giventhe substantial short-term synaptic depression in MSO (Couchman etal. 2010). Phase-locking was achieved by choosing a synaptic eventtime in a given tone period as a Gaussian random number centered onzero with SD � sqrt(�2logR)/(2f) (Mardia and Jupp 2000). Ipsilat-eral excitatory synaptic event times were shifted by the appropriateITD (spaced every 20 �s spanning 1/f), then combined with thecontralateral event times, and convolved with gmini(t) to produce gE(t).Similarly, inhibitory synaptic event times were shifted by a delay, �tI,relative to the timing of contralateral excitation, then convolved withgmini(t) to produce gI(t). The current-balance equation was numeri-cally integrated by the forward Euler method at a time step of 10 �s.Halving the time step produced no noticeable difference in the voltagetrace. Output spike times were chosen when the voltage trace crossedupward through a threshold of �30 mV.

RESULTS

We recorded from 91 ITD-sensitive units in the left and rightbrain stems of 15 anesthetized gerbils. ITD sensitivity wasmeasured in response to 1-Hz binaural beats: dichotic puretones presented to each ear with a 1-Hz frequency difference,equivalent to a binaural pure tone undergoing continuous 1cyc/s interaural phase shift. We report data from units thatdisplayed unimodal period histograms with respect to theperiod of the beat and with respect to the periods of theipsilateral and contralateral tones, i.e., units that were both ITDsensitive and phase-locked (n � 68). Non-phase-locking unitswere infrequently encountered (n � 5).

The anatomical locations of all recording sites were identi-fied with respect to electrolytic lesions placed at or near therecording site (Fig. 2A). Units localized to the dorsal or ventralnuclei of the lateral lemniscus (n � 10) were excluded fromfurther analysis. Units within 200 �m of the center of the MSO



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column were classified as MSO (n � 30) and the rest asnon-MSO SOC (n � 28) (Fig. 2B).

ISIs from units localized to the SOC were collected intohistograms (see e.g., Fig. 5A, inset) to exclude multiunitspiking or triggering off the neurophonic, identifiable as asubstantial amount of submillisecond ISIs, normally absentbecause of the refractory period of a single unit. The half-widthof the depolarization associated with spike events (from thefiltered neural signal) was always �0.5 ms (see, e.g., Fig. 5A,inset; Fig. 6F, inset); therefore any submillisecond ISIs asso-ciated with multiunit spiking or neurophonic triggering wouldbe readily observable in an ISI histogram. Three MSO unitswere excluded for possible multiunit contamination because oftheir having �1% of their ISIs �1 ms. Altogether, the datareported here come from single units in the MSO (n � 27) andnon-MSO SOC (n � 28).

Figure 3A shows the distribution of BFs across the popula-tion. As mentioned in METHODS, single unit isolation could notbe maintained near threshold, and frequency tuning was mea-sured at 60 or 70 dB SPL. This raises concern that some of ourresponses may have come from higher-CF units excited at highlevels in their low-frequency tails (Joris et al. 1994b). Forexample, Yin and Chan (1990) reported one 2.3-kHz CF MSOneuron in the cat whose BF shifted to 800 Hz at higher levels(their Fig. 15c). We measured responses to binaural beats at BFat different sound levels; Fig. 3B shows that for about half(26/55) of the SOC population an ITD-sensitive response couldbe elicited below 60 dB SPL while still maintaining single unitisolation. The threshold of response in the low-frequency tailsof high-CF MSO neurons is not known; however, an inspectionof individual threshold frequency tuning functions of gerbilAN fibers (Schmiedt 1982, 1989) suggests that the 1-kHzthresholds of high-CF AN fibers (CF � 3 kHz) are similar tothat of cat (Kiang and Moxon 1974), which in the extreme canbe as low as 45 dB SPL. Therefore, we cannot rule out thepossibility of high-CF units based on the lowest sound levelseliciting an uncontaminated single unit response. We will comeback to the issue of high-CF units below with our resultsrelated to interaural cochlear delays.

In the cat, the CFs of MSO units are tonotopically arrangedalong the dorsoventral axis of MSO, with lowest CFs dorsaland highest CFs ventral (Guinan et al. 1972). In the gerbil, thesheet of MSO neurons viewed in the sagittal plane is tilted andextends from dorsorostral to ventrocaudal (see Fig. 2B, inset).All units localized to the MSO were concentrated in thedorsorostral half of the MSO (Fig. 2B) and had BFs �2 kHz.The absence of units localized to the ventrocaudal end of theMSO sheet may suggest that neurons located there are tuned tohigher frequencies. There was a weak correlation between aunit’s dorsoventral location and BF (Fig. 4; � � �0.28, P �0.06, n � 27, Kendall’s rank correlation). Units with BFsbelow 700 Hz were all located at the dorsal end, while thoseabove were scattered dorsally and ventrally. In our localizationprocedure, dorsoventral location was measured in histologicalsections with reference to a zero location at the dorsal tip of theMSO column—a reference that systematically shifts ventrallyfor progressively caudal sections (see Fig. 2B, inset). Theventral shifting of the zero reference may have biased thelocation of caudal units to values more dorsal than theirabsolute dorsoventral location, which would weaken the sig-nificance of correlation between BF and dorsoventral location.Despite this, the scatter in location of units above 700 Hz BF(Fig. 4) is consistent with a recent plot of the tonotopic map in

Fig. 3. A: best frequencies (BF) measured at 60 or 70 dB SPL(MSO: n � 27; non-MSO SOC: n � 28). B: lowest level atwhich an ITD-sensitive response could be elicited to a binauralbeat at BF and still maintain single unit isolation.

Fig. 4. Best frequency vs. dorsoventral location in the MSO column. Location0 indicates the dorsal end of MSO (n � 27).



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cat MSO derived from axonal terminations (Karino et al. 2011;their Fig. 9).

Frequency-dependent interaural delays. The BD of an ITDtuning function is determined by an internal interaural delaybetween the paths of phase-locked excitatory inputs leading toa coincidence detector. Jeffress (1948) proposed that the inter-nal interaural delay was formed by a difference between inputipsilateral and contralateral axonal conduction times. Such aninternal delay is thought to be independent of frequency, i.e.,the delay is the same regardless of the frequency content of thestimulus. For a coincidence detector neuron with a frequency-independent interaural delay, ITD tuning functions measured atdifferent frequencies will have a common peak correspondingto the ITD that compensates for the internal delay by placingthe excitatory inputs in phase. Figure 5, C and D, show datafrom a MSO neuron with ITD tuning functions at differentfrequencies having a common peak near �600 �s (negativeITD indicates an ipsilateral-leading sound). The ITD tuningfunction in response to a binaural beat is periodic; thereforeITD may be transformed into an equivalent IPD and BD to anequivalent BP. The information contained in multiple ITDtuning functions can be summarized by the BP-frequencyrelation (Yin and Kuwada 1983) (Fig. 5E), which for frequency-independent interaural delays between excitatory inputs willhave the following three characteristics: the relation is linear;the y-axis intercept of the fit line, termed the characteristicphase (CP), is zero cycles, and the slope of the fit line, termedthe characteristic delay (CD), is equal to the internal interauraldelay. Neurons with these characteristics, such as in Fig. 5, aretermed “peak type” because of their having a common ITDpeak across frequency. Importantly, any phase-frequency rela-tion that has a nonzero CP or is nonlinear indicates a frequency-dependent interaural delay (assuming bilateral excitatoryinputs).

Based on an assumption of frequency-independent interauraldelay, we expected all MSO neurons to be peak type. Surpris-ingly, we found many MSO neurons with decidedly non-peak-type phase-frequency relations. Figure 6, A and B, show datafrom a MSO neuron with a CP near 0.5 cyc. For a 0.5-cyc CP(or equivalently, �0.5 cyc), the overlaid ITD tuning functionsat multiple frequencies align at a common trough instead of acommon peak, termed a “trough-type” neuron. “Intermediate-type” neurons were also present in our sample (Fig. 6, C andD), with a CP between 0 and 0.5 cyc or between �0.5 and 0cyc and a common ITD at a point along the tuning functionslope. Several neurons displayed strongly nonlinear phase-frequency relations with a bulge in one direction, as in Fig. 6F.These nonlinear neurons were observed in three differentanimals, including two MSO neurons (BFs 1.6 and 2 kHz) andthree non-MSO SOC neurons (BFs 0.65, 1.25, and 1.25 kHz).There was no clear division between neurons with linear andnonlinear phase-frequency relations; while some neurons hadstraight relations (Fig. 5E, Fig. 6, B and D) or dramaticallynonlinear relations (Fig. 6F), many had small, reproduciblenonlinearities, such as the relation in Fig. 6H from a peak-typeMSO neuron (note the magnified y-axis range). We calculateda CP only for those neurons that passed a linear goodness-of-fitthreshold (root-mean-squared residual � 0.044 cyc) chosen toexclude the most nonlinear relations, as in Fig. 6F. Thedistribution of CP for MSO units depended on BF (Fig. 7), withmainly peak-type neurons for BFs below 800 Hz and the fullrange of CPs above. The dispersion of MSO CPs below 800 Hzdiffered significantly from the dispersion of the remainingMSO CPs (P � 0.005). The CPs of non-MSO SOC units alsotook on a wide range of values at high BFs; however, thedependence of CP on BF was only clear in the MSO samplethat contained a greater number of units at low BFs. The datain Fig. 7 do not lend themselves to a clear division between

Fig. 5. ITD tuning functions from a “peak-type”MSO neuron. A: raster plot showing spike responsesto a binaural beat with 1.1-kHz center frequency (f).Duration of stimulus indicated by black bar. Inset,top: interspike interval (ISI) histogram showing noISIs � 1 ms. Inset, bottom: voltage traces of 5triggered spike events. Dotted line indicates the cho-sen voltage trigger, in this case a downsweep trigger.Bar, 1 ms. B: period histogram of spike responseswrapped into the 1-s beat period. The period histo-gram is the interaural phase difference (IPD) tuningfunction and may be transformed into the ITD tuningfunction by dividing IPD by the binaural beat centerfrequency. Arrow indicates best phase/best delay.Positive IPDs/ITDs indicate contralateral-leadingsound. C: ITD tuning functions were obtained forfrequencies between 0.9 and 1.7 kHz and overlaid(BF � 1 kHz). Tuning functions derived from bin-aural beats are periodic on the center frequency toneperiod. D: normalized ITD tuning functions show acommon peak characteristic of a “peak-type” neu-ron. E: information from multiple ITD tuning func-tions is reduced to a best phase-frequency relation.For a peak-type neuron, the relation is linear withslope [characteristic delay (CD)] equal to the com-mon peak and y-axis intercept [characteristic phase(CP)] of �0 cyc.



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peak-type and trough-type neurons; if we arbitrarily chooseCPs within �0.1 cyc as indicative of peak-type behavior, thenonly 37% (10/27) of MSO neurons and 29% (8/28) of non-MSO SOC neurons fall within the range. Our evidence fornon-peak-type neurons is consistent with previous SOC studies(Batra et al. 1997; Spitzer and Semple 1995) yet is demon-strated here for neurons specifically anatomically localized tothe MSO.

Trough-type phase-frequency relations have been shown toarise in the lateral superior olive (LSO) from the interaction ofphase-locked, ipsilateral excitation and contralateral inhibition(Finlayson and Caspary 1991; Tollin and Yin 2005). Fortrough-type neurons, ITD tuning functions at multiple frequen-cies have a common trough corresponding to the ITD thatminimizes firing rate by placing the excitatory and inhibitoryinputs in phase. We considered the possibility that trough-typephase-frequency relations in our sample arose from a purely

excitatory-inhibitory (EI) interaction. We recorded responsesto 100-ms monaural tone pips at the BF of each neuron. Onlytwo neurons indicated inhibition in their monaural responsesby a suppression in spiking during stimulation and/or a postin-hibitory rebound at stimulus offset (1 MSO, CP � �0.15 and1 localized to the superior paraolivary nucleus, CP � 0.09). Anexcitatory monaural spiking response was evoked from at leastone ear for all but one neuron (1 MSO). Monaural unrespon-siveness or weak responses were common, likely becauseMSO functions as a binaural coincidence detector. For an EImechanism, the binaural spike rate should always be less thanthe higher monaural spike rate since the addition of contralat-eral inhibition can only reduce the rate evoked by ipsilateralexcitation. In our population, the maximal binaural spike rate(the rate at the best ITD) was greater than the monaural rate forall but three neurons (1 MSO neuron that had bilateral, excit-atory monaural responses and 2 non-MSO SOC; Fig. 8). Note

Fig. 6. Prevalence of neurons with non-peak-type phase-frequency relations. A, top: ITD tuning functions at multiplefrequencies surrounding BF (1.6 kHz) of a trough-type MSOneuron. Bottom: same functions normalized by maximumrate. B: phase-frequency relation of the same neuron. y-Axisintercept of the straight-line fit to data (gray) is the CP. Cand D: data from an intermediate-type MSO neuron (BF �1.25 kHz). E and F: data from a MSO neuron (BF � 2 kHz)with an extremely nonlinear phase-frequency relation. Inset,spike waveforms. Dotted line indicates the chosen voltagetrigger. Bar, 1 ms. G and H: data from a peak-type MSOneuron with a small, reproducible nonlinearity (BF � 1.6kHz). Error bars included in all relations represent 95%confidence intervals.



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that the binaural data in Fig. 8 came from long-durationbinaural beats while the monaural data came from short tonebursts over many repetitions. It is likely that monaural rateshad not undergone as much rate adaptation as binaural rates;nevertheless, binaural rates still exceeded monaural rates inalmost all cases. This implies that neurons in our samplereceived bilateral excitation, and that subthreshold excitationunderlies those cases in which a neuron did not respond tosound presentation on one side. Interestingly, this included the12 units localized to the LSO (see Fig. 2B), of which 7 hadevoked spiking responses to both ipsilateral and contralateralsound and 4 had CPs within �0.1 cyc (peak type).

The absence of inhibitory indications in monaural responsesdoes not exclude the presence of inhibitory inputs amongbilateral excitation, and the presence of such inhibition is likely(Grothe and Sanes 1993). However, the evidence for bilateralexcitation indicates that frequency-dependent interaural delaysin our sample (including trough-type, intermediate-type, andnonlinear phase-frequency relations) do not arise from a purelyEI interaction. We address the possible influence of inhibitionconcurrent with bilateral excitation below.

Interaural cochlear delays are consistent with frequency-dependent delays. Bonham and Lewis (1999) demonstrated theability of interaural cochlear delays to produce nonlinearphase-frequency relations through a simple MSO model basedon cross-correlation of AN responses. We used a similar modelto fit our phase-frequency data in the SOC. In our model, a puretone sound pressure waveform was simultaneously input into

ipsilateral and contralateral AN modules that were allowed tohave different CFs corresponding to different distances alongthe basilar membrane (Fig. 9A). The output of the ipsilateralAN module was time-shifted by a frequency-independent in-teraural delay (e.g., an axonal conduction time difference, orperhaps the delay associated with inhibition). This frequency-independent delay allowed the inclusion of other mechanismsof internal delay, whereas the frequency-dependent behaviorarose solely from the interaural cochlear delay. The time-varying ipsilateral and contralateral AN spike rate outputs(poststimulus time histograms) were cross-correlated at differ-ent ITDs to simulate coincidence detection at the MSO. TheITD that maximized the cross-correlation was divided by thetone frequency to yield the BP, and BPs were computed foreach frequency.

The basilar membrane is a dispersive medium, and differentfrequency components of the cochlear traveling wave havedifferent latencies at a given location along the membrane(Robles and Ruggero 2001). In particular, recordings from theAN show that latency becomes longer for stimulus frequenciesnear the CF (Pfeiffer and Molnar 1970; van der Heijden andJoris 2003, 2006; Versteegh et al. 2011). Figure 9B demon-strates that the AN module used in our model exhibits a longerlatency for stimulus frequencies near CF. Shown is the phaseof the AN module response to various tone frequencies for twolocations along the basilar membrane (two CFs near 1.5 kHzseparated by 0.1 oct). The slope of this phase plot (the latencyor group delay) increases near the CF. When the phase differ-ence between the two locations is converted into a time delay(Fig. 9B, bottom), the frequency dependence of the interauraldelay is evident. The frequency dependence arises because thelatency associated with the AN input with the lower CF beginsincreasing at a lower stimulus frequency than the input with thehigher CF. Therefore, a frequency-dependent interaural delaywould result if ipsilateral and contralateral inputs originatefrom slightly different locations on the basilar membrane.Furthermore, the interaural cochlear delays possible from asmall mismatch in CF may be large (Fig. 9B; Bonham andLewis 1999; Joris et al. 2006) compared with the azimuth-relevant range of ITDs of the gerbil (�130 �s) (Maki andFurukawa 2005).

On the basis of interaural cochlear delays alone, modelphase-frequency relations could be highly nonlinear (Fig. 9C),similar to the most extreme observed nonlinear relations (Fig.6F). The phase-frequency relation became more nonlinearwhen the mismatch between CFs was increased. While mod-

Fig. 7. Distribution of CP across best frequency for MSO neurons (Œ, n � 25)and non-MSO SOC neurons (�, n � 21).

Fig. 8. Maximal binaural rate is greater than monaural rate.Monaural rate was derived from response to a BF puretone. Binaural rate at the peak of the ITD tuning functionwas derived from a BF binaural beat at the same soundlevel as monaural. A: ipsilateral (MSO, Œ: n � 12; non-MSO SOC, �: n � 25). B: contralateral (MSO: n � 23;non-MSO SOC: n � 17). Dashed line, identity line.



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eled phase-frequency relations with pure interaural cochleardelay were highly nonlinear, adding an additional frequency-independent interaural delay and selecting a subset of frequen-cies surrounding the CFs created relations that were approxi-mately linear but with a CP shifted away from zero to that ofan intermediate- or trough-type neuron (Fig. 9D).

We fit the interaural cochlear delay model to the phase-frequency relations of 12 neurons (10 MSO and 2 LSO) thatexhibited deviation from peak-type behavior. The three param-eters of the model (ipsilateral and contralateral CFs, frequency-independent interaural delay) were adjusted to minimize themean absolute residual of the fit. Fits to data were remarkablyaccurate, with most mean absolute residuals �0.015 cyc (Table 1).Figure 10, A and B, show fits to data from a trough-type MSO

neuron (same as in Fig. 6, A and B) and an intermediate-typeMSO neuron, respectively, which both had observable excit-atory responses to ipsilateral and contralateral stimulation. Tovisually demonstrate the advantage of fitting data with a modelthat incorporates the frequency-dependent interaural cochleardelay, we also plotted in all panels the best fit assuming onlyfrequency-independent delay (i.e., a best-fit line with zero CP).Figure 10, C and D, show fits to two MSO phase-frequencyrelations exhibiting large nonlinearities (data in Fig. 10D sameas in Fig. 6, E and F). Figure 10, E and F, show fits to twophase-frequency relations with smaller nonlinearities (note themagnified y-axis range). Both of these MSO neurons (CP ��0.29 and 0.06 cyc, respectively) had relations that werereasonably linear; however, the interaural cochlear delaymodel captured the subtle nonlinearities. This suggests thatinteraural cochlear delays may underlie small nonlinearitiesoften apparent in peak-type phase-frequency relations, such asFig. 10F.

A previous experimental study showed that the interauraldelay created by a CF mismatch of cross-correlated AN fiberresponses decreased with CF (Joris et al. 2006), consistent withthe dependence of latency on log CF being steeper for low-CFAN fibers than for high-CF fibers [e.g., Versteegh et al. (2011)for gerbil]. Our model reproduced this dependence of interau-ral cochlear delay on CF. For an ipsilateral CF of 200 Hz, a0.05-oct CF mismatch (CFcontra � CFipsi) created a modeledmaximal interaural delay of 250 �s. The same CF mismatch (inoctaves, approximately the same mismatch in cochlear dis-tance) at an ipsilateral CF of 1.5 kHz created a maximalinteraural delay of 91 �s. The interaural time delay caused bya fixed CF mismatch decreases with CF; however, the delay interms of phase of the tone period increases with CF, as notedby Joris et al. (2006). This can be seen in Fig. 9C, where thesame CF mismatch (in octaves) produces slightly greater phasedelays at higher CFs. The decreased ability of interauralcochlear delay to cause large phase shifts at low CFs mayexplain the predominance of peak-type CPs at low BFs in oursample (Fig. 7). Interaural cochlear delays may be present (andeven larger) at low CFs or BFs but not produce significantdeviations in the phase-frequency relation from peak-typebehavior.

Model-estimated monaural CFs could not be compared withmeasured monaural CFs because single unit isolation could notbe maintained at threshold sound levels (see METHODS), nor wasmonaural spiking prevalent enough at high sound levels off theBF to construct adequate isolevel frequency tuning functionswhile maintaining unit isolation. Most CF mismatches esti-mated in our model (as small as a 30-Hz mismatch at 1.4 kHz)would be difficult to observe in a comparison of noisy, exper-imentally derived monaural frequency tuning functions. Thefits in Fig. 10 demonstrate that the interaural cochlear delaymodel can quantitatively account for some observed phase-frequency relations with high precision by using model CFsnear the measured BF (see Table 1). However, an evaluation ofrecent data from the gerbil AN suggests that interaural cochleardelays may also occur far from the CF. Versteegh et al. (2011)reported phase plots for gerbil AN fibers with high CFs (�2kHz) which had increased latencies at the CF and separately atfrequencies below 1 kHz. Furthermore, two example fibers(their Fig. 8) with CFs near 2 kHz had BFs that shifted below1 kHz as level was increased to �60 dB SPL, i.e., into the

Fig. 9. Interaural cochlear delay model produces non-peak-type phase-fre-quency relations. A: interaural cochlear delay model. A pure tone was inputinto ipsilateral and contralateral auditory nerve (AN) models that may bemismatched in characteristic frequency (CF). The time-varying output rate onthe ipsilateral side was optionally time-shifted by a frequency-independentdelay. The 2 rates were cross-correlated at different IPDs. The IPD thatmaximized the cross-correlation (BP) was the final output. B, top: mean phaseof the phase-locked output of the AN model for the case of 0.1-oct CFmismatch: ipsilateral CF � 1.5 kHz (solid line) and contralateral CF � 1.61kHz (dashed line). Bottom: difference of AN mean phases converted into timeshows that the delay produced by the CF mismatch is dependent on frequency.C: model phase-frequency relations for the case of no frequency-independentdelay (pure cochlear delay). Ipsilateral CF was held constant in each panel,while contralateral CF was varied to produce CF mismatches of 0.15, 0.1, 0.05,0, �0.05, �0.1, and �0.15 oct (top to bottom). Zero CF mismatch in eachpanel is in gray. Bold line indicates the same parameters as in B. D: modelphase-frequency relations with a 200-�s frequency-independent delay. Linefits show the varied CP at the intersection with the y-axis. Ipsilateral CF washeld at 1.6 kHz, while contralateral CF was varied to produce CF mismatchesof 0.15, 0.1, . . . , �0.1 oct (top to bottom).



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off-CF range where there was another increase in latency.Given that BFs in our sample were measured at 60–70 dB SPL,it is possible that some of the frequency-dependent delaysobserved in our sample below 1 kHz came from CF mis-matches of neurons with CFs � 2 kHz. The AN module usedin our interaural cochlear model only exhibits an increase in

latency near CF and would not accurately model an interauralcochlear delay occurring far from CF. However, the majorityof frequency-dependent delays in our sample occurred forstimulus frequencies above 1 kHz (Fig. 7 and Fig. 10), wherethere is no evidence of an additional region of increasedlatency for high-CF AN fibers.

Inhibition and frequency-dependent interaural delay. Be-sides interaural cochlear delay, the other mechanism that hasbeen proposed to account for non-peak-type phase-frequencyrelations in MSO neurons that exhibit bilateral excitation is theinteraction of fast, phasic inhibition with bilateral excitation(Batra et al. 1997; Leibold 2010). Glycinergic inhibition hasbeen demonstrated as a mechanism of interaural delay (Brandet al. 2002; Pecka et al. 2008); however, the manner in whichinhibition has been modeled to account for delay (i.e., shortduration synaptic inhibition) has been contested (Zhou et al.2005). We examined the ability of a biophysical MSO modelincorporating fast synaptic contralateral inhibition [and similarto the model in Brand et al. (2002)] to produce frequency-dependent interaural delays. Specifically, both excitatory andinhibitory miniature postsynaptic conductances were modeledas -functions with fast 0.1-ms time constants.

As shown in Fig. 11A, increasing the strength of synapticinhibition shifted the ITD tuning function in the contralateral-leading direction for a 1-kHz input frequency when inhibitionled the contralateral excitation by 200 �s [compare to Fig. 4Ain Brand et al. (2002)]. The model also predicted that fastinhibition could shift the ITD tuning function in differentdirections for different values of delay between contralateralinhibition and contralateral excitation (Fig. 11B). Interestingly,at some inhibitory delays the firing rate exceeded the excitato-ry-only case, possibly because of postinhibitory facilitation(Fig. 11B). We computed phase-frequency relations of themodel from 1.2 to 1.8 kHz, where non-peak-type behavior wasoften observed (e.g., Fig. 10), while varying the strength andrelative timing of synaptic inhibition. When inhibition led thecontralateral excitation by 200 �s, increasing the strength ofinhibition systematically increased the CP while maintaining alinear phase-frequency relation (Fig. 11C). When the relativetiming of inhibition was varied, the phase-frequency relationalso remained linear and the CP could take on the full range ofpossible values (Fig. 11D). The addition of a frequency-independent interaural delay, such as from axonal conduction

Table 1. Fit parameters of interaural cochlear delay model

Unit Location Measured BF, kHz Ipsilateral CF, kHz Contralateral CF, kHz CF Mismatch, octFrequency-Independent Interaural

Delay, �sMean AbsoluteResidual, cyc

30.2 MSO 0.80 0.80 0.746 �0.100 �600 0.00830.7 MSO 1.60 1.40 1.432 0.033 0 0.00731.0 MSO 1.60 1.60 1.524 �0.070 �130 0.00931.2 MSO 2.00 1.60 1.503 �0.090 �50 0.02631.3 MSO 1.60 1.40 1.460 0.060 400 0.01531.4 MSO 1.25 1.15 1.111 �0.050 �620 0.00931.6 MSO 1.60 1.40 1.439 0.040 25 0.01231.9 MSO 1.60 1.20 1.159 �0.050 �20 0.01033.0 MSO 0.80 0.80 0.752 �0.090 �500 0.01134.2 LSO 1.25 1.10 1.204 0.130 300 0.03237.4 LSO 1.50 1.60 1.540 �0.055 525 0.01337.7 MSO 1.55 1.55 1.600 0.045 250 0.011

Fit model parameters and a measure of error are in italics. MSO, medial superior olive; LSO, lateral superior olive; BF, best frequency; CF, characteristicfrequency. CF mismatch is the ratio of the contralateral CF to the ipsilateral CF, in octaves.

Fig. 10. Interaural cochlear delay model fits to data. A: phase-frequencyrelation of a trough-type MSO neuron (gray line; same unit as Fig. 6, A and B;BF � 1.6 kHz) and its fit with the interaural cochlear delay model (�).Included in all panels is the best-fit line assuming a CP of zero (dotted line).B: fit to data from an intermediate-type MSO neuron (BF � 1.55 kHz). C andD: fits to data from 2 MSO neurons with strongly nonlinear phase-frequencyrelations (BFs � 1.6 and 2 kHz). E and F: fits to data from 2 MSO neuronswith small, reproducible nonlinearities in the phase-frequency relations (notethe magnified y-axis range; BFs � 1.6 and 1.6 kHz). Error bars in all panelsindicate 95% confidence intervals of the BP data.



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time difference, would change the CD of the phase-frequencyrelation while maintaining the same CP. Therefore, it is likelythat with three parameters (inhibitory strength and timing,frequency-independent delay) the fast inhibition model mightreasonably fit the linear, non-peak-type phase-frequency rela-tions in our data set. This would include CPs as large as �0.5,as shown in Fig. 11, while a previous linear model includinginhibition only fit relations with CPs � 0.25 (Leibold 2010).Our fast inhibition model did not predict any nonlinearities inthe phase-frequency relation, such as in Fig. 10, C–F.

The above results were based on an extremely fast inhibitorysynaptic time constant. When we increased the inhibitorysynaptic time constant to 0.4 ms, the ability of inhibition tocreate nonzero CPs was eliminated. CPs remained within � 0.1cyc regardless of the relative timing of inhibition (Fig. 11E) orthe strength of inhibition (gI could not be increased muchlarger than gE without reducing the model output to minimumbecause of the greater effective inhibition at �inh � 0.4 ms).Since the publication of the fast inhibition model in Brand et al.(2002), the time course of synaptic inhibition onto gerbil MSOhas been reported. Magnusson et al. (2005) measured miniatureinhibitory postsynaptic currents under voltage clamp and re-ported an average rise time of 0.34 ms and exponential decaytime constant of 2.5 ms. We plot this synaptic time coursealong with the 0.1- and 0.4-ms -function synaptic conduc-tances used in our model in Fig. 11F. The 0.4-ms -functionhas a faster rise time and a shorter decay time (0.7 ms) than the

experimentally derived synaptic input yet was still not able tocreate frequency-dependent interaural delays. Therefore, a bio-physical model of MSO incorporating inhibition with realisticsynaptic dynamics would not explain the presence of frequency-dependent interaural delays in our data.

Distribution of interaural delays. Mechanisms of internalinteraural delay such as axonal conduction differences, inhibi-tion, and cochlear delays ultimately shape the distribution ofBDs. An interesting observation in the IC (the main recipientof output from the MSO) is that the distribution of BDs inresponse to noise across CF is overwhelmingly contralateralleading and scattered below the “-limit”—a boundary equalto half the period of the CF (Hancock and Delgutte 2004; Joriset al. 2006; McAlpine et al. 2001).

Figure 12A shows a scatterplot of BDs in response to puretones at BF against BF for units in our MSO sample. Forbinaural beat stimuli, as used here, the ITD function is periodicand the BD is chosen as the peak closest to zero ITD, which isnecessarily inside the “-limit” (in this case half the period ofthe BF). A comparison to the distribution in IC is limitedbecause of our use of tone stimuli at BF instead of noise andthe possibility that the BF measured here is not the same as theCF. Nonetheless, it is interesting to note the absence of nega-tive (ipsilateral leading) BDs below 1.4 kHz in our data.Random interaural cochlear delays alone would predict BDsscattered across negative and positive delays. However, ourmodel fit data well by incorporating a frequency-independent

Fig. 11. Modeled synaptic inhibition and interauraldelay. A: synaptic inhibition shifts the ITD tuningfunction in the contralateral-leading direction wheninhibition leads contralateral excitation by 200 �s.Same result as in Brand et al. (2002). gE and gI are theunitary excitatory and inhibitory peak synaptic con-ductances (in nS), with gE � 5 nS. B: synaptic inhi-bition shifts the ITD tuning function with the peak ITDdependent on the timing of inhibition relative to con-tralateral excitation, �tI (in �s, positive indicates in-hibition leading excitation). gE � 8 nS and gI � 24 nS.C: with a fast inhibitory synaptic time constant �inh,inhibition creates frequency-dependent interaural de-lay, shifting the phase-frequency relation to greaterCPs (triangles) with increased synaptic strength. gE �8 nS and �tI � �200 �s. D: altering the relativetiming of inhibition shifts the phase-frequency relationto span the range of CPs. gE � 8 nS and gI � 24 nS.E: with a slower inhibitory synaptic time constant, theability of inhibition to shift the phase-frequency rela-tion is eliminated. gE � 8 nS and gI � 8 nS.F: comparison of the time courses of the synapticinhibitory conductances used in our model and thetime course of synaptic inhibition derived experimen-tally (Magnusson et al. 2005). The decay time of theexperimentally reported inhibition is much longer thanthe decay times used in our model.



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delay in addition to interaural cochlear delay; a contralateralbias of BDs could exist with random interaural cochlear delaysif the mechanisms underlying the frequency-independent de-lays were biased toward contralateral delays.

Surprisingly, BDs from units with BF above 1.4 kHz werescattered across positive and negative delays, with a majorityof negative delays. Joris (2003) found that cat IC units withCFs between 1 and 3 kHz could exhibit ITD tuning to both thefine structure and envelope of noise. It is possible that our unitswith BF above 1.4 kHz exhibit this kind of ITD tuning, i.e., theBDs derived from tones would not be the same as from noise,which would include envelope ITD tuning. In Fig. 12B, wecombine our data with data extracted from Pecka et al. (2008;their Supplemental Fig. 2A), who also measured BD for tonesat BF in the gerbil MSO (their reported CFs ranging from 165to 4,800 Hz). The combined plot, for BFs below 1.4 kHz,shows BDs scattered between the upper -limit and zero ITD,similar to the IC plots of BD versus CF.

As mentioned in METHODS, spike isolation could not bemaintained with noise stimulation to collect traditional noise-delay functions. As an alternative, we constructed compositeITD tuning functions: an average of pure tone ITD tuning

functions collected at several equally spaced frequencies (Fig. 13,A and C). Composite functions have been shown to be similarto noise-delay functions (Yin and Chan 1990; Yin et al. 1986).Plotted in Fig. 13E is the distribution of composite peak ITDsacross BF for units in our MSO sample. All trough-type andmany intermediate-type units had composite functions inwhich the central peak was ambiguous (Fig. 13C). In suchcases, we plotted both peaks (Fig. 13E)—all were associatedwith trough-type, intermediate-type, or nonlinear units. All butone of the units with unambiguous peaks had peaks within the-limits. The exception was a peak-type unit with a large,negative BD whose ITD tuning function is presented in Fig. 5.A comparison of Fig. 13E with Fig. 12A reveals that compositepeaks were generally located at the same delay as BDs mea-sured at BF. This is unsurprising given the ITD function at BFelicits the greatest spike rate and therefore contributes the mostto the composite. Similar to Fig. 12A, there was an absence ofpeaks with negative delays within the -limit for BFs below1.4 kHz. Regardless of whether the BFs of units in our samplematched their actual CFs, it is clear that units that elicit strongresponses below 1.4 kHz prefer contralateral-leading (positive)delays at these frequencies. Composite peaks of units with BFabove 1.4 kHz were scattered across positive and negativedelays. Composite tuning functions only capture fine-structureITD tuning; therefore if these units (or others in our sample)were also tuned to envelope ITDs, the envelope componentwould not be represented in their composite functions.

DISCUSSION

We showed that a majority of neurons anatomically local-ized to the gerbil MSO exhibited frequency-dependent inter-aural delays (i.e., non-peak-type phase-frequency relationsarising from neurons with bilateral excitation). We furtherdemonstrated that an excitatory coincidence detection modelincorporating interaural cochlear delay (in addition to frequency-independent delay) was sufficient to reproduce observed fre-quency-dependent delays, while a biophysically realistic model ofinhibition was not. Several previous studies of the SOC haveshown the existence of frequency-dependent interaural delays inthe form of non-peak-type CPs (i.e., 0.1 � CP � 0.9) (Batra et al.1997; Pecka et al. 2008; Spitzer and Semple 1995; Yin and Chan1990), yet data have been interpreted as indicative of peak-typebehavior since CP population histograms generally have a modenear zero. Previous studies of neurons anatomically localized tothe MSO have shown a larger concentration of peak-type neuronsthan the present study (Pecka et al. 2008; Yin and Chan 1990),likely because most neurons in these studies had BFs below 1kHz—frequencies at which interaural cochlear delays may belarge but create smaller shifts in phase. Interaural cochlear delayeffects fed-forward from the MSO may also explain some of thenon-peak-type behavior prevalent in the IC (Yin and Kuwada1983), although some of this behavior is likely due to convergenceof ITD-sensitive inputs with different BDs (McAlpine et al. 1998).

Pentobarbital, one of the anesthetics used in the presentstudy, has been shown to potentiate the current of the glycinereceptor (Daniels and Roberts 1998). Blockage of inhibitoryglycinergic transmission at MSO neurons has been demon-strated to alter the BD (Brand et al. 2002; Pecka et al. 2008);therefore it is possible that pentobarbital altered some BDs inthe present study. However, in a study of the unanesthetized

Fig. 12. Distribution of best delays (BD). A: BD (measured at the BF) plottedagainst BF for all MSO units (n � 27). BDs are derived from periodic ITDtuning functions and are necessarily contained within the -limit (half a toneperiod from zero ITD; black curves). Shaded area is azimuth-relevant ITDrange. Symbols indicate type of phase-frequency relation: peak-type (circles),intermediate-type (squares), trough-type (triangles), and nonlinear or indeter-minate (asterisks). B: same distribution of MSO BDs as in A plotted along withthe BD-BF distribution from Pecka et al. (2008; their Supplemental Fig. 2A).



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rabbit SOC, Batra, Kuwada, and Fitzpatrick (1997) foundmany clear examples of intermediate-type, trough-type, andnonlinear phase-frequency relations—i.e., these non-peak-typerelations occur regardless of any possible alteration of inhibi-tion.

Batra et al. (1997) concluded that trough-type neurons in therabbit came from a low-frequency area of the LSO; however,the precise location of their neurons within the SOC wasindeterminate because of the use of an awake animal prepara-tion. Similar to our study, they found almost no evidence of anexclusive EI interaction in ITD-sensitive units. It is likely thatsome trough-type units in the Batra et al. study assumed to befrom the LSO were actually from the MSO. The assumeddichotomy of peak-type neurons in the MSO and trough-typeneurons in the LSO has endured, especially since low-fre-quency, trough-type phase-frequency relations derived from anEI interaction have been reported in the LSO (Tollin and Yin2005). One consequence of the assumed dichotomy is thatneurons that do not exhibit peak-type phase-frequency rela-tions may be excluded from a sample because their response isnot considered to come from the MSO (Seidl and Grothe2005).

Studies in the barn owl have provided some evidence againstthe existence of interaural cochlear delays (Fischer and Pena2009; Pena et al. 2001), but the specific evidence has beenagainst an exclusive model of interaural cochlear delay, e.g.,measured CF mismatches in barn owl nucleus laminaris neu-

rons were not predictive of the direction of interaural delay. Incontrast, our model assumes both cochlear and frequency-independent delays that may or may not be in the samedirection. For example, one of our units whose data was fitto the interaural cochlear delay model had a modeled CFmismatch (�0.055 oct) opposite in direction to the modeledfrequency-independent delay (525 �s) and opposite to theobserved composite peak delay (439 �s). Interaural cochleardelays shifting in a direction opposite to other mechanismsof internal delay would be expected if CF mismatchesresulted from random imprecision in the tonotopic matchingof afferents onto a target MSO neuron. Nonetheless, inter-aural cochlear delays may not be significant in barn owls,which are unique in that they extract ITDs at comparativelyhigh frequencies (3– 8 kHz) (Pena et al. 2001). In the barnowl AN (and also in mammals), the dependence of latencyon CF is steeper for low CFs than for high CFs (Koppl1997), and at high CFs in the barn owl range the time neededto traverse a fixed cochlear distance may be small comparedwith the azimuth-relevant ITD range (Pena et al. 2001),while the time needed to traverse the same cochlear distanceat lower CFs would be substantial. CF mismatches in birdsthat use low-frequency ITDs, such as the chicken (andperhaps the small, low-CF range of barn owl), may producesizeable interaural cochlear delays compared with their az-imuth-relevant ITD range. Indeed, a study in chicken (Koppland Carr 2008) showed that nearly half of nucleus laminaris

Fig. 13. Composite ITD tuning functions. A: ITD tuningfunctions at different pure tone frequencies (top) and compos-ite function (bottom) for a MSO unit (BF � 0.65 kHz). Centralpeak of composite is unambiguous. B: phase-frequency re-lation of the unit in A; CP in cycles and CD in microsec-onds. C and D: same layout as in A and B for a differentMSO unit (BF � 0.8 kHz). Central composite peak isambiguous. E: composite peak plotted against BF. Œ, Un-ambiguous peaks; X, ambiguous peaks (both peaks plotted).



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recordings had CF mismatches greater than 50 Hz and amajority of recordings with non-peak-type CPs (0.1 � CP �0.9), indicative of interaural cochlear delay.

Our interaural cochlear delay model used an AN module thatexhibited an increase in latency (group delay) near the CF. Arecent study on responses of low-CF AN fibers in the gerbilshowed that phase plots could be complex, with an additionalincrease in latency at frequencies below CF (Versteegh et al.2011). It would be straightforward to look at the difference ofphase plots between AN fibers or spherical bushy cells of theAVCN as a simulation of interaural delay, similar to our Fig.9B, to search for indications of frequency-dependent interauraldelays at frequencies further from CF as well as near CF. Oneinteresting possibility is that interaural cochlear delays couldoccur without CF mismatches: differences in the shape of thephase plots at a similar location along the cochlea in each earcould create frequency-dependent interaural delays, eventhough the CFs would be the same.

In this study, we show how certain aspects of data from theMSO can be qualitatively and quantitatively accounted for byinteraural cochlear delay. However, direct evidence of interau-ral cochlear delays in the form of mismatches between theipsilateral and contralateral CFs of MSO neurons has yet to bereported. The general paucity of data on the MSO comparedwith other auditory brain areas is due to the difficulty inisolating MSO units by extracellular recording techniques.Recent reports of successful MSO recordings using in vivojuxtacellular techniques (Van der Heijden et al. 2011) mayprovide the opportunity to record responses to difficult stimuli,e.g., monaural pure tone frequency thresholds and noise-delayfunctions. Small CF mismatches would likely be difficult todiscern at low frequencies where threshold frequency tuning isbroad and the exact position of the CF is questionable. How-ever, an important test of the interaural cochlear delay modelwould be in the case of a relatively large CF mismatch; themeasured CF mismatch could be compared with the model CFmismatch after fitting the model to the measured phase-fre-quency relation.

ACKNOWLEDGMENTS

We thank B. Delgutte and K. Hancock for a critical reading of themanuscript and D. Polley for a critical reading of an earlier version.

DISCLOSURES

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

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