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All procedures were performed in accordance with the University of California, Santa Cruz (UCSC) Institutional Beastly Care and Use Committee.



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To admeasurement the HRTF of the mouse, a brace of Golay codes38 (216 = 65,536 credibility for each) were played at a sampling bulk of 500 kHz through a digital-to-analog advocate (DAC; National Instruments (NIs), PCIe-6341), an amplifier (Tucker Davis Technology (TDT), ED1), and an open-field electrostatic apostle (ES1) against a decapitated abrasion arch amid 25 cm away. The acknowledgment was recorded with a microphone (Bruel & Kjaer, 4138-L-006, abundance response: 6.5 Hz to 140 kHz) accompanying with the aback of the ear aqueduct of the mouse, amplified (Bruel & Kjaer, 1708), low-pass filtered (Thorlabs, EF502, 100 kHz), and digitized (NI, PCIe-6341) with a sampling bulk of 500 kHz. The head-related actuation acknowledgment (HRIR) was reconstructed from the responses to the Golay codes38. The altitude was performed in an anechoic alcove (a cube with 60-cm-long sides) with egg-crate-shaped polyurethane cream absorbed to the ceiling, walls, and the attic of the chamber, as able-bodied as added surfaces such as the date for the abrasion head, the microphone and its cable, and the arm that holds the microphone.



Before barometer the HRTFs, the abrasion was euthanized and again decapitated. The cochleae and the eardrums were removed from the ear aqueduct and the microphone was accompanying to the aback of the ear aqueduct application a ~1-cm-long coupling tube. In adjustment to accumulate the tissue from dehydration and ensure a connected allowance amid the ear aqueduct and the microphone, a baby bulk of mineral oil was activated on the tissue about the ear canal. To admeasurement the HRTF as a action of the adventure angle, the abrasion arch was army on a date that was accompanying to a stepper motor that was apprenticed by an Arduino board. The date was rotated by the stepper motor and agee by a hinge, afterwards defective to abstract the microphone (Supplementary Fig. 1a). We abstinent the HRTF for filigree credibility of 10 elevations (0–90° with 10° steps) and 101 azimuths (0–180° with 1.8° steps), 1010 credibility in total, in the aerial appropriate division of the abrasion head. Note that the arctic arbor of the alike for this altitude is the rostral administration (Supplementary Fig. 7a). Afore the microphone was detached, the HRTF of the bureaucracy with earphone (earphone HRTF, EHRTF) was additionally measured. This EHRTF was subtracted during the electrophysiological recording in adjustment to abstain the added abundance acknowledgment due to the earphone setup. The aforementioned action was again for the larboard ear to accomplish binaural HRTFs. Barometer the HRTFs from three changeable abrasion alive showed acceptable reproducibility (the boilerplate aberration was 5.3 ± 0.8 dB). We estimated the aberration of HRTFs amid animals as an angular absurdity (~±14°; see “Estimation of added analytical errors of the RF parameters” in “Data Analysis”) and congenital this into our absurdity measurements. The HRTFs were calm from changeable mice, but stimuli based on them were presented to both macho and changeable mice. We did not see a aberration in the topographic map ambit amid macho and changeable groups (Supplementary Fig. 8). In addition, alike admitting their boilerplate anatomy weights were decidedly altered (male: 28.2 ± 0.7 g (n = 6), female: 21.3 ± 1.5 g (n = 6), p = 2 × 10−3 (two-tailed t test)), the ear sizes were not decidedly altered (the numbers represent [right ear continued axis, appropriate ear abbreviate axis, larboard ear continued axis, larboard ear abbreviate axis]; male: [13.0 ± 0.3, 7.8 ± 0.2, 13.2 ± 0.2, 7.5 ± 0.1]; female: [12.6 ± 0.3, 7.9 ± 0.3, 12.6 ± 0.3, 7.9 ± 0.2]; p = [0.39, 0.90, 0.12, 0.26]). The LabView and Arduino programs accounting for HRTF abstracts and the abstinent HRTFs are accessible online39,40 (see Code availability and Abstracts availability sections).



Using the abstinent HRTFs, we developed a VAS dispatch that creates bang complete with backdrop constant with the complete advancing from a specific antecedent direction. This access has been auspiciously acclimated in humans16, marmosets4, guinea pigs11, and ferrets2,17. The bang complete is aboriginal filtered by a zero-phase afflicted clarify of the ES1 apostle and the EHRTF, to abrade the abundance responses of the ES1 and the earphone setup. Next, the bang is filtered by a abstinent HRIR, including phase, to assemble the complete acreage that is constant with the adventure bend for which the HRIR is measured. We alone reproduced the abundance acknowledgment in the ambit amid 5 and 80 kHz because the ES1 apostle did not aftermath a acceptable amplitude alfresco this range. Within this range, the reconstructed complete reproduces the ITDs, ILDs, and ashen cues.

Sound is delivered to the aerial through a DAC (NI, PCIe-6341), an amplifier (TDT, ED1), and closed-field electrostatic speakers (EC1) accompanying with a baby artificial horn. The tip of the horn was aggressive against the ear aqueduct (~40° elevation, ~110° azimuth) and placed ~1 cm from it. With this angle, the EHRTF does not accommodate a able cleft and appropriately abandoning by an afflicted clarify was easy.

Full-field VAS stimulus: The full-field bang acclimated filigree credibility of bristles elevations (0–80° with 20° steps) and 17 azimuths (−144° to 144° with 18° steps), accretion 85 credibility in the two-dimensional directional acreage (Supplementary Fig. 7a). We abstinent the HRTFs alone in the aerial appropriate division because of the limitation of the altitude stage. In adjustment to assemble the HRTFs in the aerial larboard quadrant, we afflicted the alteration action of the adverse ear, flipping larboard and right. This is done afterwards acknowledging that the larboard ear HRTF and appropriate ear HRTF are agnate in the accumbent alike (left–right agreement of the ear shapes). The abstinent ILDs and ITDs for the aerial appropriate division are advised in Supplementary Fig. 1c, d. The baseline bang arrangement was 100-ms white babble with beeline cone-shaped windows in the aboriginal and aftermost 5 ms. The bang was presented every 2 s and again 30 times per administration (total continuance was 85 min). The bang acuteness was 50 dB SPL. We generated a new arrangement of white babble at every point of amplitude and on every balloon (the arrangement is not “frozen”). Archetype stimuli are accessible in our Figshare repository41 (see Abstracts availability section).

Because we acclimated an amphitheater blazon earphone, some complete from the earphone is additionally detected by the contralateral ear. We abstinent this cross-talk amplitude to be ~−10 dB at 5 kHz and <−30 dB at 30 kHz and above, about to the angry ear.

Freezing anniversary complete localization cue: Freezing a specific complete localization cue was accomplished by acclimation the cue for all adventure complete admonition while abrogation the added cues to change their backdrop artlessly as a action of complete direction. Stimuli with arctic cues were about interleaved so that the abiding change of the recording action does not access the differences of the RFs. For this experiment, we again the stimuli 20 times per administration instead of 30 times to abbreviate the absolute continuance (with 5 conditions, 85 directions, and 2 s intervals, the absolute continuance was 4.7 h). To benumb the ITDs, we aboriginal abstinent the aiguille timings of the HRIR for anniversary breadth in anniversary ear and confused the larboard HRIR to set the timing aberration to zero. To benumb the boilerplate ILDs, we afflicted the boilerplate amplitudes amid 5 and 80 kHz in larboard and appropriate HRTFs and adapted their amplitudes to be the boilerplate of the larboard and appropriate HRTFs so that they accept according all-embracing complete levels beyond this ambit of frequency. To benumb the ashen cues, we replaced the HRIR with a distinct sample actuation to abrade the spectrum while the all-embracing complete akin and timing were kept constant with the aboriginal sound. To actualize monaural stimuli, we artlessly beatific no arresting to the ipsilateral (left) speaker. This finer kept the ILD at a aerial amount for all complete directions.

Note that freezing a complete localization cue does not beggarly abatement the cue. The arctic cue is still present at every breadth and may accord advice that contradicts added cues. For example, aught ILDs are constant with a complete that comes from the midline, and some neurons may acknowledge in a non-natural address back this is accumulated with ashen cues that alter in the basic space.

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Extended ILD stimulus: To assay whether the neurons are acquainted to beyond ILD values, we acclimated the aforementioned 100-ms white babble bursts with a collapsed spectrum but afflicted the ILD about amid ±40 with 2 dB increments. The bang for anniversary ILD amount was again 30 times.

Dynamic accidental ambit stimulus: To admeasurement ashen affability backdrop of the neurons with localized RFs, we acclimated activating accidental ambit stimuli20 and afflicted the STA of the stimuli for anniversary neuron. The stimuli abide of 48 tones alignment from 5 to 80 kHz (12 tones per octave). Anniversary arrangement was 10 ms continued with 3 ms beeline cone-shaped at the alpha and the end (i.e., plateau for 4 ms). We acclimated a abbreviate continuance of the patterns to ascertain fast (<20 ms) responses of the SC neurons. In anniversary pattern, the tones were about set to either ON or OFF with a anticipation of 0.5. The absolute cardinal of tones per arrangement was not fixed. The amplitude of anniversary accent was anchored and set to be 50 dB SPL back averaged over time. One presentation of the stimuli was 2-min continued (12,000 patterns) and this presentation with the aforementioned set of patterns was again 20 times to aftermath a 40-min-long stimulus. Tones from the larboard and appropriate speakers were not activated with anniversary added in adjustment to admeasurement the affability to adverse amid the ears. We did not use a specific HRTF for this experiment, but artlessly canceled the earphone HRTF so that the bang complete was filtered to accept a collapsed abundance acknowledgment abreast the eardrums.

We acclimated 2–5-month-old CBA/CaJ (The Jackson Laboratory, 000654) mice of anniversary sex. The mice were kept in cages at 20–23 °C temperature, 30–70% clamminess level, and a 12-h light/dark cycle. Mice were co-housed whenever accessible and acceptable aliment and baptize were provided all the time. One day afore the recording, we built-in a custom-built titanium arch bowl on a mouse’s skull, which accustomed us to fix the mouse’s arch to the recording rig afterwards affecting the ears. On the day of the recording, the abrasion was anesthetized with isoflurane (3% induction, 1.5–2% maintenance; in 100% oxygen) and a craniotomy was fabricated (~1.5–2 mm diameter) in the larboard hemisphere aloft the SC (0.6 mm crabbed from the midline, on the lambdoid suture). We did not use ear confined to attach a arch bowl or to accomplish craniotomy in adjustment to abstain damaging the ears. The abrasion was accustomed >1 h to balance from the anesthesia afore recording. The cavity was covered with 2% low-melting-point agarose in acrid and a band of mineral oil on top of it to accumulate the academician from drying. A 256-channel silicon delving (provided by Prof. Masmanidis42) was amid through the case into the SC with its four shanks accumbent forth the A–P arbor (Fig. 1b; the electrodes were adverse against the crabbed direction). Back the brand enters the apparent SC, the positions of multi-unit beheld RFs on anniversary brand are recorded. We again lower the delving until the able multi-unit beheld responses disappear. As a consequence, the top of the alive breadth of the best apparent brand is amid at ~300 µm from the apparent of the SC. Afore acclimation the delving at the final location, the delving was overshot by ~120 µm and rewound in adjustment to abate delving clearing during the recording. Recordings were started 20–30 min afterwards inserting the probe. The mice were euthanized afterwards the recording session.

During the recording, the abrasion was accustomed to run advisedly on a annular treadmill fabricated of polystyrene cream (Fig. 1a). The apparent of the butt was covered with self-adherent blanket (CVS pharmacy) to abate locomotion noise. The movement of the butt was recorded by a shaft encoder (US Digital, H5-100-NE-S).

In bristles of ten abstracts in the “Mice accept spatially localized audition RFs that are topographically organized” section, we amid the delving three times per abrasion in adjustment to amount the recordings in altered M–L positions to admeasurement the acclivity tuning. Anniversary assimilation was afar by 400 µm forth the M–L axis. The adjustment of assimilation in the M–L arbor was randomized for anniversary agreement to abstain a alternation amid a abasement in recording affection with the delving location. All the added mice had alone one delving insertion.

Blind analysis: We performed a dark assay of our data, which is able for abbreviation a false-positive advertisement of results43,44. First, we looked for specific appearance application bisected of the neurons about subsampled from anniversary agreement (exploratory dataset). Afterwards chief which ambit to attending at, we performed the aforementioned assay on the hidden bisected of the abstracts (blinded dataset) to affirm if the after-effects agreed with the basic dataset. All of the after-effects appear in the present abstraction anesthetized a acceptation assay both in the basic dataset and the addled dataset unless acclaimed otherwise.

Spike sorting: We acclimated custom-designed software for fasten sorting. Raw analog signals were high-pass filtered (cutoff ~313 Hz) and thresholded for fasten detection. Detected spikes were amassed application the arch basic assay to its waveforms on the detected electrode and its surrounding electrodes. A admixture of Gaussians archetypal was acclimated for array identification. Clusters with abounding spikes in the adverse aeon and bifold clusters for the aforementioned neuron (determined by abreast distance, L-ratio, cross-correlation analysis, and affinity of the waveform shapes) were afar from the analysis. Added capacity are accessible in appear articles45,46.

When we appraise absolute populations such as a atom of neurons with a fast response, we afflicted a binomial distribution. If the anticipation that a neuron is in a class is p, its absurdity is estimated by (sqrt {p(1 – p)/N}), breadth N is the absolute cardinal of neurons.

We estimated the about position of the silicon probes in assorted abstracts application the beheld RF positions abstinent in the apparent SC. Back we amid a silicon probe, we abstinent the positions of the beheld RFs on anniversary brand in the apparent SC application multi-unit activity. We extrapolated the beheld RFs to acquisition an A–P position breadth the beheld RF azimuth was 0°, and authentic this point as the aught of the A–P position. To appraisal the A–P position of the audition neurons we assumed: (1) the best apparent electrode of the silicon delving was at 300 µm in depth; and (2) the admittance bend of the delving into the SC was 25°. (1) is justified by consistently endlessly assimilation at the position breadth beheld responses predominantly abandon from all of the electrodes; and (2) is justified by the post-recording observations of the admittance bend (Fig. 1c). The position of a neuron about to the delving was bent by a two-dimensional Gaussian fit to its fasten amplitude beyond assorted electrodes46. We alone analyzed neurons with a absolute A–P position in adjustment not to accommodate neurons alfresco the SC.

We acclimated quasi-Poisson statistics for acceptation tests of the audition responses of alone neurons47. Simple Poisson statistics was not acceptable because the post-stimulus battlefront bulk about had a beyond trial-by-trial about-face than that accepted from Poisson statistics (overdispersion) due to factors such as beginning of the neural action and/or locomotion/movement of the animal. These added fluctuations can annual added apocryphal positives. (The overdispersion constant was estimated by the about-face of the fasten calculation disconnected by the mean, which should be 1 if the neuron is Poissonian. The boilerplate of the overdispersion ambit of all neurons was 5.61 ± 0.10. These ambit during anchored and active periods were 4.99 ± 0.08 and 5.11 ± 0.10, respectively, advertence that locomotion is one of the sources, but not a sole antecedent of overdispersion.)

To actuate the acceptation of the response, we aboriginal estimated an overdispersion constant and advised a acknowledgment to be cogent if the p amount of the neuron’s fasten calculation is beneath 0.001 (p = 1 − CDF(N), breadth CDF is a accumulative administration action of the quasi-Poisson administration and N is the fasten calculation of the neuron). We accept called to use quasi-Poisson statistics over a abrogating binomial administration (another administration that permits overdispersion) because of its simplicity. We do not apprehend a ample aberration in after-effects because of the best amid these two distributions.

We acclimated a maximum-likelihood fit of the Kent distribution18 to appraisal the azimuth, the elevation, and the ambit of an RF. The Kent administration is a spatially localized administration in a two-dimensional directional space. We accept called the Kent administration over the two-dimensional Gaussian administration because we accede a ample ambit of angles in the directional amplitude in which the nonlinearity of the alike arrangement should be taken into account.

The blueprint of the Kent administration is accustomed by:

$$f({mathbf{x}}) = frac{1}{{{mathrm{exp}}left( kappa right)}}{mathrm{exp}}{ kappa {mathbf{gamma }}_1 cdot {mathbf{x}} beta [({mathbf{gamma }}_2 cdot {mathbf{x}})^2 – ({mathbf{gamma }}_3 cdot {mathbf{x}})^2]},$$

where ({mathbf{{x}}}) is a three-dimensional assemblage vector, κ is a absorption constant that represents the admeasurement of the RF (κ > 0), β is an ellipticity constant (0 < 2β < κ), the agent γ1 is the beggarly administration of the RF, and vectors γ2 and γ3 are the aloft and accessory axes of the Kent distribution. These three assemblage vectors are erect to anniversary other. This action is normalized to 1 back x = γ1. At the absolute of ample κ, this administration becomes asymptotically abutting to a two-dimensional Gaussian. At anniversary point of the directional field, the likelihood amount was afflicted based on quasi-Poisson statistics47. The absurdity of anniversary constant was estimated from the Hessian cast of the likelihood function.

We acclimated the front-Z alike arrangement (Supplementary Fig. 7a) for the HRTF altitude and the bang presentation, but acclimated the top-Z alike arrangement (Supplementary Fig. 7b) for the Kent administration fitting. We had to use the front-Z alike arrangement for the HRFT altitude because of the brake of our altitude date (Supplementary Fig. 1a). However, the front-Z alike arrangement has a aperture of the azimuth beyond the midline that gives a botheration in applicable and estimation of the abstracts abreast the midline. We abhorred this affair by switching to the top-Z alike system. Because the Kent administration in agent architecture is absolute of the alike system, likelihood ethics and ambit in the agent architecture are not afflicted by this change back the fit is successful. To abstain an breadth breadth two alike systems are abundantly different, we alone acclimated neurons with their acclivity abate than 30° for azimuthal cartography (Fig. 2e). To accomplish abiding fits, we belted β to amuse 4β < κ, set the azimuthal ambit to be from −144° to 144°, and set the acclivity ambit to be from 0° to 90°.

We acclimated the afterward blueprint to ascertain the ambit ρ from the absorption constant κ:

$$rho = {mathrm{cos}}^{ – 1}left( {1 – frac{1}{{2kappa }}} right).$$

With this definition, the amount of the administration becomes ({mathrm{exp}}left( { – frac{1}{2}} right)) of the aiguille amount back (left| {{mathbf{x}} cdot {mathbf{gamma }}_1} right| = {mathrm{cos}}(rho )) and β is negligible, a behavior agnate to a two-dimensional Gaussian.

We estimated added analytical errors that may affect the RF parameters. First, the abrasion was active and advisedly active on a annular treadmill during the neural recording session. Locomotion modulates the anatomic backdrop of the visually acknowledging neurons46,48,49 and the audition cortical neurons50,51. To actuate the furnishings of locomotion on the audition SC neurons, we afar the affair into segments back the abrasion was active (speed >1 cm s−1) and back it was stationary. The abrasion was running, on average, 30% of the time (Fig. S6a). During locomotion, the ad-lib action added and the audition responses decreased both in the fast and apathetic timescales (Supplementary Fig. 6b–g). However, it did not change the alone RF structures or the map of audition amplitude (Supplementary Fig. 6h, i). Therefore, we did not accede this as a antecedent of analytical error. Second, the abrasion was affective its eyes during the experiment. In primates, eye movement influences the audition RF of the SC neurons52. However, this acreage has not been characterized in mice and the ambit of the abrasion eye movement is small. The accepted aberration (SD) is ~2–3° and the saccade amplitude is <10° forth the accumbent arbor and the movement forth the vertical arbor is alike smaller48,53. Therefore, it is absurd that this is a aloft antecedent of analytical errors. Based on the SD value, we booty ±3° to be the estimated analytical error. Third, the HRTFs can be articulate by the movement of the abrasion pinnae. To appraisal the aftereffect of the calamus movement on the HRTF, we abstinent the amplitude of the ear movement application an bittersweet video camera (Basler acA640-120 um) while the abrasion listened to the audition stimuli. We quantified the calamus bend in 100 about called images of the video recording. Overall, the abrasion confused the calamus by 13° (SD). Fourth, our VAS stimuli ability not be absolute because we acclimated a distinct set of HRTFs for all the mice instead of barometer them individually. In adjustment to quantify this effect, we abstinent HRTFs from three mice and compared the differences (Supplementary Fig. 1b). The all-embracing aberration (RMS) was 5.3 ± 0.8 dB, and this corresponds to an angular about-face of ±14°.

To appraisal the topographic map parameters, demography into annual both the analytical and statistical errors, the analytical errors acclaimed aloft were added in quadrature to accord ±19°. This is beyond than the boilerplate statistical errors associated with the alone neurons (±5.8°). However, a beeline fit to the topographic map forth the azimuthal arbor (Fig. 2e) resulted in a ample χ2 per amount of abandon (24.1), which is in the administration of either underfitting or aberration of the error. In adjustment to appraisal the abruptness and account parameters, we added, in quadrature, the estimated analytical absurdity of ± 19° to anniversary abstracts point. The χ2 per amount of freedom, based on a beeline fit, is now 0.69, advertence that the analytical errors are a reasonable accession to the statistical errors.

We acclimated cosine affinity to analyze the affinity of the audition RFs afore and afterwards freezing anniversary cue. We advised the audition responses at 85 basic antecedent locations as an 85-dimensional agent and normalized it so that it has a assemblage breadth and aught mean. Again we took an abutting artefact of the responses to the aboriginal bang and the added stimuli (control, arctic ITD, arctic ILD, arctic spectrum) to account the cosine SIs. The statistical errors of the fasten calculation at anniversary basic antecedent breadth (estimated by Poisson statistics) were broadcast to the final absurdity of the SIs. The SIs of the cue freezing abstracts are added normalized by adding by the SI of the ascendancy stimuli (NSI). The aforementioned cosine SI was additionally acclimated to admeasurement the affinity amid the ipsilateral and contralateral STRFs (BSI).

We estimated the STRFs of neurons application the STA afflicted from the spiking acknowledgment to the activating accidental ambit bang declared above. First, the spikes of anniversary neuron are discretized in time with 10 ms bins (the aforementioned as the bang articulation size) and the boilerplate of the bang patterns that preceded anniversary fasten was calculated. The bang was advised as 1 if there is a accent in the abundance and 0 otherwise. The acceptation tests for the STRFs were performed by analytical whether the aberration amid the beggarly of the bang and the STA is significant. Namely, the p amount was afflicted for anniversary pixel application a accumulative administration action of the binomial administration (in Matlab, this is application a action binocdf(S*N, N, M), breadth S is the afflicted STA, N is the cardinal of spikes, and M is the beggarly amount of the bang over time). The beggarly amount of the bang is abutting to 0.5, but not absolutely because of the accustomed aberration of the stimulus. This amount was evaluated for anniversary abundance separately. If the p amount is added than 1 − 0.001/Npixels/2, the pixel is advised to accept a decidedly absolute structure; if it is <0.001/Npixels/2, the pixel is advised to accept a decidedly abrogating structure. Npixels is the cardinal of pixels that we advised for a cogent anatomy (Bonferroni alteration factor), and in this experiment, it was 960 (10 time bins, 48 frequencies, and 2 ears). The added agency of 2 is all-important because this is a alternate test. This affirms p < 0.001 beginning akin for the absolute STA for the neuron. Neurons with <20 spikes during the bang were not analyzed.

Further advice on analysis architecture is accessible in the Nature Analysis Advertisement Summary affiliated to this article.

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