Cooperative population coding facilitates efficient sound source separability by adaptation to spatial statistics

Our sensory environment changes constantly. Accordingly, neural systems continually adapt to the concurrent stimulus statistics to remain sensitive over a wide range of conditions. Such dynamic range adaptation (DRA) is assumed to increase both the effectiveness of the neuronal code and perceptual sensitivity. However, direct demonstrations of DRA-based efficient neuronal processing that also produces perceptional benefits are lacking. Here we investigated the impact of DRA on spatial coding in the rodent brain and the perception of human listeners. Naturalistic spatial stimulation with dynamically changing source locations elicited prominent DRA already on the initial spatial processing stage, the Lateral Superior Olive (LSO) of gerbils of either sex. Surprisingly, on the level of individual neurons, DRA diminished spatial tuning due to large response variability across trials. However, when considering single-trial population averages of multiple neurons, DRA enhanced the coding efficiency specifically for the concurrently most probable source locations. Intrinsic LSO population imaging of energy consumption combined with pharmacology revealed that a slow-acting LSO gain control mechanism distributes activity across a group of neurons during DRA, thereby enhancing population coding efficiency. Strikingly, such “efficient cooperative coding” also improved neuronal source separability specifically for the locations that were most likely to occur. These location-specific enhancements in neuronal coding were paralleled by human listeners exhibiting a selective improvement in spatial resolution. We conclude that, contrary to canonical models of sensory encoding, the primary motive of early spatial processing is efficiency optimization of neural populations for enhanced source separability in the concurrent environment. Author summary The renowned efficient coding hypothesis suggests that neural systems adapt their processing to the statistics of the environment to maximize information while minimizing the underlying energetic costs. It is further assumed that such neuronal adaptations also confer perceptual advantages. Yet direct demonstrations of adaptive mechanisms or strategies that result both in increased neuronal coding efficiency and perceptual benefits are lacking. Here we show that an auditory spatial processing circuit exploits slow-acting gain control to distribute activity across the neuronal population, thereby enhancing coding efficiency based on single-trial population averages. This population-efficiency maximization also results in improved neuronal spatial resolution for the concurrently most probable source locations, which was resembled in a focally improved spatial acuity of human listeners.


Abstract 14
Our sensory environment changes constantly. Accordingly, neural systems continually adapt to the 15 concurrent stimulus statistics to remain sensitive over a wide range of conditions. Such dynamic 16 range adaptation (DRA) is assumed to increase both the effectiveness of the neuronal code and 17 perceptual sensitivity. However, direct demonstrations of DRA-based efficient neuronal processing 18 that also produces perceptional benefits are lacking. Here we investigated the impact of DRA on 19 spatial coding in the rodent brain and the perception of human listeners. Naturalistic spatial 20 stimulation with dynamically changing source locations elicited prominent DRA already on the initial 21 spatial processing stage, the Lateral Superior Olive (LSO) of gerbils of either sex. Surprisingly, on the 22 level of individual neurons, DRA diminished spatial tuning due to large response variability across 23 trials. However, when considering single-trial population averages of multiple neurons, DRA 24 enhanced the coding efficiency specifically for the concurrently most probable source locations. 25 Intrinsic LSO population imaging of energy consumption combined with pharmacology revealed that 26 a slow-acting LSO gain control mechanism distributes activity across a group of neurons during DRA, 27 thereby enhancing population coding efficiency. Strikingly, such "efficient cooperative coding" also 28 improved neuronal source separability specifically for the locations that were most likely to occur. 29 These location-specific enhancements in neuronal coding were paralleled by human listeners 30 exhibiting a selective improvement in spatial resolution. We conclude that, contrary to canonical 31 models of sensory encoding, the primary motive of early spatial processing is efficiency optimization 32 of neural populations for enhanced source separability in the concurrent environment. 33 Author summary: 34 The renowned efficient coding hypothesis suggests that neural systems adapt their processing to the 35 statistics of the environment to maximize information while minimizing the underlying energetic 36 costs. It is further assumed that such neuronal adaptations also confer perceptual advantages. Yet 37 direct demonstrations of adaptive mechanisms or strategies that result both in increased neuronal 38 coding efficiency and perceptual benefits are lacking. Here we show that an auditory spatial 39 processing circuit exploits slow-acting gain control to distribute activity across the neuronal 40 population, thereby enhancing coding efficiency based on single-trial population averages. This 41 population-efficiency maximization also results in improved neuronal spatial resolution for the

Introduction 47
Our ability to distinguish individual objects in complex and dynamic environments is a fundamental 48 brain function (1,2). Conversely, the functional requirements of sensory systems are shaped by the 49 physical properties of the outside world: only if the neural sensitivity matches the current statistics of 50 the sensory inputs, the coding of relevant stimulus features will be both informative and 51 energetically efficient, and consequently evolutionary viable. Because realistic complex 52 environments exhibit highly non-uniform occurrence probabilities of stimulus cues (3,4), sensory 53 neurons adapt their action potential ("spike") responses according to the probability of concurrent 54 stimulus properties. This "dynamic range adaptation" (DRA) is thought to render neuronal firing 55 maximally sensitive to changes in the stimulus range that is most likely to occur ( Fig. 1) (5-7), while 56 keeping activity rates low. Consequently, DRA to stimulus statistics is believed to reflect a neuronal 57 adjustment to optimize stimulus encoding efficacy while simultaneously mediating improved 58 perceptional resolution within the relevant cue range. However, direct demonstrations of DRA-based 59 neuronal coding that causes both in increased neuronal efficiency and the resulting perceptual 60 benefits are lacking. 61 In the auditory system, rapid (sub-second) DRA to stimulus statistics has been revealed on multiple 62 processing levels from primary auditory cortex (8-11), to midbrain (12-15), and even brainstem ( Fig.  63 1A). Specifically, DRA is prominently exhibited already by auditory nerve fibers (ANF) (16,17) (Fig. 1B), 64 which consequently should affect the processing of all downstream centers, but might potentially be 65 most crucial for spatial computations: To infer the location of a sound source, brainstem neurons of 66 the Lateral Superior Olive (LSO) compare the difference in sound level at the two ears (interaural 67 level difference, ILD) that is generated by a location-specific sound-attenuating effect of the head. 68 LSO neurons respond according to the relative strength of excitatory and inhibitory inputs from the 69 ipsi-and contralateral ear, respectively (Fig. 1A). The ensuing sigmoidal ILD-response functions 70 (average action potential rate as a function of ILD) are regarded to represent the neuronal basis of 71 auditory space encoding based on intensity difference cues (18) (Fig. 1A To answer these questions, we studied the effects of naturalistic, i.e. spatially complex, stimulation 112 on ILD processing in the LSO of gerbils and on the perception of human listeners. We extended a 113 well-established monaural stimulus paradigm for studying DRA (10,12,16,17) and present rapidly 114 changing ILDs that switched periodically between favoring either the left or right azimuthal space 115 (Fig. 1C,D). In response to these spatially dynamic stimuli, we observed prominent DRA in LSO 116 neurons, which demonstrates a lack of absolute encoding of space by average neuronal firing rate. 117 Surprisingly, DRA in single neurons resulted in large response variability to a given ILD across trials. 118 However, we find that when considering single-instance population coding, DRA maximized the 119 efficiency of neuronal separability for specifically those ILDs that were most likely to occur in the 120 concurrent statistical environment (high probability region, HPR, Fig. 1C,D). These stimulus-specific 121 enhancements in neuronal coding were paralleled by human listeners exhibiting a selective 122 improvement in just noticeable differences for ILDs within the respective HPR. Intrinsic LSO 123 population imaging of energy consumption and a simple LSO model further explained that a slow-124 acting gain control mechanism enhances the population efficiency by distributing activity across a 125 group of neurons during DRA. We conclude that, already on the primary detector level, the 126 processing of ILDs is not tuned towards an absolute representation of space but optimizes efficient 127 sound source separation in the concurrent acoustic environment by population coding of ILDs. To explore the role of DRA on spatial coding in complex environments, we designed a stimulus 154 paradigm with constantly varying ILDs in the context of two related but statistically distinct listening 155 conditions. We used continuous broadband noise (identical on the two ears) and changed the ILD 156 every 50ms, with ILD values drawn from one of two non-uniform distributions. The two distributions 157 covered an identical range of ILDs but favored predominately (80% of time) either the ipsi-or 158 contralateral ear (ILDs of +20±8dB and -20±8dB, named the +20dB HPR and -20dB HPR respectively, 159 Fig. 1C, and Methods). This way, we simulated dynamic spatial environments with dominant sound 160 sources located either left or right of midline (Fig. 1D). The two conditions switched periodically ( Fig.  161 1C, one run consisted of 19 switches every ~6s, the sequence of ILDs was different for each switch 162 but identical across repetitions, 3 runs were recorded for each cell).
To assess to what extent changes 163 in spatial statistics alter the neuronal detection and encoding of ILDs, we first carried out 164 extracellular recordings from single neurons in the LSO of anesthetized gerbils while presenting the 165 stimuli via calibrated earphones (see Methods). 166 Following previous studies of DRA (12,14-16), we first assessed the average neuronal spike rates 167 (calculated across occurrences of each ILD) separately for -20dB to the +20dB HPR conditions. We 168 observed that the resulting ILD-response functions differed between the two conditions (a single 169 neuron example is shown in Fig. 1E). Specifically, a clear shift of the ILD-spike rate functions was 170 observable that entailed a change in the average spike rate in the respective HPRs (red and blue 171 areas in Fig. 1E and throughout). To quantify these shifts, which appeared highly reminiscent of DRA 172 to accommodate the change in the range of overrepresented ILDs, we computed the minimal ILD 173 that triggered significant spiking ("threshold ILD", see Methods) in the respective condition for each 174 neuron. Threshold ILDs significantly increased when switching from the -20dB to the +20dB HPR ( Fig.  175 1F, n=13 neurons, P=0.001, paired Wilcoxon signed rank test). For the population, the median shift in 176 threshold ILD between the two conditions was 8dB (interquartile range [IQR] 16dB; Fig. 1F inset). To 177 further characterize the extent and specificity of the DRA, we also generated two additional "un-178 natural" ILD distributions. These additional conditions confirmed that the observed shifts in 179 threshold ILDs were dependent on the concurrent binaural statistics (Fig. S1, n=18 neurons and n=19 180 neurons). This presence of DRA-related shifts in ILD-functions in the LSO directly demonstrates a lack 181 of absolute encoding of sound source locations by the average neuronal firing rate already on the 182 level of cue detection. 183

DRA optimizes single observation population coding 184
So far, we followed previous studies of DRA in the auditory system (12,14-16) and evaluated the 185 spatial sensitivity of individual LSO neurons by its average spike rate given the repeated presentation 186 of each ILD. However, in reality, processing must be able to compute the location of a sound source 187 from observation of a single instance of the stimulus. Therefore, we next focused on the direct 188 response by each neuron to each occurrence of a particular ILD. Examining individual spike counts for 189 75 recurrent instances of +20dB and -20dB ILD in the respective HPR condition revealed two 190 interesting findings ( Fig systematic relationship between ILD sequences and their likelihood to trigger a spike (Fig. S2). 206 Crucially, this lack of consistent responses to ILDs with naturalistic probability statistics resulted in a 207 very limited modulation of the average spiking probabilities in either HPR condition. That is, the 208 probability to observe a particular mean average spike count across the sample population was very 209 similar for all ILDs (Fig. 2B). 210 In contrast, however, more specific ILD population tuning emerged from our data set when 211 considering the population response for a single occurrence of a particular ILD (i.e. averaging across a 212 column in Fig. 2A; Fig. 2C, compare also bottom lines in right-hand panels of Fig. 2A but not MLE(mean) (Fig. 3A,B; improvement of 9dB and 0dB, respectively). 225 Such relative enhancement in the neuronal precision of ILD estimation implies -but does not 226 confirm -a relative improvement in the ability to resolve nearby sound locations. To quantify the 227 impact of the differences in population tuning (Fig. 2B,C) on resolution directly, we next determined 228 the informational content of each neurons' response towards the separability of ILDs. We followed 229 previous studies on ILD coding (15,34) and calculated the standard separation (35) ("D"), which 230 quantifies the separability of adjacent ILDs based on the ratio of slope steepness and response 231 variability. We first calculated D(mean), i.e. using the mean of average single neuron tunings. Since 232 the two spatial conditions that we presented were mirror-symmetric to each other, the two LSOs on 233 each side of the brain would provide complementary spatial information for each HPR condition 234 towards D. We therefore summed the D-ILD functions of each condition with the mirror-image of the 235 function of the other condition (Fig. 3C, dashed lines indicate single-hemisphere data, solid line 236 represents sum of both hemispheres). In remarkable contrast to previous midbrain studies (12,15), 237 we found that the average neuronal separability was not enhanced by the DRA, but actually 238 considerably lower within the respective HPRs ( To test whether the increased performance as predicted by analyzing MLE(pop) and D(pop) also 267 results in an improved ability to resolve sound source locations, we performed a spatial separability 268 test with human listeners via calibrated headphones (Fig. 3E). The subjects (N=5) were presented 269 with a 2s long snippet of the same stimulus used in the electrophysiological experiments, taken 270 alternatively from the +20dB and -20dB ILD HPR condition (only +20 dB is illustrated in Fig. 3f). 271 Shortly after (0.35s) this adapting period, the listeners were presented with two probe ILDs (each 272 consisting of 50ms broadband noise, spaced apart by 100ms) and were asked to indicate which of 273 the two was perceived more lateralized. Using an adaptive tracking paradigm (see Methods), the 274 difference in ILD between the two probe ILDs was systematically reduced to determine the just 275 noticeable difference (JND) in ILD for each subject. The probe ILDs were centered either on +20db ILD 276 or -20dB ILD (Fig. 3F), to allow deciphering the influence of matching and miss-matching the adapter 277 HPRs with the probe ILD. In agreement with the prediction made on the basis of D(pop), we observed 278 a significant improvement in JND when probe center ILDs matched the HPR of the adapter (single 279 subject example in Fig. 3G: -20db adapter and -20dB probe, red, or +20dB adapter and +20dB probe, 280 blue; P=0.004, Friedman test). On average, JNDs of the five listeners improved by 52.6% (Fig. 3H stimulus statistics in other centers of the auditory system (12,14,16), we observed an exponential 290 time course of rate adaptation (Fig. 4A). Yet in contrast to all previous reports, we found that 291 adaptation kinetics were best described not by a single, but by two time constants (Fig. 4B) analysis revealed a hemispheric specificity of response efficiency for the concurrent spatial 312 conditions (Fig. 4E). Thus, the slow gain control mechanism associated with the second time constant 313 of DRA that we found might serve to maximize the efficiency of neuronal processing within the range 314 of most likely occurring ILDs. To investigate this potential role of slow gain control on ILD coding in 315 more detail, we generated a simple model of the LSO based on existing models of DRA. Specifically, 316 we extended an existing auditory nerve model that included both threshold and gain adaptation (17) 317 by adding a binaural subtraction stage to reflect LSO processing (Fig. S3). As expected, this simple 318 model exhibited clear DRA in response to the binaural HPR stimuli (Fig. 4G, dotted lines). However, 319 since this version of the model lacked a binaural gain control stage, it captured only the fast time 320 course of rate adaptation and quickly reached a steady state spike rate (<1s, Fig. 4F, gray trace). To 321 account for the second, slow adaptation component in the neuronal data, we included an additional 322 slow negative feedback stage after binaural comparison in the model (Fig. S3). This modification 323 resulted in a close match in the dynamics of rate adaptation between model and LSO neurons (Fig.  324 4F, black trace) and led to lowered overall spike counts during DRA (Fig. 4G, solid lines). This effect of 325 slow gain control had little effect on the overall amount of spatial information (Fig. 4H), but 326 specifically increased D/spike of model responses within the concurrent HPR (Fig. 4I, compare dotted  327 and solid lines). These modeling results thus suggest that the main function of slow gain control in 328 the LSO is the optimization of coding efficiency (i.e. separability per unit of neuronal activity). 329

Intrinsic imaging reveals energetic benefits of slow GABAergic gain control 348
To directly test the model prediction that slow feedback signaling may minimize energy expenditure 349 in the LSO, we took advantage of the intrinsic autofluorescence of NADH as key metabolic 350 intermediate (40,41). We monitored the relative change in NADH levels with high spatial resolution 351 in LSO brain slices (21µm x 23µm per region of interest, "ROIs", 1200 ROIs per field of view; Fig. 5A,B, 352 see Methods). Using 20 second long fiber stimulation at 200 Hz, we determined the spatial 353 distribution of energy consumption in the LSO (6 brain slices). As expected, large parts of the imaged 354 LSO area displayed a monotonic increase in energy consumption with a single minimum (SM) in 355 response to the 20 second long stimulation (Fig. 5C, red region, Fig. 5D, lowest trace). However, we 356 also frequently observed areas in which energy consumption declined after a few seconds of 357 stimulation, before ultimately increasing again ("Double minima, "DM", Fig. 5D, and Fig. 5F). This 358 non-monotonic progression of energy consumption combined with its apparent slow time course 359 (4.58s; IQR: 2.36s, Fig. 5E) is highly suggestive of the known GABA-B receptor mediated, activity-360 dependent gain control mechanism. Accordingly, application of the specific antagonist CGP 55845 361 hydrochloride (CGP, 10µM) to the bath revealed that DMs largely disappeared during blockade of 362 GABA-B signaling, resulting in considerable larger energy consumption (Fig. 5G). In accordance with 363 the assumed gain control function of GABA, on the population level (i.e. across all ROIs per slice), 364 CGP had differential effects on the prevalence of observed DMs. A spatial diversity in the effect of 365 blocking GABA-B mediated inhibition was clearly observable within individual brain slices (Fig. 5H). 366 Specifically, DMs were either more or less likely to appear during CGP dependent on the fraction of 367 DMs during control (Fig. 5I). 368 Application of CGP also had a striking effect on the overall energy consumption in the LSO: Across the 369 entire imaged area, the block of GABA-B signaling on average almost doubled the energy 370 consumption (median CGP-control ratio: 1.6, IQR: 1.5; n= 6 slices, Fig. 5J). Moreover, similar to the 371 history-dependency observed for the DMs, the magnitude of change in the energy consumption 372 during CGP application was highly correlated with the prior activity level during control conditions 373 (Spearman correlation, P<0.0001, Fig. 5K), providing further corroboration for the activity-374 dependency of the gain control mechanism.Together, these data strongly suggest that the spatially 375 variable, slow gain control mediated by GABA-B in the LSO serves for the efficient population coding 376 of ILDs. 377

Discussion 394
Our findings advocate a novel concept for the neuronal coding of auditory space that significantly 395 differs from the canonically assumed mapping of absolute locations (42). We observed that LSO 396 neurons strongly adapted their ILD-rate functions in response to changes in the spatial statistics. 397 Consequently, auditory spatial representation is dynamic and devoid of absolute mapping of sound 398 source locations already on the detector level. We further discovered that the average rate tuning of 399 single LSO neurons conveys little spatial information during naturalistic stimulation due to high 400 response variability. However, if responses to individual instances of an ILD were averaged across 401 neurons, DRA optimized the efficiency of responses, which resulted in improved separation of ILDs 402 within the concurrent HPRs. Correspondingly, human listeners showed evidence of a focal 403 improvement in ILD resolution specifically for HPR ILDs. Importantly, this study is -to our knowledge 404 -the first to demonstrate stimulus-specific benefits by DRA both for the efficiency of neuronal 405 coding as well as human perception. Finally, a simple LSO model and intrinsic energy imaging 406 explained that the efficiency of the enhancement in spatial separability is facilitated by a slow gain 407 control mechanism involving GABAergic signaling downstream to binaural integration. 408 The canonical concept of spatial coding assumes that specific average response rates of sensory 409 neurons are mapped onto a particular physical cue to allow for a faithful encoding of the 410 corresponding source location (19-21). By introducing a more naturalistic likelihood-distribution of 411 spatial statistics, we determined a prominent role of DRA for binaural processing that refutes the 412 idea of an absolute representation of space already on the detector level and instead promotes a 413 relative coding of sound source positions. Moreover, our evaluation of the impact of DRA on 414 neuronal information suggests that the basic principle of LSO spatial coding is the preservation of 415 ecologically relevant coding efficiency by providing high separability of nearby sound sources within 416 the statistically predominant range of ILDs (5,38). These findings corroborate the generality of these 417 perceptual effects of stimulus history independent of the specific binaural cue(42), and provide an 418 mechanistic explanation on the detector level that had so far been linked to secondary processing at 419 higher stages (13,15,43-45). 420 Because the LSO represents the initial binaural stage of ILD detection, our findings stand out for two 421 more reasons: (1) Adaptive processing at the spatial cue detector should result in absolute 422 localization errors due to a missing reference frame. This notion is supported by reports of human 423 listeners producing significant absolute localization errors when presented with biased spatial 424 statistics (33,42,44,46). (2) While adaptation with the purpose to preserve a large dynamic coding 425 range within the predominant stimulus range can be found across sensory systems (7), we showed 426 that in the auditory spatial system, DRA is likely to be inherited to a large degree by adaptation to 427 intensity statistics in the monaural LSO inputs (e.g. the auditory nerves from each ear). We 428 furthermore show that the major computational modification after binaural integration serves to 429 optimize the efficiency of coding for the concurrent spatial statistics. Such processing of naturalistic 430 statistics to maximize the efficiency of information transmission (by redundancy reduction) had so far 431 been associated with midbrain and cortex, i.e. processing that is secondary to the initial detection of 432 the respective feature (47-51). In contrast, ILD detection and efficiency optimization are realized 433 concurrently by the LSO (and subsequent negative feedback, see below). Interestingly, adaptation to 434 binaural statistics to optimize spatial sensitivity has also been described for the detector neurons of 435 the second important binaural cue, the interaural time differences (28,52). However, in contrast to 436 the short-term changes of the LSO, these adaptations take place over days during maturation and 437 entail long-term morphological changes. 438 Different to prior studies on adaptation to spatial statistics in the midbrain (12,15), MLE(mean) 439 declined within the concurrent HPR due to the high response variability of individual neurons. An 440 informational gain was only revealed by applying a single observation population coding concept in 441 the form of MLE(pop). In this regard, our data provide physiological support for the framework of 442 cooperative population decoding (36), which had been developed to explain the apparent noisiness 443 of cortical processing. Specifically, the framework suggested that recurrent inhibition with slow time 444 constant can be utilized to maximize the efficiency of an average population code to the expense of 445 increased response variability of individual neurons. Congruent with such a coding regime, individual 446 LSO neurons responded sparsely (intermitted and with few spikes) and therefore decreased the 447 redundancy of firing in the population for a given ILD. A potential limitation for such an 448 interpretation of our data is that the population of neurons was not recorded at the same time (also 449 due to methodological limitations for brainstem recordings of highly stimulus-time-locked 450 responses). However, our in vitro recording of large population of LSO neurons conclusively supports 451 the single neuron data and moreover, it is known that spiking in auditory brainstem nuclei occurs 452 independently (53). Accordingly, population analyses of single neuron recordings are assumed a valid 453 approximation and thus commonly performed (12,13,15). 454 In conclusion, our findings suggest a new concept for auditory spatial coding: the detection and 455 processing of spatial cues, particularly ILDs, is not geared for an absolute representation of space, but 456 optimizes efficient sound source separation in a given stimulus context by sparse population coding. 457 458 All the stimuli were digitally generated using MatLab (The MathWorks Inc., USA) and fed into TDT 509 hardware using Brainware. were used to achieve a flat spectrum over the entire range of the respective headphones. 517 When spikes of single cells were identifiable, the characteristic frequency (CF) and absolute threshold 518 were determined using a pure-tone stimulus having the same length as the search stimulus. For 519 further characterization of a neuron, a baseline ILD function was obtained and a broad-band noise 520 rate-level functions were recorded in response to 50ms bursts presented on the ipsilateral excitatory 521 ear only. These recordings were used for determining a cell's latency (see below). To measure DRA in 522 LSO neurons, a bimodal HPR stimulus was created. The intensity of continuous broadband noise was 523 drawn from a pseudo-randomized predefined distribution every 50 ms (see Fig. 1). The range of 524 monaural intensities spread from 20 to 80 dB SPL in 2 dB steps, similar as used monaurally (16,17). 525 The predefined distribution consisted of two HPRs intensity levels around center-intensities of 50 dB 526 ±4 dB SPL and 70 dB±4 dB SPL, resulting in 5 values per HPR with a cumulative occurrence probability 527 of 0.8. To generate ILDs, the stimulus intensities were mirrored at 60 dB for presentation on the 528 other ear, resulting in HPR center regions of -20 dB ILD and +20 dB ILD, respectively. A single 529 condition epoch was 6.55 seconds long and was repeated ten times with different pseudo-530 randomizations each time (but identical cumulative probabilities). A 131 seconds long stimulus was 531 generated by alternating the two HPR conditions repeatedly, resulting in 10 HPR epochs per sweep 532 for each condition. 533 534 Neuronal data analysis 535 Recorded data files were analyzed offline using custom-made analysis in MatLab and Python. First, 536 the average latency of each cell was determined on the basis of its monaural rate-level functions to 537 allow for subsequent spike-triggered analysis of responses to the HPR stimuli. To this end, spikes 538 were assigned to 50 ms bins of the respective ILD that elicited the spikes (taking into account the 539 latency of the cell). This resulted in a mean ILD-response rate function for each HPR condition. 540 Spike-triggered averages where calculated by selecting all bins with a non zero response and 541 recording the ILD values presented in the nine previous bins plus the bin that showed the non zero 542 response. The average response in each of the ten bins was then used as the Spike-triggered average. 543 The non-spike triggered average was calculated the same way but based on bins that did not show 544 any response. The data are plotted relative to the mean ILD of the last bin in time. 545 The standard separation D is calculated as previously described (35): 546 D_n = |mu_n+1 -mu_n| / (sqrt(sigma_n+1 * sigma_n)) 547 where mu_n+1 and mu_n are the mean values of the responses to two ILD values while sigma_n+1 548 and sigma_n are their standard deviation. D_n was subsequently smoothed using a 5-sample moving 549 average filter. 550 The metric D/spike was calculated as: 551 D_n,spike = (2 * D_n) / (mu_n+1 + mu_n) 552 In case of the model, we calculated D based on the assumption of an underlying Poison process 553 where the variance would equal the mean response. 554 Maximum likelihood estimations (MLE) were used to find the most probable ILD to result in a specific 555 observed response given all other observed responses R. For this, the joint probability density 556 functions , of the observed spike counts R and the presented ILDs was calculated for all 557 responses of one neuron excluding . The ILD that maximizes , was than used as 558 the MLE for . 559 To characterize shifts in ILD functions due to HPR statistics, the threshold ILD, defined as the ILD at 560 which the firing rate differentiates more than 10 % from baseline firing, was determined. 561 Time courses of adaptation were measured by fitting a single-or double-exponential function to the 562 mean responses rates averaged over all 30 repetitions of a HPR condition. Inbuilt functions in Matlab 563 for the root-mean-square error (rmse) and the adjusted coefficient of determination (R 2 ) were used 564 to evaluate the goodness of fits. 565 Psychophysical measurements and data analysis 566 5 normal hearing (within 20dB of ISO/TR 389-5:1998) listeners (2 males and 3 females, mean age 567 26±4years, right-handed) participated in the measurement of just noticeable ILD differences. The 568 signals consisted of bandpass filtered noise (center frequency 10 kHz, bandwidth 2.208 kHz) which 569 was generated in MatLab (The Mathworks, Inc, Natick, Massachusetts, US) at a sampling rate of 44.1 570 kHz. The signals were digital to analog converted (Audio 2 Dj, Native Instruments GmbH, Berlin, 571 Germany) before being presented over calibrated circumaural headphones (HDA 200, Sennheiser 572 Electronic GmbH & Co. KG., Wedemark, Germany). The signals where presented at 60 dB SPL average 573 diotic sound pressure level and ILDs were introduced by symmetrically amplifying and attenuating 574 the right and left ear signals by half the desired ILD. Within the experiment, a 2 s long adapter 575 stimulus was followed, after 350ms, by two 50ms probe stimuli which were separated by 100ms. 576 Similar to the physiological experiments, the adapter consisted of concatenated diotic noise busts, 577 each 50 ms in duration, with ILDs that were randomly drawn from one of the two non-uniform HPR 578 distributions. ILD JNDs were determined at two reference ILDs (i.e -20dB ILD and +20dB ILD, see Fig.  579 2d and e). One of the two probe stimuli was randomly presented at one of the two reference ILDs 580 while the other probe stimulus was systematically varied using a transformed up-down procedure, 581 following a one-up three-down rule, as implemented by the MatLab AFC package(54). To determine 582 the JND, listeners were asked to specify the perceived direction of the probe pair sounds, which 583 allows deducing which of the two probe stimuli was perceived more lateralized. Following the 584 subject's answer, the variable probe ILD was adjusted until reaching the termination criterion (6 585 reversals) of the one-up three-down rule. ILD JNDs for each listener, each probe position and each 586 listening condition (i.e. HPR) were calculated as median over six sessions (each session consisting of 3 587 measurements). For each subject, the effect of listening condition was expressed as normalized 588 change in ILD JND due to co-location of probe position and preceding HPR. 589

LSO model 590
The LSO was modeled using a phenomenological rate model similar to the one used by Wen and 591 colleagues (17) to model adaptation in the ANF (see Fig. S1) . The LSO is implemented as a 592 subtraction stage with inputs from the ipsi-and contra lateral ANFs and a sigmoidal activation 593 function (CN and MNTB were omitted to minimize model complexity). The firing rate in 594 spikes per second (sps) of the LSO is calculated as following: 595 1 • Where and are the maximum and the minimum firing rates, is the rate at zero input 596 and k is the steepness of the sigmoid. and are the firing rates from the ipsi-and 597 the contra-lateral ANFs and is a gain factor to weight the relative strength of the excitatory and 598 inhibitory input. The ANF inputs where each calculated using a dual adaptation model (17), which 599 was fitted to the data shown in figure 2 of (16). As we only fitted the response of one ANF, we 600 switched the saturating nonlinearity used in the original model with a simple logistic function. The 601 parameters for the LSO model where determined by calculating the ILD-rate function of the model 602 and fitting it to the ILD-rate function given by figure 4 in (55