Robust representation and non-linear spectral integration of simple and complex harmonic sounds in layers 4 and 2/3 of primary auditory cortex

Auditory processing, harmonic stacks, functional connectivity, in vivo imaging , 20 spectral integration 21 22

& Contributions: YC and POK designed research. YC performed imaging 23 experiments and analysis. YG performed imaging analysis. CC and YC performed 24 electrophysiological experiments and analysis. YC and POK drafted paper. All authors edited the 25 manuscript. Supported by NIH RO1DC017785 and NIH RO1DC009607 (POK). 26 .CC-BY-NC-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted August 27, 2025. ; https://doi.org/10.1101/2025.08.26.672221doi: bioRxiv preprint 2

27 Sound harmonicity is foundational in complex auditory stimuli like music and vocalizations but it 28 remains unclear how such spectrally complex stimuli are processed in the auditory cortex (ACtx). 29 Subregions of the auditory cortex process are thought to process harmonic stimuli differently, and 30 secondary ACtx (A2) layer (L) 2/3 is believed to be the most selective. Selective responses to 31 sound features in ACtx are thought to emerge hierarchically starting from A1 L4. Since the spectral 32 complexity of harmonic stacks can range from two to more than ten components, harmonic 33 selectivity and sensitivity might also arise hierarchically across layers and areas . We studied 34 responses to simple and complex harmonic stacks across A1 L4, A1 L2/3 , and A2 L2/3 in adult 35 mice using in vivo two -photon microscopy . We found harmonic -sensitive neurons (HN) 36 responding only to harmonic stacks but not to their pure -tone components in all areas at similar 37 proportions. HNs showed non-linear processing of component tones with onset-responsive HNs 38 showing greater nonlinearity, which decreased with harmonic complexity. Co-tuned HNs in A1 39 L4 exhibited the highest signal correlation, regardless of harmonic complexity. A1 L4 HNs also 40 showed the lowest noise correlation with other neurons. Moreover, A1 L4 HNs achieve robust 41 spectral integration and harmonic sensitivity by receiving diverse inputs and maintaining high 42 signal correlation, ensuring independent, strong responses to harmonic stimuli. Therefore, 43 harmonic sensitivity is present in A1 L4 and is not a unique feature of A2. Thus, tuning to complex 44 spectral sounds is a fundamental property of ACtx and is already established in A1 L4. 45 46 Significance statement 47 Harmonics are essential in auditory perception, influencing how we process complex sounds like 48 music and speech. This study reveals that neurons in the primary auditory cortex (A1) and 49 secondary auditory cortex (A2) integrate simple and complex harmonic structures with distinct 50 mechanisms of neuron al recruitment. A1 L 4 harmonic-sensitive neurons (HNs) demonstrated 51 strong, independent responses through high signal correlation and minimal noise correlation, 52 suggesting a robust mechanism for spectral integration . Our results show that harmonic 53 relationships are already extracted at the input layers of A1, and that HN s show non -linear 54 facilitative integration. Thus , tuning to sounds of complex spectral contents might be a 55 fundamental processing function of the auditory cortex and is already established in A1 L4, which 56 receives major thalamic inputs. 57 58

59 Harmonicity is a fundamental feature of human speech , music and animal vocalization 60 (Ehret and Riecke, 2002) . Harmonic stacks are compound sounds made up of one or more 61 frequencies that have a positive integer multiple of the fundamental frequency (F0) (Terhardt, 1974; 62 Plack, 2010; McLachlan et al., 2013) . Both simple sounds such as pure tones and sweeps and 63 complex sounds like animal vocalizations are represented in the cochlea and, more sparsely, in the 64 central nervous system (Nelken, 2004; Hromadka et al., 2008; Chechik and Nelken, 2012). In mice, 65 ultrasonic and middle frequency vocalization usually consist of a few frequency components, 66 .CC-BY-NC-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted August 27, 2025. ; https://doi.org/10.1101/2025.08.26.672221doi: bioRxiv preprint 3 whereas vocalization in low frequency harmonics is composed of multiple frequencies. Behavioral 67 studies reveal that a high proportion of low frequency harmonic vocalizations are associated with 68 stress in mice (Grimsley et al., 2013; Grimsley et al., 2016) and serve as a distress call to listeners 69 (Chen et al., 2009). As a central hub for sound processing, the auditory cortex (ACtx) encodes the 70 spectral and temporal information in harmonic stacks to form a neural representation of presented 71 auditory stimuli (Zatorre and Belin, 2001; Kadia and Wang, 2003; Linden et al., 2003; Bendor et 72 al., 2012; Herdener et al., 2013) . Studies in animal models have shown that the ACtx represents 73 various sound types-such as sweeps, white noise, and pure tones-through sparse coding (Hromadka 74 et al., 2008; Liang et al., 2019; Kang and Kanold, 2024). Specifically, neurons that are selective to 75 harmonic stacks have been identified in both the core and belt areas in ACtx of ferrets (Bizley et 76 al., 2010), the primary auditory cortex (A1) of cats (Abeles and Goldstein, 1970; Phillips and 77 Irvine, 1981; Sutter and Schreiner, 1991) , in A1 of marmosets (Kadia and Wang, 2003; Bendor 78 and Wang, 2005; Song et al., 2016). In mouse A1, L2/3 and L4 display distinct responses of pure 79 tones and unique integration patterns for the spectral content of harmonic stacks (Sołyga and 80 Barkat, 2022). Others suggested that A2 L2/3 shows a preferential response to harmonics than 81 individual pure tone components compared to A1 and anterior auditory field (AAF) (Kline et al., 82 2021). Thus, harmonic processing might vary between ACtx subareas and layers. The mammalian 83 brain contains two hemispheres and in mice, imaging has shown that A2 in the left hemisphere of 84 mice exhibits a stronger response to high -frequency tones and vocalizations than the right 85 hemisphere, analogous to human left-hemisphere specialization for speech (Calhoun et al., 2023), 86 suggesting that harmonic processing might also vary between hemispheres. 87 Furthermore, studies suggest that neurons may integrate simpler and more complex 88 harmonic stacks differently. In marmosets, neurons in A1 have been shown to respond to more 89 complex harmonic structures selectively, exhibiting non-linear facilitation compared to responses 90 to pure tones or two -tone harmonic stacks (Song et al., 2016; Feng and Wang, 2017) . This 91 sensitivity is further underscored by the disruption of neuronal activation when the spectral content 92 of perfect-octave harmonic stacks is shifted, indicating high sensitivity for precise spectral 93 composition. While sparse coding in the cortex is well -documented, it remains unclear how this 94 coding differs for simple versus complex harmonic stacks. Specifically, it is unknown whether a 95 fundamental neural network recruits additional neurons or strengthens neuronal connections to 96 process more complex harmonics that are composed of simpler harmonics. 97 The mammalian ACtx is organized into layers. In rodents, layer (L) 4 (L4) neurons receive 98 primary thalamic inputs (Winer et al., 2005; Sherman et al., 2013; Ji et al., 2016) , while L2/3 99 neurons receive inputs from both L4 and other L2/3 neurons within auditory cortical subregions 100 through horizontal connections (Oviedo et al., 2010; Covic and Sherman, 2011; Watkins et al., 101 2014; Meng et al., 2017; Chang and Kanold, 2021). Since inputs and outputs of each ACtx subarea 102 are unique (Hackett, 2011) , harmonic stimuli might be processed differentially by specialized 103 neuronal populations distributed across layers in both primary and higher-order auditory fields. 104 While the spectral integration of complex sounds in A1 L2/3 and L4 has been investigated 105 using electrophysiology (Sołyga and Barkat, 2022), there is a lack of a direct comparison of how 106 .CC-BY-NC-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted August 27, 2025. ; https://doi.org/10.1101/2025.08.26.672221doi: bioRxiv preprint 4 selectively tuned neuron populations across layers and subregions are recruited and interconnected 107 to process the same harmonic stacks . Moreover, it remains an open question whether the 108 integration of complex harmonic stacks builds upon the integration of simpler harmonic stacks, 109 and whether this integration occurs hierarchically or in parallel across A1 L4, A1 L2/3 , and A2 110 L2/3. 111 In this study, we aimed to determine (i) whether harmonics of varying spectral complexity 112 are represented in similarly sparse manner across A1 L4, A1 L2/3 , and A2 L2/3, (ii) whether 113 harmonic-sensitive neurons encode harmonic stacks with comparable consistency across these 114 subregions, and (iii) whether functional connectivity between harmonic -sensitive neurons and 115 other sound-responsive neurons differs among three populations. We analyzed sound -evoked 116 activity in mouse left ACtx subregions using in vivo two-photon Ca2+-imaging to capture the 117 simultaneous activity of large neuron populations. We used awake adult CBAxThy1GCaMP6s F1 118 mice that have good high-frequency hearing (Frisina et al., 2011; Bowen et al., 2020) and express 119 the calcium indicator GCaMP6s in excitatory neurons. We find that harmonic-sensitive neurons 120 (HNs) are present in similar proportions in A1 L4, A1 L2/3, and A2 L2/3, regardless of harmonic 121 complexity. However, co-tuned HNs in A1 L4 displayed the highest functional connectivity, the 122 highest signal correlation, and the lowest noise correlation compared to A1 L2/3 and A2 L2/3. We 123 also observed nonlinear integration of the harmonic component frequencies. The integration of 124 component frequencies became more linear with increasing spectral complexity . These results 125 suggest that while HNs maintain similar sparseness across cortical subregions , A1 L 4 uniquely 126 supports efficient, robust integration of spectral contents through strong co -tuning and minimal 127 noise, enabling consistent encoding of both simple and complex harmonic structures. Thus, 128 harmonic stimuli are processed in all auditory subareas , starting with the input layers of ACtx , 129 suggesting that harmonic processing might be a core function of ACtx. 130 131

132 Animal Preparation 133 For in vivo two photon imaging, mice were 12-24 weeks old at the time of the experiments. Mice 134 (n=28) of both sexes were first generation (F1) of CBA/CaJ (Jax # 000654) and C57BL/6J -135 Tg(Thy1-GCaMP6s)GP4.3Dkim/J (Jax # 024275) crosses. For electrophysiology recording, mice 136 were Tlx3-Cre;Rosa26-LSL-GCaMP6s;cdh23Ahl/ahl mice on a C57BL/6J background with fixed-137 hearing (Babola et al., 2025) All mice were housed with a reverse light cycle (12h light, 12h 138 darkness). All experiments were conducted during the dark cycle of the mice. All animal 139 procedures were approved by the Johns Hopkins University Animal Care and Use Committee. 140 141 Surgery 142 In brief, mice were prepared for surgery by inducing anesthesia with 4% isoflurane in 100% 143 oxygen and later reduced to 1 -2% isoflurane for maintenance until the surgery ended. 144 Dexamethasone (2mg/mL) was injected 1 hour before the surgery started to prevent inflammation. 145 During the surgery, body temperature was maintained with a feedback -controlled heating pad 146 .CC-BY-NC-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted August 27, 2025. ; https://doi.org/10.1101/2025.08.26.672221doi: bioRxiv preprint 5 maintained at 35-36oC. Hair on the top of the head was shaved and removed using a hair remover 147 (Nair) followed by disinfections with 70% ethanol and iodine. The skin and soft tissues were then 148 exposed by detaching and pushing away muscle on the surface of the skull. Craniotomy of a 149 circular area with 4mm diameter was performed above the left ACtx, covering both A1 and A2, 150 by using a dental drill. A stack of round glass coverslips (one 4mm glass, catalog #640724-CS4R, 151 Warner Instruments, on two stacked 3mm glasses, catalog #64-0720-CS-3R, Warner Instruments, 152 and fixed with optic glue, catalog #NOA71, Norland Products) was secured onto the exposed brain 153 with SuperGlue around the edge of the window. The exposed skull was covered with dental cement 154 (C&B Metabond). To prepare mice for imaging, a customized metal headplate was fixed onto the 155 cement along the midline of the skull. After the surgery, 5 mg/kg carprofen and 500 mg/kg 156 cefazolin were injected subcutaneously after the surgery and in the following 1-2 days of surgery. 157 Mice rested in the home cage and recover ed for at least 14 days before the first imaging session. 158 The s urgical procedure for acute electrophysiological experiments was similar to the imaging 159 experiments described above, except that the circular craniotomy was done with dura removed . 160 The exposed brain was covered by a 4mm glass with saline filling the gap . We used silicone 161 adhesive (KWIK-SIL, World Precision Instruments ) to seal the cranial window for the ease of 162 removal before the experiment. Cefazolin, dexamethasone, and m eloxicam (5mg/mL) were 163 injected after surgery, and the animal was put in a recovery cage for at least one hour before the 164 experiment started. 165 166 Sound Stimuli 167 All sound stimuli were pre-generated using MATLAB (Mathworks, version R2023a). 168 Stimuli were loaded into a Tucker-Davis Technologies (TDT) RX6 processor and presented by a 169 ES1 speaker, via a PA5 attenuator, 10 cm away from the right ear of the mouse. The speaker was 170 first calibrated using customized MATLAB (Mathworks, version R2020b) scripts by recording 4–171 64 kHz pure tone frequencies at 70 decibels (dB) sound pressure level (SPL), with a calibrated 172 microphone to find the natural transfer function of the speaker. We then calculated the inverse of 173 the function, which when added to the natural transfer function of the speaker, will equalize the 174 speaker’s output, giving a flat frequency/dB curve. We then used the calibration curve to generate 175 each pure tone frequency at 70 dB SPL and attenuated each frequency to 60 dB SPL. We ensured 176 that the recorded sound level of each frequency component was <1 dB from the target for all 177 sounds played using MATLAB (Mathworks, version R2023a) . To study the effect of the 178 complexity of the spectral contents in a harmonic complex, we generated harmonic complexes that 179 are composed of two to ten frequencies with base frequency 4kHz as well as complexes that are 180 composed of two to five frequencies with base frequency 8kHz. Similar to multiple published 181 studies that focus on the encoding of complex sounds in mice (Wang et al., 2020; Kline et al., 2021; 182 Sołyga and Barkat, 2022; Kang and Kanold, 2024; Efron et al., 2025) , we chose this frequency 183 range because sounds composed of low -to-mid frequencies have been shown in mouse 184 vocalizations, pup calls, and alarm calls in mice , which makes the encoding of these sounds 185 relevant and potentially critical to social behaviors (Ehret and Bernecker, 1986; Ehret and Riecke, 186 .CC-BY-NC-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted August 27, 2025. ; https://doi.org/10.1101/2025.08.26.672221doi: bioRxiv preprint 6 2002; Grimsley et al., 2013; Grimsley et al., 2016) . To generate harmonic stacks with varied 187 spectral complexities, each frequency component was generated at 60dB SPL and stacked to 188 generate the harmonic stacks without further attenuation. By doing this, each frequency component 189 during presentations of harmonic stacks or pure tones has the same sound intensity. The sound 190 intensity of resulting harmonic stacks can vary from 63 dB (two -tones harmonic) to 70dB (ten -191 tones harmonic). For spectrally shifted two-tone harmonic stacks (SH), we generated each 192 frequency component similarly and stacked two 60dB SPL frequency components, so the sound 193 intensity of the resulting two -tone JH was 63dB SPL, comparable to two -tone harmonic stacks. 194 During two-photon imaging, each session started with a 10-second of silence period to record the 195 spontaneous activity of neurons. Each trial comprises of 0.5 s of pre-stimulus silence, 1 s of sound 196 presentation, followed by 3.5 s post-stimulus silence (Fig. 1A). The order of sound presentation, 197 including harmonic stacks and pure tones, is pseudo -randomized to ensure all stimuli are played 198 once before beginning the next randomized sequence . Each sound was repeated for 10 times to 199 increase statistical confidence. 200 201 In vivo two-photon calcium imaging 202 The lo cation of the ACtx and subareas , including A1, A2, and AAF , was acquired by the 203 characteristic tonotopic axes using widefield imaging (Liu et al., 2019). During wide field imaging, 204 mice were head-fixed on a customized imaging station under the 2x objective. Mice were presented 205 with 100ms 4kHz to 64kHz pure tone frequencies in three sound levels (60-, 75-, and 90-dB SPL). 206 For two-photon imaging, mice were head -fixed on a customized imaging station under the 16x 207

attached to the two -photon microscope within a sound -attenuating chamber. In one 208 imaging session, harmonic stacks and the stack components were randomized and played as 209 described above. GCaMP6s was excited at 940 nm, and the field of view contained 1024 x 1024 210 pixels covering 1120 x 1120 μm2. Images were acquired from either L2/3 (150-230 um below the 211 surface) or L4 (370-430 μm below the surface) using the Prairie View software at 15 frames per 212 second. Data from each subarea was acquired in separate sessions. For recording in A2 L2/3, 1.1x-213 1.5x zoom is used to restrict the field of view to contain only the tonotopy -mapped A2. Sound 214 stimulation was synchronized with the image acquisition using a hardware trigger signal. 215 216 Two-photon data analysis 217 Motion correction and cell extraction were performed using the suite2p software with denoising 218 (Pachitariu et al., 2017) . Neuron fluorescence traces and neuropil fluorescence traces were 219 extracted by processing recorded signals with Suite2P software. Pixels that overlapping more than 220 one cell were excluded from processing. Denoising was enabled for data processing in Suite2P. 221 Neuron fluorescence were further corrected as: F cell, corrected = Fcell – 0.9 * F neuropil. We calculated 222 the change of fluorescence (∆F/F) during response period by dividing fluorescence 3 seconds after 223 the sound onset from each trial by the average fluorescence of silent frames in 0.5 seconds 224 preceding the sound onset (F0). To determine that a neuron has facilitated response to a sound, we 225 calculated the confidence for F 0 and ∆F/F in all trials of one sound , respectively, and set our 226 .CC-BY-NC-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted August 27, 2025. ; https://doi.org/10.1101/2025.08.26.672221doi: bioRxiv preprint 7 criterion to be that the lower bound of ∆F/F must be larger than the upper bound of F0 at 5% 227 confidence level. The suppressed response is not considered in this study. 228 229 Classification of neurons by sound-evoked response 230 To categorize neurons into harmonic -, pure tone -, or both -sensitive neurons, we compared their 231 sound-evoked response calculated as described above. Neurons with no significant facilitative 232 response to any pure tone but with significant response to any harmonic stacks were categorized 233 as harmonic-sensitive neurons (HNs). Similarly, those with no significant facilitative response to 234 any harmonic stacks but with significant facilitative response to any pure tone sounds were 235 categorized as pure tone-sensitive neurons (PTNs). Those with significant facilitative response to 236 both harmonic stacks and pure tone sounds were considered as both-sensitive neurons (BNs). 237 238 Linearity analysis 239 To evaluate the linearity and nonlinearity of harmonic neurons responding to harmonic stacks, we 240 used customized MATLAB scripts to perform univariate and multivariate linear regressions as 241 well as Support Vector Regression for nonlinear regression on the mean response to pure tone 242 frequencies and harmonic stacks. For univariate linear regression, we used the MATLAB function 243 “polyfit” with degree of 1 to linearly reconstruct harmonic response , y n, by adjusting the 244 coefficient assigned to each pure tone response X separately. n represents reconstructed harmonic 245 response by response to pure tone n. We reported the highest R2 values of all univariate regressions 246 for one harmonic response. 247 𝑦! = 𝑎!𝑋! 248 249 For multivariate linear regression, we used MATLAB function “regress” to perform linear 250 reconstruction by response to all corresponding pure tone components. 251 𝑦 = & 𝑎!𝑋! " !#$ 252 To evaluate the effects of varied number of predictors on the multivariate regression, we permuted 253 predictor data, or response to pure tone, then performed multivariate regression again and 254 compared the R2 between original data and permuted data. To perform Support Vector Regression 255 analysis, we used the MATLAB function “fitrsvm” with the radial basis function (“rbs”) kernel 256 and data standardization. 257 258 Granger causality analysis 259 We investigated functional connectivity by performing Granger causality analysis on the 260 ∆F/F traces of HNs and BNs. We used the multivariate Granger causality framework implemented 261 in the MVGC toolbox (Barnett and Seth, 2014). For neuron in this analysis, we extracted all trials 262 for all sounds and concatenate all traces into one time-series data, which were then detrended and 263 z-scored. To reduce the effect of slow fluctuations, we applied a first-order difference filter to each 264 time-series data. GC was then estimated using vector autoregressive (VAR) models fit to each pair 265 .CC-BY-NC-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted August 27, 2025. ; https://doi.org/10.1101/2025.08.26.672221doi: bioRxiv preprint 8 of neuron traces between every HN and every BN within each FOV. The optimal model order was 266 selected to be 1 due to the slow calcium dynamics. 267 Statistical significance of GC links between one HN and any BN within the same FOV was 268 determined by comparison to a nonparametric null distribution generated through bootstrapped 269 surrogate data. For each BN-HN pair, we generated 5 surrogate traces by permutating frames of 270 the BN’s time series data, totally disrupting the temporal dependency between the pair. GC values 271 from real data were considered significant if they exceeded the 9 5th percentile of the surrogate 272 distribution (p < 0.05, one-tailed). To obtain ∆GC values, we subtracted the real GC value of each 273 BN-HN pair by the mean of GC values of surrogate data. 274 All GC values were calculated across the entire stimulus period (or spontaneous window, 275 where relevant), and results were analyzed at the individual neuron -pair level and aggregated to 276 quantify the distribution of ∆GC strength across sound conditions and subareas. Only neuron pairs 277 with sufficient activity (above threshold signal variance and number of time points) were included 278 in the final analysis. The distance between BN-HN is normalized by dividing the absolute distance 279 by the maximum value of distances of all BN -HN pairs within the same FOV. To perform 280 Spearman correlation analysis, we used the built -in MATLAB function “corr” with type of 281 correlation being “Spearman”. 282 283 Onset-offset bias index (OBI) 284 We investigated the onset -offset bias index using the same methods described in our 285 previous study (Liu et al., 2019) . We defined the onset response window to be the 0.5 seconds 286 immediately following sound onset, and the pre -onset baseline window to be 0.5 seconds before 287 the sound onset. Similarly, we defined the offset response window to be 0.5 seconds immediately 288 following the sound offset, and the baseline for the offset response to be 0.5 seconds before the 289 sound offset. For each neuron, we first averaged the ∆F/F of ten trials for each window, then 290 calculated the onset response as the mean activity in the onset window minus the mean of the pre-291 onset window, and the offset response as the mean activity in the offset window minus the mean 292 of the pre-offset window. These values were then used to compute the OBI as: 293 OBI = (offset response – onset response) / (offset response + onset response) 294 295 Electrophysiology experiment and data preprocessing 296 Extracellular recordings were performed with a 4-shank high-density probe ( Neuropixels 2.0 ) 297 (Steinmetz et al., 2021) in a n anechoic chamber , where the animal was head -fixed and awake 298 during the recording. Audio stimuli were presented with a free-field speaker (ES1, TDT) 299 positioned 10cm from the animal’s right ear , contralateral to the recording hemisphere . The 300 speaker was driven by a pre-amplifier (ED1, TDT) receiving input from a data acquisition device 301 (NI USB-6343). Neuropixels recordings were acquired using the SpikeGLX software system, and 302 the data was digitized at 30kHz . The neural recording system and the sound stimulation were 303 coordinated by custom scripts in MATLAB. For spike analysis, a global demuxed CAR (common 304 average referencing) filter and a bandpass filter (300 Hz -9000 Hz) were applied to correct for 305 .CC-BY-NC-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted August 27, 2025. ; https://doi.org/10.1101/2025.08.26.672221doi: bioRxiv preprint 9 temporal misalignment across channels due to multiplexing during analog-to-digital conversion at 306 the electrode sites and remove irrelevant signals using post-processing tool CatGT. Spike sorting 307 was done by Kilosort4 (Pachitariu, 2023) , and we only included those clusters that were classified 308 as single units in the analysis. Current source density (CSD) was derived from the second 309 derivative of local field potential (LFP) (Mitzdorf and Singer, 1978)with a spacing of 200𝜇m. The 310 LFPs were obtained from applying a bandpass filter at lower frequencies (0.1Hz-500Hz) to the 311 recordings of all channels. We used CSDs to localize the relative laminar po sition of each 312 recording site. L4 was characterized by a short latency sink after the stimulus onset, whereas the 313 peaks of current sources marked L2/3 and L5. 314 315 Analysis of electrophysiology data 316 To determine if the single unit was responsive to the stimuli, we counted the spike number before 317 and after the stimulus onset for each trial and used paired t -test to determine whether the spike 318 count within 0.2s after the sound onset is significantly different from the spike count within 0.2s 319 before the sound onset. Similarly, to account for the offset response, we used a paired t-test to 320 determine whether the spike count within 0.2 before the sound offset is significantly different (p < 321 0.001) from the spike count within 0.2 after the sound offset. Clusters with significant onset or 322 offset response with increased spike counts were then further classified into three categories: PTN, 323 HN, and BN based on whether the clusters had evoked facilitated response to pure tones and/or 324 harmonic stacks. 325 326 Correlation analysis 327 To compute signal correlation s, the pair-wise cross-correlation of sound-evoked activity was 328 calculated between co-tuned neurons using 2 seconds after the sound onset , covering the offset 329 period, similar to our previously published studies (Winkowski and Kanold, 2013) . To compute 330 the pair-wise noise correlation s between each neuron pair, ∆F/F of each trial of a sound is 331 subtracted by the mean ∆F/F of all trials of the sound, then the cross correlation between the time 332 sequences was calculated for each trial between paired neurons with significant sound -evoked 333 facilitated response by using the MATLAB function “xcorr” at zero lag and normalized by using 334 “coeff” as the normalization parameter. 335 336 Statistical analysis 337 All statistical tests were performed in MATLAB R2024b. The Anderson-Darling test was used on 338 each data group to test for normal distribution. For data that does not form normal distribution, a 339 two-sided Wilcoxon rank sum test or a Kruskal-Wallis test was performed and corrected by 340 Bonferroni correction for statistics obtained by multiple comparisons Dunn’s test followed by 341 Dunn-Sidak multiple comparison correction. For data that follows normal distribution, an N-way 342 Analysis of Variance ( ANOVA) test is performed followed by post -hoc t-test and corrected by 343 Tukey-Kramer. 344 345 .CC-BY-NC-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted August 27, 2025. ; https://doi.org/10.1101/2025.08.26.672221doi: bioRxiv preprint 10

346 To explore the neural representation of harmonic stacks across three auditory subregions (A1 L4, 347 A1 L2/3, and A2 L2/3), we first used widefield imaging to identify tonotopic maps and localize 348 A1 and A2 in each mouse (Fig. 1B) as described previously (Liu et al., 2019). We then performed 349 in vivo two-photon imaging in A1 L4, A1 L2/3, and A2 L2/3 in separate sessions (3 sessions per 350 animal) on awake young adult mice (A1 L4: n=11; A1 L2/3: n=10; A2 L2/3: n=10 animals). We 351 used F1 mice with a CBA background, which retain high -frequency hearing into adulthood 352 (Frisina et al., 2011; Bowen et al., 2020), to ensure responses to the high sound frequencies in 353 complex harmonic stacks. We presented either pure tones (PT) or harmonic stimuli (H) with varied 354 numbers of components (2 –10 components), covering frequencies from 4 –40 kHz at 60 –70 dB 355 SPL. Harmonic complexes were centered on fundamental frequencies (F0) of 4 kHz and 8 kHz 356 (Fig. 1C). 357 358 HNs exhibit high sensitivity for harmonic tuning at one sound level 359 The ACtx is thought to have a sparse representation of sound features, so we first 360 investigated whether a subset of excitatory neurons responded exclusively to harmonic stimuli 361 without responding to any pure -tone components of the harmonic stacks at one sound level and 362 whether different subfields displayed a varying fraction of harmonically responsive neurons . We 363 recorded sound-evoked responses to harmonic stimuli with varied component numbers, as well as 364 to individual pure tones (A1 L4: 10 animals, 4974 neurons; A1 L2/3: 12 animals, 10,913 neurons; 365 A2 L2/3: 7 animals, 1792 neurons). Imaging sessions in A1 L4, A1 L2/3, and A2 L2/3 were 366 conducted when the targeted subarea was clearly identified in widefield imaging and suitable for 367 two-photon imaging. Each frequency was presented at the same sound intensity to ensure the same 368 intensity of each component of one harmonic sound compared to when each frequency is played 369 at pure tone stimulus. 370 We classified neurons into three types based on their facilitated (positive DF/F) responses 371 to sounds : pure -tone neurons (PTNs; responsive only to pure tones), harmonic neurons (HNs; 372 responsive only to harmonic stimuli), and broadly -tuned neurons (BNs; responsive to both pure 373 tones and harmonic stacks) (Fig. 1D). All three subregions exhibited similar proportions of HNs, 374 PTNs, and BNs (Fig. 4A-C), suggesting comparable sparseness in harmonic encoding across these 375 areas. We further quantified the proportion of neurons activated by different levels of harmonic 376 complexity in each individual recording session, and found that the number of neurons with 377 facilitated responses remained largely consistent between areas as the harmonic stacks became 378 more complex (Fig. 4). Male and female mice had the same proportions of sound-evoked neurons 379 (Fig. 4A-C); therefore, data from both sexes were combined in further analyses. Even though we 380 did not observe an effect of increasing the spectral complexity of harmonic stacks, we found that 381 the proportion of neurons activated by harmonic stacks sound in A2 L2/3 was higher than those in 382 A1 (Fig. 4D, left). When we considered the tuning properties, A2 L2/3 also contained a larger 383 fraction of BNs than A1 L4 and L2/3 across a range of complexities (Fig. 4D, middle), while A1 384 L4 contained a smaller fraction of HNs than A1 L2/3 and A2 L2/3 (Fig. 4D, right). These results 385 .CC-BY-NC-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted August 27, 2025. ; https://doi.org/10.1101/2025.08.26.672221doi: bioRxiv preprint 11 indicated that all subareas contain a similar proportion of neurons responsive to only the harmonic 386 stacks, but that A2 contains more neurons responsive to pure tones and harmonic stacks (BNs). 387 The proportion of activated neurons reflects the network size representing harmonic stacks, 388 while response amplitudes of individual neurons may reflect the robustness of the sound 389 representation by the neuronal network, which is crucial for stable perception. We thus calculated 390 the response amplitude of each HN to its "best harmonic" —the harmonic stimulus eliciting the 391 strongest average response. Our results revealed that HNs in A1 L2/3 showed significantly higher 392 response amplitudes to their best harmonic stacks compared to HNs in A1 L4 (Fig. 4E). Together, 393 these findings suggest that neurons in all three subregions exhibit sensitive tuning to harmonic 394 stacks, with HNs in A1 L2/3 showing the highest activation by harmonic stacks. Additionally, our 395

also show that the sensitivity is observed at the thalamorecipient layer (A1 L4), suggesting 396 that the source of selectivity could reflect both cortical processing and thalamic inputs. However, 397 the higher response amplitudes in A1 L2/3 suggest a more robust representation of the harmonic 398 stacks in this layer compared to A1 L4. We observed no differences in amplitude between A2 L2/3 399 and the other two subareas, which suggests that A2 L2/3 HNs are more heterogeneous in terms of 400 response amplitude to the same sounds that are represented significantly differently in A1 L2/3 401 and A1 L4. 402 To identify the sensitivity of HN neurons to harmonic stacks as opposed to sounds having 403 multiple frequency components that are not harmonically related, we performed separate imaging 404 sessions presenting two-tone harmonic stacks and non-harmonic two-tone sounds with the upper 405 frequency component spectrally shifted downward (SHs) (Fig. 5A). We found that in all three 406 subareas fewer HNs responded to both the harmonic and its spectrally shifted counterpart (Fig. 407 5B). We observed no differences in the proportion of neurons responsive to 25%, 50%, and 75% 408 spectrally shifted harmonic stacks across the three subareas (Fig. 5C). These results suggest that a 409 subset of excitatory neurons in three imaged subregions have sound-evoked facilitative response 410 only to the specific frequency combination forming a harmonic stack and are sensitive to the 411 downward spectral shifts of the higher frequency in a two-tone harmonic stack. 412 Our findings show that HNs display high selectivity to harmonic stacks , and the 413 representation of more complex harmonic stacks does not rely on recruiting additional HNs that 414 respond to simpler harmonic stacks, as shown by similar proportions of neurons evoked by 415 harmonic stacks of varied complexity. This further supports the hypothesis that ACtx neurons are 416 finely tuned to spectral information within harmonic stacks and represent these features in a sparse 417 and selective manner. 418 419 Electrophysiology recording of HN response to harmonic stacks in both L4 and L2/3 420 Two-photon imaging in deeper layers has the potential of contamination by neuropil signal 421 from more superficial layers. Thus, to confirm our observation about harmonic-sensitive neurons 422 in L4 by two-photon imaging, we performed electrophysiology recording in awake hearing-fixed 423 mice mice on a C57BL/6J background (Babola et al., 2025). To record across the depth of A1 we 424 used Neuropixel arrays (REF) and identified cortical layers using CSD analysis (Fig. 2B). We 425 .CC-BY-NC-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted August 27, 2025. ; https://doi.org/10.1101/2025.08.26.672221doi: bioRxiv preprint 12 identified recording locations in L4 as sites showing the first current sink shortly after sound onset 426 as L4 and sites 200 µm above the early current sink as L2/3. We then identified clusters with 427 significant sound response within 0.2 after onset or offset and found clusters that show similar 428 sensitivity to harmonic sounds (HNs) but not to pure tones (Fig. 2C). We found HNs in both A1 429 L2/3 and L4 (Fig. 2D). This result is consistent with our in vivo two photon imaging results (Fig. 430 1) and suggest the existence of neurons that are responsive selectively to harmonic stacks but not 431 to any individual pure tones in both L4 and L2/3 of A1. 432 433 BN shows broader frequency response profiles compared to PTN 434 In our previous work (Liu and Kanold, 2021; Maximov and Kanold, 2025) , we identified 435 six distinct shapes of frequency response area (FRA) of neurons that respond to pure tones of 436 different frequencies at different sound levels . We here again studied the FRAs of the neurons 437 responding to pure tones and/or harmonic stacks as a separate experiment. We imaged A1 L2/3 438 and A1 L4 in hearing-fixed mice and played pure tones and harmonic stacks at three sound levels, 439 40dB, 55dB and 70dB. For harmonic stacks, each frequency is calibrated to 40dB, 55dB or 70dB 440 then combined to generate the harmonic stacks. We found the best frequency for each BN and 441 PTN and used the best frequency as the center of the FRA. We then clustered the centered FRA of 442 each BN and PTN similarly, as in our previous work (Liu and Kanold, 2021) , into one of the 443 clusters V, H, I, S1, S2, S3 (Fig. 3D). We found that tSNE plot exhibited distinct clusters (Fig. 444 3A). BN and PTN occupied different regions of the tSNE plots (Fig. 3B) which is further analyzed 445 by quantifying the proportions of BN and PTN in each cluster (Fig. 3C). We found that proportions 446 of PTNs in S1 and S3 clusters are significantly higher than the proportions of BNs (Fig. 3C). For 447 cluster S2, proportion of PTNs showed a trend to be higher but not significant compared to the 448 proportion of BN. This result indicates that PTNs usually respond to their best frequency at one 449 level and have much narrower tuning regarding pure tones compared to BNs. Additionally, for 450 cluster H, proportion of PTNs showed a trend to be lower but not significant compared to the 451 proportion of BNs. This result further suggests that, compared to PTNs, BNs tend to have broader 452 tuning reflected by FRA shape and they respond to more neighboring frequencies around the best 453 frequencies when the sound becomes louder. 454 Together with our criteria to classify neurons as BNs in Figure 1, these result s further 455 suggest that BNs may contribute more to the encoding of spectral combinations and may serve as 456 an intermediate population bridging basic and complex spectral features , whereas PTNs serve in 457 precise frequency resolution at one sound level. 458 459 Nonlinear and linear integration of pure-tone components in harmonic sensitive neurons 460 How does the sensitivity to harmonic stacks emerge? Harmonic responses can occur via 461 linear or non-linear processing of the individual sound components. Given that we identified HN 462 neurons in all areas, these processes might vary between areas. We examined if the responses of 463 HN neurons to harmonic stacks could be due to processes beyond the simple summation of 464 responses to each pure -tone component, which suggests a potential nonlinearity that might vary 465 .CC-BY-NC-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted August 27, 2025. ; https://doi.org/10.1101/2025.08.26.672221doi: bioRxiv preprint 13 with increasing spectral complexity of harmonic stimuli. We thus investigated whether HN 466 responses to harmonic stacks were constructed linearly or non -linearly from the individual pure-467 tone components . We classified harmonic responses as linear if they could be accurately 468 approximated by a weighted sum of these components as a first -order polynomial function (Fig. 469 6A). Conversely, if the sum could not fully account for the harmonic response, we inferred the 470 presence of nonlinear processing. 471 To quantify linearity, we first isolated HN responses to their optimal harmonic stimuli and 472 their constituent pure-tone components (Fig. 6B). Using these responses, we reconstructed the HN 473 response to harmonic stacks by summing the pure-tone responses through first-order polynomial 474 fitting (Fig. 6C). Additionally, we employed support vector regression (SVR) to capture further 475 nonlinear relationships between harmonic and pure -tone responses (Fig. 6D). To assess the 476 linearity, we calculated the R² as a measure of the goodness of fit for each polynomial function. 477 To control for the number of predictors in the multivariate function’s effect on R², we permuted 478 values across the averaged neuron al responses and conducted the same linear reconstruction, 479 allowing us to perform a three -way ANOVA to compare R² across spectral complexity, cortical 480 subareas (A1 L4, A1 L2/3, and A2 L2/3), and data type (original versus permuted) (Fig. 6E). Our 481 ANOVA revealed significant effects for spectral complexity, data type, and their interaction . 482 However, no significant differences were found between subareas, suggesting that HNs in these 483 regions integrate individual frequencies similarly across simple and complex harmonic stacks. 484 The analysis further revealed that R² values increased with harmonic complexity, 485 indicating that more responses to spectrally complex harmonic stacks are due to a more linear 486 computation to integrate individual frequency components. We then examined whether this linear 487 reconstruction was driven by responses to one or multiple frequency components by comparing 488 R² values from single -component and multi -component reconstructions (Fig. 6F). For more 489 complex harmonic stacks, all-components reconstructions yielded significantly higher R² values, 490 implying that the response integration for complex harmonic stacks leverages the contributions of 491 multiple frequency components more linearly. 492 To probe further into the nonlinear aspects of harmonic processing, we applied SVR to 493 account for nonlinearities in HN responses. We observed improved R² with SVR relative to linear 494 reconstruction. However, the degree of improvement diminished as harmonic stacks became more 495 complex (Fig. 6G), supporting our finding that HNs exhibit greater linearity with increasing 496 spectral complexity. This heightened linearity in complex harmonic stacks may be due to reduced 497 inhibitory modulation in HNs, while nonlinearity might stem from two primary sources: (i) 498 threshold effects due to intrinsic properties (e.g., ion channel density, leaky conductance, and 499 inhibitory inputs) (Gerstner et al., 2014) , and (ii) amplification effects from positive feedback 500 mechanisms that exponentially boost the pure -tone response into a harmonic response (Wu and 501 Zenke, 2021). In conclusion, our data suggest that HNs processing complex harmonic stacks might 502 experience reduced inhibition and positive feedback compared to those processing spectrally 503 simpler harmonic stacks (Fig. 6E-G). To summarize these effects, we propose a simple model 504 microcircuit (Fig. 6H) in which an excitatory HN tuned to two-tone harmonic stacks receives both 505 .CC-BY-NC-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted August 27, 2025. ; https://doi.org/10.1101/2025.08.26.672221doi: bioRxiv preprint 14 inhibitory and excitatory inputs from PTNs. When only one pure tone is present, the HN is non -506 responsive due to balanced excitation from a single PTN and inhibition. However, when both tones 507 are presented as a two-tone harmonic, the HN’s response is facilitated by simultaneous excitation 508 from both PTNs and the disinhibition effect, leading to a nonlinear, harmonic -sensitive response. 509 Given that all subareas show similarities in the HNs we propose that such a circuit is present across 510 ACtx. 511 512 A1 L4 shows the highest BN-HN directed functional connectivity 513 As we revealed that the response of HN to harmonic stacks cannot be reconstructed by a 514 linear weighted sum of the neuron’s response to pure tone components, we performed the same 515 analysis for BNs. This analysis showed that the reconstructed response of BN to harmonic stacks 516 is more linear (Fig. 7A-C). Combined with its broad tuning, BN might play a critical role in 517 enabling selective response to harmonic stacks in HNs. Here, we proposed a micronetwork to 518 explain the source of harmonic -sensitive tuning of HNs as excitatory neurons (Fig. 7D). We 519 focused on investigating the potential differences of functional connectivity (FC) from BN to HN 520 by applying Granger Causality (GC) analysis on the sound-evoked response of BNs and HNs. We 521 aimed to answer two questions: first, does BN -HN have significant FC compared to the shuffled 522 control? Second, does the FC differ between subareas and across distances? 523 To answer these questions, we performed the Granger causality analysis on every pair of 524 BN-HN to explore their functional connectivity. We used the metric, ∆GC link strength, to 525 quantify the relative strength of GC links by subtracting absolute GC link values of the real data 526 by the mean of absolute GC link values of the surrogate data . By doing this, we extracted the 527 strength of GC links in real data compared to chance, which would still generate values of GC 528 links. To answer the first question of significant GC link between BN and HN, we found that more 529 than one BN-HN pair for each mouse showed significant GC links (Fig. 7F), despite the absolute 530 values of GC links being small (<0.05), which can be due to the slow calcium dynamics or sparse 531 functional coupling. We then answered the second question by performing statistic tests on two 532 main factors: subareas and distances. We found no significant effect of distances between BN and 533 HN on the strength of GC links (Fig. 7G). However, the test revealed a significant effect of 534 subareas (Fig. 7G). Post-hoc test further showed that BN-HN in A1 L4 had the strongest significant 535 GC links compared to A1 L2/3 and A2 L2/3, respectively. This result suggests that the proposed 536 micronetwork is more well-represented in A1 L4 compared to the upper cortical layers. 537 Additionally, we explored the potential trend of decreased FC as the distances between BN 538 and HN increases by performing Spearman correlation analysis. While A1 L4 and A2 L2/3 showed 539 no significant trend as the distances changed, A1 L2/3 showed a small but significant trend of 540 decrease of the mean values of top 5% GC links as the distance increased. Such result suggests 541 that BNs in A1 L4 and A2 L2/3 does not preferably transfer information only to HNs in its 542 neighborhood but also coordinate with HNs that are farther in the FOV. 543 Together, we showed that BNs can have significant but small directed excitatory influence 544 onto HNs which is stronger in A1 L4 and weaker in L2/3 of A1 and A2. Specifically, the relatively 545 .CC-BY-NC-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted August 27, 2025. ; https://doi.org/10.1101/2025.08.26.672221doi: bioRxiv preprint 15 stronger functional connectivity from BN to HN compared to randomized data could indicate that 546 the linear inputs from BNs can serve as essential and meaningful building blocks for the nonlinear 547 integration performed by HNs, ultimately shaping their sensitive responses to harmonic stacks. 548 Such BN-HN connectivity is more well-represented in A1 L4. 549 550 Parallel pathway contributions to response properties and nonlinear integration in ACtx neurons 551 ACtx receives parallel ascending inputs from the lemniscal and non -lemniscal pathways 552 (Hackett et al., 2011; Saldeitis et al., 2014; Liu et al., 2019). These pathways shape the functional 553 properties of ACtx neurons, with lemniscal input from the ventral medial geniculate body (MGBv) 554 preferentially driving onset responses (Aitkin and Webster, 1972; Imig and Morel, 1983; Redies 555 and Brandner, 1991; Hackett et al., 2011) , while non-lemniscal input from the dorsal medial 556 geniculate body (MGBd) is thought to preferentially driving offset responses (He, 2001; Liu et al., 557 2019). We investigated whether the temporal response properties of the three neuron types —558 harmonic-sensitive neurons (HNs), pure -tone neurons (PTNs), and broadly -tuned neurons 559 (BNs)—aligned with lemniscal or non -lemniscal input patterns, focusing on their responses to 560 sound onset and offset. 561 To characterize these temporal properties, we applied K -means clustering to the temporal 562 response profiles of neurons, revealing distinct clusters dominated by onset or offset responses 563 (Fig. 8A-B). We further quantified each neuron's onset-offset bias using the offset bias index (OBI, 564 OBI = (offset response – onset response) / (offset response + onset response)) (Liu et al., 2019) 565 and compared OBIs across neuron populations (Fig. 8C-E). We observed differences in the OBI 566 of sound-evoked responses of BNs from A1 L 4 to A2 L2/3 and then to A 1 L2/3 from onset - to 567 offset- bias, with progressively greater onset bias for BNs in A2 L2/3 versus A1 L4 . BNs in A1 568 L2/3 displayed significantly less onset bias than those in A1 L4 and A2 L2/3, with A2 L2/3 569 exhibiting an intermediate onset response (Fig. 8C). These findings suggest that BNs in A1 L4 570 may be more specialized in encoding the onset of sounds, while BNs in A1 L2/3 showed less 571 preference for the onset of sounds. In contrast, OBIs for HNs were similar across areas (Fig. 8D), 572 which indicates the similarity between harmonic -responsive neurons in A1 L4, A1 L2/3 , and A2 573 L2/3 in detecting the initiation and termination of the harmonic stacks. The OBIs of PTNs in A2 574 L2/3 exhibited a significantly higher onset bias than A1 L4 (Fig. 8E), consistent with previous 575 findings that A2 L2/3 neurons are more onset -biased in response to pure tones (Liu et al., 2019). 576 We next analyzed OBIs of HNs to harmonic stacks of varied complexity (Fig. 8F) and found that 577 OBIs of HNs were largely independent of both subareas and sound complexity. In summary, BNs 578 show the most obvious subareal differences in onset-offset bias, PTNs in A1 L4 are significantly 579 shifted to offset response compared to A2 L2/3, and HNs have homogeneous OBIs among the 580 three subareas. 581 HNs exhibit nonlinear responses to simpler harmonic stacks, consistent with underlying 582 mechanisms such as thresholding, where responses are only elicited when the summed input from 583 multiple components exceeds a certain activation threshold, and rectification, where only positive 584 or suprathreshold inputs drive significantly increased spiking activity, resulting in the increase of 585 .CC-BY-NC-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted August 27, 2025. ; https://doi.org/10.1101/2025.08.26.672221doi: bioRxiv preprint 16 fluorescence change from the baseline in this study. Thus, t o explore whether these nonlinear 586 dynamics vary with response timing—particularly by extending response latency toward sound 587 offset rather than onset —we analyzed the linearity of HNs with different OBIs. Specifically, we 588 selected HNs with higher biases toward onset ( shaded in beige) or offset (shaded in light purple) 589 and examined their response linearity, respectively (Fig. 8G). Offset-biased HNs (off-HNs) in A1 590 L2/3 exhibit a more linear response profile compared to onset -biased HNs (on -HNs) (Fig. 8H), 591 while HNs in A1 L4 showed a marginal trend toward this profile (p=0.0667), and HNs in A2 L2/3 592 showed no significant difference (p = 0.3650). These findings suggest that while HNs are similarly 593 distributed across these cortical subregions, their response dynamics vary, with A1 HNs 594 demonstrating a more linear onset response. This linearity may result from reduced inhibitory 595 modulation and minimal positive feedback during spectral integration. Overall, this variation in 596 response profiles across subregions highlights region -specific processing differences, potentially 597 supporting distinct roles in auditory perception. 598 599 Enhanced signal correlation and coordinated activity of harmonic neurons in A1 L4 600 Building upon our investigation of individual HN responses, we next aimed to characterize 601 the collective activity of neurons sensitive to harmonic stacks but not to their pure tone components. 602 While the proportion of HNs was similar across the three subareas (Fig. 4), prior widefield imaging 603 studies revealed distinct activation patterns for tones and vocalizations in these regions (Calhoun 604 et al., 2023) . These differences may stem from varying reliability in how sound stimuli engage 605 neuronal networks in each subarea. The sound -evoked response comprises a stimulus -driven 606 component representing the overall response to the stimulus and a variable component that reflects 607 the network’s activation pattern. The contributions of these components can be separated by 608 calculating signal and noise correlations: signal correlations capture shared stimulus -driven 609 responses, while noise correlations reflect functional connectivity between neurons (Averbeck et 610 al., 2006; Averbeck and Lee, 2006; Cohen and Kohn, 2011; Winkowski and Kanold, 2013; Hazon 611 et al., 2022) . We calculated the signal correlation between HNs coactivated by each harmonic 612 sound and compared across harmonic complexity and imaged subregions. Our results showed that 613 increasing harmonic complexity did not significantly alter the signal correlation among HNs (Fig. 614 9A). Thus, more spectrally complex harmonic processing does not rely on recruiting additional 615 neurons (Fig. 4D) or increasing synchronization of coactivated HNs as the harmonic becomes 616 more spectrally broad (Fig. 9A). However, we observed that A1 L4 exhibited significantly higher 617 signal correlations than A1 L2/3 and A2 L2/3, regardless of harmonic complexity (Fig. 9B). SCs 618 were similar between A1 L2/3 and A2 L2/3. Thus, HNs in A1 L4 respond to harmonic stacks more 619 synchronized than HNs in L2/3, potentially enabling A1 L 4 to facilitate a more efficient, robust 620 encoding of harmonic stacks through the heightened level of coordination. This high degree of 621 coordination in A1 L4 may reflect a specialization for processing spectrally complex sounds, such 622 as harmonic stacks, at an early stage of auditory processing. 623 624 Distinct functional connectivity and network sparsity of harmonic neurons in A1 L4 625 .CC-BY-NC-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted August 27, 2025. ; https://doi.org/10.1101/2025.08.26.672221doi: bioRxiv preprint 17 Noise correlations capture how fluctuations in neuronal activity, independent of stimulus-626 evoked response, are shared between pairs of neurons . High noise correlation indicates a high 627 probability of shared connectivity between neurons, and thus noise correlation can serve as a proxy 628 for measuring functional connectivity between neuron pairs. To further investigate network 629 dynamics in harmonic processing, we examined the functional connectivity inferred by pairwise 630 noise correlations between HNs and other neuron types, BNs, and PTNs. 631 To characterize stimulus-dependent network engagement, we compared noise correlations 632 within HN pairs (HN-HN), between HNs and BNs (HN-BN), and between HNs and PTNs (HN-633 PTN) (Fig. 10). For HN-HN pairs, the ANOVA showed significant effects from both subareas and 634 sound conditions on positive and negative noise correlations of HN -HN (Fig. 10B) despite that 635 post-hoc test showed no significant differences among varying harmonic conditions on positive or 636 negative correlations. We then examined whether there is a difference in the distribution of noise 637 correlation coefficients between subareas and observed that HN-HN pairs in A1 L4 exhibited 638 significantly lower positive and negative noise correlations compared to A1 L2/3 and A2 L2/3 639 (Fig. 10A), indicating that HNs in A1 L4 are less likely to form interconnected networks. 640 Similarly, we examined HN-PTN and HN-BN noise correlations. For HN-PTN pairs, the 641 ANOVA revealed significant effects of subareas and sound condition on negative noise 642 correlations but not on positive noise correlation (Fig. 10D). Post hoc analysis showed HN-PTN 643 noise correlations were lowest in A1 L4 compared to A1 L2/3, and A2 L2/3, which had the highest 644 noise correlation among the three areas (Fig. 10C). For HN-BN pairs , the harmonic sound 645 condition had no significant effect, but subarea remained a key factor, with A1 L4 displaying 646 significantly lower noise correlations compared to A1 L2/3 (Fig. 10F). No significant differences 647 were found between A1 L4 and A2 L2/3, or between A1 L2/3 and A2 L2/3 (Fig. 10E). 648 Together, our analysis of noise correlations among neuron types across subareas suggests 649 that HNs in A1 L4 are more likely to receive distinct synaptic inputs, forming sparser and more 650 selective networks than HNs in L2/3, which exhibit stronger noise correlations. This network 651 sparsity in A1 L4 remained consistent despite increasing spectral complexity of harmonic stacks, 652 supporting the idea that the ACtx encodes sounds sparsely and selectively adapts to varying 653 spectral complexity. 654 655

656 We investigated the population coding of spectrally simple and complex harmonic stacks 657 in different auditory cortical subfields. We find harmonic-sensitive neurons (HNs), that respond 658 to harmonic stacks but not to single frequency. We find that multiple subareas, including A1 L4, 659 A1 L2/3 and A2 L2/3, in the ACtx contain HNs, and that the fraction of HNs is similar across A1 660 and A2. Thus, harmonic sensitivity is already present in A1 L4 and is not a unique feature of A1 661 L2/3 and A2 L2/3 . HNs show sensitivity to particular stacks of harmonic frequencies and are 662 characterized by nonlinear integration of the component frequencies. 663 Simple sounds, such as pure tones or harmonic stacks of few frequencies, serve as the 664 fundamental building blocks of more intricate stimuli, such as harmonic stacks of more than five 665 .CC-BY-NC-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted August 27, 2025. ; https://doi.org/10.1101/2025.08.26.672221doi: bioRxiv preprint 18 frequencies found in speech. Although previous studies have examined the neural representation 666 of specific sound features in the ACtx of humans, rats, and mice (Lewis et al., 2009; Okada et al., 667 2010; Carruthers et al., 2015; de Heer et al., 2017; O'Sullivan et al., 2019; Staib and Fruhholz, 668 2023), the question remains of if the spectral integration of harmonic stacks with simpler to more 669 complex structures varies across ACtx layers and subareas. Our results show that A1 L4, A1 L2/3, 670 and A2 L2/3 contain neurons that are sensitive to harmonic stacks with no significant response to 671 any pure tone, and that proportions of HNs are largely similar across subareas while their 672 functional connectivity differs. Thus, HNs seem to be independently assembled in multiple ACtx 673 areas but form distinct networks. 674 Intrinsic imaging has suggested that A2 L2/3 preferentially activated by harmonic (Kline 675 et al., 2021). In contrast, we found that the proportion of neurons activated by harmonic stacks was 676 similar across A1 L4, A1 L2/3, and A2 L2/3, regardless of number of harmonic frequencies in the 677 stack or the sex of the mice. The differences between our study and the prior study (Kline et al., 678 2021) likely lie in the imaging specificity, duration of sounds, as well as mouse lines . Instead of 679 intrinsic imaging with low spatial resolution, w e used in vivo two -photon imaging and 680 electrophysiologywith single cell resolution . Instead of short duration sounds (100–300 ms), we 681 utilized sound with longer duration (1000 ms). Certain proportions of neurons may be sensitive to 682 the duration of the sound (Theunissen et al., 2000; Buonomano and Maass, 2009), or require longer 683 stimuli to trigger the significant changes in calcium traces. The prior study utilized C57Bl/6 mice 684 and there are also sex-dependent age-related changes in hearing (Shilling-Scrivo et al., 2021, 2022), 685 and thus the differences could also be due to C57Bl/6 mice having early -onset high-frequency 686 hearing loss (Ison et al., 2007; Jendrichovsky et al., 2024) . In contrast, we use mice that retain 687 good high-frequency hearing across age. Moreover, given the behavioral importance of natural 688 stimuli containing harmonic stacks, the sensory experience of animals could shape the responses 689 in ACtx, thus differences in the rearing environment (Chang and Merzenich, 2003; Sanes and Bao, 690 2009; Homma et al., 2020; Chang and Kanold, 2021) could underlie the observed differences. 691 Among HNs in three imaged auditory subfields, we showed that spectral shift of frequency 692 disrupted their response to the non -shifted harmonic two -tone stacks. In this study, the spectral 693 shift was applied only in the downward direction, disrupting harmonicity and narrowing spectral 694 bandwidth. As a result, the diminished responses could reflect sensitivity to either the altered 695 frequency relationship or changes in bandwidth. Nonetheless, the consistent reduction in activity 696 across regions suggests that these neurons respond preferentially to specific frequency 697 combinations with harmonic structure. Future studies incorporating upward or bidirectional shifts 698 could be utilized to distinguish the relative contributions of harmonicity and spectral bandwidth. 699 The harmonic-sensitive response of HNs can be explained by their nonlinear integration of 700 component responses . HN responses become more linear with increased number of harmonic 701 frequencies, suggesting that broader frequency integration is associated with increased linearity. 702 Consistent with studies reporting supra-linear and sublinear integration in A1 L2/3 and A2 L2/3 703 for harmonic representation (Kline et al., 2023), our results provided insights of how the linearity 704 of spectral integration can change depending on the spectral contents. We observed that neurons’ 705 .CC-BY-NC-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted August 27, 2025. ; https://doi.org/10.1101/2025.08.26.672221doi: bioRxiv preprint 19 responses to harmonic stacks with fewer frequencies were highly nonlinear in A1 L4, A1 L2/3 and 706 A2 L2/3 (Fig. 6). Such nonlinear integration emerges earlier than L2/3 and might also be 707 observable in auditory thalamus. This nonlinearity in spectral integration diminished as the number 708 of harmonic frequencies increased in a stack in all imaged subfields. This is potentially due to 709 reduced thresholding in the local network as the number of harmonic frequencies increases . It is 710 also possible that the representation of simpler and more complex harmonic stacks are through the 711 two different pathways, linear and nonlinear pathways , emerging from the cochlear nucleus (Yu 712 and Young, 2000) . These findings under score the dynamic nature of spectral integration in the 713 ACtx, adapting to the varied complexity of auditory stimuli. 714 As we characterized the nonlinear spectral integration of frequencies by HNs, we proposed 715 a micronetwork model, delineating potential structural and functional connectivity that might 716 underly the harmonic-sensitive response tuning of HNs. (Fig. 7). Notably, broadly-tuned neurons 717 (BNs) appear critical for establishing harmonic-sensitive tuning: they display lower sensitivity for 718 particular harmonic stacks, and their pure -tone response reconstruct s harmonic responses with 719 higher linearity. This suggest that BNs may generalize across frequencies and facilitate the 720 harmonic sensitivity in HNs. Granger causality (GC) analysis revealed a small but significantly 721 stronger directed influence from BNs to HNs in A1 L4 compared to L2/3 of A1 and A2. This result 722 suggests that the underlying network may not be confined to A1 L4, but rather originate earlier in 723 the auditory pathway which is known to shape and refine representations of complex acoustics 724 (Patterson et al., 2002; Nelken, 2008; Bartlett, 2013) . Moreover, signal correlations among A1 725 L2/3 neurons are patchy and stimulus-dependent, suggesting upstream convergence and nonlinear 726 integration (Jendrichovsky et al., 2025) . Given the spatial en coding of single frequencies in 727 mammalian cochlea (Dallos, 1996) and the sparse representation of vocalization features observed 728 in cortex across multiple species (Hromadka et al., 2008; Bandyopadhyay et al., 2010; Bowen et 729 al., 2020; Montes -Lourido et al., 2021) , we speculate that the BN -> HN micronetwork spans 730 multiple brain regions and enables the special tuning profiles of HNs in the auditory cortex. 731 To explore the sources of nonlinearity, we examined whether nonlinear neurons might 732 show preference to the sound onset or offset, which are essential for auditory scene analysis 733 (Bregman, 1994). Our study showed that BNs and PTNs are more onset-biased in A1 L4 compared 734 to A2 L2/3. Specifically, BNs in A 2 L2/3 also show significantly more onset bias compared to 735 those in A1 L2/3. Which is consistent with our previous finding that A1 neurons were more off-736 set biased to pure tones compared to those in A2 (Liu et al., 2019), without evaluating the responses 737 to harmonic stacks; thus, neurons in the previous study likely were a combination of PTNs and 738 BNs in this study . As A1 L2/3 receives inputs from both A1 L4 and A2 L2/3, it may be an 739 integrative hub for processing diverse spectral information in sustained auditory stimuli . The 740 observed hierarchy across layers and regions likely reflects specialized roles in temporal 741 processing. Notably, in A1 L2/3, onset-biased HNs tended to be more linear, while offset -biased 742 HNs were more nonlinear. These results suggest that the onset pathway may encode spectrally 743 complex sounds more linearly, with increased nonlinearity in the non-lemniscal offset pathway. 744 .CC-BY-NC-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted August 27, 2025. ; https://doi.org/10.1101/2025.08.26.672221doi: bioRxiv preprint 20 Coactivated HNs in A1 L4 exhibit the highest signal correlations compared to those in A1 745 L2/3 and A2 L2/3. This result contradicts to the hypothesized hierarchy of harmonic processing 746 from A1 L4 to A1 L2/3 and finally to A2 L2/3. An alternative explanation for this non-hierarchical 747 transformation is that neurons in L2/3 may engage in a more distributed representation of harmonic 748 features, resulting in a lower synchronized sound-evoked response compared to A1 L4. This could 749 indicate that as sound information progresses from L4 to L2/3, it undergoes further abstraction, 750 leading to reduced coordination among L2/3 neurons. This distinction suggests that A1 L4 may 751 play a foundational role in the initial encoding of harmonic structure, while L2/3 may contribute 752 to higher-order processing of sound features. The neuronal network involving all sound-evoked 753 neurons in A1 L4 was the sparsest, showing the lowest noise correlation . This is consistent with 754 our previous study which found pure -tone responsive neurons in A1 L4 showed higher signal 755 correlations and lower noise correlations than those in A1 L2/3 (Winkowski and Kanold, 2013) . 756 Here A1 L4 HNs also showed low noise correlations with pure-tone and broadly-tuned neurons 757 compared to L2/3 suggesting that A1 L4 neuron populations show less of the shared synaptic 758 inputs regardless of their sound-response profiles. 759 Our results show that harmonically sensitive neurons are ubiquitous in A1 and A2 , 760 indicating the importance of harmonic integration for auditory processing . Thus, already, A1 L4 761 functions as a center for integrating spectral information for complex sounds, supporting robust 762 encoding through coordinated but sparsely connected networks. 763 764

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It is made The copyright holder for this preprintthis version posted August 27, 2025. ; https://doi.org/10.1101/2025.08.26.672221doi: bioRxiv preprint 25 958 959 .CC-BY-NC-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted August 27, 2025. ; https://doi.org/10.1101/2025.08.26.672221doi: bioRxiv preprint 26 Figures 960 961 Figure 1: Excitatory neurons in A1 L4, A1 L2/3, and A2 L2/3 are found sensitive to harmonic 962 stacks but not to individual frequencies. 963 A: In vivo two-photon imaging schematic (top) and sound stimulus trial (bottom). F0: baseline of 964 fluorescence change in the window of neuron response to the sound stimulus. Solid line indicates 965 sound onset and dashed line indicates sound offset. The gray shaded area indicates when sound is 966 present. 967 B: Left: Tonotopy map (A1, A2, AAF) identified by widefield imaging on sound -evoked areas. 968 Right: Example field of view of in vivo two photon calcium imaging on A1 L2/3 excitatory 969 neurons. 970 .CC-BY-NC-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted August 27, 2025. ; https://doi.org/10.1101/2025.08.26.672221doi: bioRxiv preprint 27 C: A decision chart of classifying neuron into three categories based on their facilitative response 971 to types of sounds. 972 D: Schematic of stimuli design. Pure tone frequency, for example the base frequencies 4kHz and 973 8kHz, is shown in black. Harmonic stacks that consist of more than one frequencies are shown in 974 blue. 975 E: Examples of fluorescence changes compared to baseline (∆F/F) of neurons responding to only 976 pure tones (PTN), only to the harmonic stacks (HN) with onset or offset response , or both 977 harmonic(s) and pure tone(s) (BN) (from top to bottom). For HN and BN, their ∆F/F responses to 978 the pure tone frequency components are stacked and shown as black traces as the leftmost plot. 979 F: Example of one HN responding to pure tones and harmonic stacks played at three sound levels, 980 70dB (top row), 55dB (middle row), and 40dB (bottom row). Arrows indicate detected significant 981 facilitated response to the corresponding stimulus. 982 983 .CC-BY-NC-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted August 27, 2025. ; https://doi.org/10.1101/2025.08.26.672221doi: bioRxiv preprint 28 984 Fig. 2: Electrophysiology recording confirms existence of harmonic -sensitive neurons in 985 ACtx. 986 A: Example waveform of spikes from the electrophysiology recording. Grey lines show the 987 200 example traces aligned based on spikes. Red line show the average of the 200 aligned 988 traces. 989 B: Example plot of current source density (CSD) analysis for identifying L4 which shows current 990 sink after sound onset, and L2/3 which shows current source and is located above L4. 991 C: Example raster plots of a recorded cluster that show significantly increased counts of spikes 992 within 0.2s window after the sound onsets of harmonic stacks (bottom) and non -significantly 993 changed spike counts after sound onset. Gray area indicates the presence of sound (1s). 994 D: Distribution of clusters in a representative mouse that show significantly increased spike counts 995 to pure tones and/or harmonic stacks. Same criteria for classification as in vivo two -photon 996 imaging is applied to classify clusters as HN (red), PTN(blue), or BN(purple). Gray are clusters 997 that have no significant sound-evoked response to any sound. Yellow shaded area indicates L4. 998 E: Quantification of proportions of classified clusters in different cortical layers of the same mouse 999 in (D). 1000 1001 .CC-BY-NC-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted August 27, 2025. ; https://doi.org/10.1101/2025.08.26.672221doi: bioRxiv preprint 29 1002 Fig. 3: Distinct frequency response area (FRA) profiles of broadly tuned neurons (BNs) and 1003 pure-tone neurons (PTNs) in A1 L2/3. 1004 A: t-SNE visualization of k -means clustering applied to centered FRA profiles from sound -1005 responsive neurons (n = 3 animals, 1418 neurons). 1006 B: Same t-SNE plot as in (A), now colored by BN and PTN identity, illustrating the distribution 1007 of neuron subtypes across FRA-based clusters. 1008 C: Proportion of BNs and PTNs within each cluster, showing differential cluster occupancy by 1009 neuron subtype. Error bars indicates standard errors. *: p < 0.05. Two-sample t-test on proportions 1010 of BN versus PTN for each cluster: V, p = 0.4125; I, p = 0.4543; H, p = 0.1531; S1, p = 0.0445; 1011 S2, p = 0.0680; S3, p = 0.0249. 1012 D: Average centered FRA maps for each of the six clusters, revealing distinct spectral and intensity 1013 tuning profiles. Vertical bars indicate peak response frequency. 1014 .CC-BY-NC-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted August 27, 2025. ; https://doi.org/10.1101/2025.08.26.672221doi: bioRxiv preprint 30 1015 Figure 4: Harmonic neurons are similarly sparse in three imaged auditory subareas. 1016 A: Left: Proportions of BNs in A1 L4, A1 L2/3 and A2 L2/3. %BN: A1 L4, 28.50%±11.60%; A1 1017 L2/3, 34.80% ± 4.09%; A2 L2/3, 37.52% ± 5.42%. One-way ANOVA on the effect of subregions: 1018 F(2,26) = 3.17, p = 0.059. Middle and right: comparisons of BN proportions in females and males 1019 in subregions. A1 L4: Female, 27.54%±10.17%; Male, 29.92%±15.05%. One -way ANOVA on 1020 the effect of sex: F(1,8) = 0.0907, p = 0.77. A1 L2/3: Female, 34.44%±4.56%; Male, 1021 35.17%±3.96%. One-way ANOVA on the effect of sex: F(1,10) = 0.0877, p = 0.7732. A2 L2/3: 1022 Female, 37.22%±6.6%; Male, 38.26%±0.34%. One -way ANOVA on the effect of sex: F(1,5) = 1023 0.0443, p = 0.8416. Error bars show mean ± SEM. 1024 B: similar to ( A), but proportions of HNs. %HN: A1 L4, 35.54%±8.09%; A1 L2/3, 31.12% ± 1025 4.68%; A2 L2/3, 31.94% ± 7.83%. One-way ANOVA on the effect of subregions: F(2,26) = 1.24, 1026 p = 0.307. A1 L4: Female, 35.81%±5.62%; Male, 35.12%±11.97%. One -way ANOVA on the 1027 effect of sex: F(1,8) = 0.0157, p = 0.9035. A1 L2/3: Female, 30.86%±5.44%; Male, 31.37%±4.3%. 1028 One-way ANOVA on the effect of sex: F(1,10) = 0.0326, p = 0.8604. A2 L2/3: Female, 1029 32.89%±9.22%; Male, 29.58%±3.54%. One-way ANOVA on the effect of sex: F(1,5) = 0.2211, 1030 p = 6580. 1031 C: similar to (A), but proportions of PTNs. %PTN: A1 L4, 35.97%±8.49%; A1 L2/3, 34.08% ± 1032 4.70%; A2 L2/3, 30.54% ± 3.12%. One-way ANOVA on the effect of subregions: F(2,26) = 1.67, 1033 p = 0.21. A1 L4: Female, 36.64%±10.31%; Male, 34.96%±6.06%. One-way ANOVA on the effect 1034 of sex: F(1,8) = 0.0850, p = 0.7780. A1 L2/3: Female, 34.70% ±5.68%; Male, 33.46%±3.93%. 1035 One-way ANOVA on the effect of sex: F(1,10) = 0.1907, p = 0.6692. A2 L2/3: Female, 1036 29.89%±3.01%; Male, 32.15%±3.88%. One-way ANOVA on the effect of sex: F(1,5) = 0.7131, 1037 p = 0.4369. 1038 D: Proportions of neurons responding to harmonic stacks with varied spectral complexity in A1 1039 L4 (left), A1 L2/3 (middle), and A2 L2/3 (right). Two-way ANOVA: %neurons: Subareas, F(2,234) 1040 = 11.5, p = 1.72E -5; component numbers, F(8,234) = 1, p = 0.43; interactions between subareas 1041 .CC-BY-NC-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted August 27, 2025. ; https://doi.org/10.1101/2025.08.26.672221doi: bioRxiv preprint 31 and component numbers, F(16,234) = 0.61, p = 0.87. %BN: Subareas, F(2,234) = 19.52, p = 1.44E-1042 8; component numbers, F(8,234) = 0.31, p = 0.96; interactions, F(16, 234) = 0.31, p = 0.99. %HN: 1043 Subareas, F(2,234) = 4.99, p = 0.0076; component numbers , F(8,234) = 1.97, p = 0.051; 1044 interactions, F(16,234) = 1.21, p = 0.26. Post -hoc t -test with corrected p -values on 1045 subareas: %neurons: A1 L4 v.s. A1 L2/3, p = 0.75; A1 L2/3 v.s. A2 L2/3, p = 1.67E-4; A1 L4 v.s. 1046 A2 L2/3, p = 1.84E-5. %BN: A1 L4 v.s. A1 L2/3, p = 0.0028; A1 L2/3 v.s. A2 L2/3, p = 0.0014; 1047 A1 L4 v.s. A2 L2/3, p = 1.33E-9. %HN: A1 L4 v.s. A1 L2/3, p = 0.013; A1 L2/3 v.s. A2 L2/3, p 1048 = 0.99; A1 L4 v.s. A2 L2/3, p = 0.029. All data are represented as mean ± SEM. Symbols indicate 1049 significance with post-hoc t-test with Bonferroni correction. *: p<0.05, **: p<0.01, ***: p<0.001. 1050 * indicates comparison between A1 L2/3 and A2 L2/3. # indicates comparison between A1 L2/3 1051 and A1 L4. $ indicates comparison between A1 L4 and A2 L2/3. 1052 E: Response amplitude of HNs responding to the characteristic harmonic sound. Error bars show 1053 mean ± SEM. A1 L4: 6.95 ± 0.27; A1 L2/3: 8.21 ± 0.29; A2 L2/3: 6.42 ± 1.00. Wilcoxon rank -1054 sum test with Bonferroni-corrected p-values: A1 L4 v.s. A1 L2/3: p=0.012; A1 L2/3 v.s. A2 L2/3: 1055 p = 0.36; A1 L4 v.s. A2 L2/3: p = 0.056. 1056 1057 .CC-BY-NC-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted August 27, 2025. ; https://doi.org/10.1101/2025.08.26.672221doi: bioRxiv preprint 32 1058 Figure. 5: Most of HNs are sensitive to frequency shifts in harmonic stacks and faithfully 1059 respond to the harmonic stacks. 1060 A: Example of one two-tone harmonic and its spectrally shifted stacks (top) and example of ∆F/F 1061 of neurons only responding to the harmonic (blue) but not spectral shifts (orange), as well as shift-1062 tolerant harmonic neurons ( SHN) with facilitated response to both the harmonic and its spectral 1063 shifted versions but not to any pure tone frequencies that makes up the composite sounds. 1064 B: Prevalence of HNs and SHNs in three subareas. One-way ANOVA: A1 L4 (7 mice), F(1,16) = 1065 22.74, p = 4.58E-4; A1 L2/3 (6 mice), F(1,16) = 111.56, p = 9.61E -7; A2 L2/3 (9 mice), F(1,16) 1066 = 39.01, p = 1.17E-5. 1067 C: Distribution of SHN across spectral shifts within the HN population in A1 L4, A1 L2/3 and A2 1068 L2/3. One-way ANOVA: A1 L4 (7 mice), F(2,16) = 1.56, p = 0.24; A1 L2/3 (6 mice), F(2,16) = 1069 0.31, p = 0.74; A2 L2/3 (9 mice), F(2,16) = 0.47, p = 0.63. 1070 1071 .CC-BY-NC-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted August 27, 2025. ; https://doi.org/10.1101/2025.08.26.672221doi: bioRxiv preprint 33 1072 Figure 6: Non -linearity of response of HNs diminishes when harmonic becomes more 1073 spectrally complex. 1074 A: Schematic showing the linear reconstruction of the simulated output signals by taking the sum 1075 of gain-adjusted simulated input signals. Cases of high linearity (top) and low linearity (bottom) 1076 are shown. 1077 B: Example response to harmonic stacks and pure-tone components of a HN with best harmonic 1078 being 4kHz + 8kHz stack. 1079 C: Linear reconstruction of the example HN response to harmonic by using both the response to 1080 the pure tones 4kHz and 8kHz as variables (left), as well as by the response to each pure tone 1081 separately (right). Higher R 2 tells higher similarity between reconstructed harmonic response by 1082 component response and the original response to harmonic. 1083 .CC-BY-NC-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted August 27, 2025. ; https://doi.org/10.1101/2025.08.26.672221doi: bioRxiv preprint 34 D: Nonlinear reconstruction with Support Vector Regression (SVR) that accounts for nonlinearity 1084 in the relationship between three responses, which shows higher R2 score. 1085 E: Quantification on the similarity between reconstructed response to harmonic and original 1086 response in A1 L4, A1 L2/3, and A2 L2/3. Left: Similarity by using linear reconstruction improves 1087 as the harmonic becomes more spectrally complex, which is not shown in permuted response data 1088 while the same number of independent variables are used in the reconstruction. Three -way 1089 ANOVA (factors: subareas, harmonic stacks, permutation): Subareas, F(2,6406) = 0.0058, p = 1090 0.9942; harmonic stacks, F(8,6406) = 372.44, p = 0; permutation, F(1, 6406) = 24375.9, p = 0; 1091 Subareas x Harmonics, F(16,6406) = 0.52, p = 0.9404; Subareas x Permutation, F(2,6406) = 0.71, 1092 p = 0.49; Harmonics x Permutation, F(8,6406) = 147.0647, p = 5.8806E-228. 1093 F: The similarity between reconstructed response and original response when the reconstruction 1094 uses response to all components as variables versus response to single component. Two -way 1095 ANOVA (factors: subareas, harmonic stacks ): Subareas, F(2, 3195) = 0.7822, p = 0.4575; 1096 harmonic stacks, F(8, 3195) =167.9672, p = 0; interaction, F(16,3195) = 0.9670, p = 0.4907. G: 1097 Right: The similarity between reconstructed response and original response when SVR that 1098 accounts for more non-linearity in the data was used compared to linear reconstruction. Two-way 1099 ANOVA (factors: subareas, harmonic stacks): Subareas, F(2, 3195) = 0.54, p = 0.5822; harmonic 1100 stacks, F(8, 3195) =111.86, p = 0; interaction, F(16,3195) = 0.43, p = 0.9763. 1101 1102 .CC-BY-NC-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted August 27, 2025. ; https://doi.org/10.1101/2025.08.26.672221doi: bioRxiv preprint 35 1103 Fig. 7: BN-HN in A1 L4 has the highest functional connectivity. 1104 A: Example realistic neural responses of BNs at different pure -tone sounds and corresponding 1105 harmonic sounds. Case of harmonic response (4 kHz plus 8 kHz) and pure-tone responses (4 kHz 1106 and 8 kHz) are shown. 1107 B: Linear reconstruction of the example BN response to harmonic sound by using both the 1108 response to the pure tones as variables (left), as well as by the response to each pure tone separately 1109 (right). Higher R 2 indicates higher similarity between reconstructed harmonic response by 1110 component response and the original response to harmonic. 1111 C: Nonlinear reconstruction of BN responses to HN response by Support Vector Regression (SVR). 1112 D: Schematic showing the proposed micronetwork that can encode how HN responses to sounds 1113 with different components. Along the auditory pathway, PTN activates inhibitory neurons when 1114 pure-tone sound is played, further inhibits the HN (left). BN directly activates BN without any 1115 inhibition from PTN, which triggers the high responses of HN when harmonic is played. We next 1116 investigated the functional connectivity between BN and HN by applying Granger Causality 1117 (GC) analysis. 1118 E: Example field-of-view images showing the spatial location of PTNs, HNs and BNs in A1 L2/3. 1119 Left: PTNs are located heterogeneously across imaged A1 L2/3. Color indicates best frequency 1120 of the plotted neuron. Right: BN and HN are plotted on the same field-of-view. Larger dots indicate 1121 an example coactivated pair of HN and BN to one stimulus, in which the BN achieves the highest 1122 .CC-BY-NC-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted August 27, 2025. ; https://doi.org/10.1101/2025.08.26.672221doi: bioRxiv preprint 36 R2 reconstructing the response of HN to the stimulus. The black line indicates the distance between 1123 the HN and BN. 1124 F: ΔStrengths of significant GC links between all BNs within the same FOV (left Y-axis, blue) as 1125 an example HN plotted with the distances between each BN and the example HN (right Y -axis, 1126 red). The distances are normalized by the maximum distance among all BN-HN pairs for all HNs 1127 for each animal. 1128 G: Quantification of top 5% GC links between any BN-HN pair plotted against binned normalized 1129 distances in three subareas. A1 L2/3, n = 11 mice. A1 L4, n = 7 mice. A2 L2/3, n = 7 mice. Two 1130 separate Kruskal-Wallis tests revealed the significant main effect of subareas ( χ²(2) = 35.3033, p 1131 = 2.16E-8) and non-significant effect of distances (χ²(8) = 13.2486, p = 0.1036) on the Δstrength 1132 of top 5% GC links. Post-hoc Dunn’s test with Dunn-Sidak correction showed that A1 L4 has the 1133 highest functionally connected BN-HN pairs compared to A1 L2/3 (p = 1.03E-8) and A2 L2/3 (p 1134 = 5.71E-4). Spearman correlation performed on the GC links as the distances increase reveals 1135 significant trend of decrease of GC links in A1 L2/3 (ρ = -0.2170, p = 0.0388) and nonsignificance 1136 in A1 L4 (ρ = -0.1202, p = 0.3731) and A2 L2/3 (ρ = -0.2132, p = 0.1254). 1137 1138 1139 1140 .CC-BY-NC-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted August 27, 2025. ; https://doi.org/10.1101/2025.08.26.672221doi: bioRxiv preprint 37 1141 Figure 8: Neurons with offset-bias in A1 L4 has more linear integration. 1142 A: K-means clustering with varied numbers of clusters on the average sound-evoked response of 1143 HN to harmonic stacks. Each dot is the mean of 10 trials of sound-evoked response to one harmonic 1144 stack. Number of clusters is chosen using the elbow method for each subarea. In A1 L4, n = 2141 1145 average traces from 1565 neurons. In A1 L2/3, n = 4811 traces from 3167 neurons. In A2 L2/3, n 1146 = 1002 average traces from 631 neurons. 1147 B: K-means clustering results that show distinct response types as offset response (magenta), onset 1148 response (orange). 1149 A Centroids of clusters C OBI of %HNs OBI of %BNs OBI of %PTNs On Off R2 Linear G Off On H -1 0 1 F 2 4 6 8 10 -0.3 OBI v.s. Complexity Mean OBI Number of frequencies in harmonic stacks % cells A1 L4 A1 L2/3 A2 L2/3 R2 Linear % cells D B PCA with k-means Clustering A1 L4 A1 L2/3 A2 L2/3 A1 L4 A1 L2/3 A2 L2/3 PC 1 PC 2 -0.2 -0.1 0 0.1 Onset Offset Response types: 0 100 E -1 0 1 -1 0 1 A1 L4 A1 L2/3 A2 L2/3 -1 0 1 A1 L2/3 vs A2 L2/3: *** A1 L4 vs A1 L2/3: *** Medians A1 L4 vs A2 L2/3: ** A1 L4 vs A1 L2/3: ** ******** On-Hn Off-Hn 0 1 0 100 0 1 0 100 0 1 0 100 n.s. ** n.s.Medians * n.s. n.s. 0 1 -1 0 1 0 1 -1 0 1 0 1 OBI .CC-BY-NC-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted August 27, 2025. ; https://doi.org/10.1101/2025.08.26.672221doi: bioRxiv preprint 38 C: Cumulative probability of OBI of HNs. On the x -axis, -1 shows total onset biased, 1 shows 1150 total offset biased. Y-axis shows the cumulative probability of the OBIs. Dotted line shows median 1151 of OBIs in each subarea. Kruskal -Wallis test is performed due to the non -normal distribution of 1152 data. χ²(2) = 0.2177, p = 0. 8969. Dunn’s post -hoc test with Bonferroni -corrected p -values on 1153 subareas: A1 L4 v.s. A1 L2/3, p = 1; A1 L2/3 v.s. A2 L2/3, p = 0. 9539; A1 L4 v.s. A2 L2/3: p = 1154 0.9755. Two-sample Kolmogorov -Smirnov test is performed on paired curves with post -hoc 1155 Bonferroni correction. Reported p -values are corrected. A1 L4 v .s. A1 L2/3, p = 0.2687; A1 L4 1156 v.s. A2 L2/3, p = 0.2857; A1 L2/3 v.s. A2 L2/3, p = 1. D: Similar to C but for BNs in three subareas. 1157 Kruskal-Wallis test is performed due to the non -normal distribution of data. χ²(2) = 35.3030, p = 1158 2.16E-8. Dunn’s post-hoc test with Bonferroni-corrected p-values on subareas: A1 L4 v.s. A1 L2/3, 1159 p = 1.45E-7; A1 L2/3 v.s. A2 L2/3, p = 9.75E-4; A1 L4 v.s. A2 L2/3: p = 0. 9441. Cumulative 1160 distribution plot, two sample Kolmogorov-Smirnov test: A1 L4 v.s. A1 L2/3, p = 2.96E-17; A1 1161 L4 v.s. A2 L2/3, p = 0.0734; A1 L2/3 v.s. A2 L2/3, p = 7.55E-5. 1162 E: Similar to C but for PTNs in three subareas . Kruskal-Wallis test is performed due to the non -1163 normal distribution of data. χ²(2) = 10.8272, p = 0.0045. Dunn’s post-hoc test with Bonferroni -1164 corrected p-values on subareas: A1 L4 v.s. A1 L2/3, p = 0.2101; A1 L2/3 v.s. A2 L2/3, p =0.0554; 1165 A1 L4 v.s. A2 L2/3: p = 0.0033. Cumulative distribution plot, two sample Kolmogorov-Smirnov 1166 test: A1 L4 v.s. A1 L2/3, p = 0.0093; A1 L4 v.s. A2 L2/3, p = 0.0752; A1 L2/3 v.s. A2 L2/3, p = 1167 0.0034. 1168 F: OBI of HNs that respond to harmonic stacks with varied spectral complexity. Two -way 1169 ANOVA: Subareas: F(2,6144) = 0.73, p = 0.48; Harmonics: F(8,6144) = 1.96, p = 0.048; 1170 interaction: F(16, 6144) = 0.98, p = 0.48. Post -hoc t -test with corrected p -values show no 1171 significant among OBIs of HNs responding to different harmonic stacks. Solid line indicates the 1172 mean and the shaded area indicates the SEM. 1173 G: Scatter plots show linearity of response and OBI of every HN to the best harmonic sound in A1 1174 L4, A1 L2/3 and A2 L2/3. The response linearity of HN with higher preference to onset-response 1175 (shaded by orange) or to higher offset-response (shaded by purple) are selected and plotted. 1176 H: Cumulative probability of R2 of linearity reconstruction on HNs response to harmonic sound 1177 by the response to pure -tone components in A1 L4, A1 L2/3 and A2 L2/3. Dotted line indicates 1178 the median of the distribution. Two-sample Kolmogorov-Smirnov test on the curves of on-HN and 1179 off-HN: A1 L4, p = 0.0667, A1 L2/3, p = 0.0091; A2 L2/3, p = 0.3650. Ranksum test on the 1180 medians of off-HN and on-HN: A1 L4, p = 0.0344; A1 L2/3, p = 0.2884; A2 L2/3, p = 0.3095 1181 1182 .CC-BY-NC-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted August 27, 2025. ; https://doi.org/10.1101/2025.08.26.672221doi: bioRxiv preprint 39 1183 Figure 9: Hierarchical transformation of pair -wise signal correlation between coactivated 1184 HN pairs. 1185 A: Means of correlation coefficients (left) of pair-wise signal correlation between coactivated HNs 1186 responding to the activating harmonic stacks with varied numbers of components in A1 L4 (gray), 1187 A1 L2/3 (red) and A2 L2/3 (blue) , as well as scatter plot (right) that shows the average signal 1188 correlation coefficients across different harmonic complexes. Each data point represents the mean 1189 coefficients of one subject. Two-way ANOVA on the left plot: Subareas, F(2,233) = 3.3990, p = 1190 0.0351; harmonics, F(8, 233) = 1.5078, p = 0.1552; interactions, F(16, 233) = 0.8349, p = 0.6451. 1191 Post-hoc t-test with Tukey-Kramer correction on the scatter plots: A1 L4 v.s. A1 L2/3: p = 0.1552; 1192 A1 L4 v.s. A2 L2/3: p = 0.0280; A1 L2/3 v.s. A2 L2/3: p = 0.4656. 1193 B: Cumulative probability of pair-wise signal correlation coefficients in (A) between coactivated 1194 HNs in A1 L4 (gray), A1 L2/3 (red) and A2 L2/3 (blue ). Two-sample Kolmogorov-Smirnov test 1195 on cumulative distribution curves with Bonferroni-corrected p-values: A1 L4 v.s. A1 L2/3: p = 1196 1.1179E-53; A1 L4 v.s. A2 L2/3: p = 6.6488E-30; A1 L2/3 v.s. A2 L2/3: p = 5.0582E-6. 1197 1198 .CC-BY-NC-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted August 27, 2025. ; https://doi.org/10.1101/2025.08.26.672221doi: bioRxiv preprint 40 1199 Figure 10: Noise correlation is the lowest in A1 L4, and similar in L2/3 of A1 and A2. 1200 A: Cumulative probability of the noise correlation coefficients of paired-neurons with significant 1201 facilitative response to any sound in three areas. Kolmogorov-Smirnov test for multiple groups 1202 .CC-BY-NC-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted August 27, 2025. ; https://doi.org/10.1101/2025.08.26.672221doi: bioRxiv preprint 41 with Bonferroni-corrected p-values: A1 L4 v.s. A1 L2/3: p = 4.52E-233; A1 L4 v.s. A2 L2/3: p = 1203 2.93E-100; A1 L2/3 v.s. A2 L2/3: p = 1.78E-11. 1204 B: Positive (left) and negative (right) noise correlation coefficients between pairs of sound-1205 responsive neurons in A1 L4 (gray), A1 L2/3 (red) or A2 L2/3 (blue) when different harmonic 1206 sound is present. Smaller box charts as insets shows the average noise correlation coefficients 1207 across sounds. Each data point is one animal in both plots. Positive correlation: Two-way ANOVA: 1208 Subareas, F (2,23 2) = 38.5750, p = 3.44E-15; harmonics, F (8, 23 2) = 0.6330, p = 0. 7497; 1209 interactions, F (16, 23 2) = 0.5479, p = 0. 9190. Post-hoc t-test with Tukey-Kramer-corrected p-1210 values: A1 L4 v.s. A1 L2/3, p = 6.57E-7; A1 L4 v.s. A2 L2/3, p = 0; A1 L2/3 v.s. A2 L2/3, p = 1211 3.58E-5. Negative correlation: Two-way ANOVA: Subareas, F (2,232) = 30.3274, p = 1.99E-12; 1212 harmonics, F (8, 232) = 1.1879, p = 0.3077; interactions, F (16, 232) = 0.8270, p = 0.6542. Post-1213 hoc t-test with Tukey-Kramer-corrected p-values: A1 L4 v.s. A1 L2/3, p = 1.2E-4; A1 L4 v.s. A2 1214 L2/3, p = 0; A1 L2/3 v.s. A2 L2/3, p = 3.54E-5. 1215 C: Cumulative probability of the noise correlation coefficients in three areas with presence of any 1216 harmonic sound. Kolmogorov -Smirnov test for multiple groups with Bonferroni -corrected p -1217 values: A1 L4 v.s. A1 L2/3: p = 1.9493E-188; A1 L4 v.s. A2 L2/3: p = 7.3765E-48; A1 L2/3 v.s. 1218 A2 L2/3: p = 0.2990. 1219 D: Positive (left) and negative (right) noise correlation coefficients between pairs of HNs in A1 1220 L4 (gray), A1 L2/3 (red) or A2 L2/3 (blue) when different harmonic sound is present. Smaller box 1221 charts as insets shows the average noise correlation coefficients across sounds. Each data point is 1222 one animal in both plots. Positive correlation: Two-way ANOVA: Subareas, F (2,234) = 24.8330, 1223 p = 1.6588E-10; harmonics, F (8, 234) = 2.0914, p = 0.0374; interactions, F (16, 234) = 1.2075, p 1224 = 0.2629. Post-hoc t-test with Tukey-Kramer-corrected p-values: A1 L4 v.s. A1 L2/3, p = 1.3102E-1225 5; A1 L4 v.s. A2 L2/3, p = 0; A1 L2/3 v.s. A2 L2/3, p = 7.622E-3. Negative correlation: Two-way 1226 ANOVA: Subareas, F (2,234) = 13.0619, p = 4.1897E -6; harmonics, F (8, 234) = 2.1196, p = 1227 0.0348; interactions, F (16, 234) = 1.0262, p = 0.4296. Post -hoc t -test with Tukey-Kramer-1228 corrected p-values: A1 L4 v.s. A1 L2/3, p = 0.03349; A1 L4 v.s. A2 L2/3, p = 9.4061E-7; A1 L2/3 1229 v.s. A2 L2/3, p = 6.533E-3. 1230 E: Similar to (C), but between pairs of HN and PTN. Kolmogorov -Smirnov test for multiple 1231 groups with Tukey-Kramer-corrected p-values: A1 L4 v.s. A1 L2/3: p = 1.0340E-239; A1 L4 v.s. 1232 A2 L2/3: p = 1.1758E-77; A1 L2/3 v.s. A2 L2/3: p = 8.2345E-5. 1233 F: Similar to (D) but between pairs of HN and PTN. Positive correlation: Two -way ANOVA: 1234 Subareas, F (2,234) = 45.7036, p = 1.7549E -17; harmonics, F (8, 234) = 0.9572, p = 0.4703; 1235 interactions, F (16, 234) = 0.7702, p = 0.7185. Post -hoc t-test with Tukey-Kramer-corrected p-1236 values: A1 L4 v.s. A1 L2/3, p = 0; A1 L4 v.s. A2 L2/3, p = 0; A1 L2/3 v.s. A2 L2/3, p = 3.0922E-1237 5. Negative correlation: Two -way ANOVA: Subareas, F (2,234) = 23.9604, p = 3.4150E -10; 1238 harmonics, F (8, 234) = 2.2323, p = 0.0259; interactions, F (16, 234) = 0.9387, p = 0.5256. Post -1239 hoc t-test with Tukey-Kramer-corrected p-values: A1 L4 v.s. A1 L2/3, p = 3.3942E-4; A1 L4 v.s. 1240 A2 L2/3, p = 0; A1 L2/3 v.s. A2 L2/3, p = 7.1524E-4. 1241 .CC-BY-NC-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted August 27, 2025. ; https://doi.org/10.1101/2025.08.26.672221doi: bioRxiv preprint 42 G: Similar to (C), but between pairs of HN and BN. Kolmogorov-Smirnov test for multiple groups 1242 with Tukey-Kramer-corrected p-values: A1 L4 v.s. A1 L2/3: p = 6.6985E-8; A1 L4 v.s. A2 L2/3: 1243 p = 0.0818; A1 L2/3 v.s. A2 L2/3: p = 0.5404. 1244 H: Similar to (D), but between pairs of HN and BN. Positive correlation: Two -way ANOVA: 1245 Subareas, F (2,229) = 9.8325, p = 8.0033E -5; harmonics, F (8, 229) = 0.5160, p = 0.8439; 1246 interactions, F (16, 229) = 0.9143, p = 0.5535. Post -hoc t-test with Tukey-Kramer-corrected p-1247 values: A1 L4 v.s. A1 L2/3, p = 0.0230; A1 L4 v.s. A2 L2/3, p = 3.2149E-5; A1 L2/3 v.s. A2 L2/3, 1248 p = 0.06987. Negative correlation: Two-way ANOVA: Subareas, F (2, 229) = 3.6435, p = 0.0277; 1249 harmonics, F (8, 229) = 0.6496, p = 0.7354; interactions, F (16, 229) = 0.4749, p = 0.9573. Post -1250 hoc t-test with Tukey-Kramer-corrected p-values: A1 L4 v.s. A1 L2/3, p = 0.2106; A1 L4 v.s. A2 1251 L2/3, p = 0.0211; A1 L2/3 v.s. A2 L2/3, p = 0.4225. Whiskers in larger box charts represent SEM. 1252 Whiskers in smaller box charts within the larger charts represent standard deviation. 1253 1254 .CC-BY-NC-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted August 27, 2025. ; https://doi.org/10.1101/2025.08.26.672221doi: bioRxiv preprint