Synchronized LFP rhythmicity in the social brain reflects the context of social encounters

Mammalian social behavior is highly context-sensitive. Yet, little is known about the mechanisms that modulate social behavior according to its context. Recent studies have revealed a network of mostly limbic brain regions which regulates social behavior. We hypothesize that coherent theta and gamma rhythms reflect the organization of this network into functional sub-networks in a context-dependent manner. To test this concept, we simultaneously record local field potential (LFP) from multiple social brain regions in adult male mice performing three social discrimination tasks. While LFP rhythmicity across all tasks is dominated by a global internal state, the pattern of theta coherence between the various regions reflect the behavioral task more than other variables. Moreover, Granger causality analysis implicate the ventral dentate gyrus as a main player in coordinating the context-specific rhythmic activity. Thus, our results suggest that the pattern of coordinated rhythmic activity within the network reflects the subject’s social context.


Introduction
state preference (EsP) (Fig. 1E) and sex preference (SxP) (Fig 1I) tasks [46]. (See timeline in Fig. 100 S1B). Each task comprised a five min-long baseline period involving empty chambers located at 101 opposite corners of the arena, followed by a five min-long encounter period, when a distinct 102 stimulus was introduced into each chamber [42]. Mice performing the SP task tended to interact 103 with social stimuli (conspecifics) for significantly more time than with objects throughout the 104 encounter period (Fig. 1B-D). Similarly, mice performing the EsP task preferred to interact with 105 socially isolated rather than group-housed stimuli (Fig. 1E-H), while mice performing the SxP task 106 tended to interact more with female than with male stimuli (Fig 1I-L). Thus, in each task, the 107 subjects discriminated between a preferred and a less-preferred stimulus. Importantly, the same 108 type of stimulus (a group-housed male mouse) that was the preferred stimulus in the SP task was 109 the less-preferred stimulus in the other two tasks. Therefore, this set of tasks allowed us to analyze 110 brain-wide neural activity patterns in association with either the type of stimulus (i.e., a group-111 housed male vs. an object/group-housed female/isolated male) or its valence (i.e., preferred vs. 112 less-preferred), or the social context (i.e., SP, EsP or SxP task). It should be noted, that in our 113 hands ICR female mice do not discriminate between group-housed and isolated stimuli, hence we 114 conducted this study using male subjects only. 115 We further compared multiple behavioral parameters across the various tasks. There were no 116 significant differences between the tasks in terms of total time dedicated to stimuli investigation 117 (Fig. 1M), the total number of transitions made by the subjects between the two stimuli ( Fig. 1N) 118 or the distance traveled by the subjects during a task (Fig. 1O). Nonetheless, the preference 119 (reflected by the relative discrimination index, RDI) between the two stimuli was lower in the EsP 120 task, as compared to the SP task (Fig. 1P). Overall, subject behavior was similar across the various 121 tasks. 124 The power spectral density (PSD) profiles of LFP signals recorded during the encounter period 125 ( Fig. 2A-B), differed among the various tasks performed by the same subject in a brain region-126 specific manner (Fig. S1C). For quantitative comparison, we calculated the mean theta (θP) and 127 gamma (γP) power separately for the baseline and encounter periods of each task for each brain 128 region. While the mean power during baseline across all regions did not significantly differ 129 between the tasks (Fig. 2C-D), the change in power during the encounter for both theta (∆θP) and 130 6 gamma (∆γP) rhythms was highest for the SP task, compared to the other two (Fig 2E-F). Thus, 131 despite the generally similar behavior exhibited by subjects across the tasks (Fig. 1), their system-132 level brain LFP signals significantly and consistently differed in power across tasks. Specifically, 133 despite involving only one social stimulus, the SP task induced the strongest LFP rhythmicity. 134 When considering each brain region separately, we found that in almost all cases, the mean power  To examine the temporal dynamics of LFP rhythmicity during the various tasks, we plotted ∆θP 143 and ∆γP as a function of time for each task and brain region. In accordance with our previous study 144 in rats [32], we found that both ∆θP and ∆γP began to rise several seconds before stimulus 145 introduction, peaked within 20 s from this point and gradually declined in all brain regions and 146 tasks (Fig. S2). Thus, the dynamics of LFP rhythmicity across the session were similar among the 147 various tasks and did not seem to reflect the behavioral dynamics (shown in Fig. 1D, H, L). We 148 also found no significant correlation (Pearson's, p>0.05) between the mean power change and 149 speed of the subject during any task for either ∆θP or ∆γP ( Fig. S3A-F). 150 Overall, these results suggest that theta and gamma rhythmicity during the encounter period are 151 driven by an internal brain state that shows similar temporal dynamics across tasks, independent 152 of the behavioral dynamics.  156 Despite the uniform dynamics of LFP rhythmicity in the social brain during the encounter period, 157 it may be differentially modulated during specific behavioral events, such as stimulus 158 investigation. We thus examined the possibility that during investigation bouts, ∆θP and ∆γP 159 (henceforth termed ∆ θP and ∆ γP) differ between the various stimuli and tasks. As exemplified by 160 signals recorded from the amygdalo-hippocampal area (AhiAl) shown in Fig. 3A-F, a Z-score 161 7 analysis revealed elevation in theta power during investigation bouts towards social but not the 162 object stimuli in the SP task, during investigation of both stimulus types in the EsP task and during 163 investigation of female but not male stimuli in the SxP task. Very similar results were obtained for 164 gamma power (Fig. S4A-F). This analysis thus suggests a bias in the response towards specific 165 stimuli, in a task-specific manner. Interestingly, even though the same type of stimulus (a group-166 housed male) was used in all tasks, this stimulus elicited a clear elevation in LFP rhythmicity only 167 during the SP and EsP tasks, but not during the SxP task. These results suggest that at least for the 168 AhiAl, the change in LFP power was not dictated by either the stimulus type nor by its valence.

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To explore the stimulus-specific bias in LFP power change during each task, we calculated the 170 difference in ∆ θP and ∆ γP between the two stimuli, separately for each brain region. Since a 171 possible bias of LFP rhythmicity of a given brain region may be associated with a behavioral bias 172 towards a specific stimulus, we examined the correlation between the two variables. To this end, 173 we correlated the ∆ θP bias (preferred minus less-preferred) to the RDI values of each task. We 174 found a negative correlation in a specific set of brain regions (i.e, extended amygdala (EA) and 175 lateral septum (LS),) only for the SP task. In contrast, a positive correlation was found in a distinct 176 set of brain regions (nucleus accumbens shell (AcbSh), AhiAl, ventral pallidum (VP) and 177 dorsomedial hypothalamic nucleus (DMD)) during the EsP and SxP tasks. Specifically, the VP 178 exhibited a very strong and highly significant linear correlation with RDI values during both the 179 EsP and SxP tasks ( Fig 3G). These results suggest a link between stimulus-specific bias in ∆ θP and 180 behavioral preference in a task-specific manner.

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To further explore this link, we plotted ∆ θP bias across all tasks on a 3D plot, separately for each 182 brain region. We found that almost no region showed bias towards the object stimulus in the SP 183 task, with the various regions being equally distributed between the two stimuli in the EsP and SxP 184 tasks (Fig. 4B). In contrast, when ∆ γP was analyzed (Fig. 4C), we observed an opposite picture.

185
Here, almost all brain regions exhibited stronger responses to the grouped and male stimuli in the 186 EsP and SxP tasks, yet were rather equally distributed between the two stimuli in the SP task.

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Thus, for ∆ γP, most brain regions (14/18) were equally divided between those biased towards less-188 preferred stimuli (i.e., object+grouped+male) and those biased towards the type of stimulus used 189 in all three tasks (i.e, social+grouped+male). The probability of such an arrangement to occur by 190 chance is smaller than 0.001 (1-binomial test) for each of these two groups. The results thus suggest 191 that a bias in gamma power is mostly associated with the characteristics (i.e, valence or type) of 192 8 the stimulus. They also generally demonstrate opposite stimulus-dependent bias patterns between 193 the theta and gamma rhythms during stimulus investigation, in contrast to their significant 194 correlation when measured during the entire encounter period (Fig. 2E-G). This implies the 195 existence of an independent active state in the social brain during stimulus investigation. Notably,196 of all brain regions considered, the vDG stood out as the only region biased to the combination of 197 object/isolated/female stimuli. Moreover, this region showed an strong bias for all these stimuli in 198 both ∆ θP and ∆ γP ( Fig. 3H-I). These results suggest a unique position for the vDG in the social 199 brain, as also supported by results presented below. between all pairs of brain regions (99 pairs with ≥5 sessions from at least two subjects in all three 208 tasks, see Table S2)) was similar across all tasks (Fig. 4A). Thus, the subjects displayed similar 209 global brain synchronization while exploring the arena without stimuli, in all tasks. However, the 210 change in theta coherence (∆θCo) during the encounter period differed significantly between tasks.

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While almost all pairs of brain regions exhibited increased θCo during the SP task, we observed 212 significantly milder increases during EsP and SxP tasks, with many paired regions showing 213 reduced θCo (Fig. 4B, E-G). Similar relationships among tasks were observed for changes in 214 gamma coherence (γCo), although here the general tendency was one of decreased coherence 215 during the encounter period ( Fig. 4C-G). Notably, there was almost no correlation between the 216 baseline period coherence and the change in coherence during the encounter period for any task 217 (apart a weak correlation for SP gamma coherence; r=-0.21, p=0.0111; not shown). This suggests 218 that the encounter-induced coherence change represents an internal state, independent of the 219 resting state. Finally, when calculating the correlations in ∆θCo across all paired regions between 220 the various tasks, we found a statistically significant high correlation between SxP and EsP, while 221 no correlation was found between SP and SxP. A milder but significant correlation was found 222 between SP and EsP (Fig. 4H). In contrast, all correlations were found significant for ∆γCo. These 223 9 results suggest a gradual shift from SP to EsP and to SxP when in ∆θCo brain pattern is measured 224 across the whole encounter. 225 We, therefore, examined the encounter-induced coherence changes for each brain region 226 separately, by comparing the change in coherence between a given region and all other regions 227 across tasks in the theta (Fig. S5A) and gamma (Fig. S5B) bands. We found that differences 228 between tasks were brain-region specific, with most (13/18) regions showing significant 229 differences (after FDR corrections) between at least two tasks in ∆θCo and one third (6/18) 230 showing differences in ∆γCo. Notably, in all cases, we found significantly higher coherence 231 changes during the SP task, as compared to at least one task, and in many cases, to both other tasks.

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Thus, a subset of the recorded brain regions displayed differential changes in theta or gamma 233 coherence among the social contexts, with this change being majorly increased in the SP task, as 234 compared to the other two tasks. 237 To explore possible modulation of LFP coherence during investigation bouts, we calculated the 238 mean ∆ θCo between each pair of brain regions during all investigation bouts towards a given 239 stimulus, similarly to how we analyzed the power changes (Fig. 3). Since data had been collected 240 for a large number of brain-region pairs (99 pairs), we focused on pairs showing a mean coherence 241 change that crossed a cutoff value ± 1.5*standard deviation (SD) for each stimulus (about 20% of 242 the pairs). When plotting the bias in ∆ θCo and ∆ γCo between the two stimuli in each task on a 3D . Surprisingly, the three stimuli of the same type (i.e, social, grouped, male) did not share even 247 a single pair of brain regions that passed the ∆ θCo cutoff value. Similarly, the preferred stimuli 248 (i.e, social, isolated, female) also did not share even a single pair among them. In contrast, multiple 249 pairs of brain regions shared similar changes in theta coherence between both stimuli used in each for both male and female stimuli. Similar results were observed for ∆ γCo (Fig. S6C). Thus, changes 254 in coherence during stimulus investigation seem to be dictated by the social context rather than by 255 stimulus characteristics, such as its type or valence.

256
For quantitative examination of this possibility, we calculated the correlation across all brain 257 regions for either ∆ θCo (Fig. 5B) and ∆ γCo (Fig. 5C), between pairs of stimuli which share common 258 context, type or valence. We found strong and highly significant correlations between all pairs of 259 stimuli used in the same task (sharing context). In contrast, among the three stimuli of the same 260 type, only grouped (ESP) and male (SxP) showed significant correlation. Similarly, among 261 preferred stimuli, only isolated (EsP) and female (SxP) showed significant correlations. Notably, 262 in both of these cases the correlation was weaker than the correlation between any pair of stimuli 263 sharing the same context (Fig. 5B). Similar results were found for ∆ γCo (Fig. 5C). Thus, coherence 264 changes during stimulus investigation in both bands had the strongest association with the context 265 of the social interaction, relative to any characteristic of the stimulus.

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Finally, we employed a Decision trees (multi-class Random forest) classifier to examine if ∆ θCo 267 and ∆ γCo contain information which may be used to discriminate between the various contexts or 268 stimuli. First, we validated that the model achieved good (~60%) and significant accuracy in 269 predicting the social stimulus vs. object in the SP task using either ∆ θCo or ∆ γCo. Notably, the 270 classification of the object vs. social was not accurate, suggesting that the presence of the social 271 stimulus (social context) mask the object classification ( Fig. S7A-B). Then, we used the same 272 model for predicting the social context (SP, EsP and SxP) and found that using ∆ θCo (Fig. 5D), 273 but not ∆ γCo (Fig. 5E), allowed the model to predict the right context better than any other context, 274 and that this prediction was the only one achieving more than a chance level (33.3%) accuracy 275 (although only SxP classification was statistically significant). In contrast, the same model worked

Analysis of Granger causality suggests that specific brain regions serve as hubs
The coherent LFP rhythmicity in the social brain can be dominated by specific regions serving as 286 hubs, thereby preceding other regions in terms of rhythmic neural activity. To identify hub 287 candidate regions, we first selected brain regions which are statistically over-represented (see 288 Methods) among pairs of regions exhibiting strong (mean ± 1.5*SD) bias in any task, separately 289 for ∆ θCo (Fig. 6A) and ∆ γCo (Fig. 6B). We then examined the dependence of LFP rhythmicity of  Interestingly, theta GC changes from vDG to AhiAl increased during a SP task but decreased 298 during a EsP task, while theta GC changes from PrL to vDG decreased during both EsP and SxP 299 tasks. These results suggest that these brain regions dictate LFP rhythmicity in the social brain 300 during social investigation.

301
To further explore this possibility, we have calculated the difference in GC change during 302 encounter between the two directions (from area 1 to area 2 and vice versa), for all couples of brain 303 regions across all tasks and rhythms ( Fig. S8A-C). After applying FDR correction for multiple 304 comparisons, we found only vDG to LS, for gamma rhythmicity of the EsP task, which was 305 significantly higher in the vDG-LS direction than in the opposite direction (Fig. S8D).

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Context-specific synchronization of LFP rhythmicity in the ventral dentate gyrus with precise 308 behavioral events 309 To further examine the candidate hub regions, we exploited our ability to determine the exact 310 timing of each investigation bout to quantify the synchronized modulation of LFP rhythmicity, 311 relative to these events. Thus, we compared the modulation of theta and gamma power in all 312 regions associated with significant GC changes ( Fig. 6) relative to a defined battery of specific 313 behavioral events (Fig. 7A). These events included the beginning and end of investigation bouts 314 towards specific stimuli, as well as transitions between stimuli. We found a main effect in ANOVA 315 for multiple events, although in most cases, none of the regions showed significance in post-hoc 316 12 analysis (see Table S3). One region, the vDG, did, however, exhibit significant differences 317 between stimuli. The vDG displayed significantly higher theta and gamma powers at the end of 318 investigation bouts of social stimuli, as compared to object stimuli, specifically in the SP task (Fig.   319 7B-G and S7A-B). The same region also exhibited decreased theta and gamma powers at the 320 beginning of transitions from isolated to grouped stimuli, as compared to non-transitional bouts,  In this study, we used multi-site electrophysiological recordings from the murine social brain to 328 seek system-level neural correlates of three distinct aspects of social interaction, namely, the type 329 of the social stimulus, its relative valence (preference) and the social context. To distinguish 330 between these three aspects, we relied on three social discrimination tasks (i.e., SP, EsP, and SxP) 331 in which male mice clearly prefer one of two distinct stimuli. This design enabled us to employ 332 the same type of social stimulus, a novel group-housed male mouse, in all three tasks, with this 333 stimulus being the preferred stimulus in the SP task and the less-preferred stimulus in the other 334 two tasks. Importantly, all three tasks took place in the same experimental arena, which enables 335 uniform interactions between the subject and the stimuli, i.e., stimulus investigation by the subject 336 [42]. Consequently, as much as we could measure, subject behavior was almost identical in all 337 three tasks. Therefore, behavioral differences cannot explain the significant differences in the 338 patterns of rhythmic LFP signals observed among the different tasks. 339 We analyzed LFP signals at three different time resolutions, specifically, across the whole session, 340 during stimulus investigation, and during specific behavioral events, such as at the beginning and 341 end of investigation bouts. When analyzing the power of both theta and gamma rhythms over an 342 entire session, some aspects seemed to be dictated by a general internal state. In accordance with 343 previous studies by us and others [31, 32], virtually all brain regions exhibited higher level of theta 344 and gamma power during the encounter period, as compared to the baseline period. Our 345 observation that the level of enhanced power was both brain region-and task-specific strongly 346 suggests that the power elevation was not caused by enhanced electrical noise or any other artifact  This state did not seem to be caused by subject movement, as we found no correlation between 356 subject speed and changes in theta or gamma power for any brain region.

357
While the dynamics of the internal state seemed to be similar across the distinct contexts, other 358 aspects of the general (session-wise) changes in theta and gamma power exhibited context-specific 359 characteristics. For example, the general changes in both power and coherence were highest in the 360 SP task, suggesting a higher level of the internal state. Assuming that the general state reflects 361 social motivation, these results are somewhat surprising, given how the SP task involved only one 362 social stimulus and reasoning that among the various stimuli tested, the female would be the most 363 attractive to the male subjects. Our interpretation is that the SP task is simpler in terms of social 364 motivation, as it requires the animal to choose between an inanimate object and a conspecific, 365 while the other two tasks involve two social stimuli, thereby presenting the subject with a more 366 challenging dilemma. The higher confidence of the subject during the SP task is in accord with the 367 simpler pattern of theta coherence changes observed during this task (seen as a general increase 368 across almost all brain region pairs). Overall, these results suggest that the internal state level may 369 distinguish between some contexts, which is in accordance with the ability of the Random forest 370 model to predict only the SP context based on the arousal-induced LFP power. Nevertheless, the 371 changes in theta and gamma power across the encounter period did not differ between the EsP and 372 SxP tasks, and thus cannot be the sole basis for the context-specific responses to social cues.

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Notably, a recent paper [22] that employed similar recordings during the SP test, used the power, 374 coherence and GC data (termed Electome network) from various regions of the social brain in a 375 machine-learning model to discriminate between social and object investigation. In accordance 376 with our results, this study reported that the model's precision was higher for the social than for 377 14 the object, thus suggesting that the social stimulus masks the object, which may be attributed to 378 the context effect.

379
Analysis of the power change, specifically during stimulus investigation, yielded a different 380 picture than did session-wide analysis. First, we found no correlation between theta and gamma 381 power changes during these periods, suggesting a distinct state of active sensing which 382 characterizes stimulus investigation. Moreover, although both theta and gamma power changes 383 across brain regions showed bias to specific combinations of stimuli, they did so in distinct 384 manners. While theta power was biased towards the preferred stimulus in the SP task, with almost 385 no region (other than hippocampal areas) showing a higher level during investigation of object 386 stimuli, the gamma power was clearly biased towards the less-preferred stimuli in the EsP and SxP 387 tasks (grouped and male stimuli), while showing a mixed preference between stimuli in the SP 388 task. Thus, as related to gamma power, the social brain may be divided between regions associated 389 with the valence of stimulus (biased towards less-preferred stimuli) and brain regions associated 390 with the type of stimulus. It should be noted that theta rhythmicity is thought to reflect top-down 391 processes, such as arousal and attention, which are regulated by brain wide-active neuromodulators  In accordance with our hypothesis, that coherent theta and gamma rhythms couple various regions 397 of the social brain in a social context-dependent manner, we found that the correlation in the 398 coherence change during stimulus investigation was strongest between the two stimuli in each 399 task, even the EsP and SxP tasks. In contrast, there were weaker correlations, if any, among the 400 three stimuli of the same type (social, grouped, male) or the preferred stimuli (social, isolated, 401 female). The fact that the same correlation pattern was observed for the coherence of both theta 402 and gamma rhythms supports the validity and significance of the observation. Moreover, using a 403 Decision Tree classifier, we demonstrated that the theta coherence between the recorded areas 404 could generate predictions regarding the social context, but not the specific stimulus, which are 405 accurate above the chance level. The limited accuracy of the model may be attributed to the 406 restricted number of recorded regions. Thus, we expect that a more comprehensive analysis of the 407 coherence within the social brain will be able to generate highly accurate prediction of the social 408 context. Moreover, GC analysis, representing causal time relationships between various brain 409 regions, also suggests distinct patterns of changes across the various contexts. Altogether, these 410 results are in accordance with the idea that the social brain processes information during stimulus 411 investigation in a context-dependent manner dictated by the context-dependent pattern of 412 coherence within the network. Such a mechanism may explain how the same stimulus induces 413 distinct patterns of brain activity in different social contexts, which then elicits distinct behavioral 414 responses to a stimulus. 415 Finally, the coherence changes and GC analyses led us to identify a small subset of brain regions 416 that seem highly influential within the network during the various tasks. Of these, the vDG and

434
In conclusion, our results suggest that the distribution of LFP rhythmic activity in the social brain 435 and, most specifically, the synchronization between the various regions is context-specific and 436 may thus mediate context-specific processing of social information, leading to social context-437 dependent social responses and behavior.   The skull covering these marked coordinates was removed using a dental drill, and the exposed EAr was lowered onto the surface of the exposed brain using a motorized manipulator (MP200; 464 Sutter instruments). The dorsoventral coordinates were marked using the depth of the electrode 465 targeting the PVN (AP= -1 mm, ML= -0.3), which was lowered slowly to -4.7 mm. The EA and 466 exposed skull with the screws were secured with dental cement (Enamel plus, Micerium). Mice 467 were sub-cutaneously injected with Baytril (5mg/kg; Bayer) and Norocarp (5 mg/kg; Carprofen, 468 Norbrook Lab) post-surgery and allowed to recover for three days.   481 We recorded the behavior and neural activity of 14 males in the SP task, 13 males in the EsP task, 482 and 11 males in the SxP task (Table S1), while targeting 18 distinct brain regions. All the stimuli 483 used for the tasks were unfamiliar to the subject mice. In experiments, the mice were briefly 484 exposed to isoflurane, and the EAr was connected to the evaluation system. After 10 minutes of  Subjects were transcardially perfused, and their brains was kept cold in 4% paraformaldehyde for 503 48 h. Brains were sectioned (50 µm) horizontally (VT 1200s, Leica). Electrode marks were 504 visualized (DiI coated, Red) against DAPI-stained sections with an epifluorescence microscope 505 (Ti2 eclipse, Nikon). The marks were used to locate the respective brain regions, based on the 506 mouse atlas. Out of all implanted electrodes (256), 9% (23 electrodes from 14 mice) were found 507 to be mistargeted and 36% (93) were non-functional (Table S1). Only brain regions recorded for more than 5 sessions across at least 3 mice were analyzed. All 517 signals were analyzed with codes custom-written in MATLAB 2020a. We excluded the signals 518 recorded during 30 seconds around stimulus removal and insertion times, to avoid any effect of 519 this action. First, the signals were down-sampled to 5 kHz and low-pass filtered to 300 Hz using a 520 Butterworth filter. The power and time for the different frequencies were estimated using the 521 'spectrogram' function in MATLAB with the following parameters: Discrete prolate spheroidal 522 sequences (dpss) window = 2 s; overlap = 50% ; increments = 0.5 Hz; and time bins = 0.5 s. The 523 power of each frequency band (theta: 4-12 Hz and gamma: 30-80 Hz) was averaged for both the 524 baseline and encounter periods (5-min long each). Changes in theta (∆θP) and gamma (∆γP) 525 powers for each brain region were defined as the mean difference in power between the encounter 526 and baseline periods (Fig. 2C-D, H-I). For Z-score analysis of Δ θP and Δ γP during investigation 527 bouts for a given stimulus we used the pre-bout 5 s period as baseline, and averaged the Z-score 528 across all bouts with the same stimulus in each session. Notably, throughout the study we have 529 analyzed only investigation bouts that were longer than 2 s, for two reasons: 1) only >2 s bouts 530 showed statistically significant differences between the stimuli in the various tasks and 2) only >2 531 s bouts allow a reliable calculation of theta coherence. LFP power ( Δ θP and Δ γP) for specific bouts 532 19 with each stimulus was estimated by calculating the difference between the average power per 533 second during an investigation bout (which was longer than 2 s) during the encounter period and 534 the average power per second for investigation of both empty chambers in the baseline period of 535 the same session, followed by averaging these values over all sessions (Fig. 4).

537
Coherence analysis 538 We used the 'mscohere' function of MATLAB to estimate coherence values using Welch's 539 overlapped averaged periodogram method. The magnitude-squared coherence between two 540 signals, x, and y, was defined as follows: where is the cross-power spectral density of x and y, is the power spectral density of x 543 and is the power spectral density of y. All coherence analysis was quantified between brain 544 regions pairs involved in at least five sessions of behavior tasks. Coherence for the baseline period 545 was quantified as the average coherence of all brain region pairs for each context (Fig. 5A and F).

546
Changes in coherence (ΔθCo and ∆γCo) during the encounter period ( Fig. 5B and G) between a 547 pair of brain regions were calculated as follows: where, Coherenceencounter is the absolute coherence value between a pair of regions within a all sessions ( Fig. 6A and S5C). Brain regions that displayed higher frequencies of crossing the 558 threshold of mean ± 1.5 SD Δ θCo and Δ γCo, based on a binomial distribution test, were considered 559 to be hubs in the coherent social brain (Fig. 7A-B).
560 561 20 Inter-regional pairwise conditional Granger causality 562 We employed the multi-variate GC toolbox [43] to calculate GC values separately for baseline and 563 encounter periods between brain regions separately for each task and rhythm. To this end, we 564 selected brain regions most represented among brain region pairs that crossed the mean ± 1.5*SD 565 threshold for the difference in coherence change between preferred and less preferred stimuli in 566 any task, separately for Δ θCo and Δ γCo. For GC analysis, LFP signals were measured at a reduced 567 sampling rate of 500 Hz. We used the "tsdata_to_infocrit" function to determine the model order for each bout, the mean power was normalized using Z-score analysis, where a pre-bout duration 585 of 5 s served as baseline (Table S2).   The data from two mice (total 14) were ignored as they had less than 40 recorded brain regions the mean value for a pair, we first averaged the mean value per stimulus (for a specific mouse) and 615 then subtracted the average of these means.

617
The average bout for each stimulus was computed for each session.

618
Data Imputation: 619 For each mouse, a slightly different set of brain areas were recorded due to slight inaccuracies in 620 placing the electrodes and slight difference in the individual mouse anatomy. This resulted in 621 missing entries from some of the brain regions pairs. We used a data imputation strategy to restore 622 these missing entries. Note that before this step, we subtracted the mean value per brain region per

948
The gray areas mark the theta and gamma ranges. The inset shows the theta range in higher 949 resolution.