 bottom-up in the case of PAC (or AAC). This definition is in accordance with a previous approach [Fontolan et al., 2014].
We first examined PAC and AAC across the four sectors, in auditory evoked potentials to 20 conspecific vocalizations (VOC). Both CFC measures peaked in the θ frequency range and showed relatively strong coupling across all the target amplitude frequencies (Fig. 2A,B,D,E). The field potential signal showed the highest power in the same frequency band decaying with the typical 1/f pattern thereafter (Fig S1), thus satisfying a pre-requisite for the presence of physiologically meaningful CFC [Aru et al., 2015].
Among PACs, both top-down and bottom-up coupling was dominant between θ phase and broadband amplitude (Fig. 2A,B). Examining differences in coupling strength in the two directions more closely (Fig. 2C), PACs showed dominant top-down coupling in the low-frequency space (θ, α, β phase to θ, α, β amplitude), as well as between low frequency phase and high-γ (>67.5Hz) amplitude. Bottom-up PAC was dominant between low frequency phase and low-γ (47.5-62.5Hz) amplitude. The same trends were found when computing significance at p=0.01 using cluster-permutation testing (Fig. S4A). In addition, bottom-up coupling was dominant between θ phase and θ amplitude, low β (12.5-22.5) phase and high-γ amplitude (127.5-132.5Hz), and between high γ phase and high γ amplitude. These interactions did not show up significant with cluster-permutation testing (Fig. S4A) [Maris and Oostenveld, 2007].
AACs showed a similar pattern to PACs in both directions, but coupling strength and differences in coupling strength were overall lower than for PACs (Fig. 2D,E). AACs replicated the pattern oveserved in PACs with dominant θ to broadband coupling in both directions. Additionally, and unlike in PACs, coupling strength among same-frequency couplings was pronounced in both directions with strongest coupling in the low-frequency range (Fig. 2D,E). Examining differences in coupling strength in the two directions more closely (Fig. 2F), AACs displayed a similar pattern to PACs but showed less significant frequency pairs than PACs across the entire frequency spectrum. AAC coupling differences did not show up significant with cluster-permutation testing (Fig. S4B) [Maris and Oostenveld, 2007].
To examine cross-regional patterns in coupling across the auditory hierarchy (Fig. 1) more closely, we analyzed differences between top-down and bottom-up coupling strength separately across the six cross-regional pairs (Fig. 3). This revealed that the overall coupling pattern (Fig. 2) was mostly driven by interactions between S1 (A1/ML) and S2-S4 (higher-order sectors) (Fig. 3 A,B,C), rather than by interactions among higher-order sectors (Fig. 3 D,E,F).
More specifically, interactions between S1 (A1/ML) and S2 (R/AL) show dominant top-down coupling only (Fig. 3A), which is overall less widespread across low and high frequency amplitudes than for the cross-regional pairs S1 (A1/ML)-S3 (RTL) (Fig. 3B) and S1 (A1/ML)-S4 (RTp) (Fig. 3B). The full pattern as manifested in Fig. 1 only gains full prominence among cross-regional pairs S1-S3 (3B) and S1-S4 (3B), which also include predominant bottom-up coupling between low frequency phase and low-γ amplitude. Interactions between higher-order sectors (3 D,E,F) show fewer differences between top-down and bottom-up coupling. A similar trend was observed among AACs, though differences were overall smaller compared to PACs and there was less widespread low frequency to highγ coupling among S1-S3 and S1-S4 (Fig. S5).
To examine whether the observed coupling patterns are a general feature of inter-areal communication, we also analyzed coupling strength in two types of synthetic stimuli derived from the natural vocalizations. Envelope-preserved sounds (EPS) were obtained by leaving the original temporal envelope of the vocalization intact but flattening its spectral content, while spectrum-preserved sounds (SPS) were obtained by leaving the spectral information of the original vocalization intact but flattening its temporal envelope [Anonymous, 2014] (see Methods and Materials 3.2).
EPS and SPS stimuli showed similar bottom-up and top-down coupling patterns to natural stimuli, with pronounced θ-to-broadband coupling strength in both directions (Fig. S6,S10). Examining differences between top-down and bottom-up coupling strength in both types of synthetic stimuli (Fig. 4,S7, S11), we found that they reflected the same coupling asymmetries across the frequency spectrum as natural stimuli did (Fig. 2). This was true for PAC (Fig. 4A,C) and AAC (Fig. 4B,D) alike. More specifically, both types of synthetic stimuli showed dominant top-down coupling among low-to-low frequency and low-to-high γ interactions, and dominant bottom-up coupling among low-to-low γ interactions, like natural stimuli did. Both types of synthetic stimuli also showed similar coupling asymmetries to natural stimuli when examining cross-regional pairs separately (Fig. S8, S9, S12, S13), with most of the pattern driven by interactions between A1 and higher-order sectors, as in natural vocalizations.
To examine differences in coupling strength between natural and synthetic stimuli more closely, we compared coupling strength across stimuli separately in the top-down and bottom-up direction (Fig. 5).
EPS stimuli showed lower coupling strength than natural stimuli in both directions for both PACs and AACs (Fig. 5). Among PACs more specifically (Fig. 5A-B), natural stimuli showed higher coupling strength in the top-down direction for select frequency pairs in the low frequency space as well as among low frequency to high-γ coupling (Fig. 5A). In the bottom-up direction, coupling strength for natural stimuli was enhanced among low frequency to low and high γ couplings (Fig. 5B). There were also select coupling values in the low and high γ frequency target amplitude space for which coupling was stronger in EPS stimuli.
Among AACs, coupling strength was increased for natural stimuli across the entire frequency spectrum in both directions (Fig. 5 C-D); compared to PACs, AACs showed more significant differences between natural and EPS stimuli in the high-frequency space, in both directions (Fig. 5 C,D). Altogether, coupling strength is enhanced for natural stimuli over envelope-preserved but spectrally flat synthetic stimuli (EPS) in both directions and across the entire frequency spectrum, with AACs displaying more significant differences in the high-frequency space.
SPS stimuli showed more similar coupling patterns to VOC stimuli. Among PACs, there were much less significant differences in both directions (Fig. 6A-B) than there were between EPS and natural stimuli (Fig. 5A-B). This also held true among AACs (Fig. 6C-D), especially in the top-down direction (Fig. 6C) which displayed much less significant differences across the frequency spectrum than for EPS stimuli (Fig. 5C). SPS and natural stimuli still showed differences among AACs in the bottom-up direction (Fig. 6D) across the entire frequency spectrum, mostly with increased coupling strength for natural stimuli. Altogether, spectrally rich (but envelope flat) stimuli (SPS) showed less widespread differences to natural stimuli in both directions for both types of coupling; most of the differences were observed in the bottom-up direction among AACs, with natural stimuli showing higher coupling strength across the frequency spectrum.
Overall, top-down and bottom-up cross-frequency coupling signatures were preserved among synthetic stimuli, albeit at overall reduced coupling strength. Envelope-flattened (but spectrally intact) SPS stimuli showed smaller differences in coupling strength to VOC stimuli than spectrally-flat (but envelope preserved) EPS stimuli. AACs revealed more widespread differences in coupling strength than PACs among synthetic stimuli, in particular in the γ frequency range.
To examine the pattern of PAC coupling over time in more detail, we focused on the θ frequency phase band which showed the highest coupling strength (Fig. 2A-B). We bandpassed the signal and obtained instantaneous phase and amplitude information by applying the Hilbert-transform (as described in Methods and Materials 3.7). We then computed PAC for every time window separately, obtaining a time-resolved picture for coupling between the θ (2.5-7.5Hz) phase band in the source sector and θ/α (2.5Hz-12.5Hz) amplitude band in the target sector (Fig. 7).
(A) θ (2.5-7.5Hz) phase to θ/α (2.5-12.5Hz) amplitude PAC over the duration of stimulus presentation, separately in the bottom-up direction (blue) and the top-down direction (red) (B) Differences in top-down and bottom-up low frequency PAC (θ (2.5-7.5Hz) phase to low γ amplitude coupling) over the duration of stimulus presentation.  Results are depicted averaged