The spatial scale of somatostatin subnetworks increases from sensory to association cortex

Summary

Incoming signals interact with rich, ongoing population activity dynamics in cortical circuits. These intrinsic dynamics are the consequence of interactions among local excitatory and inhibitory neurons and affect inter-region communication and information coding. It is unclear whether specializations in the patterns of interactions among excitatory and inhibitory neurons underlie systematic differences in activity dynamics across cortex. Here, in mice, we compare the functional interactions among somatostatin-expressing (SOM) inhibitory interneurons and the rest of the neural population in auditory cortex (AC), a sensory region of cortex, and posterior parietal cortex (PPC), an association region. The spatial structure of shared variability among SOM and Non-SOM neurons differs across regions: correlations decay rapidly with distance in AC, but not PPC. However, in both regions, activity of SOM neurons is more highly correlated than Non-SOM neurons’ activity. Our results imply both generalization and specialization in the functional structure of inhibitory subnetworks across cortex.

Introduction

The mammalian neocortex is a hierarchically organized and highly interconnected network that can be subdivided into regions with functional specializations. Sensory cortices process incoming signals from a single modality, while downstream association areas integrate inputs from multiple modalities to guide behavior. Incoming signals interact with rich, ongoing population activity dynamics throughout the brain. A well-studied feature of population activity, the shared variability of activity between neurons that is unrelated to stimulus-evoked responses, can limit the information neural populations encode (Averbeck et al., 2006; Bartolo et al., 2020; Moreno-Bote et al., 2014), but also improves the stability and consistency of representations over time (Runyan et al., 2017; Valente et al., 2021).

The timescale of information processing increases systematically along the cortical hierarchy, which allows sensory and association regions to specialize in cortical computations with distinct temporal scales (Chaudhuri et al., 2015; Chen et al., 2015a; Murray et al., 2014). For example, shared variability across neurons is lower in magnitude and decays more rapidly across time in auditory cortex (AC), a sensory region, than in posterior parietal cortex (PPC), an association level region. As a result, information coding has a shorter timescale in AC than in PPC (Runyan et al., 2017). The spatial scale of shared variability may also increase systematically across cortex. Pairwise noise correlations in sensory cortex, which tend to be highest among synaptically connected neurons (Ko et al., 2011), decrease sharply over intersomatic distances (Chelaru and Dragoi, 2016; Rosenbaum et al., 2017; Rothschild et al., 2010; Schulz et al., 2015; Smith and Kohn, 2008; Smith and Sommer, 2013). Although the spatial scale of noise correlations has not been well-characterized outside of sensory cortex, in primate prefrontal cortex, noise correlations do not seem to decay with distance (Safavi et al., 2018), suggesting that the spatial scale of functional connectivity may also vary across the cortical hierarchy. The spatial and temporal scales of cortical microcircuits may thus be tailored to the computational demands of each region, such as transforming topographically organized feedforward inputs in sensory cortex or integrating multimodal information over time in association cortex.

The spatial and temporal properties of population activity depend on the interactions among a rich diversity of excitatory and inhibitory cell types, which are not yet well understood, especially outside of sensory cortex. Cortical inhibitory neurons can largely be divided into three nonoverlapping subtypes, which express parvalbumin (PV), somatostatin (SOM), or vasoactive intestinal peptide (VIP), and participate in distinct local circuit motifs (Tremblay et al., 2016). SOM neurons can powerfully influence correlated variability in local networks (Chen et al., 2015b; Veit et al., 2017), due to their broad lateral pooling of excitatory inputs (Adesnik et al., 2012) and dense innervation of local neurons (Fino and Yuste, 2011), and disinhibit excitatory neurons through PV neurons (Pfeffer et al., 2013). Though many aspects of inhibitory microcircuitry are conserved across cortical areas, the relative density of SOM to PV neurons increases from sensory to association cortex (Dienel et al., 2020; Kim et al., 2017). Theoretical work suggests that this difference underlies flexible coding properties of association cortex (Wang and Yang, 2018). Other properties of local inhibitory circuits, such as the spatial decay of synaptic connectivity, may also be tailored to specific regions’ roles in sensory processing, decision-making, or the control of behavioral output.

Here, we test the hypothesis that local inhibitory population activity is differently structured in sensory and association cortex. We transgenically labeled SOM neurons in auditory and posterior parietal cortices and performed two-photon calcium imaging in both areas to compare the activity of SOM and Non-SOM neurons, the majority of which are excitatory. Though the spatial scale of SOM and Non-SOM functional interactions was larger in PPC than AC, SOM neurons were most strongly correlated with each other in both regions. Together, our results suggest both specializations and generalized principles in the functional properties of SOM subnetworks across cortex, that SOM neurons act locally as highly coordinated subpopulations throughout cortex, but that the spatial scale of their coordinated activity is increased in association cortex.

Results

To compare the structure of local interactions among SOM and Non-SOM neurons in sensory and association regions, we used two-photon calcium imaging to measure spike-related fluorescence changes of the calcium reporter GCaMP6f in in layer 2/3 (~150–300 μm depth) of auditory cortex (AC) and posterior parietal cortex (PPC), in six mice of both sexes. Mice were head-fixed and ran voluntarily on a spherical treadmill during imaging (Figure 1A) and were passively exposed to sound stimuli (1 and 2 second dynamic ripples, see STAR methods) that were presented from 8 locations (Figure 1B). Sounds were separated by a 240 ms interstimulus interval and repeated three times at each location. There were 57.4±7.1 (mean and standard deviation) trials (including all three repetitions) at each sound location during an imaging session.

Figure 1: Imaging spike-related activity in SOM and Non-SOM neurons during sensory stimulation.

(A) Mice were headfixed over a spherical treadmill and allowed to run voluntarily. An infrared camera was used to image the pupil, and a rotating two-photon microscope objective was focused on either AC or PPC. (B) Sound stimuli were randomly presented from eight locations during the session. (C) Example field of view from auditory cortex, with intermingled tdTomato+/SOM+ (magenta) and tdTomato-/SOM- neurons, co-expressing GCaMP6f (green). (D) Example aligned behavioral and neural signals collected for the session in C, including running speed (black), pupil area (gray), and z-scored ΔF/F from Non-SOM (top) and SOM (bottom) example neurons during sound presentations, sorted by mean sound responsiveness across all locations. Bars indicate sound stimulus timing and are colored by location using the convention in (B). (E) As in C, for an example PPC field of view. Scalebar from (C) applies. (F) As in D, for the PPC field of view in (E).

Cells were classified as either somatostatin-positive (SOM) or somatostatin-negative (Non-SOM) by the presence of the fluorophore tdTomato, which was expressed transgenically in SOM neurons (SOM-Cre × flox-tdTomato, Figure 1C, E). While the majority of neurons classified as Non-SOM were likely excitatory neurons, this population also included other inhibitory subtypes. Fields of view were 500 μm² and contained 187±95 (mean±standard deviation) neurons, 20±10 of which were classified as SOM. Analyses included data from 2,645 Non-SOM neurons and 359 SOM neurons from 24 fields of view in AC, and 4,719 Non-SOM neurons and 525 SOM neurons from 20 fields of view in PPC. Neural activity was aligned with sound presentations, running speed, and pupil area (Figure 1D, F). Throughout all analyses, we used deconvolved neural activity, reported in arbitrary units (a.u.), rather than dF/F to minimize the impact of calcium indicator decay kinetics on results.

Noise correlations were strongest within the SOM population

To examine the functional interactions among SOM and Non-SOM neurons in AC and PPC, we computed pairwise noise correlations, the correlation between two neurons’ trial-to-trial response variability (Cohen and Kohn, 2011). As expected from our previous work (Runyan et al., 2017), pairwise noise correlations overall, among the full population of SOM and Non-SOM neurons, were lower in AC than in PPC (p<.0001, Table S1). Here, we calculated noise correlations based on trial-to-trial fluctuations around the mean response to the first sound location repetition to minimize the potential effects of sound adaptation on noise correlations. To characterize the patterns of functional interactions within and between cell types, we computed the pairwise noise correlations between Non-SOM/Non-SOM pairs, SOM/SOM pairs, and Non-SOM/SOM pairs (Figure 2A–C). In both regions, noise correlations differed significantly across these three cell type combinations (Kruskal Wallis: AC, p<.0001; PPC, p<.0001, Table S1), and SOM/SOM correlations were higher than both Non-SOM/Non-SOM correlations (p<.0001 for AC and PPC) and Non-SOM/SOM correlations (p<.0001 for AC and PPC). The high SOM/SOM noise correlations that we have observed in both regions suggest that functional subnetworks of SOM neurons described previously in sensory cortex (Karnani et al., 2016) persist across the cortical hierarchy. These differences could not be accounted for by differences in firing rates (Figure S1).

Figure 2: The Spatial Scale of Correlated Variability in AC and PPC.

(A) The pairwise noise correlations considered in following analyses. (B) Cumulative probability distributions of the noise correlations in Non-SOM/Non-SOM pairs (N=160,241), Non-SOM/SOM (N=41,473), and SOM/SOM (N=2,788) pairs in AC. SOM/SOM correlations were higher on average than other cell type pairs. (C) As in B, for PPC neurons (Non-SOM/Non-SOM, N=620,319; Non-SOM/SOM, N=129,319; SOM/SOM, N=7,644). Similar to AC, SOM/SOM pairs tended to be more correlated. (D) Mean pairwise noise correlations binned by intersomatic distance in AC (red) and PPC (blue). From left to right: Non-SOM/Non-SOM pairs, Non-SOM/SOM pairs, and SOM/SOM pairs. n.s.: no significant difference; ****p<.0001. Points indicate mean, lines are 95% bootstrapped confidence intervals of the mean, here and throughout. (E) Lambda, the decay constant of a single exponential function fit to the correlation vs. distances in D. Each point represents the lambda values for one pair type from one dataset, error bars show 95% bootstrapped confidence interval of the mean. AC N=24 datasets; PPC, N=20 datasets. See Figure S2 for analogous results using spontaneous running bouts as trials and trials including all three repetitions.

The spatial scale of functional connectivity was wider in PPC than in AC

As the activity of somatostatin neurons was highly coordinated in both AC and PPC, we next considered the spatial scale of these cell-type specific interactions. To characterize the spatial extent of shared variability in AC and PPC, we related pairwise noise correlations, based on sound responses, to intersomatic distance (Figure 2D–E). Surprisingly, noise correlations among Non-SOM/Non-SOM pairs within 100 μm were higher in AC than PPC (p<.0001). Non-SOM/SOM and SOM/SOM pairs at this distance did not significantly differ between the two areas (Non-SOM/SOM, p=.91; SOM/SOM, p=.014, α=.0125, Table S1). However, at distances greater than 100 μm, AC pairwise noise correlations were significantly lower than in PPC for all pair types (Figure 2D).

To quantify the rate of decay in pairwise noise correlations over cortical distance, we fit an exponential equation to determine the decay constant lambda (λ), across binned pairwise distances. Within regions, there was no significant difference in the decay rate across pair types (Kruskal Wallis: AC, p=0.46; PPC, p=0.35). Across regions, spatial decay of pairwise noise correlations among all cell type combinations was faster in AC than PPC (Figure 2E). Because correlations could be influenced by trial-to-trial fluctuations in behavioral variables such as running speed, we also examined pairwise activity correlations in the absence of sensory stimulation, at the onset of “running bouts”, when mice transitioned from stillness to running. Spatial patterns of noise correlations were similar when noise correlations were calculated based on these running bout “trials” in the spontaneous context rather than sound stimulus presentations, and when using all three sound repetitions (Figure S2, Table S2). Additionally, we obtained similar results when limiting noise correlation measurements to sound location conditions that elicited significant responses in both neurons (Figure S3, Table S3). We conclude that the spatial scale of shared variability is overall larger in PPC than in AC.

Discounting behavioral and sensory influences to measure functional coupling

Though useful for characterizing shared variability across neurons, pairwise noise correlations cannot easily discount the effects of ongoing fluctuations in behavioral variables such as running direction, speed, and pupil size, which could modulate neuronal activity in AC and PPC differently. To measure shared variability while also accounting for both sensory stimuli and behavioral variables, we adopted a generalized linear model (GLM) approach, computing the level of functional “coupling” among SOM and Non-SOM neurons in AC and PPC (See STAR Methods and Figure S4). The coupling measurement shares the goal of noise correlation analyses, while discounting many external variables simultaneously.

To measure the activity coupling of each neuron to simultaneously imaged SOM and Non-SOM neurons, we trained and tested variants of the encoding model and compared their prediction performance of each neuron’s activity. The uncoupled model included time varying predictors based on running velocity, pupil area, and sound stimulus presentation. The coupled variants of the model included these in addition to predictors based on the activity of subsets of the simultaneously imaged neurons. The “SOM coupled model” used the activity of SOM neurons in the field of view as predictors, and the “Non-SOM coupled model” used the activity of a subsampled population of Non-SOM neurons, chosen to match the size and distance distribution of the SOM population within that field of view. To avoid the effects of overfitting, cross-validation was used when quantifying models’ prediction performance (See STAR Methods).

We calculated each neuron’s coupling to the SOM population by subtracting the single trial prediction performance of the uncoupled model (fraction deviance explained, compared to the null model) from the prediction performance of the SOM coupled model, using data that had not been used to train the model. This difference measured the improvement in model performance when including SOM activity. Similarly, each neuron’s Non-SOM coupling was calculated by subtracting the performance of the uncoupled model from the performance of the Non-SOM coupled model (Figure 3A). This approach allowed us to isolate functional coupling of each neuron to local SOM and Non-SOM subpopulations that could not be explained by sound stimuli, running behavior, or pupil area fluctuations (i.e., the difference in the y and x axes for each neuron in Figure 3B–D).

Figure 3: Functional Coupling among SOM and Non-SOM Neurons.

(A) Left: Schematic of the Generalized Linear Model (GLM) used to measure functional coupling between neuron types. Behavioral predictors and coupling predictors from either SOM or Non-SOM neurons were used to predict each neuron’s activity. Right: Types of coupling assessed. (B) Performance improvement when adding Non-SOM coupling to the model to predict activity of Non-SOM neurons in AC (left, N=2,428) and PPC (right, N=4,048) neurons. X axis: uncoupled model prediction performance (fraction of deviance explained). Y axis: coupled model prediction performance, using Non-SOM neurons as coupling predictors. (C) As in B, when using Non-SOM neurons to predict each SOM neuron’s activity (AC, N=320; PPC, N=485). (D) As in B-C, when using SOM neurons to predict each SOM neuron’s activity (E) Mean coupling (model performance improvement when adding coupling: Y-axis minus X-axis for each neuron in B-D), measured with the three coupled model types in AC (red bars) and PPC (blue bars) neurons. (F) Comparison of Non-SOM and SOM coupling to SOM neurons in AC. (G) As in F, for PPC SOM neurons. Note that in C-D, and F-G coupling is measured in SOM neurons, either using Non-SOM activity to predict SOM activity (C), or using SOM activity to predict SOM activity. Accordingly, all pentagrams correspond to SOM neurons. Error bars indicate SEM, **** p<0.0001. See Figure S4 for model details, and Table S4 for full values and statistics.

We calculated three types of coupling: 1) Non-SOM/Non-SOM (Figure 3B); 2) Non-SOM/SOM (Figure 3C); and 3) SOM/SOM coupling (Figure 3D). As expected from previous results (Runyan et al., 2017), coupling among Non-SOM neurons was higher in PPC than AC (p<.0001, Figure 3E), as was SOM-SOM and Non-SOM/SOM coupling (p<0.0001). Consistent with the noise correlation results (Figure 2A–C), coupling among SOM neurons was higher than coupling between other cell types in both AC and PPC (p<.0001, Figure 3E–G, Table S4). In summary, even when accounting for co-modulation of neural activity by changes in running speed, pupil size, and sound stimulation, coupling among neurons was high in PPC relative to AC, and coupling among SOM neurons was higher than coupling among other cell types within both regions.

Discussion

We imaged spike-related calcium changes in somatostatin (SOM) and Non-SOM neurons in auditory (AC) and posterior parietal (PPC) cortex of mice, revealing both common principles as well as region-specific differences in the functional interactions among cell types across cortex. In both AC and PPC, activity within the SOM subpopulation was highly coordinated when compared to the Non-SOM population. However, functional interactions among all cell types decayed more slowly over distance in PPC compared to AC, suggesting that the spatial scale of functional subnetworks may increase systematically across the cortical hierarchy.

The highly coordinated activity of the SOM population in both regions is consistent with previous findings within primary visual cortex, in which shared variability is overall higher within inhibitory cell types than between types (Karnani et al., 2016; Khan et al., 2018; Knoblich et al., 2019). Higher noise correlations among GABAergic neurons in general relative to excitatory neurons have also been observed in PPC (Najafi et al., 2020). Our similar results in AC and PPC, sensory and association level regions of cortex, suggest that a highly coordinated somatostatin population is a general feature of cortical circuits, which may allow the SOM population to influence local network dynamics more effectively (Chen et al., 2015b; Veit et al., 2017).

Despite the high shared variability among SOM neurons in both AC and PPC, the spatial scales of these functional interactions among neurons differed markedly between in the two regions. In AC, the magnitude of pairwise noise correlations decayed rapidly with distance (Figure 2), as has been well established in sensory cortex (Chelaru and Dragoi, 2016; Rosenbaum et al., 2017; Rothschild et al., 2010; Schulz et al., 2015; Smith and Kohn, 2008; Smith and Sommer, 2013). In contrast, pairwise noise correlations among SOM and Non-SOM neurons remained high over longer distances in PPC. Similarly high noise correlations across long distances in primate prefrontal cortex (Safavi et al., 2018) suggest that in general, the spatial scale of correlated variability may be wider in association cortex than sensory cortex, and that this trend extends to inhibitory subnetworks.

Noise correlations can arise from recurrent connectivity and shared or correlated inputs. Given that SOM neurons are not synaptically interconnected (Pfeffer et al., 2013), their coordinated activity likely arises from shared or correlated inputs. SOM neurons pool excitatory input laterally, which assists in their role in sharpening excitatory sensory responses through lateral inhibition in sensory cortex (Adesnik et al., 2012; Kato et al., 2017). We propose that in AC and PPC, heightened noise correlations among SOM neurons are the consequence of overlapping synaptic input from local excitatory neurons (Figure 4A–B). The spatial scale of noise correlations among SOM neurons is then determined by the distance over which SOM neurons pool excitatory inputs. We hypothesize that in AC, SOM neurons integrate excitatory inputs across shorter distances than in PPC. Future work can test these hypotheses directly to determine how synaptic connectivity patterns contribute to the spatial structure of functional subnetworks in AC and PPC, and whether the spatial scale of connectivity increases systematically from sensory to association cortex.

Figure 4: Proposed Excitatory-SOM subnetworks in AC and PPC.

(A) We propose that SOM neurons (circles) in PPC receive input from overlapping and spatially broad pools of excitatory neurons (triangles) (left), which results in the elevated correlations that we have observed among SOM neurons at greater distances in PPC (right) (B) We propose that SOM neurons in AC receive input from spatially narrower pools of excitatory neurons (left), and that only nearby SOM neurons will have overlapping inputs, leading to correlations that decay more rapidly over distance (right).

Taken together, our results demonstrate key differences in the spatial extent of coordinated inhibitory subnetworks across cortex, adding to a growing body of evidence that cortical microcircuits are functionally specialized across cortical regions (Dienel et al., 2020; Kim et al., 2017; Runyan et al., 2017). The underlying spatial patterns and dynamics of population activity may be tailored to specialized roles for cortical areas in processing incoming sensory information or generating behaviors. Sensory areas, such as AC, encode fine-grain details of time-varying sensory stimuli, and are organized topographically. Meanwhile, multisensory inputs converge in association-level regions such as PPC, which then flexibly integrates sensory information over time and transforms it to influence behavioral choices (Fitzgerald et al., 2011; Goard et al., 2016; Huk and Shadlen, 2005; Pho et al., 2018; Runyan et al., 2017). The flexible, task-dependent integration of diverse feedforward signals in PPC may require larger scale network dynamics, as we observed in SOM and Non-SOM populations.

Limitations of the Study

Our methods allowed us to identify SOM and Non-SOM neurons. While most Non-SOM neurons are excitatory, this population also includes PV and VIP expressing inhibitory neurons, which are highly correlated subpopulations in sensory cortex (Karnani et al., 2016; Hofer et al., 2011). It is possible that in our study, the most strongly correlated Non-SOM pairs (Figure 2B,C) correspond to PV/PV or VIP/VIP interactions. Future work will be required to determine if this is the case, or if coordination within the SOM population is uniquely conserved between sensory and association cortex. Finally, differences in the spatial scale of noise correlations can theoretically be explained by differences in the extent of recurrent connectivity, as we propose in Figure 4. In the current study, we are unable to distinguish this possibility from other potential contributions, such as an extrinsic input that is more strongly correlated and/or more spatially diffuse in PPC than in AC. Future work mapping the spatial scale of synaptic connectivity in AC and PPC will be required to determine whether differences in recurrent connectivity patterns underlie differences in functional connectivity across cortical regions.

STAR Methods

Resource Availability

Lead Contact

Further information and requests for resources and reagents should be directed to and will be fulfilled by the lead contact, Caroline Runyan (runyan@pitt.edu).

Materials Availability

This study did not generate unique new reagents.

Data and code availability

Neural and behavioral data and have been deposited at Mendeley Data and are publicly available as of the date of publication. DOIs are listed in the key resources table.

Key resources table.

REAGENT or RESOURCE	SOURCE	IDENTIFIER
Bacterial and virus strains
AAV1.Syn.GCaMP6f.WPRE.SV40	Chen et al., 2013	Addgene Cat#: 100837-AAV1
Deposited data
DF/F, deconvolved, and behavioral data	This study	DOI: 10.17632/yhr8vhk6yv.1
Experimental models: Organisms/strains
Mouse: Ssttm2.1(cre)Zjh/J	Jackson Laboratories	RRID: IMSR_JAX: 013044
Mouse: B6.Cg-Gt(ROSA)26Sortm14(CAG-tdTomato)Hze/J	Jackson Laboratories	RRID: IMSR_JAX: 007914
Software and algorithms
Matlab	Mathworks	RRID: SCR_001622
R Glmnet package	Friedman et al., 2010	https://cran.r-project.org/web/packages/glmnet/index.html
OASIS	Friedrich et al., 2017	https://github.com/j-friedrich/OASIS
Suite2p	Pachitariu et al., 2017	https://github.com/cortex-lab/Suite2P
Wavesurfer	Janelia Research Campus	https://www.janelia.org/open-science/wavesurfer
Original Code	This study	DOI: 10.5281/zenodo.6964753

All original code has been deposited at Zenodo and is publicly available as of the date of publication. DOIs are listed in the key resources table.

Any additional information required to reanalyze the data reported in this paper is available from the lead contact upon request.

Experimental Model and Subject Details

All procedures were approved by the University of Pittsburgh Institutional Animal Care and Use Committee. Homozygous SOM-Cre mice (Sst-IRES-Cre, JAX Stock #013044) were crossed with homozygous Ai14 mice (RCL-tdT-D, JAX Stock #007914) obtained from Jackson Laboratory, ME, USA, and all experiments were performed in the F1 generation, which expressed tdTomato in SOM+ neurons. Mice were group housed in cages with between 2 and 4 mice. Adult (8–24 weeks) male and female mice were used for experiments (4 male, 2 female). Mice were housed on reversed 12 hr light/dark cycle, and all experiments were performed in the dark (active) phase.

Method Details

Surgery

Mice were anesthetized with isoflurane (4% for induction, and 1–2% maintenance during surgery), and mounted on a stereotaxic frame (David Kopf Instruments, CA). Ophthalmic ointment was applied to cover the eyes (Henry Schein, NY). Dexamethasone was injected 12–24 hours prior to surgery, and carprofen and dexamethasone (Covetrus, ME) were injected subcutaneously immediately prior to surgery for pain management and to reduce the inflammatory response. Two 2 × 2 mm craniotomies were made over left AC (centered at 3.0 mm posterior and 4.3 mm lateral to bregma) and PPC (centered at 2 mm posterior and 1.75 mm lateral to bregma). 1–4 evenly spaced ~60 nl injections of AAV1-synapsin-l-GCamp6f (Addgene, MA stock #100837 (Chen et al., 2013)) that had been diluted to a titer of ~1×10^12 vg/mL using sterile PBS were made in each cranial window, centered on the same coordinates listed above. A micromanipulator (QUAD, Sutter, CA) was used to target injections ~250 μm under the dura at each site, where ~60 nl virus was pressure-injected over 5–10 minutes. Pipettes were not removed until 5 minutes post-injection to prevent backflow. Dental cement (Parkell, NY) sealed a glass coverslip (3mm) over a drop of Kwik Sil (World Precision Instruments, FL) over the craniotomy. Using dental cement, a one-sided titanium headplate was attached to the right hemisphere of the skull. After mice had recovered from the anesthesia, they were returned to their home cages, and received oral carprofen tablets (Fisher Scientific, MA) for 3 days post-surgery.

Two-photon microscope

Images were acquired using a resonant scanning two-photon microscope (Ultima Investigator, Bruker, WI) at a 30 Hz frame rate and 512 × 512 pixel resolution through a 16x water immersion lens (Nikon CF175, 16X/0.8 NA, NY). On separate days, either AC or PPC was imaged at a depth between 150 and 300 μm, corresponding to layers 2/3 of cortex. For AC imaging, the objective was rotated 35–45 degrees from vertical, and for PPC imaging, it was rotated to 5–15 degrees from vertical, matching the angle of the cranial window implant. Fields of view contained 187.4±95.0 neurons, 20.1±9.6 of which were classified as SOM. Excitation light was provided by a femtosecond infrared laser (Insight X3, Spectra-Physics, CA) tuned to 920 nm. Green and red wavelengths were separated through a 565 nm lowpass filter before passing through bandpass filters (Chroma, ET525/70 and ET595/50, VT). PrairieView software (v5.5, Bruker, WI) was used to control the microscope.

Behavioral monitoring

Running velocity was monitored on pitch and roll axes using two optical sensors (ADNS-98000, Tindie, CA) held adjacent to the spherical treadmill. A microcontroller (Teensy, 3.1, Adafruit, NY) communicated with the sensors, demixing their inputs to produce one output channel per rotational axis using custom code. Outputs controlling the galvanometers were synchronized with running velocity using a digital oscilloscope (Wavesurfer, Janelia, VA).

Pupil images were acquired at 1280 × 1024 pixels, at 10 Hz from an infrared (IR) camera focused on one eye (Flea3 FL3-U3-13Y3M-C ½” Monochrome USB 3.0 Camera, 1.0x SilverTL Telecentric Lens, FOV = 6.74mm × 5.39mm, Edmund Optics, NJ). The pupil was illuminated by the IR light emitted by the two-photon laser and required no additional IR illumination. Movies were acquired with Matlab Image Acquisition Toolbox (Mathworks, MA). Pupil area was determined in each pupil movie frame post-hoc using custom Matlab code (Mathworks, MA). The pupil was constricted by controlling ambient illumination with an array of LCD screens (LG LP097QX1, South Korea), to maintain a moderate pupil area baseline from which increases and decreases could be measured.

Experimental protocol

Imaging began 3–5 weeks post-surgery once robust expression of the GCaMP6f virus was observed. Imaging sessions lasted 45–90 min total, divided in half between spontaneous activity and passive listening (ordering was random), and alternated between AC and PPC across days. Fields of view were selected based on co-expression of viral GCaMP6f (all neurons) and transgenic tDTomato (SOM neurons). Multiple imaging sessions were performed in each cranial window, focusing slightly different depths and lateral/posterior locations within the imaging windows across sessions. AC and PPC were each imaged in six mice (biological replicates). Each cranial window was imaged up to 11 times (technical replicates). Imaging from a given cranial window was suspended when we observed nuclear inclusion in 2 or more cells in the field of view, which indicates an over-expression of GCaMP6f. In each imaging session, GCaMP6f fluorescence changes were imaged in SOM (tDTomato+) and Non-SOM neurons, while mice ran freely on a spherical treadmill. In the “spontaneous context”, no sensory stimuli were delivered, while in the passive listening context, location-varying sound stimuli were presented. Spontaneous and passive listening contexts lasted ~25–50 minutes each. The order in which the contexts occurred was random.

Sound stimuli

Either immediately before or following spontaneous activity context, the same field of view was imaged for 25–50 minutes during passive listening. Four magnetic speakers were positioned in a semicircular array, centered on the mouse’s head (MF1-S, Tucker-Davis, FL). The speakers were positioned at −90, −30,+30 and +90 degrees in azimuth and driven by digital/analog converter (National Instruments). Speakers were calibrated to deliver similar sound levels (~70 db) in a sound isolation chamber using a microphone at the same distance from the speakers as the mouse’s head using a random incidence microphone (4939, Brüel & Kjær, Denmark). During passive listening, 1 or 2 second dynamic ripples (broadband stimuli created in Matlab by summing 32 tones spaced across 2–32 kHz, which fluctuated at 10–20 Hz (Elhilali et al., 2004)) were presented from one of eight locations. Four of the sound locations corresponded to the locations of the four speakers (−90, −30, +30, +90 degrees), while the other four sound locations (−60, −15, +15, +60 degrees) were simulated using vector-based intensity panning, where the same sound stimulus was delivered to two neighboring speakers simultaneously, scaled by a gain factor (Runyan et al., 2017). Dynamic ripples were chosen to optimally drive populations of neurons in auditory cortex with diverse frequency tuning preferences. Each sound repeated three times at one location before switching to another. Each ripple would play from all eight locations in randomized order continuously throughout the session with a 240 ms gap between each sound. Output controlling the audio speakers was aligned with two-photon imaging and running velocity offline using Wavesurfer (Janelia, VA).

Data Processing

Imaging datasets from 24 AC fields of view and 20 PPC fields of view were included from 6 mice. We excluded any datasets where we observed significant photobleaching or filled cells. We excluded any AC or PPC dataset from analysis if fewer than 1/3 of neurons were significantly responsive (according to our definition above) to at least one sound location. For AC datasets, we analyzed single-cell responses to pure tones on a subset of fields of view from each mouse, and then anatomically aligned all fields of view from datasets collected from each window, to ensure each field of view lay in a region representing tone frequencies in the sonic range of the tonotopic axis. We eliminated any datasets where >50% of tone-responsive neurons had a preferred frequency was in the ultrasonic range (>20kHz), as well as any fields of view that were aligned anterior to a field of view where this was observed, to assure that we were seeing sound responses in the range of frequencies primarily represented by our dynamic ripples. We collected widefield fluorescence responses to pure tones in all AC cranial windows and observed ample pure tone responses in the sonic range for all AC windows; however, the extent of the viral expression within windows was too spatially limited to allow for mapping of specific regions.

Image Processing

For each field of view, the raw calcium movies collected during the spontaneous activity and passive listening contexts were concatenated for motion correction, cell body identification, and fluorescence and neuropil extraction. These processing steps were performed using Suite2p 0.9.3 in Python (Pachitariu et al., 2017). Suite2p first registered images to account for brain motion, and clustered neighboring pixels with similar time courses into regions of interest (ROIs). ROIs were manually curated using the Suite2p GUI, to ensure that only cell bodies as opposed to dendritic processes were included in analysis, based on morphology. Cells expressing tdTomato (SOM cells), were identified using a threshold applied in the Suite2p GUI based on mean fluorescence in the red channel after bleed-through correction applied by Suite2p’s cell detection algorithm, along with manual correction. For each ROI, Suite2p returned a raw fluorescence timeseries, as well as an estimate of neuropil fluorescence that could contaminate the signal. For each cell, we scaled the neuropil fluorescence by a factor by 0.7 and subtracted this timeseries from the ROI’s raw fluorescence timeseries to obtain a neuropil-corrected fluorescence signal for each selected cell.

ΔF/F and deconvolution

Once the neuropil corrected fluorescence was obtained for each neuron, we calculated ΔF/F for each cell in each frame by calculating (F-F_baseline)/F_baseline for each frame, where F is the fluorescence of a given cell at that frame and F_baseline was the eighth percentile of that cell spanning 450 frames before and after (~15s each way, 30 s total). ΔF/F timeseries were then deconvolved to estimate the relative spike rate in each imaging frame using the OASIS toolbox (Friedrich et al., 2017). We used the AR1 FOOPSI algorithm and allowed the toolbox to optimize the convolution kernel, baseline fluorescence, and noise distribution. A threshold of .05 a.u. was applied to remove all events with low magnitude from deconvolved activity timeseries. All analyses were performed with both ΔF/F and deconvolved activity and showed the same trends. Outside of Figure 1D and 1F, only results using deconvolved activity are shown.

Sound Responsiveness

Sound responsiveness was calculated based on the mean z-scored deconvolved activity of each neuron aligned on sound onset. For each neuron, we calculated the difference between the mean activity during the sound presentation at a certain location (either 1 or 2 seconds) and the mean activity in the 240 milliseconds prior to sound onset. We calculated sound responsiveness separately for each sound location as the difference in mean activity between these two windows for each neuron. We then compared the observed sound responsiveness of each neuron for each sound location to a shuffled distribution. Each cell’s activity was shifted randomly by at least 5 seconds in time relative to sound location time series, and for 1000 time-shifted iterations, sound responsiveness to each sound location was recalculated. Each sound responsive neuron had a positive sound responsiveness value for at least one location that was greater than the 95^th percentile of that cell’s shuffled distribution for that location. All other neurons were not considered sound responsive. For Figure 1, example neurons were sorted by the mean of their sound responsiveness values across all eight locations.

Pairwise Noise Correlations

Pairwise noise correlations were initially calculated based on trial-to-trial fluctuations around mean sound-evoked responses. For the analysis presented in Figure 2 sound trial included only the first repeat of a given sound stimulus. We calculated mean sensory-evoked activity for each neuron at each location and binned the activity of each neuron by 10 frames (~330 milliseconds) over the course of the sound trial. Mean responses were calculated separately for each duration/location condition. For each neuron, we subtracted the corresponding mean sensory-evoked responses from single trial activity, and then concatenated these mean-subtracted trial responses. For each pair of neurons, we computed the Pearson correlation coefficient between these binned, mean-subtracted activity timeseries. We also calculated a shuffled distribution of pairwise noise correlations by shuffling the identity of trials for each neuron independently within sound location/duration condition and then computing the Pearson correlation coefficient in the same way. We also computed signal correlation between each pair of neurons, as the Pearson correlation between the pair of neurons’ mean sound-evoked responses to each sound duration/location after they had been binned into 10 frame (~330 milliseconds) bins and concatenated. In Figure S2C–D, we performed the same analysis, but in this case, we included all three repetitions in the same trial. In Figure S3, we limited analysis to pairs of neurons that were significantly sound responsive to at least one of the same sound locations, and only considered co-fluctuations on trials with a sound location for which both neurons were significantly responsive according to the definition in Sound Responsiveness.

During the spontaneous context, a similar approach was used to find running-based noise correlations (Figure S2A–B). Running bout onsets were defined as transitions in speed from below 10 cm/s to above 10 cm/s and required that the mean running speed in the 1 s following the transition was three times greater than the 1 s prior to running bout onset, and that the mouse maintained a speed of a minimum of 15 cm/s for the following two seconds. The three seconds following each running bout onset was defined as a “trial”, and the Pearson correlation was computed based on the binned (~330 ms) activity of pairs of neurons after subtracting mean running-related activity from each neuron’s timeseries.

Correlation Decay over Distance

We considered pairs of neurons in four separate distance bins, pairs of neurons within 0–100, 100–200, 200–300, 300+ μm from each other. For all neuron pairs, as well as by dataset, we fit decay constant λ based on the mean noise correlations of pairs in each bin using the following equation:

$$\frac{\mathit{\delta }\mathit{\rho }}{\mathit{\delta }\mathit{\mu }\mathit{m}}=-\mathit{\lambda }\mathit{\mu }\mathit{m}$$

Where ρ is the pairwise noise correlation between cells, and λ is a decay constant that describes the rate of decay over distance (μm). We calculated this decay constant, λ, using noise correlations based on trial-to-trial fluctuations centered either on mean sound-location related responses during the passive listening context (Figure 2E), or on mean running bout related responses during the spontaneous context (Figure S2B). This decay constant, λ, was calculated considering the means of each distance bin using all pairs from all datasets, as well as for each dataset considered separately.

Encoding Models

Using Generalized Linear Models (GLMs), the time-dependent effects of all measured external variables and activity of neighboring neurons on each neuron’s activity were estimated (Pillow et al., 2008; Runyan et al., 2017). For this approach, several classes of predictors were used in different combinations: running, pupil, sound location, and activity of SOM or Non-SOM neurons. We used a Bernoulli-based GLM to weight various combinations of predictors based on these variables to predict each neuron’s binarized activity (timeseries of relative spike rates were thresholded at 0.05). The encoding model is also described in our previous work (Runyan et al., 2017)

Pupil and Running Predictors

Running velocity was measured at a higher time resolution than imaging and was binned to match the sampling rate of two-photon images (30 Hz). We included the velocity along the pitch and roll axes of the treadmill (relative to the mouse’s body axis). Running velocity measurements were separated into four channels, (1) forward, (2) reverse, (3) left, (4) right directions based on rotation along these axes. Running velocity changes could both precede or follow activity of individual neurons, so time series of running velocity were convolved with four evenly spaced Gaussian basis functions (240 milliseconds half-width at half-height) extending 1s both forward and backward in time (8 basis functions total for each running direction: forward, reverse, left, and right, Figure S4). Changes in pupil area were modeled similarly. Because pupil is a slower signal, the pupil area trace was convolved with 16 evenly spaced Gaussian basis functions 4s forward and backward in time to allow either prediction or response to pupil area changes.

Sound Stimulus Predictors

For sound stimulus onsets at each of the possible sound locations, 12 evenly spaced Gaussian basis functions (170 millisecond half width at half height) extended 2 s forward in time from each sound onset. First, second, and third repeats were represented separately due to potential adaptation-related effects. This resulted in 12 basis functions per repeat per sound location × 3 repeats × 8 locations for 288 sound predictors.

Coupling Predictors

For a given neuron being fitted, the relative spike rate of all individual SOM neurons as well as their activity averaged across cells was convolved with two boxcar functions extending ~66 milliseconds forward in time from the activity of the predictor neurons (each boxcar was non-zero for only a single imaging frame or ~33 milliseconds). Because in all datasets there were more Non-SOM neurons than SOM neurons, to estimate Non-SOM coupling, a separate set of Non-SOM predictors was randomly selected for each neuron to match the population size and distance of the SOM neurons from that neuron. Creating these separate sets of predictors allowed us to compare functional coupling within and between the SOM and Non-SOM populations within each field of view.

GLM Fitting and Cross-Validation Procedures

All predictors were maximum normalized before the fitting procedure. Beta coefficients for the predictors were fitted to each neuron’s activity individually, using the glmnet package in R (Friedman et al., 2010) with elastic-net regularization, which smoothly interpolated between L₁ and L₂ type regularization according to the value of an interpolation parameter α, such that α=0 corresponded to L₂ and α=1 corresponded to L₁. We selected α=.25.

The GLMs were fit separately for the spontaneous and passive listening contexts. Within each context, trials were randomly split into training (70% of trials) and test (remaining 30% of trials) sets, while balancing the distribution of sound locations. Fitting was performed on the training set, and within each training dataset, cross validation folds (3x) were also pre-selected so that sound locations were evenly represented. Model performance (see below, GLM Model Prediction Performance) was assessed on the test set. Each model was thus fitted and tested on entirely separate data to prevent over-fitting from affecting our assessment of model performance. This train/test procedure was repeated ten times, with random subsamples of the data included in train and test segments. Each model’s overall performance was assessed as its mean across all 10 iterations.

GLM Model Prediction Performance

Each model’s performance for each cell was defined as the fraction of explained deviance of each model (compared to the null model). In the null model, only a constant (single parameter) was used to fit the neuron’s activity and no time-varying predictors were included. We calculated the deviance of the null and behavior and coupling model variants. For each model, the fraction of null model deviance explained by the model was then calculated ((null deviance – model deviance)/null deviance). A layered cross-validation approach was used, as described above in GLM Fitting and Cross-Validation Procedures. Deviance calculations were then performed on a test dataset (30% of the data), which had not been included in the fitting procedure, and this train/test procedure was repeated ten times on randomly subsampled segments of the data.

Coupling

We previously demonstrated that by comparing the model performance (fraction of explained deviance) in the coupled model to the performance of the uncoupled model, we could estimate the level of correlation between a given neuron and the neurons in the simultaneously imaged population, while considering the contributions of behavior and stimulus-related variables (Runyan et al., 2017).

Here, we computed several types of “coupling” by comparing the model performance (fraction deviance explained) of each coupled variant of the model to the behavior-only model. We computed three types of coupling: (1) Non-SOM/Non-SOM coupling, (2) SOM/SOM coupling, (3) Non-SOM/SOM coupling. Each type of coupling was computed in the same way, as the difference between the fraction deviance explained of the full behavior model and the fraction deviance explained of a coupled model using other neurons as predictors. However, for each type of coupling, there was a different combination of the type of cell being fit and the type of predictors being used to fit that cell, as follows:

1. Non-SOM/Non-SOM coupling: Defined as the improvement in model performance when using Non-SOM predictors to explain Non-SOM activity, compared to the behavior-only model, d_Non-SOM−d_behav

2. SOM/SOM coupling: Defined as the improvement in model performance when using other SOM predictors to explain SOM activity, compared to the behavior-only model, d_SOM−d_behav

3. Non-SOM/SOM coupling: Defined as the improvement in model performance when using Non-SOM predictors to explain SOM activity, compared to the behavior only model, d_Non-SOM−d_behav.

These various types of coupling allow a characterization of the functional relationships among distinct classes of neurons across cortical areas.

Histology

After all imaging sessions had been acquired, each mouse was transcardially perfused with saline and then 4% paraformaldehyde. The brain was extracted, cryoprotected, embedded, frozen, and sliced. Once slide mounted, we stained brains with DAPI to be able to identify structure. We used anatomical structure to verify the locations of our injections in AC and PPC.

Quantification and Statistical Analysis

All pairwise comparisons were done with two-sided paired or unpaired permutation (i.e. randomization) tests with 10,000 iterations as indicated, where p<.0001 indicates the highest significance achievable given the number of runs performed. All permutation tests were performed for differences in means. For statistical comparisons involving more than two groups, we used Kruskal-Wallis (non-parametric ANOVA) and used unpaired permutation tests post-hoc to determine which groups differed from each other. Data fell into natural groupings by 1) brain area (AC or PPC) and by 2) cell-type (SOM or Non-SOM), as indicated by expression of the red fluorophore, tdTomato. All bar plots show mean and bootstrapped 95% confidence intervals unless otherwise indicated. When multiple comparisons were made between groups, p values were Bonferroni-corrected.

Fields of view were 500 μm² and contained 187±95 neurons, 20±10 (mean and standard deviation) of which were classified as SOM. Analyses included data from 2,645 Non-SOM neurons and 359 SOM neurons from 24 fields of view in AC, and 4,719 Non-SOM neurons and 525 SOM neurons from 20 fields of view in PPC. Depending on the analysis, cells, pairs of cells, or fields of view were used as the n, as indicated in figure legends. Sample sizes were chosen based on previous studies comparing population activity dynamics across brain areas or cell types (Khan et al., 2018; Runyan et al., 2017). Full values and statistical details from all figures are most thoroughly summarized in Tables S1–S4.