We implanted cranial windows covering sensorimotor cortex (Figure 1A, B) in six male mice expressing GCaMP8s in most cortical pyramidal cells (Zhang et al., 2023). Dense sampling of layer 2/3 neurons was achieved using two-photon calcium imaging across 98 fields of view (FOVs) spanning the forelimb, hindlimb, and trunk representations (Figure 1D). FOVs were aligned to the Allen Mouse Brain Common Coordinate Framework version 3 (Allen CCF; Wang et al., 2020) using a combination of anatomical landmarks and widefield imaging with paw vibration mapping (Methods; Figure 1B). A total of 39,398 neurons were extracted across the five relevant regions in the sensorimotor cortex (Figure 1E). A larger number of neurons were imaged in M2 and M1 (31,453 neurons) than in somatosensory areas (7945; Figure 1C).

To quantify the overall temporal profile of single neurons, we measured when activity for each neuron ramped up. To compute these onset times, we first averaged the activity for each modulated neuron across all trials, creating a single grand-mean trace per neuron, then found the time to half-max. We next asked whether onset times differed by anatomical area (Figure 4A). These distributions over neurons revealed clear differences in the overall profile of activation: early onsets were more prevalent in S1 trunk and hindlimb regions, perhaps due to activity related to the animal shifting or stabilizing itself even if the neurons became more active later; then M2, and finally S1-fl and M1. Nevertheless, each area contained neurons activated at any given time in the trial.

Next, we leveraged our dense spatial sampling to build a map of the time of activation across the cortex. The temporal onset metric was computed for each neuron, neurons were binned into pixels, then this map was lightly smoothed (Methods). The resulting temporal onset map revealed a number of sub-area features (Figure 4B). The earliest activations, occurring during the delay (after the target had moved in but well before the Go cue), were in S1 at the juncture of the trunk, hindlimb, and forelimb regions; and in the portions of M1 and M2 that correspond somatotopically to the hindlimb. As suggested by the area-level result above, these zones presumably reflect the animal preparing its body to support the reach. Shortly after, there was activation in a small zone of S1 that corresponded closely with the tactile subregion of the forelimb region, and in the vibrissal subregion of M2 (see Figure 1A; Esmaeili et al., 2021; Mayrhofer et al., 2019). This latter activation might relate to the animal whisking, possibly to find the target; or because the incoming spout simply triggers a whisking response; or because the animal is engaged (Steinmetz et al., 2019) and anticipating movement. Next, activation spread through much of M2, part of the forelimb portion of M1, and into other parts of S1; and then finally to more lateral parts of M1 and M2 that relate to the face and oromanual feeding (Figure 1A; An et al., 2026).

To quantify the heterogeneity of tuning profiles across single neurons, we developed several summary metrics that captured the most salient variations in observed properties across our inspection of thousands of PETHs. This provides greater interpretability than using unsupervised methods such as Principal Component Analysis (PCA), and is consistent with the practice of feature engineering to extract known-meaningful structure from data where more generic methods fail to capture this structure (e.g., in spikesorting; Caro-Martín et al., 2018, Lee et al., 2021, Lewicki, 1994). Brief intuition is given for each metric below, with complete explanations of each in the Methods.

Each of our PETH feature maps varied across the sensorimotor areas, and appeared to change more abruptly in some locations. We wished to ask whether there were in fact relatively discrete transitions in the PETH feature values across cortical space, or whether these values changed only smoothly. To do so, for each PETH feature we computed the gradient: the vector-valued derivative of the PETH feature with respect to two-dimensional cortical space. We then took the magnitude of this gradient computed at every point in the map (Methods; Figure 6A). Intuitively, this simply asks how quickly the PETH feature is changing at each point on the map. Each map revealed a ridge at the edge of the high-value region (Figure 6A–E), suggesting that the PETH feature maps had edges, albeit soft ones, as opposed to smoothly falling off in value. In the target tuning linearity’s gradient map (Figure 6A), this boundary was strongest along the border between M1 and S1-fl, cut through the anterior horn of S1-hl (consistent with projection neuron patterns; Ueno et al., 2018 and Yang et al., 2023), and separated what is presumably the forelimb representation from both the hindlimb representation posteromedial and the orofacial representation anterolateral. Other PETH features strongly separated M1 and M2 and somatotopic zones (Figure 6B, D and E). Each of the candidate functional boundaries was present in at least two of the gradient maps. We therefore pooled the identified boundaries by computing an overall gradient magnitude (the quadratic mean of the individual PETH feature maps; Figure 6F). This map makes clear that the PETH features of single cells changed most sharply along both area and somatotopic boundaries. Notably, these boundaries did not correspond with ‘edges’ in the map of where more or fewer cells were modulated (Figure 3B).

This gradient method has the advantage of producing a smooth map with simple operations. However, to validate the result, we also used a decoding approach. For each of 10,000 randomly placed candidate boundaries, we attempted to classify which side of the boundary nearby neurons were on using their PETH features (Figure 6G; Methods). We expected that classification would be better when the random boundary happened to match places where PETH features were changing more rapidly. The top-performing 2.5% of random boundaries are plotted in Figure 6H. They aligned well with the boundaries revealed by the gradient method.

From the PETH feature maps and distributions (Figure 5), it was clear that areas exhibited distinct response profiles on average. However, within each area, neurons’ responses were heterogeneous. To better understand the distribution of response profiles within and across areas, we used nonlinear dimensionality reduction (t-distributed Stochastic Neighbor Embedding, t-SNE; Hinton and Roweis, 2002). Specifically, we summarized each neuron’s response with a five-dimensional feature vector comprising the five PETH features described above, then applied t-SNE to these vectors for the full neural population spanning all five brain areas (Figure 7A). Finally, we found where the neurons from each area were embedded in the t-SNE space (Figure 7B). The resulting two-dimensional t-SNE projection led to three findings. First, single neurons from each region were found across most of the t-SNE space (Figure 7B). This makes clear that much of the diversity of neuron activity patterns was observed in each area. Second, when looking at where neurons in each area most commonly appeared in the t-SNE space, most areas had peaks centered at different locations – although with overlapping distributions (Figure 7C; all pairwise comparisons p<0.005, two-dimensional Kolmogorov-Smirnov test). The largest differences were between motor and somatosensory areas, with S1-fl bridging the other S1 subregions and M1. This implies that areas had distinct distributions of their PETH features, but also that there was an interpretable spectrum of typical properties from M2 to M1 to forelimb S1 to hindlimb and trunk S1. Third, the distributions of PETH features within-area were strongly multimodal for several areas. This suggests that the heterogeneity of neurons within each area may form loose response ‘types’, especially in M2, M1, and S1-fl. This multimodality motivated further analysis targeted at understanding the range of neural response profiles in each area, and whether neurons with specific response profiles were preferentially found in localized regions of each cortical area.

The multimodality of feature vector distributions within-area opens a range of possibilities for how PETH response features could be organized across the cortex, both within and across areas. To work with these multimodal distributions, we fit a generative model to the PETH feature vectors defined above for each area’s population of neurons. This approach modeled the feature vectors of an area’s neurons as arising from a Gaussian Mixture Model (GMM). Doing so explicitly models different peaks in the distribution as arising from different Gaussian distributions, and retains probabilistic interpretability. In agreement with the t-SNE results, M1, M2, and S1-fl were best modeled by the GMM as having multiple components (Methods): four for M2, three for M1, and two for S1-fl, while S1-hl and S1-tr were best modeled as being unimodal. The Gaussians fitting different modes were well-separated, as expected when fitting a multimodal distribution (Figure 8—figure supplement 1).

We hypothesized that even though the distributions of response profiles were multimodal within-area, different areas might still be well separated. To test this, we computed a data likelihood for each neuron – p(neuron i’s PETH features | GMM_area) – as arising from each area’s distribution (Figure 8A). Intuitively, this produces a measure of how similar each neuron is to the population of neurons in an anatomically-defined area. We then binned and smoothed over neurons by cortical location to produce the maps in Figure 8B–F. This mapping approach is explicitly biased toward finding feature differences between areas, allowing for a direct test of the hypothesis that response profile distributions are area-specific.

When computing this likelihood map using neurons in M2 to define the distribution (Figure 8B), the highest likelihood zone was, as expected, in M2. However, we found that a patch of M1 was strongly similar. If we instead defined the distribution using M1 neurons (Figure 8C), again the highest-likelihood zone was within the defining area. However, two additional features were salient. First, the anterior portion of S1-fl was also strongly similar to M1, in line with previous results (Grier et al., 2026). Second, the posteromedial portion of M1 differed strongly from the rest of M1, consistent with a difference between forelimb and hindlimb somatotopic regions (Maurer et al., 2023). Considering other areas, defining the distribution with S1-fl led to high likelihoods in adjacent M1 and S1-hl (Figure 8D), while defining the distribution with S1-hl or S1-tr produced similar spatial layouts and bled over mostly into the other sensory areas (Figure 8E, F). These results make clear that the working hypothesis – of areas with well-separated feature distributions – is incorrect. Even when building models explicitly from neurons in one area, neurons in portions of some areas were similar to neurons in portions of other areas, and two dissimilar areas could both be similar to the same third location in cortex. These neural populations therefore warranted further dissection.

The likelihood maps above suggested that populations of neurons with similar response profiles were not always confined to the anatomically-defined areas. For example, portions of M1 and S1-fl were strongly similar (Figure 8C, D). This hinted at a second hypothesis: that a peak in the multimodal distribution from one area might correspond to a peak in the multimodal distribution of a different area. If this were due to a subpopulation that was shared across the areas, we would expect that the M1 GMM would contain a component (a one-area estimate of the subpopulation) with similar characteristics to a component in the S1-fl GMM (Figure 9A). We therefore computed a distance metric (Methods) between each pair of GMM components (Figure 9B). This analysis revealed that many components identified independently in different areas were indeed highly similar and formed four clusters. We therefore combined components within each of the four clusters (Methods) and took the neurons belonging to each cluster as the subpopulations.

These four subpopulations differed in two major ways. First, by construction, different subpopulations were characterized by distinct PETH features (Figure 9G). Second, their spatial likelihood maps differed strongly as well (Figure 9C–F). One subpopulation, which we refer to as the ‘Anterior’ subpopulation, was almost unique to M2 (Figure 9C). It had uniquely high tuning persistence and tuning sharpness along with highly linear target tuning, arguing for a relatively abstract and external target representation (Galiñanes and Huber, 2023). A second subpopulation, the ‘Forelimb motor’ subpopulation, spanned M2 and the forelimb portion of M1 (Figure 9D). These neurons were also strongly linear in their target tuning, but less sharply tuned and with tuning that was somewhat less persistent (i.e., changed more over the course of the movement). The ‘Forelimb somatomotor’ subpopulation spanned M1 forelimb and orofacial zones and the anterior portion of S1-fl (Figure 9E). This subpopulation was more broadly tuned, was less linearly tuned to target location, changed tuning over the course of the movement (low tuning persistence), and responded very briefly (low response duration). Nevertheless, each neuron in this subpopulation still responded at its own characteristic time in the movement (low peak time variation). Finally, a ‘Hindlimb somatomotor’ subpopulation (Figure 9F) was centered on S1-hl and spilled into S1-tr, the posterior portion of S1-fl, and the posterior tips of M1 and M2. This subpopulation was similar to the Forelimb somatomotor subpopulation, but each neuron no longer fired at a specific time point in the movement; instead, neurons fired at different times for different targets (high peak time variability). As a qualitative depiction of the response profiles identified with each subpopulation, we plotted the two highest-likelihood cells for each area/subpopulation combination (Figure 9—figure supplement 1). These examples reveal stereotypy in the subpopulation responses across areas, but also show variation across areas, especially for the two somatomotor subpopulations.

To better understand whether the subpopulations were well separated in feature space or not, we examined our clustering further using two approaches. First, for each pair of subpopulations, we trained a logistic regression classifier to separate the 5D feature vectors of the neurons in one subpopulation from the feature vectors of the neurons in another subpopulation, then projected the feature vectors onto this axis (Figure 9—figure supplement 2A). The resulting distributions were well separated along this axis in all but one of the pairwise comparisons (Hindlimb somatomotor vs. Forelimb somatomotor subpopulations). Second, we re-examined our t-SNE of the features, contouring density by subpopulation membership instead of area membership (Figure 9—figure supplement 2B). Despite t-SNE being a quite different nonlinear operation than applying a GMM, subpopulations were again distinct. Interestingly, here the strongest separation was between the Hindlimb somatomotor subpopulation and all other subpopulations. To assess an orthogonal property, we examined the distributions of activity onset times by subpopulation (Figure 9—figure supplement 2C). These distributions appear to be more distinct for the subpopulations than for the areas (compare with Figure 4A). Overall, these analyses support the interpretation that the subpopulation distributions are distinct in feature space.

To confirm that this identification of area-spanning subpopulations was not simply due to our choice of PETH features, we validated these findings by repeating some of our analyses using the top 20 PCs of the PETHs instead of the PETH feature vectors. Using PCA as a preprocessing step in this way is more common in the field. Performing t-SNE on the PCs, analogously to Figure 7, again yielded multimodality (Figure 9—figure supplement 3A). Repeating the analysis of Figure 8 on the PCs produced likelihood maps that were substantially patchier and less distinct between areas, but recapitulated that parts of each area were strongly similar to parts of other areas (Figure 9—figure supplement 3C–G). This indicates that although our choice of PETH features enabled a sharper view of the distinctions between subpopulations, these features were not necessary to detect them.

To determine whether finding distinct subpopulations required recordings from a large area, we directly examined a smaller patch of M1 (480 µm diameter) in an overlap zone (Figure 9—figure supplement 3B, left). Applying t-SNE to either our PETH features (Figure 9—figure supplement 3B, center) or to the top 20 PCs of the PETHs (Figure 9—figure supplement 3B, right) again yielded multimodality. This demonstrates that even with a single ordinary-size field of view, distinct subpopulations in overlapping zones could be readily detected in the context of our behavior.

To validate the clustering itself, we fit a GMM to all neurons without consideration of their area membership. This process produced three components with maps that were nearly identical to three of the four subpopulations identified with the area-aware method (Figure 9—figure supplement 4). The only noticeable difference was that the Anterior subpopulation was lost when all areas were fitted together, likely due to having a lower membership than the other subpopulations. Using this area-agnostic model we also demonstrated that these three main subpopulations were reliably detected in subsets of our data. To do so, we evaluated how similarly two GMMs fit to 50/50 area-wise splits of the data clustered the neurons. The median Adjusted Rand Index (Hubert and Arabie, 1985), a measure of clustering similarity, was 0.856 across splits, indicating highly similar clusterings from the data subsets. Together, these controls indicate that the clustering was reliable.

Notably, the high-likelihood regions for different subpopulations spatially overlapped. The Anterior and Forelimb motor subpopulations overlapped throughout M2; the Forelimb motor and the Forelimb somatomotor subpopulations overlapped in the forelimb portion of M1; and the Forelimb somatomotor and Hindlimb somatomotor subpopulations overlapped in a band along the S1-fl and S1-hl border. This indicates that although several of the PETH feature boundaries found in Figure 6 aligned with area borders, several of these boundaries corresponded to the edges of subpopulations that spanned other borders. To confirm this interpretation, we computed the gradients of the likelihood maps directly (Figure 9—figure supplement 5). These maps closely matched those computed from the PETH feature gradients directly (Figure 6), as expected.

The overlaps in the subpopulation likelihood maps above imply that members of different subpopulations are spatially intermingled, but it is less clear whether each subpopulation has homogeneous response profiles across space. In particular, the use of likelihoods mixes two properties: the fraction of neurons in a given neighborhood that are members of each subpopulation, and the heterogeneity of response profiles amongst members of that subpopulation. These properties could vary systematically with respect to one another, and the spatial structure shown by the likelihood map does not disentangle them.

We therefore assessed the distribution of subpopulation memberships across cortex independently from response profile variability within subpopulation. To do so, we first classified each neuron into its maximum-likelihood subpopulation, then mapped the subpopulation identity of neurons (Figure 10A). As expected, members of the different subpopulations were locally salt-and-pepper intermingled, including in overlap zones. Also consistent with the likelihood maps, the fraction of each subpopulation in each area differed (Figure 10B). Critically, we found that the prevalence of subpopulation membership across cortex matched the likelihood maps (Figure 10D), implying that the spatial structure in the likelihood maps reflects the spatial variation in prevalence of each subpopulation and not some other structure in the heterogeneity of response profiles.

Finally, we looked for heterogeneity in the PETH features within the footprint spanned by each subpopulation. If the PETH features within a subpopulation varied substantially across areas, a model built on neurons from one area (e.g., M2) would assign lower likelihoods to neurons in other areas (e.g., M1), and vice versa (Figure 10C). To determine if this was the case, we produced likelihood maps for each GMM component of the models fit to each area separately, thresholded these maps to produce a contour, and compared their shapes. Subpopulations had nearly identical spatial footprints no matter which area was used to identify them (Figure 10E). This was true even in cases where only a small fraction of neurons in an area were members of that subpopulation: for example, the Forelimb somatomotor and Hindlimb somatomotor subpopulations could be identified using M2 data, even though there was no high-likelihood zone for these subpopulations within M2 (see Figure 9E–F). Note that this consistency mirrors the low Bhattacharyya distances between corresponding GMM components in Figure 9B, and further validates the use of clustering to combine components from different areas. Together, these results argue that the overlap zones for different subpopulations contained locally intermingled members, and that the PETH features within each subpopulation were similar across the territory covered by that subpopulation.

All procedures were approved by the University of Chicago Institutional Animal Care and Use Committee. For two-photon imaging, six male mice aged 8–12 weeks were used. Mice were crosses of Slc17a7-IRES2-Cre-D (JAX strain 037512; Harris et al., 2014) and TIGRE2-jGCaMP8s-IRES-tTA2 (JAX strain 037719; Sweeney et al., 2025), which express GCaMP8s in most glutamatergic neurons (Wang et al., 2023a). Each animal underwent a single surgery, then were individually housed on a reverse 12 hr light/dark cycle, with an ambient temperature of 22 °C and a humidity of 58%. Experiments were conducted in the afternoon, during the animal’s dark cycle.

Anesthesia and basic surgical preparation were as described in Grier et al., 2026. A circular craniotomy was outlined with a 5-mm biopsy punch and completed with a dental drill, centered over the left forelimb M1 at approximately 0.4 mm anterior and 1.5 mm lateral of bregma. The craniotomy was cleaned with SurgiFoam (Ethicon) soaked in phosphate-buffered solution (PBS). If the dura remained intact, a durotomy was performed with a needle.

A retrograde virus carrying a tdTomato construct (AAVretro-tdTomato, diluted to 5×10¹² particles per mL in PBS, Addgene stock 59462-AAVrg) was injected in S1-fl (mice 1–3; 0.0 mm A, 2.65 mm L relative to Bregma) or the center of the forelimb representation of M1 (mice 4–6; 0.4 mm A, 1.5 mm L). 100 nL of virus was pressure injected (NanoJect III, Drummond Scientific) at a depth of 300 µm from the cortical surface over 5 min. The injection pipette was kept in place for another 3–6 min to ensure viral dispersion before being removed slowly over 2–3 min. This injection retrogradely labeled cell bodies in other areas that sent projections to the injected area. In this paper, the labeling was used solely for stabilizing the imaging plane (see below) throughout the cortex.

The craniotomy was sealed with a 5 mm #1 round cover glass (Thomas Scientific) glued in place first with tissue glue (VetBond, 3 M) and then with cyanoacrylate glue (Krazy Glue) mixed with black dental acrylic powder (Ortho Jet; Lang Dental). In all mice, two layers of MetaBond (Parkell) were applied, and then a custom water jet-cut stainless steel head bar was affixed to the skull with black dental acrylic. Animals were awoken by administering atipamezole via intraperitoneal injection and allowed to recover at least 3 days before water restriction.

The behavioral task (Figure 2A) was a variant of the multi-target water-reaching task of Galiñanes and Huber, 2023. Water-restricted mice were head-fixed with their forepaws on paw rests (bent partially threaded screws) and the hindpaws and body supported by a custom 3D-printed translucent seat. Trials were triggered after the animal held both paw rests for 100ms. After an additional 100 ms hold period, a water spout (22 gauge, modified 90 degree bent, 1-in blunt dispensing needle, McMaster) was moved into one of 15 positions in front of the mouse’s face via a set of three motors (LSM050B-T4A, Zaber). The spout was customized, with ~2 mm of the side facing away from the animal ground down; this caused the water to cling to the last few mm of the spout and not just hang from the tip. The animals were then required to hold the paw rests continuously for an additional 400–600 ms delay period to trigger the delivery of a water droplet on the spout. If the animals released the paw rests briefly during this time, the delay was reset. If the paw rest release exceeded 1 s contiguously, the trial was aborted and a 10-s penalty period occurred. Brief releases occurred at variable rates across animals (20–85% of trials), and delay-aborted trials rarely occurred (<1% of trials). Animals were allowed a maximum of 2000 ms to achieve paw rest contact for the entire delay; if this did not occur, the spout was removed to the neutral location and a 5000 ms time-out was triggered (<3% of all trials across animals). Once the paw rests were held continuously for the variable delay time, a 4000 Hz tone was played by stereo speakers as the Go cue, and a 2–3 μl droplet of water appeared on the spout. The cue tone lasted 500 ms or until the mouse made contact with the water spout, whichever came first. The mouse could grab the water droplet and bring it to its mouth to drink anytime after the tone began. The spout was removed 4000 ms after first contact, triggering a variable ITI of 3000–7000 ms, and automatically wiped against a small sponge to remove any remaining water. Both the paw rests and spouts were wired with capacitive touch sensors (Teensy 3.2, PJRC). Control software was custom-written in MATLAB R2018a using PsychToolbox 3.0.14. Touch event monitoring and task control were performed at 60 Hz using the Teensy.

The mice were trained to make all reaches with the right paw and to keep the left paw on the paw rest during reaching. For the first 1–3 days, mice were head-fixed and provided water directly to their mouths to acclimate them to head-fixation and reward collection. During this period, the animals were encouraged to make consistent contact with both paw rests to trigger water delivery to their mouths. After acclimation and consistent trial initiation, the spout was withdrawn to a position on the right side of their face intended to elicit forelimb reaching with the right arm. If animals were reluctant to reach, small droplets of water were placed on their right whisker pad with a blunt syringe to induce grooming and water collection. After animals reliably performed reaches toward the rightward spout location (80–90% success), its position was moved medially and anteriorly in gradual increments within a single session until it aligned with the midline. Once mice could reliably reach to the central spout position, two new target locations were introduced on either side (approximately 1 mm from center). Once in this three-target training stage, each target was cued in blocks of 50 trials. The size of the blocks was reduced as the mice progressed in their training until targets were interleaved randomly. After 80–90% success at the three target configuration, two additional targets were added further lateral on the left and right sides, creating a five target semicircle. The targets were then progressively spaced apart along the semicircle until they reached their final azimuthal spacings of ~1.72 target-to-target and ~6 mm total. Variation in the Z position was introduced by adding an additional row of targets above and below the existing row and gradually increasing the inter-row distance until the final Z spacing of 1 mm was achieved. This training procedure took 10–20 days. Data presented here were collected after 3–6 weeks’ experience with the task.

Calcium imaging procedures were similar to those described previously (Grier et al., 2026). Briefly, imaging was performed with a Neurolabware 2 p microscope running Scanbox 4.1 and a pulsed Ti:sapphire laser (Vision II, Coherent). Depth stability of the imaging plane was maintained using a custom plugin that made automatic movements of the objective up to every ~10 s based on comparing red-channel data with an initially-acquired image stack. Offline, images were run through Suite2p to perform motion correction, region-of-interest (ROI) detection, and fluorescence extraction. ROIs were manually curated using the Suite2p GUI. Fluorescence was neuropil-corrected using a coefficient optimized by minimizing the mutual information between the corrected trace and the neuropil trace (Allen, 2025). As previously described (Grier et al., 2026; Zhu et al., 2022), fluorescence was then detrended and passed through OASIS using the ‘thresholded’ method, AR1 event model, and limiting the tau parameter to be between 300 and 800 ms. To put events on a more useful scaling, for each ROI, we found the distribution of event sizes, smoothed the distribution (ksdensity in MATLAB, with an Epanechnikov kernel and log transform), found the peak of the smoothed distribution, and divided all event sizes by this value. This rescales the peak of the event size distribution to have a value of unity.

As previously described, when time-locking the data for visualization, modulation testing, or further analyses, the deconvolved events were resampled into 10 ms bins. This resampling was performed by assigning a fraction of each event into the new 10 ms bins proportionally to how much the 10 ms bins overlapped the original ~32.2 ms frames, and taking into account the exact time each ROI centroid was sampled based on its position within the field of view (FOV).

All cells were imaged between 140 and 210 µm below the cortical surface, in superficial layer 2/3. We chose this depth range both because it yielded large numbers of modulated neurons, and because GCaMP expression in these animals was lower in deeper layer 2/3 of S1. Imaging in this limited depth range therefore produced more comparable data across areas.

To determine whether a neuron was modulated in the task, we used an adapted ZETA method (Montijn et al., 2021) as described in Grier et al., 2026. Briefly, trial-averaged responses were compared to shuffled trial-averages computed by circularly permuting each trial by a random offset. Modulation was computed as the maximum difference between the real and shuffled data. This procedure was performed separately for each target and for locking data to the cue (–200 ms to +400 ms), lift (–200 ms to +400 ms), and first contact (–300 ms to 300 ms). For each locking event (cue, lift, and first contact), neurons with any p-values ≤0.01 were considered modulated. For all analyses, only neurons modulated by the relevant locking event were included. Note that this measure looks for modulation over time to any target; it is indifferent to whether the neuron exhibits tuning across targets.

Each 2p FOV was aligned based on the vasculature to an image of the entire window captured via widefield imaging. S1-fl was identified by paw vibration (Alonso et al., 2023), with imaging and preprocessing performed exactly as described in Grier et al., 2026 except that the camera was upgraded to a pco.edge 5.5 CLHS sCMOS camera (Excelitas). The vibration map was aligned to the widefield vasculature image via shared vasculature landmarks. This composite image was then scaled and translated to best align the S1-fl activation shape to its CCF boundary, while aligning the central sinus vasculature to the midline overlapping bregma. See Figure 1—figure supplement 1 for vibration map to Allen CCF alignment across animals. 2p images from the cortical surface from each session were then scaled to 720 µm width by 980 µm height and aligned to the registered vasculature via rigid transformations. This series of transformations produced global coordinates for each ROI from its location within the 2p FOV.

To produce the map in Figure 1A, outlines of subregions described by prior literature were extracted. Our review of the literature is non-exhaustive and serves simply to illustrate the heterogeneity of function that has been described in previous studies. Corresponding figures were overlaid with the Allen CCF and rigidly transformed to qualitatively match anatomical boundaries as closely as possible. Outlines were then extracted by tracing the subregion boundaries by hand.

From anterior to posterior, we describe the acronyms and the corresponding citations as follows: secondary motor cortex (M2), or MOs in the Allen CCF. Anterior lateral motor area (ALM), as originally described in Komiyama et al., 2010 and further delineated in Guo et al., 2015 and Chen et al., 2017. Rostral Forelimb Area (RFA) as described in Tennant et al., 2011 and further delineated in Carmona et al., 2024. Rostral Forelimb Orofacial area (RFO) as described in An et al., 2026, and referred to as tjM1 in Mayrhofer et al., 2019. Secondary vibrissal motor area (M2-vb) as described in Mayrhofer et al., 2019 as the frontal region activated by C2 vibrissal stimulation, and called medial motor area or MM in Chen et al., 2017. Primary motor cortex (M1) or MOp in Allen CCF. Primary forelimb motor cortex (M1-fl) as described in Muñoz-Castañeda et al., 2021 via tracing and characterized in Grier et al., 2026. Primary hindlimb motor area (M1-hl) as traced from hindlimb musculature by Maurer et al., 2023, and sensory cortical areas by Zingg et al., 2014. Primary forelimb somatosensory area (S1-fl), or SSp-ul in Allen CCF. Primary proprioceptive and tactile forelimb somatosensory areas (S1-pro and S1-tac) as originally identified in Alonso et al., 2023. Primary hindlimb somatosensory area (S1-hl), or SSp-ll in Allen CCF. Primary trunk somatosensory area (S1-tr), or SSp-tr in Allen CCF. Primary mouth somatosensory area (S1-m), or SSp-m in Allen CCF. Primary nose somatosensory area (S1-n), or SSp-n in Allen CCF. Primary vibrissal somatosensory area (S1-bfd) or SSp-bfd in Allen CCF. Anterior visual cortex (A) or VISa in Allen CCF. Retrosplenial cortex (RSC), or RSPagl, RSPd, and RSPv in Allen CCF. Cortical cervical spinal cord (CSC) and lateral rostral medulla (latRM) projections as traced in Yang et al., 2023.

To quantify and visualize the spatial distribution of properties of imaged neurons, we used a binning procedure to prevent biases due to uneven sampling. We binned the neurons into 80 µm-wide square pixels, then averaged the property of interest over all neurons within the pixel. Pixels that contained zero neurons were excluded from further analysis. The images were then Gaussian smoothed (s.d. 150 µm). To Gaussian-smooth the images while excluding empty pixels and accommodating irregular map edges, the final normalization for each pixel was the sum of the weights of contributing pixels, excluding empty pixels. For modulation images, each neuron was assigned a zero if not statistically modulated or a one if modulated. For PETH feature maps, each neuron was assigned its PETH feature value. The one-dimensional pixel values were then mapped onto a perceptually linear colormap (Kovesi, 2015).

In Figures 4A, 5 and 9G, Figure 8—figure supplement 1, distributions of features were smoothed with Kernel Density Estimation (KDE). Specifically, for a distribution, the density f^h\begin{document}$\hat{f}_h$\end{document} at point x\begin{document}$x$\end{document} was computed asf^h(x)=1nh∑i=1nK(x−xih)\begin{document}$$\displaystyle \hat{f}_h(x)=\frac{1}{nh}\sum\limits_{i=1}^{n}{K}\left(\frac{x-x_i}{h}\right) $$\end{document}

where {x1,x2,x3,...,xn}\begin{document}$\left\{x_1, x_2, x_3,...,x_n\right\} $\end{document} represent the distribution of interest, K is the Gaussian kernel, and the bandwidth h was set by Silverman, 1988:h=1.06An1/5,A=min(s,IQR(x)1.34)\begin{document}$$\displaystyle h=1.06\frac{A}{n^{1/5}},\,A={\rm min}\left(s, \frac{IQR(x)}{1.34}\right) $$\end{document}

with n being the number of observations and S being the sample standard deviation.

As an alternative to our feature extraction method for summarizing population structure in trial-averaged activity, we applied PCA to the vectorized PETHs of all modulated neurons (the matrix of shape N x CT) and used the first 20 coefficients of each neuron as a feature space. For increased interpretability, we performed a VARIMAX rotation on the first 20 coefficients to sparsify them without distorting the space. The rotated scores’ spatial structure was visualized in . The likelihood maps for clustering based on the PC coefficients were shown in Figure 9—figure supplement 3C–G.

In Figure 6, we asked whether the single neuron PETH feature values changed more over the same spatial distance in some locations than others. This corresponds to a spatial derivative of the feature map. To compute this for each map in Figure 6, we first smoothed the spatial distribution of the feature map with a Gaussian kernel. as described in the section ‘Computing map images from single-cell properties’. We then gridded the smoothed map values into square bins as described above, and filled missing interior values with linear interpolations of their neighbors. At each pixel, we then computed the 2D gradient magnitude using MATLAB’s centered finite-difference method. Specifically, if M(x,y)\begin{document}$M(x,y)$\end{document} denotes the gridded feature map, then the gradient magnitude |∇M(x,y)|\begin{document}$\left|\nabla M(x, y)\right| $\end{document} was calculated as:|∇M(x,y)|=(∂M(x,y)∂x)2+(∂M(x,y)∂y)2\begin{document}$$\displaystyle \left|\nabla M(x,y)\right| =\sqrt{\left(\frac{\partial M (x,y)}{\partial x} \right)^2 + \left(\frac{\partial M (x,y)}{\partial y} \right)^2 } $$\end{document}

This produced a scalar map of local changes in the corresponding feature map. For the version in Figure 9—figure supplement 5, the two partial derivatives (x and y) were computed for each of the four subpopulation likelihood maps. The quadratic mean was then calculated as above over the set of individual feature (or likelihood) gradient magnitude maps.

In Figure 6G and H we generated random boundaries through rejection sampling. Potential midpoint coordinates were randomly selected uniformly within the bounding box of the map, and an orientation was selected from a uniform distribution of 0–360°. We then computed the endpoints for a 1 mm line segment with that center and orientation. This boundary candidate was accepted if two criteria were met. First, both endpoints must have been within a non-empty pixel. Second, at least 200 neurons must have been in the valid zones on each side of the boundary (between 50 µm and 500 µm from the boundary). To account for non-uniform distributions of neurons, we downsampled neurons on the denser side of each random boundary to match the count on the sparser side.

To assess how well we could classify neurons as above or below a random boundary using the neurons’ feature vectors, we trained a binary SVM with a radial basis function kernel and parameter optimization via Bayesian hyperparameter search. Decoding performance was evaluated using 5-fold cross-validation.

We used t-SNE to visualize the structure of our neural population’s feature space. Each neuron was represented by a five-dimensional feature vector comprising the PETH feature values described above. To improve the representation of large-scale structure, we seeded the t-SNE optimization with the top two principal components of the feature matrix (Kobak and Linderman, 2021). The affinity metric was chosen to be the Pearson correlation. t-SNE perplexity hyperparameter was chosen according to the N/100 rule of thumb (Kobak and Berens, 2019). The t-SNE space produced a two-dimensional projection of our neural data with coordinates of Yi=(yi,1,yi,2)\begin{document}$Y_i=(y_{i,1},y_{i,2})$\end{document} for each neuron i.

To produce contours in the t-SNE space for each area, we first selected the points for a given area and performed two-dimensional Gaussian KDE on these points to produce an estimate of probability density. We then drew contours (contour in Matlab) at the 90th, 95th, and 98th percentiles of the peak. To verify that our results were not specific to t-SNE, we also applied two-dimensional Uniform Manifold Approximation and Projection (UMAP; McInnes et al., 2020) and obtained qualitatively similar results.

For the analyses in Figures 8—10, we modeled the PETH feature vectors from each area using Gaussian Mixture Models (GMMs). For each candidate number of clusters k, we fit a GMM with full covariance matrices using the Expectation-Maximization algorithm (fitgmdist in Matlab). To select the optimal number of mixture components, we used the Integrated Completed Likelihood (ICL) criterion (Bertoletti et al., 2015), computed as:ICL(k)=−BIC(k)−∑ijPijlog(Pij+ϵ)\begin{document}$$\displaystyle {\rm ICL}(k)=-{\rm BIC}(k)-\sum\limits_{ij}{P_{ij}{\rm log}(P_{ij}+\epsilon )} $$\end{document}

where P_ij denotes the posterior probability that neuron i belongs to cluster j, BIC represents the Bayesian Information Criterion (Schwarz, 1978), and ϵ\begin{document}$\epsilon $\end{document} was chosen as 10^–4. For each area, we fitted GMMs with one to ten components, and selected the fit that produced the maximal ICL.

Following model selection for each region, we computed the log likelihood of every neuron according to the GMM of each anatomical region. The log-likelihood Li\begin{document}$\mathcal{L}_i$\end{document} of neuron i given the full model for a single area was defined as:Li=log(∑j=1KπjN(Xi|μj,Σj)+ϵ)\begin{document}$$\displaystyle \mathcal{L}_i={\rm log}\left(\sum\limits_{j=1}^{K}{\pi_j {\mathcal{N}}(X_i|\mu_j, \Sigma_j)+\epsilon } \right) $$\end{document}

where K is the number of components in the GMM and πj\begin{document}$\pi_j$\end{document} is the mixing weight for component j. In addition to the full-mixture model, log-likelihoods were calculated for each component within an anatomical area’s full mixture model to quantify the spatial footprint of each Gaussian component and to compare this spatial map across components of different anatomical areas. These log likelihoods provide a computational approach for understanding the structure of single neuron feature properties across the sensorimotor cortex.

In Figure 9B, we computed the distance between each pair of GMM components found in different areas. To do so, we computed pairwise Bhattacharyya distances between the Gaussians. This distance captures differences in the means (as a Mahalanobis-like distance), and differences in the variances and covariances (differences in the orientations, shapes, and sizes). Each Gaussian k was represented by its mean vector μk∈RN\begin{document}$\boldsymbol{\mu}_k \in \mathbb{R} ^{N}$\end{document} and covariance matrix Σk∈RN×N\begin{document}$\Sigma_k \in \mathbb{R} ^{N \times N}$\end{document},where N is the feature dimensionality (5). The Bhattacharyya distance D_B between multivariate Gaussians i and j was defined asDB(pi,pj)=18(μi−μj)TΣ−1(μi−μj)+12ln(det(Σ)det(Σi)det(Σj)),\begin{document}$$\displaystyle D_B(p_i, p_j) =\frac{1}{8}(\boldsymbol \mu_i - \boldsymbol \mu_j)^T \Sigma^{-1} (\boldsymbol \mu_i - \boldsymbol \mu_j) + \frac{1}{2} \ln\!\left(\frac{\det(\Sigma)} {\sqrt{\det(\Sigma_i)\,\det(\Sigma_j)}} \right), $$\end{document}WhereΣ=12(Σi+Σj)\begin{document}$$\displaystyle {\rm Where} \qquad \Sigma=\frac{1}{2}(\Sigma_i + \Sigma_j)$$\end{document}

For display, the distance matrix produced by the Bhattacharyya distance was ordered using hierarchical clustering with Ward’s method (Figure 9B). The number of clusters (‘subpopulations’) was determined by simple examination of this matrix. Each cluster comprised GMM components with heavily overlapping distributions in the feature space. Clusters were further validated by comparing the spatial distributions (in cortex) of the member neurons (Figure 10E), which were very similar for the components grouped in each cluster.

As the simplest way to fairly represent the components that were grouped to form subpopulations, for further analysis we modeled each subpopulation as arising from a GMM comprising the Gaussian components that were grouped together by clustering, weighted equally.

Code used to create the figures is available on GitHub: https://github.com/kaufmanlab/SGK26-public, copy archived at Grier, 2026.