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# Hierarchical organization of cortical and thalamic connectivity

## Abstract

The mammalian cortex is a laminar structure containing many areas and cell types that are densely interconnected in complex ways, and for which generalizable principles of organization remain mostly unknown. Here we describe a major expansion of the Allen Mouse Brain Connectivity Atlas resource1, involving around a thousand new tracer experiments in the cortex and its main satellite structure, the thalamus. We used Cre driver lines (mice expressing Cre recombinase) to comprehensively and selectively label brain-wide connections by layer and class of projection neuron. Through observations of axon termination patterns, we have derived a set of generalized anatomical rules to describe corticocortical, thalamocortical and corticothalamic projections. We have built a model to assign connection patterns between areas as either feedforward or feedback, and generated testable predictions of hierarchical positions for individual cortical and thalamic areas and for cortical network modules. Our results show that cell-class-specific connections are organized in a shallow hierarchy within the mouse corticothalamic network.

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## Data availability

Data (including high-resolution images, segmentation, registration to CCFv3, and automated quantification of injection size, location, and distribution across brain structures) are available through the Allen Mouse Brain Connectivity Atlas portal (http://connectivity.brain-map.org/). Individual experiment summaries can be viewed using this link: http://connectivity.brain-map.org/projection/experiment/[insert experimental id]. Experimental ids are listed in Supplementary Table 2. In addition to visualization and search tools available at this site, users can download data using the Allen Brain Atlas API (http://help.brain-map.org/display/mouseconnectivity/API) and the Allen Brain Atlas Software Development Kit (SDK: http://alleninstitute.github.io/AllenSDK/connectivity.html). Through the SDK, structure and voxel-level projection data are available for download. Examples of code for common data requests are provided as part of the Mouse Connectivity Jupyter notebook to help users get started with their own analyses. Source data generated for this study are provided as Supplementary Tables as indicated throughout. Code and data files for hierarchical analyses are available through the Allen SDK and Github (https://github.com/AllenInstitute/MouseBrainHierarchy).

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## Acknowledgements

We thank the Animal Care, Transgenic Colony Management and Laboratory Animal Services teams for mouse husbandry and tissue preparation; all the members of the Neurosurgery and Behavior team for viral injections, including those not listed as authors: N. Berbesque, N. Bowles, S. Cross, M. Edwards, S. Lambert, W. Liu, K. Mace, N. Mastan, C. Nayan, B. Rogers, J. Swapp, C. White and N. Wong; H. Gu for cloning of the synaptophysin–EGFP viral vector; E. Lee, F. Griffin and T. Nguyen for intrinsic signal imaging; and J. Royall and P. Lesnar for schematic figure preparation. This work was supported by the Allen Institute for Brain Science and, in part, by National Institutes of Health grants R01AG047589 to J.A.H and U01MH105982 and U19MH114830 to H.Z. We thank the Allen Institute founder, Paul G. Allen, for his vision, encouragement, and support.

## Author information

Authors

### Contributions

Conceptualization: H.Z., J.A.H. and S. Mihalas. Supervision: H.Z., J.A.H., S. Mihalas, A.B., L.N., N. Gaudreault, P.A.G., J. Lecoq, S.A.S., J.W.P., A.R.J. and C.K. Project administration: S. McConoughey, S.W.O. and W.W. Investigation, validation, methodology and formal analyses: J.A.H., S. Mihalas, K.E.H., H.C., J.D.W, J.E.K., P.B., S.C., L.C., A.C., A.F., N. Gaudreault, N. Graddis, C.R.G., P.A.G., A.M.H., A.H., R.H., L.K., X.K., J. Lecoq, J. Luviano, P.L., Y.L., M.T.M., M.N., L.N., B.O., E.S., S.A.S., Q.W., A.W. and Y.W. Data curation: J.A.H., K.E.H., J.D.W., P.B., S.C., A.M.H., B.O. and W.W. Visualization: J.A.H., K.E.H., J.D.W., H.C., L.N., D.F., S. Mihalas, M.N. and Y.W. The original draft was written by J.A.H. with input from K.E.H., J.D.W, S. Mihalas, H.C., Q.W., C.K. and H.Z. All co-authors reviewed the manuscript.

### Corresponding author

Correspondence to Julie A. Harris.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Peer review information Nature thanks Claus Hilgetag, Moritz Helmstaedter and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

## Extended data figures and tables

### Extended Data Fig. 1 Similarity of connection strengths by distance, virus, hemisphere, and Emx1-IRES-Cre or C57BL/6J mice.

ad, Most experiments were done with the Cre-dependent rAAV tracer, rAAV2/1.pCAG.FLEX.EGFP.WPRE. A subset of left hemisphere injections had a duplicate injection of rAAV with a synaptophysin–EGFP fusion transgene in place of the cytoplasmic EGFP (rAAV2/1.pCAG.FLEX.SypEGFP.WPRE). This tracer allowed us to address whether labelling presynaptic terminals would improve the accuracy with which we could quantify target connection strength, particularly in brain regions that contain mostly fibres of passage. Data consisted of n = 275 experiments (137 EGFP, 138 SypEGFP). These were matched across Cre lines and areas, and represent n = 8 Cre lines and n = 26 cortical areas. For pairs of spatially matched experiments, the average projection strength (log10-transformed NPV) measured across the entire brain was lower in SypEGFP than in EGFP experiments (~0.8 log unit when <500 μm apart). However, brain-wide projection values were still highly and significantly correlated. Thus, we included the SypEGFP data sets when indicated for analyses of connectivity patterns from given source areas (but only in comparison with other SypEGFP data sets). a, Spearman correlation coefficients (r) of normalized projection volumes for all possible pairs of injections (different and same tracer, all in the same Cre line) plotted against the distance between the injection centroids. Linear regressions showed a significant negative slope (P < 0.0001) with r decreasing as distance between injections increased. b, r plotted for injections within 500 μm of each other; slopes were not significantly different from zero and means were not significantly different from each other. Average and s.d. for each group is shown by the large symbols on the left (EGFP vs EGFP: 0.81 ± 0.056, SypEGFP vs SypEGFP: 0.79 ± 0.064, SypEGFP vs EGFP: 0.79 ± 0.071). c, Quantitative differences in projection strengths measured between replicates with the same virus and between SypEGFP and EGFP (logNPV(EGFP) − logNPV(SypEGFP) injections, all <500 μm apart in the same Cre line (n = 133 within virus and 222 between virus comparisons). Boxplots show median, IQR, minimum and maximum values; + indicates mean. d, Maximum intensity projections from four experiments within 500 μm of each other illustrate overall similarities between replicate injections and tracers (r shown for each pair). Injections targeted primary visual cortex (VISp) in Emx1-IRES-Cre mice using either EGFP or SypEGFP tracers as indicated. eg, Injections into Emx1-IRES-Cre mice were made into visual areas on the left hemisphere, whereas all C57BL/6J mice received injections into the right hemisphere. Following registration to the CCF, which is a symmetric atlas, we identified three pairs of experiments in which the injection centroids were <500 μm apart after we flipped injection site coordinates from the left to the right. Cortical projections were visually similar across both lines and hemispheres, and cortical connectivity strengths (to the 86 cortical targets) from these individual experiments (normalized projection volumes) were positively and strongly correlated as indicated. Thus, in Fig. 2 we merged the Emx1 and C57BL/6J data to represent connection strengths from all layers and classes, and in some of the ‘anchor’ groups we used data from both left and right hemisphere injections.

### Extended Data Fig. 2 Characterization of cortical projection neuron classes and layer selectivity across mouse lines.

a, Brain-wide projection patterns were visually inspected for every experiment and manually classified into one of six categories on the basis of projections to ipsilateral and contralateral cortex, striatum, thalamus, and midbrain, pons or medulla structures as described for IT, PT, and CT classes. bd, Unsupervised hierarchical clustering (using Euclidean distance and average linkage) of projection weights validates and reveals major classes of cortical projection neurons. b, Each column of the heat map shows one of the 1,081 injection experiments. Colours in the ‘manual PN’ class are coded as in c for projection class. Rows show selected major brain regions that distinguish known classes of projection neurons. Values in each cell are the fractions of total brain projection volume in the given region. The dendrogram was split into nine clusters, with two subclusters identified post-hoc for cluster 5. The numbers of experiments per cluster were: 1, n = 24; 2, n = 4; 3, n = 204; 4, n = 158; 5a, n = 148; 5b, n = 230; 6, n = 174; 7, n = 12; 8, n = 16; 9, n = 111. The numbers of experiments per projection class were: CT, n = 119; IT, n = 342; IT PT, n = 158; IT PT CT, n = 189; local, n = 100; PT, n = 173. c, The relative frequency of experiments from manually assigned projection classes within each cluster is shown. There was significant enrichment of 1, or 2 related, classes in each cluster (dots; Fisher’s exact t-test, P < 0.01). d, Maximum intensity projections of GFP-labelled axons across the brain from one example per cluster. e, Characterization of layer selectivity in wild-type mice and 14 Cre lines derived from injection experiments. Number of experiments per line is listed in Supplementary Table 1. For every injection and line, we assessed layer selectivity on the basis of the manually annotated injection sites. Polygons were drawn around every injection site so that, after registration to the CCF, injection volume in each layer could be informatically derived. A layer-selectivity index was calculated for each experiment (the fraction of the total injection volume contained in each layer, scaled by the relative volume of each layer in the injection source region, because layer volumes differ by area). Plots show individual data points and the average layer selectivity index ± 95% confidence intervals (in black) for the set of 15 mouse lines. Red lines in each Cre graph show average values from C57BL/6J experiments. Red lines in the C57BL/6J graph are averages from the Emx1-IRES-Cre experiments, which also labels cells across all layers. There is a bias towards L5 neuron infection in both C57BL/6J and Emx1-IRES-Cre mice, highlighting the importance of using layer-selective Cre lines for better coverage of cortical outputs.

### Extended Data Fig. 3 Computationally removing the distance dependence of connection weights alters the modular structure of the cortex.

To test the degree to which the spatial proximity of regions affects modularity analysis, we used a power law to fit the distance component of our ipsilateral CC connectivity matrix29. Then, we repeated our modularity analysis on the ‘distance-subtracted’ matrix built from these residuals. a, Weighted connectivity matrix for 43 cortical areas showing the value of the residuals from a power law to fit the distance component. Rows are sources, columns are targets. Colours on the rows indicate distance-subtracted community structure with varying levels of resolution (γ = 0.5–1.5 on the y-axis, γ = 0.8 only on the top portion of the x-axis). Columns are coloured by their module affiliation in the distance-subtracted matrix above their module affiliation in the original matrix (Fig. 1e). The inset in the top left corner shows the modularity metric (Q) for each level of γ, along with the Q value for a shuffled network containing the same weights. The Q values for modularity in the distance-subtracted matrix were smaller than for the original cortical matrix (for example, 0.2754 versus 0.4638 at γ = 0.8) and the range of values for which Q was greater than Qshuffled was narrower (0.7 ≤ γ ≤ 1.7), but some modules were still present in the distance-subtracted cortical connectivity matrix. The difference between Q and Qshuffled was greatest for γ = 0.8. The first distance-subtracted module was comprised of the entire somatomotor module, most of the lateral module, and two regions from the prefrontal module. The second distance-subtracted module contained the visual, auditory, and medial modules, plus most of the prefrontal module and one region from the lateral module (temporal association area). Notably, these modules were like those reported by Rubinov et al.9. As γ increased past 1.0, regions began to split from the two large modules in small groups that generally did not reflect the original divisions, except for the auditory areas. b, Ipsilateral cortical network in 2D using a force-directed layout algorithm. Nodes are colour coded by module. Edge thickness shows residual values and edges between modules are coloured as a blend of the module colours. c, Cortical regions colour-coded by their distance-subtracted community affiliation at γ = 0.8 show spatial relationships.

### Extended Data Fig. 4 Whole-brain single-neuron reconstructions reveal L4 IT projections.

a, L4 neurons are classified into at least three morphological types as shown. b, Image shows sparse labelling of L2/3 and L4 neurons in the tamoxifen-inducible Cux2-IRES-CreERT2 driver crossed with the Ai166 reporter and using a low dose of tamoxifen via oral gavage for 1 day. L4 neurons were identified on the basis of their apical dendrite and local axons, using additional anatomical context when possible. Reconstruction was performed using Vaa3D-TeraVR on the high-resolution whole-brain image stack (composed of more than 10,000 images, resolution x × y × z: 0.3 × 0.3 × 1 μm) acquired with a two-photon fMOST system. c, We identified 25 L4 neurons for complete morphological reconstruction of dendrites and axons for three cell types and three cortical areas. In this Cre line at least, spiny stellate cells (SSCs) were most frequently identified. d, Dorsal surface view shows the CC projection patterns from three anterograde tracer experiments into the predominantly L4 Cre lines for somatosensory cortex (SSp-m), visual cortex (VISp) and auditory cortex (AUD). ek, Each panel shows two examples of reconstructed cells of the same L4 type in somatosensory, visual or auditory cortex. Local morphology for each cell is shown in the inset. Arrowheads indicate axon clusters outside local region. Red, axon; blue, basal dendrite; black, apical dendrite. Consistent with canonical descriptions, we found SSCs in the somatosensory cortex that had only local axon clusters (e). However, even in these cases, we frequently observed what appeared to be an aborted axon branch (no terminal cluster found; long arrow). We also found SSCs in somatosensory cortex that did have clear axon clusters in nearby areas (g), and, in auditory cortex, SSCs projected even to the opposite hemisphere (f). hk, Although we identified fewer tufted pyramidal (TPC) and untufted pyramidal (UPC) cell types in this experiment, for both types we still found cells with near and long-range projections.

### Extended Data Fig. 5 Locations and cortical projection patterns from thalamic tracer experiments.

a, Locations of the thalamic tracer injection centroids (blue dots) mapped onto virtual 2D coronal planes from the Allen CCFv3. To minimize the number of sections shown, all centroids are mapped within 200 μm of their original location. See Supplementary Table 1 (thalamus tab) for more details on Cre lines and coverage. b, Example TC projections are shown in a flat map view of the ipsilateral cortical hemisphere for different thalamic nuclei arranged by the clusters identified in Fig. 3 and related to cortical modules. Most thalamic clusters projected primarily to a single module (Fig. 3c), but some thalamic regions projected across multiple modules (for example, anteroventral nucleus (AV), ventral anterior-lateral complex (VAL), parafascicular nucleus (PF), and central lateral nucleus (CL)), or projected strongly to both prefrontal and another module; for example, somatomotor (mediodorsal nucleus (MD)-1, ventral medial nucleus (VM)), lateral (paraventricular nucleus (PVT), MD-2, parataenial nucleus (PT)) or medial regions (nucleus of reuniens (RE), anteromedial nucleus (AM)).

### Extended Data Fig. 6 Comparison of corticothalamic projection strengths derived from EGFP and SypEGFP tracer experiments.

ad, Maximum intensity projections from four experiments within 500 μm of each other targeting VISp (same experiment labelled VISp-3 below) using either EGFP or SypEGFP tracers in the Rbp4-Cre_KL100 (L5) or Ntsr1_Cre_GN220 (L6) line as indicated. a′d′, Coronal STPT images near the centre of the densest terminal zone in LGd show axon and presynaptic terminal labelling in LGd and other thalamic targets, including the ventral lateral geniculate (LGd, LGv), the intergeniculate leaflet (IGL) and the lateral posterior nucleus (LP). The anterior pretectal nucleus (APN) in the midbrain is also indicated. SypEGFP labelling is more punctate and has less fluorescence in axons and fibre tracts. a′′d′′, Coronal STPT images near the centre of one of the densest terminal zones in the middle of LP. a′′′d′′′, Coronal STPT images near the centre of the second densest terminal zone in the anterior part of LP. This image also contains a portion of the terminal zone in the lateral dorsal nucleus (LD). eh, Directed, weighted, connectivity matrices (11 × 44) showing log10-transformed normalized projection volumes for the Cre lines representing CT projections labelled from layers 5 (e, f) or 6 (g, h) with EGFP or SypEGFP tracer as indicated. True negatives (including passing fibres) at the regional level were masked and coloured dark grey. The colour map is the same as in Fig. 4. The matrix shows relative differences for connections originating from L5 versus L6 (L5 − L6/L5 + L6) for EGFP-based measures (i) and SypEGFP-based measures (j). k, Normalized projection strengths for CT targets (n = 484) were significantly correlated from matched cortical locations between EGFP and SypEGFP tracers for both Cre lines (Spearman r = 0.71, 0.73; P < 0.0001). On average, EGFP CT NPVs were ~0.5 log unit larger than SypEGFP for Rbp4 experiments, but were not different for the Ntsr1 line. l, Normalized projection strengths for CT targets (n = 484) contacted by L5 or L6 cortical neurons in matched injection locations were also significantly correlated for both EGFP and SypEGFP tracers (Spearman r = 0.51, 0.60; P < 0.0001), although more weakly than for the same line between viruses. Specific connections with different fibre to terminal ratios are coloured by source module (light blue, from VISp; orange, from SSp; dark blue, from RSPagl). m, Relative differences in projection strength to LP and LGd are plotted from n = 6 VISp injection experiments (VISp-1 to VISp-6 in matrix rows above) for each Cre line and viral tracer. n, Relative difference ratios calculated for L5 to L6 using EGFP are plotted against those obtained using SypEGFP (n = 484 CT connections, n = 278 above threshold). There is a significant correlation (Spearman r = 0.68, P < 0.0001). Specific connections are coloured by source module (from l) and labelled with the target.

### Extended Data Fig. 7 Validation of informatics-processing steps: CCF registration and quantification from segmentation.

ac, To determine the precision of the registration process on which we rely here for quantification of signal by layer in the cortex, we manually delineated layers 1 to 6b, using background fluorescence in coronal STPT images, for n = 9 cortical areas (ACAd, ORBvl, AId, PERI, SSp-bfd, MOp, VISp, RSPd, and AUDp; see Supplementary Table 3) in n = 4 mice per region. We then quantified the percentage of voxels within each manually annotated layer that were assigned to all cortical layers following automated registration to the CCFv3. a, A confusion matrix show the mean percentage of overlapping voxel labels averaged across these areas (individual region data in Supplementary Table 7). b, c, Boxplots show the median and mean (indicated with +); whiskers show the minimum–maximum range for the percentage overlap for individual experiments (b) or cortical areas (c, coloured dots). Across these cortical areas, the average percentage overlap ranged from 86 to 96% of voxels appropriately registered for all layers, except for L6b, which was not included in subsequent layer quantifications. For some areas and layers, the precision was worse than others; for example, while 66% of voxels were appropriately assigned to L2/3 in ACAd, the remaining 34% were assigned to neighbouring L5. In ORBvl, only 51% of voxels were appropriately labelled for L6a. Note, however, that delineating layer 5 from L6a in ORBvl in coronal sections using just background fluorescence was very difficult even for experienced anatomists, so some of the imprecision may in fact come from the manual drawing. Even with these exceptions noted, in all cases a large majority of voxels were registered and assigned correctly. d, e, Frequency distributions of informatically derived quantification for manually verified true negative and positive targets. d, The numbers of log10-transformed normalized projection values are plotted for all CC and TC targets manually verified as true negative (n = 24,272) or true positive (n = 12,921). Most true positive values were between log10 = −4 and log10 = 1. At log10 = −1.5 (red arrow), 639 true negatives remained (2.6%), while 7,100 true positives were still included (54.9%), resulting in a false positive rate of 8.3% at this threshold level. e, Numbers of log10-transformed normalized projection values plotted for all CC and TC targets manually verified as true negative (n = 15,789) or true positive (n = 4,503). At log10 = −2.5 (red arrow), 362 true negatives remained (2.3%), while 3,335 true positives were still included (74.1%), resulting in a false positive rate of 9.8% at this threshold level.

### Extended Data Fig. 8 CC projection patterns by layer and class between reciprocally connected areas with known hierarchy.

a, In the visual module, VISp and VISal (see Supplementary Table 3) are reciprocally connected (black line). VISp is the de facto bottom of visual cortex hierarchy. The output to VISal from VISp is feedforward (FF). The reciprocal connection (VISal to VISp) is feedback (FB). In the FF direction (top), VISp projections from L2/3, L4, and L5 IT projections were densest in L2/3–L5 of VISal, and relatively sparse in L1 and L6 (cluster 4). Rbp4 projections from VISp to VISal were densest in L4 and L6, with moderate levels in L2/3 (cluster 8). L5 PT and L6 CT cells projected, albeit sparsely, to L1 and L5 (cluster 2). In the FB direction (bottom), L2/3 IT axons were broadly distributed across layers, with a sparser region in L5 (cluster 6). VISal L4 IT cells projected noticeably more weakly to VISp (as opposed to the panel above), and terminated with a different pattern (L1 and L5/6, cluster 6). L5 IT cells projected densely to superficial layers in VISp (cluster 1). Rbp4 axons were dense in L1 and deep layers (cluster 6). Projections from L5 PT and L6 CT cells were also sparse, but present in L1 and L6 (cluster 6). b, In the somatomotor module, SSp-bfd and SSs cortex are reciprocally connected. SSp-bfd to SSs is FF; the reverse is FB. In the FF direction (top), L2/3 and L4 IT cells preferentially innervate L2/3–L5, with relatively fewer terminals in L1 and L6 (clusters 3 and 4). L5 IT projections densely innervate L1 and L2/3 (cluster 1). Rbp4 projections were densest in L4 and L6, with moderate levels in L2/3 (cluster 8). L5 PT and L6 CT cell projections were sparse, and to L1 and/or deep layers (cluster 2 and 6). In the FB direction (bottom), the patterns looked remarkably like FB projections from VISal to VISp. Note again the strong connection originating from L4 cells only in the FF direction. c, VISp (in the visual module) and ACAd (in the prefrontal module) are reciprocally connected. ACAd exerts top-down control of VISp activity (FB); the reverse (VISp to ACAd) is considered FF. In the FF direction (top), L2/3, L4, and L5 cells all preferentially innervate L1 (cluster 1). In the FB direction (bottom), L2/3 cells also predominantly terminate in L1, but L5 cells project to both L1 and deep layers (L5 and L6, cluster 6). Note also there is a potentially significant sub-layer distinction; axons from VISp to ACAd are relatively deeper in L1 (or at the border of L1 and L2/3) of ACAd, compared to the more superficial termination of ACAd axons in L1 of VISp. All panels: overall, FF projections are more often in clusters 1, 4, and 8, and FB projections in cluster 6. Cluster assignments are indicated in each panel; n/a indicates that the connection was either absent or below threshold for clustering. Areas in each module are shown in a top down cortex view and the network as a force-directed layout (edges denote normalized connection density from Fig. 1e). STPT images in the approximate centre of each target region show the laminar distribution of axons arising from labelled neurons in the different Cre lines. Images are rotated so that the pial surface is always at the top of each panel.

### Extended Data Fig. 9 TC and CT projection patterns and rules between reciprocally connected areas.

a, Schematic summarizes observed projection patterns between core thalamic nuclei (blue circle) and their reciprocally connected cortical targets (L1–L6 colour coded). Laminar patterns are from Fig. 5g. STPT images of labelled axon terminals between three pairs of core nuclei and primary sensory cortex that perfectly follow rules in both directions. In the FF direction (LGd to VISp, VPL to SSp-ll, VPM to SSp-n), projections are dense in L4 or L4 and L6 (clusters 4, 8). In the FB direction, CT projections predominantly arise from L6. b, Schematic summarizes observed projection patterns between matrix-focal thalamic nuclei (orange circle) and their reciprocally connected cortical targets. STPT images of reciprocal connections between PT and ILA, MD and ORBl, and MD and AId illustrate the schematized rules. Projections from these thalamic nuclei belong to clusters with relatively fewer L1 axons (FF-like, clusters 3, 7, 9). The reciprocal CT input is also stronger from L6 (FB), like the core nuclei above. c, Three schematics are shown to summarize observed projection patterns between matrix-multiareal thalamic nuclei (red circles) and their reciprocally connected cortical targets. The top schematic shows dense TC projections to L1 (FB) with CT projections originating from L5 (FF). The middle schematic (with relevant example images boxed) shows reciprocal connection patterns in which TC projections target mid-layers (FF-like) and the reciprocal CT input is stronger from L6 (FB). The bottom schematic shows the same TC projection pattern as the top schematic, but with CT projections originating approximately equally from L5 and L6. STPT images show reciprocal connections between multiarea-matrix thalamic regions LP, PO, RE, and VM to three cortical targets each. Some regions have target-specific projections that are either FF or FB. For example, different from the LP-to-VISp projection (FB), axons from LP to VISam and ACAd target mid-layers as opposed to L1 (clusters 8 and 5, FF), and the reciprocal connection arises more from L6 (typical for FB). Projections from PO, RE, and VM to all three cortical targets are consistent with a FB projection (denser terminations in L1 and either L5 or L6 (clusters 2 and 6). Reciprocal CT projections originate from L5 or, both L5 and L6. We did not see CT input arising equally from both layers or more from L5 when the reciprocal TC projection was considered FF, consistent with the ‘no-strong-loops’ hypothesis37. All panels: overall, FF projections from core thalamic regions are in clusters 4 and 8. FB projections from matrix-multiareal thalamic regions are in clusters 2 and 6, like CC FB. The matrix-focal results support the notion that patterns with relatively less L1 involvement (3, 5, 7, 9) are FF, particularly given the strong reciprocal input observed from L6. STPT images are from the approximate centre of the axon termination field for each target region. Cortex images were rotated so that the pial surface is at the top. Cluster assignments (for TC) are indicated in each panel. Text labels above image show FF and FB direction based on relative position in Fig. 6. Dashed lines indicate region borders.

### Extended Data Fig. 10 Robustness of the hierarchical organization results.

We constructed multiple hierarchies using only C57BL6/J and Emx1-IRES-Cre experiments (WT) or Cre data without the Cre line confidence measure to compare with results in Fig. 6. The hierarchical position of each area $${H}_{i}^{0}$$and the CC global hierarchy score hCC are defined as in Eqs. (4, 5) in Methods, but with the same confidence for all lines, that is, conf(T) = 1 for all Cre lines (T). a, b, In both cases, connection types 2 and 6 are assigned to one direction (feedback), while other clusters are grouped to the opposite direction (feedforward). Cluster 7 was not identified in the WT data set. c, CT connections were also classified as in Fig. 6b for the Cre data. CT connections were not included for WT as these are exclusively defined by Cre lines. d, e, Global hierarchy scores from the original, observed data, and the distributions of hierarchy scores obtained from shuffled data sets (n = 100) are shown for CC connections only (green), compared to scores obtained when TC and CT connections are sequentially included (pink, blue). The upper bound scores for an artificially perfect hierarchy using the WT data sets (e) are 0.630 for CC and 0.601 for CC + TC connections. f, z-scores were calculated for the global hierarchy scores compared to shuffled data for each of the three versions of cortical hierarchy (CC, CC + TC, CC + TC + CT). The highest z-scores were observed when using Cre line confidence weighting (compared to those with no confidence weighting or wild type data only). g, Predicted hierarchical positions of 37 cortical and 24 thalamic areas based on CC, CC + TC, or CC + TC + CT connections. Areas are ordered in each panel by the scores obtained using Cre line data with confidence weighting (Cre conf, black circles). Scores from Cre line data without confidence weighting (grey circles) and scores from wild type/Emx1-IRES-Cre data (open circles) are plotted for direct comparison. y-axis labels are colour coded by module assignment (for cortical areas). h, Robustness of the cortical hierarchy (w/ Cre conf) against individual Cre lines and projection classes. Left, Spearman rank correlation coefficients between the CC and CC + TC hierarchy with n = 13 layer- or class-specific Cre lines included versus each of the Cre lines removed. Right, results when data from Cre lines with the same layer and class were removed together. Removal of these lines and classes produced relatively minor deviations from the overall hierarchy determined with all data. Note that in both panels the y-axis starts at r = 0.85. For all lines and classes, the correlation with the hierarchy using the complete data set is very high. The lowest correlations occurred following removal of Cux2-IRES-Cre, Rbp4-Cre_KL100, and Tlx3-Cre_PL56.

## Supplementary information

### Supplementary Table 1

.Complete table of all Cre lines and source areas included from cortical and thalamic experiments of the Allen Mouse Brain Connectivity Atlas.

### Supplementary Table 2

.Complete table of all individual experiments with metadata that can be used to access data through the Allen SDK (http://alleninstitute.github.io/AllenSDK/connectivity.html).

### Supplementary Table 3

.Abbreviations and full structure names for all isocortical and thalamus areas in the Allen Mouse Brain Common Coordinate Framework, version 3 (CCFv3).

### Supplementary Table 4

.Corticocortical connectivity matrices. Three tabs containing (1) all anchor group experiments and metadata, (2) cortico-cortical normalized projection volumes (NPV) and manual checks for true positives, and (3) formatted data matrices from Fig. 2 with each row and column labeled with source, target, and experiment id, and including Cre lines not shown in Fig. 2.

### Supplementary Table 5

.Thalamocortical connectivity matrices. Two tabs containing (1) thalamo-cortical normalized projection volumes (NPV) and manual checks for true positive signal, and (2) formatted data matrix as shown in Fig. 3 with each row and column labeled with source, target, and experiment id.

### Supplementary Table 6

.Corticothalamic connectivity matrices. Three tabs that contain (1) cortico-thalamic normalized projection volumes (NPV) and manual checks for true positive signal, (2) formatted data matrices as shown in Fig. 4 with each row and column labeled with source, target, and experiment id, including Cre lines not shown in Fig. 4, and (3) L5 and L6 difference matrix values and labels from Fig. 4.

### Supplementary Table 7

.Confusion matrices from all nine cortical areas analyzed to measure registration precision of manually annotated layers into the CCFv3.

### Supplementary Table 8

.Relative laminar density data and cluster assignments of the 7,063 source-line-target values which passed our applied filters as described in Results and were included in Fig. 5a.

### Supplementary Table 9

.Two tabs containing (1) corticothalamic normalized projection volumes (NPV) from L5 and L6 Cre lines and results of LDA classification for Cre line confidence and no confidence weighting from Fig. 6b and Extended Data Fig. 10c, and (2) hierarchy scores for all cortical and thalamic regions using CC, CC+TC, and CC+TC+CT connections, and for Cre lines with and without confidence, and the wild type (all layers) dataset from Fig. 6d and Extended Data Fig. 10g.

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Harris, J.A., Mihalas, S., Hirokawa, K.E. et al. Hierarchical organization of cortical and thalamic connectivity. Nature 575, 195–202 (2019). https://doi.org/10.1038/s41586-019-1716-z

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• DOI: https://doi.org/10.1038/s41586-019-1716-z

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