Topographic organization of single-neuron projectome for mouse prefrontal cortex

Neurons in the prefrontal cortex (PFC) are responsible for high-level cognitive functions. Comparing to sensory and motor cortices, however, the connectivity organization of PFC is far more complex and still poorly understood. Here we report that whole-brain reconstruction of complete axonal morphologies of over 6,000 projection neurons in mouse PFC revealed ne-grained topographic relationship between the soma locations in PFC and their projection patterns before and after arriving the cortical and subcortical target regions. We rst mapped the long-range projections of intratelencephalic (IT), pyramidal tract (PT), and corticothalamic (CT) neurons, and found that each class of these neurons can be further categorized into target-based subclasses, with somata of each subclass preferentially located at different PFC domains. Furthermore, the distribution of individual axon projections within each target region exhibited subregion preference, with their somata located in specic PFC subdomains. Mapping of single axons revealed a topographic order of primary axons within IT, PT, and CT ber tracts that preserved the topography of their soma locations within PFC, and a spatial order of collateral branching points that yielded ordered clusters of collaterals aiming at specic targets. Within the target regions, we further observed subregion-specic arbor distribution that depended on the soma location. Such arbor distribution analysis of cortico-cortical PFC axons unveiled asymmetric terminal connectivity in PFC network. Our results demonstrate how large-scale single-neuron projectome analysis can provide new insights into the structural principle within the brain.


Introduction
Long-range projection neurons are essential for communication of neural information within the brain.
Diverse patterns of axon projections are the basis of distinct neuronal functions, but the pattern of axon projection for single cortical neurons is only beginning to be elucidated by recent mesoscopic reconstruction studies 1,2 . In the neocortex, long-range projection neurons are broadly divided into three top-level neuron classes: intratelencephalic (IT) neurons, pyramidal tract (PT) neurons, and corticothalamic (CT) neurons, based on their projection patterns 3,4 . However, this classi cation is not su cient to describe the functional and structural diversity of cortical projection neurons. For example, two subtypes of PT neurons in the motor cortex have been identi ed and shown to be involved in different aspects of motor functions 5 . To understand the full diversity of neuron types and the general rules of the connectivity organization requires extensive investigation of single neuron projectome within a brain region of interest. The prefrontal cortex (PFC) is believed to be responsible for high-level cognitive functions in mammalian brains and implicated in many neuropsychiatric diseases in humans 6 . It harbors diverse neuron subtypes that send axonal projections to numerous regions across the entire brain 7,8 . The complex connectivity patterns of PFC neurons, which are likely to re ect their diverse yet crucial functions, are still poorly understood due at least partially to the lack of systematic characterization at single-neuron level.
In this study, we reconstructed the axonal morphologies of over 6,000 individual projection neurons, covering extensively IT, PT, and CT neurons in PFC. Classi cation of axon projections revealed speci c projection patterns that correlated systematically with the soma locations across PFC. Mapping the single-neuron projectome allowed us to reveal new PFC subdomains, modular connectivity within PFC, and subdivisions of PFC target regions. We unveiled a variety of rules underlying the projection diversity, including the ordered arrangement of primary axons, the selection of collaterals for target regions and the ordered distribution of axon arbors within target subregions. Analysis of the axon arbors identi ed the PFC loci with differential terminal innervation. This work illustrates the importance of large-scale single neuron projectome analysis for understanding the structural principle of long-range projections in the brain.

Projectome Reconstruction of Single PFC Neurons
We sparsely labeled projection neurons of PFC 9 and imaged their whole-brain axon projections from a total of 149 mice using uorescence Micro-Optical Sectioning Tomography (fMOST) technology 10,11 (Fig. 1a, Supplementary Information 1, Methods). We developed a software system, referred to as Fast Neurite Tracer (FNT), to streamline the tracing process of long-range axon projections in TB-sized lightmicroscopic datasets (Extended Data Fig. 1). Using FNT tracing pipeline, we reconstructed the axons of 6,101 projection neurons in mouse PFC. After registering all traced neuron projections to the Allen Brain Atlas (ABA) reference brain 12 (Extended Data Fig. 2), we found that the somata of traced PFC neurons were distributed across all PFC subregions (Fig. 1b) and they exhibited extensive and diverse projections in the whole brain (Fig. 1c). We then classi ed all traced neurons based on the result of global axon alignment by an algorithm referred to as FNT-dist (Supplementary Information 2) and visualized the results by t-distributed Stochastic Neighbor Embedding (t-SNE) (Fig. 1d). In line with the conventional de nition of cortical projection neuron classes 3 , these projection neurons can be readily divided into three main classes of IT, PT and CT neurons (Fig. 1e). Consistent with previous studies 13 , the somata of IT, PT and CT neurons in PFC are preferentially distributed in different cortical layers, with IT mainly located in L2/3 and L5, PT in L5, and CT in L5/6 ( Fig. 1f). Among all PFC neurons we analyzed, IT neurons are the most abundant, followed by PT and CT neurons. All our data can be visualized on the website: https://mouse.braindatacenter.cn/.
Target-based sub-classi cation of IT, PT, and CT neurons We asked whether IT, PT and CT neurons in PFC can be further divided into subclasses, based on the pattern of their projection targets. For IT neurons, we rst obtained six combinations of projections to cortex and striatum in each hemisphere (Fig. 2a). IT neurons with these different projection patterns can be found in all PFC regions but the proportions of these neurons vary across PFC regions and cortical layers (Fig. 2b, c). The somata of IT neurons projecting to contralateral cortex or striatum, or both are located in the deeper layers. Topographic relationships with additional IT neuron targets such as amygdala, pallidum, olfactory areas, claustrum, and endopiriform nucleus have also been found (Extended Data Fig. 3a-c). We further divided the projections of IT neurons into six patterns based on their ipsi-and contra-lateral cortical projections to PFC and non-PFC regions (Fig. 2d). Somata of neurons of these six patterns also showed different distributions across PFC regions and cortical layers (Fig. 2e, f).
IT neurons with broader cortical projections such as those projecting outside of PFC are located in deeper layers than those projecting only locally within ipsilateral PFC. Meanwhile, IT neurons with contralateral projections showed high degree of symmetry between ipsi-and contra-lateral projections, with the extent of symmetry depended on the soma locations across PFC regions (Extended Data Fig. 3d, e). Finally, we focused on the IT neurons with long-range ipsilateral cortical projections outside PFC, and identi ed six subclasses of IT neurons (IT-1 to IT-6), each of which targeted a subset of 14 ipsilateral non-PFC cortical regions (Fig. 2g). Example neurons from different subclasses of neurons are illustrated in Fig. 2h. The somata of each subclass of IT neurons were largely preferentially distributed across PFC and cortical layers. For example, neurons of IT-1, IT-2, and IT-4 subclasses were differentially distributed in L5 and along dorsal to ventral direction in agranular insular cortex (Fig. 2i). The overall ipsilateral projections outside PFC from all PFC IT subclasses are summarized by the wiring diagram shown in Fig. 2j.
Abbreviation of brain structures can be found in Supplementary Information 3.
Similarly, PFC PT and CT neurons mainly projecting to subcortical regions can be divided into 12 and six subclasses respectively based on their targets (Extended Data Fig. 4a and Extended Data Fig. 5a). The somata of each subclass of PT and CT neurons also showed distinct preference for PFC regions and cortical layers (Extended Data Fig. 4b, c and Extended Data Fig. 5b, c). For example, PT-4 neurons in ACAv (projecting to SCm) were distributed in super cial layer of L5 while PT-8 neurons in ACAv (projecting to Pons) were mainly in deep layer of L5 (Extended Data Fig. 4d), similarly for PT-2 and PT-11 in AId. As shown in Extended Data Fig. 5b, c, somata of the CT-1 subclass neurons (projecting to VAL, VM, and PCN) were mainly distributed in ACAd and deep layer of L5 while those of CT-2 subclass (projecting to LD and LP) mainly in ACAv and L6. Therefore, within each of IT, PT, and CT class, neurons can be further classi ed based on their projection patterns, and these new subclasses of neurons often exhibit differential preferences in their soma locations across PFC regions or cortical layers, or both. The functional relevance of these new PFC subclasses is shown in Supplementary Information 4.
Subdivision of PFC by single-neuron projectome PFC is known to harbor subdomains with distinct functions 14 (Supplementary Information 5). Singleneuron projectome allowed us to subdivide PFC into subdomains systematically. To this aim, we investigated the spatial organization of PFC using the combined distributions of projection-de ned subclasses for IT, PT and CT neurons across ne-grained PFC subregions. We unbiasedly divided PFC into a series of cortical columns (n=40) (Methods, Fig. 3a). We then obtained the spatial density distributions of all IT, PT, and CT subclasses among the cortical columns we de ned. Using unsupervised hierarchical clustering, we found that PFC can be parcellated into medial (PFCm), lateral (PFCl), and dorsal (PFCd) subregions, each of which consists of a collection of cortical columns with similar compositions of PFC neuronal subclasses (Fig. 3b, c). Each projectome-de ned PFC subregion encompasses several PFC regions de ned in the ABA and a single PFC region in the ABA can span different projectome-de ned PFC subregions (Fig. 3d). Furthermore, we constructed a network of intra-PFC connections among the cortical columns based on single-neuron projectome. We found that the intra-PFC connectivity network has a modular structure, in which the three modules are highly similar to the three subregions de ned by PFC output projections ( Fig. 3e-g). Further analysis of this modular structure unveiled connector hubs, non-hub connectors, provincial hubs and peripheral nodes 15 .
Interestingly, we found that all cortical columns in PFCm are either connector hubs or non-hub connectors, underlining the role of PFCm as the main connector with PFCl and PFCd. Together, singleneuron projectome analysis reveals three PFC subregions de ned by PFC output projections, a modular structure of intra-PFC connectivity, and the inter-modular connectors in PFC.

Subdivision of target regions by single-neuron projectome
Many PFC downstream target regions are known to have functional subdomains 7 . We next investigated whether different subdomains of a PFC target region can receive differential projections from different PFC neurons. Brie y, we divided the target region into a 3D collection of cubes and projection strength from each individual PFC neuron was quanti ed by the total axon length within the cube. The targeted subregions were determined by unsupervised hierarchical clustering of projection strengths among all cubes (Fig. 3h). As an example, the mediodorsal thalamus (MD) receives its majority of inputs from PFC. We rst divided MD into ve subdomains: anterior-medial (MDam), dorsal-anterior (MDda), dorsal-lateral (MDdl), central (MDc), and ventral-posterior (MDvp) subregions (Fig. 3i, j). This analysis also revealed the clustering of PFC neurons with distinct MD subregion preference (Extended Data Fig. 6a, b). We found that neurons in ORBm and ORBvl preferentially project to MDam, while neurons in AId project to MDvp. Thus, the distribution of PFC projections within MD exhibited a topographic order that re ect the topography of their somata in PFC. As MD receives projections from both CT neurons and PT neurons, we further found that topographic projections to MD are highly similar between the two neuron classes, with CT projection generally stronger than PT projection (Fig. 3k, l). Using the same approach, we subdivided additional PFC downstream regions such as lateral hypothalamus (LHA) (Extended Data Fig.  6c-g). Taken together, with single-neuron projectome, we obtained detailed subdivision of PFC target regions in which we observed a clear topographic relationship with PFC soma location.
Primary axons and collaterals re ect soma topography and target locations As single neurons utilize axon branching for target selection, we next characterized the patterns of axon branching of PFC neurons. Based on previous developmental studies of cortical neurons [16][17][18][19] , we divided the axon projections into primary axons, axon collaterals, and terminal arbors (Fig. 4a, Methods). The primary axons of IT, PT and CT neurons form distinct ber bundles ( Fig. 4b and Extended Data Fig. 7). For PT neurons, the positions of primary axons on a series of cross-sections along the axon bundle remain positively correlated with soma locations, the extent of which decreases gradually as the axon bundle condenses and twists towards brain stem (Fig. 4b, c). We next clustered axon collaterals of PT neurons by FNT-dist into nine clusters, each of which extending towards a speci c direction (Fig. 4d). The collateral branch points of these clusters are sequentially distributed on the primary axons with the order of branch points along primary axons positively correlated with the order of their respective target locations ( Fig. 4e-g). Furthermore, the primary axons forming collaterals (e.g. those in collateral cluster 4) are generally closer to their respective target (SCm) than those primary axons that do not form collaterals (Fig. 4h). Finally, we found that the centers of axon arbors within the same target brain region (e.g. Striatum or Pons) are highly correlated with the branch point positions of collaterals within the same collateral cluster resulting in a more ne-grained soma-target topography ( Fig. 4i, j). Therefore, axon collaterals of PT neurons form at ordered branch points along primary axons and are topographically organized to project to speci c target locations.
Similarly, the primary axons of IT neurons within corpus callosum are topographically arranged and highly correlated with their homotypic targets in contralateral hemisphere (Extended Data Fig. 7a, b). We found IT collaterals sequentially targeting ipsilateral cortex, ipsilateral striatum, and contralateral targets along the primary axons (Extended Data Fig. 7c). Within ipsilateral cortex, IT collaterals were further sorted into clusters aiming at prefrontal, medial, somatomotor, and lateral cortical structures respectively, in line with our classi cation of IT neurons based on ipsilateral cortical projections (Extended Data Fig.  7d-f and Fig. 2g). The primary axons of CT neurons along medial to lateral direction turn roughly 90 degrees becoming anterior to posterior direction before arriving at thalamus and are highly correlated with their respective targets in thalamus (Extended Data Fig. 7g-h). Together, we found that the spatial arrangement of primary axons and collaterals of IT, PT and CT neurons re ects soma topography and target locations.

Spatial analysis of axon arbors reveals diverse modes of terminal innervation
The spatial distribution of axon terminals has important functional implications 4 . We obtained 56,825 terminal arbors using single-neuron reconstruction. We rst explored the laminar distributions of 15,593 terminal arbors of IT neurons in the cortex. We classi ed these arbors into four subclasses (L1-, L2/3-, L5-, and L6-types) based on the arbor distribution across cortical layers (Fig. 5a). We found that the arbor type usage depends on the laminar location of soma with a positive correlation between soma depth and arbor depth across layers (Fig. 5b). We further found that the IT neurons in different PFC regions showed distinct arbor type preference, with the extend of preference further depended on the target identity (Fig.  5c). In general, projections from PFC to non-PFC regions use more L1-or L6-type arbors while intra-PFC projections use more L5-type arbors, in line with the current view of laminar patterns of feedback and feedforward projections 20 . Based on the patterns of arbor type usage, we classi ed all intra-PFC connections among cortical columns we de ned in Fig. 3a into four classes, consistent between L2/3 and L5 neurons ( Fig. 5d and Extended Data Fig. 8a, b). In particular, we identi ed signi cant differential usage of arbor types among all reciprocal connections among cortical columns (Extended Data Fig. 8c). For example, the projections from column 28 (PFCd) to column 34 (PFCm) are enriched with L1-type arbors while the projections in opposite direction are enriched with L2/3-and L5-type arbors ( Fig. 5e-f). Similar asymmetric arbor usage was found between column 7 (PFCl) and column 22 (PFCm). Notably, column 28, 34, 7 and 22 are all inter-modular connectors in intra-PFC connectivity network (Fig. 3g). Moreover, similar arbor types, soma-arbor relationship and patterns of arbor type usage have been found for 2,607 cortical terminal arbors of PT neurons, with PT neurons having more L5-type arbors than IT neurons (Extended Data Fig. 8d-g). Together, our arbor analysis suggested that previously reported laminar patterns of arbor terminations at population level 21 are in fact consisted of discrete arbor types at single-axon level and we mapped the precise loci with differential usage of arbor types, providing the directionality of inter-modular connectivity in PFC.
Furthermore, we analyzed arbor distributions of PT and CT neurons in thalamus (Extended Data Fig. 9). By clustering arbors based on their spatial overlaps, we identi ed subdomains within thalamus occupied by different arbor clusters (Extended Data Fig. 9a, b). Somata of neurons utilizing arbors in different arbor clusters are also preferentially distributed in different PFC regions (Extended Data Fig. 9c, d). We found that terminal arbors of PT and CT neurons in thalamus, known to function in "driver" and "modulator" modes respectively 22 , are preferentially distributed in different arbor clusters (Extended Data Fig. 9e). Similar arbor organization has been found for PT and IT neurons in striatum (Extended Data Fig. 10). Therefore, axon arbors are spatially segregated within target brain regions in a manner depending on the soma location, and the analysis of terminal arbors provides new insights into the functional diversity of terminal innervation.

Discussion
The information ows in the brain are facilitated by the axons that can extend to a long distance.
However, how these long-range axons are spatially arranged in a highly compact brain to achieve the regulation of diverse targets is unknown. In this study, we reconstructed over 6,000 single-neuron projections in mouse PFC achieving a coverage comparable to current single-cell transcriptome studies. PFC has long been considered as the command center in the brain. Our study provided a comprehensive atlas of PFC projectome laying the structural foundation for studying diverse high-level cognitive functions. By analyzing single-neuron projectome, we unveiled a new brain map of PFC as well as PFC target regions beyond conventionally de ned brain regions. Furthermore, our study suggests that topographic relationship with soma location is maintained at all levels of axon projections including primary axons, axon collaterals, and terminal arbors. These organizational principles are likely generalizable in the whole brain and could be fundamental to the parallel processing and integration of information in the mammalian brain.

Mice
Animal experimental procedures and care were approved by the Animal Care and Use Committee of the Center for Excellence in Brain Science and Intelligence Technology (Institute of Neuroscience), Chinese Academy of Sciences, Shanghai, China. All mice used in this study were C57BL/6 male mice (8 to 10 weeks old), purchased from SLAC laboratory, Shanghai. Mice were raised under the standard condition (12-hr light/dark cycle, 22-25°C) with the access to food and water ad libitum.

Virus injection
In order to achieve sparse labeling, a mixture of a diluted virus expressing Cre-recombinase (AAV2 angle of micro-injection is relative to vertical plane of DV axis. The Bregma point is de ned as 0° (0, 0, 0) in the coordinate system of vertical injection. The detail information of injection can be found in Supplement Information 1.
fMOST imaging, data compression and image registration All mouse brain samples in this study were imaged by fMOST technology as previously described 10, 11 . The fMOST raw image data contain two channels: EGFP channel (for neurite tracing) and PI-staining channel (for image registration). A typical EGFP channel consists of around 10,000 16bit images in "tif" format of 30,00020,000 pixels in size. The raw data is processed into 1,000,000 data cubes of 256256100 voxels in size by FNT-slice2cube command. The data cubes were then compressed with HEVC method. We also downsampled the raw data to the resolution of 20µm20µm20µm for the overview of the whole brain data.
To map our reconstructed neurons onto Allen Brain Atlas (ABA) reference brain, we started with a rough registration from our PI-staining image (downsampled to 10µm10µm10µm) to ABA averaged template (10µm10µm10µm) by a ne transformation including translation, rotation, scale and shear. We then manually segmented Isocortex, Hippocampal region, Caudoputamen, Thalamus and Hypothalamus in our data image. After that, we replaced the pixel values in the segmented areas of data image into the following values: 240, 80, 120, 160, 200 for Isocortex, Hippocampal region, Caudoputamen, Thalamus and Hypothalamus respectively. ABA template image was modi ed by the same operation. Next, we used nonrigid image registration method to map our modi ed data image to modi ed ABA template image 23 (Extended Data Fig. 2d, e). Finally, our reconstructed neurons were mapped onto ABA reference brain by calculated a ne and nonrigid transformation accordingly (Fig. 1c). A ne registration and nonrigid registration were done by the software toolkit, Computational Morphometry Toolkit (CMTK).

Large-scale Single-neuron Reconstruction using Fast Neurite Tracer
Here we developed a new software tool, Fast Neurite Tracer (FNT), for e ciently tracing long-range axon projection, in tera-bytes of datasets generated by light microscopy. The work ow of FNT is shown in Extended Data Fig. 1a. The manual of FNT can be found in Supplementary Information 7. Brie y, to allow data loading into the memory of personal computer, original image data are split to smaller 3D data cubes by a program called "slice2cube" in FNT. For smooth transition during tracing, about eight neighboring cubes around the current position are loaded into computer memory automatically. Loaded cubes are visualized in 3D for tracing. Users can conveniently switch to 2D visualization to examine the ne neuronal structures. Combined with zooming and rotation, it enhances human perception of complex 3D structures. Extended Data Fig. 1b shows the graphical user interface of FNT during tracing. To provide global perspective of original data, downsampled image data can be visualized simultaneously with the 3D data cube. To accommodate the experimental data with multi-color imaging such as PI staining in fMOST technology, FNT allows up to three sets of selected imaging data channels to be visualized at the same time. Categorical data such as brain annotation from Allen Brain Atlas (ABA) can also be incorporated. After loading the brain annotation le, the brain area annotation at any chosen position in the brain can be indicated.
FNT tracing process consists of three steps: nding a putative path, examining the putative path and extending the current neurite tree as summarized in Extended Data Fig. 1c. In FNT, we included a new operation: nding a putative path only with a starting position. In FNT, users' con rmation at each step ensures the correctness of tracing. After users con rm that a branch is traced to the end, the branch is marked as nished. FNT keeps the records of all un nished branches and will automatically jump to the nearest un nished branch when the current branch is nished. A neuron tree can be traversed in this way until it is completed (Extended Data Fig. 1d). Users can easily edit existing branches or undo previous unwanted operations. A demonstration of FNT tracing process is shown in Supplementary Information 6.
FNT allows distributed tracing of the same dataset by a large number of tracers simultaneously. Image data were compressed and can be accessed locally via portable hard disk or remotely through web-based computer network. We minimized the hardware requirement to allow users to run FNT on personal laptop computers. This allows us to conduct large-scale tracing through online crowdsourcing. We parallelly distributed the tracing tasks among a team of more than 70 human tracers. 7,000 neurons were traced using roughly 60,000 human hours over one year. Among 7,000 traced neurons, over 6,000 of them fall into PFC regions.

Quality controls and evaluation
To ensure the validity of tracing result, every neuron was traced by two independent human tracers. Then the results were merged by a third human tracer. We designed a scoring scheme combining different types of errors to evaluate the quality of tracing result. The penalties for 100-score are: false negative or false positive of branches (-2, n=1; -6, n=2 or 3; -11, n4), loop forming (-6), and mis-connections to other neurons (-11) (Extended Data Fig. 2a). We found that the merge of two independent tracing result can signi cantly increase the quality score (Extended Data Fig. 2b). Among our traced neurons, we sampled 600 neurons for further evaluations by an independent team of tracers and found a median score of 94 for the tracing results of sampled neurons (Extended Data Fig. 2c).

Global alignment of single-neuron axons
We developed a dynamic programming algorithm, referred to as FNT-dist, to align axon projections of different neurons according to their morphology and geometry. The dissimilarities between the neurons were calculated by the alignment result. The detailed description of FNT-dist can be found in Supplementary Information 2.

Construction of PFC atmap
For a better visualization of soma distribution in PFC, a attened map of PFC was constructed. We rst calculated the geodesic distance between each vertex on the surface of PFC and an anchor vertex. To project these vertices onto a 2D (U, V) coordinate system, we chose the anchor vertex as the origin, the medial-lateral axis as the U axis, and the anterior-posterior axis as the V axis. For every other vertex, we computed the directional vector to the anchor vertex on the horizontal plane and obtained the (U, V) coordinate by nding the location whose distance to the origin equals their geodesic distance along the directional vector.

Target-based sub-classi cation of IT, PT, and CT neurons
To construct the projection matrix for sub-classi cation of IT, PT, and CT neurons, we quanti ed the axonal length of every neuron in each target region. As the volume of each target region varies, we rescaled the projection matrix along target regions based on their minimal and maximal values. After obtaining the normalized projection matrix, we conducted unsupervised hierarchical clustering, using 1-Spearman correlation as the distance measure and Ward's linkage to identify target-based subclasses.

Construction of PFC columns
To unbiasedly divide PFC into a series of columns (n=40), voxels on the surface of PFC were clustered using K-means algorithm based on Euclidean distance between voxels. Then labels of voxels were propagated to entire PFC volume along the laminar direction based on the "streamline" method 12

Subdivision of PFC target regions
For a given PFC target region such as MD, we rst divided it into a series of 3D cubes (n=5,525 for MD, size: 505050 µm 3 ). Then for each neuron projecting to MD, we calculated the axonal length within each cube. After obtaining the projection matrix, we conducted unsupervised hierarchical clustering, using 1-Spearman correlation as distance measure and Ward's linkage to subdivide MD domains. To generate the map in Fig. 3k showing the soma distribution of neurons projecting to each MD subdomain, each MDprojecting neuron was color-coded by the speci c MD subdomain receiving its strongest projection.

Identi cation of community and connector nodes in the intra-PFC network
We constructed the intra-PFC connectivity matrix based on the mean projection strength of neurons in each constructed PFC column. To investigate the modular structure of connectivity, we used the Louvain algorithm from Brain Connectivity Toolbox (https://sites.google.com/site/bctnet/) 24,25 . At each level of resolution with γ from 0 to 2 at the step size of 0.1, we ran the community detection algorithm for 1,000 times for the connectivity matrix and the shu ed matrix to determine the most consistent modular structures. The nal modular structure was obtained at γ=1, where the difference of modularity value between Q and Q shu ed is largest. The connectivity matrix was visualized in Gephi 26 and edges with projection strength less than 500 um was omitted (Fig. 3e). To identify the connector nodes, we computed the within-module strengths, and participation coe cients 15 for each node and the nodes with high participation coe cients were assigned as connectors.

Analysis of primary axons
In early brain development, the primary axons of IT, PT, and CT neurons extend towards contralateral hemisphere, spinal cord, and thalamus, respectively 16,18,19 . We thus designated the axon path from the

The clustering of collaterals
We obtained the collaterals by calculating the branch order for each neuron. The primary axon was assigned order as "1" and the branch orders of other branches were calculated based on branch angles. Branches were de ned as symmetry branching if both daughter branches diverged with greater than 45°o r the ratio of their branch angles is less than 1.7. In this case, the orders of both daughter branches were designated as the branch order of their parent branch +1. Otherwise, branches were de ned as collateral branching, in which the daughter branch with the smaller branching angle retained the same branch order as the parent branch while the other daughter branch was assigned as the branch order of their parent branch +1. The long branches with order of "2" were considered as collateral branches and classi ed into different collateral clusters by hierarchy clustering with Ward.2 method based on the dissimilarity scores obtained by the FNT-dist algorithm. The number of collateral clusters was determined by using the cutreeHybrid function 27 in the R package WGCNA, taking into account the branching structure of the hierarchical clustering tree while maximizing the between-cluster variation and minimizing within-cluster variation.

Detection of terminal arbors
As axon tree of a neuron is composed of connected nodes without loops, it can be viewed as a connected acyclic graph (i.e. a tree) and its terminal arbors can be viewed as its subgraphs. For an IT or PT neuron with complex structure, its branch points and end points excluding those on the primary axon were divided into several clusters by hierarchical clustering with the ward's method based on their Euclidean distance. The number of clusters was determined by using the cutreeHybrid function in the R package WGCNA. A subgraph with nodes belonging to the same cluster was de ned as a terminal arbor.
Considering the simple structure of CT neurons, the subgraphs of a CT neuron after excluding its primary axon were directly de ned as its terminal arbors.

Classi cation of cortical arbors
The projection strength in each cortical layer was de ned as the total length of a terminal arbor within that layer and normalized by the maximum value. The similarity of laminar projection pattern between terminal arbors was calculated using Ward's method with 1-Pearson correlations as the distance measure. The number of arbor clusters was determined by cutreeHybrid function in R. The classi cation of cortical connections followed the same pipeline. Intra-PFC cortico-cortical connections with no more than 10 terminal arbors were not considered in the analysis.

Quanti cation of spatial overlap between terminal arbor pairs
The coverage factor is a measure to quantify the overlap of two arbors, de ned as the overlapped volume of two arbors divided by the mean of their volumes. The overlapped volume and the volume of each arbor were obtained by the intersectn function in the R package geometry. Terminal arbors in each brain region were divided into clusters by hierarchical clustering with Ward's method based on 1-Spearman rank correlation as the distance measure. The number of clusters was determined by cutreeHybrid function.

Data and code availability
All data can be found in the website: https://mouse.braindatacenter.cn/. The FNT software and the codes used in the data analysis can be found in the website: http://yanlab.org.cn.