Genetic Single Neuron Anatomy Reveals Fine Granularity of Cortical Axo-Axonic Cells

SUMMARY

Parsing diverse nerve cells into biological types is necessary for understanding neural circuit organization. Morphology is an intuitive criterion for neuronal classification and a proxy of connectivity, but morphological diversity and variability often preclude resolving the granularity of neuron types. Combining genetic labeling with high-resolution, large-volume light microscopy, we established a single neuron anatomy platform that resolves, registers, and quantifies complete neuron morphologies in the mouse brain. We discovered that cortical axo-axonic cells (AACs), a cardinal GABAergic interneuron type that controls pyramidal neuron (PyN) spiking at axon initial segments, consist of multiple subtypes distinguished by highly laminar-specific soma position and dendritic and axonal arborization patterns. Whereas the laminar arrangements of AAC dendrites reflect differential recruitment by input streams, the laminar distribution and local geometry of AAC axons enable differential innervation of PyN ensembles. This platform will facilitate genetically targeted, high-resolution, and scalable single neuron anatomy in the mouse brain.

Graphical Abstract

In Brief

Wang et al. combine mouse genetic labeling with high-resolution, large-volume light microscopy and establish a single-neuron anatomy platform. They show that cortical axo-axonic cells, a GABAergic interneuron type that innervates pyramidal neurons at axon initial segments, consist of multiple subtypes distinguished by laminar position and dendritic and axonal arborization.

INTRODUCTION

Defining and cataloging neuronal cell types, groups of neurons that share anatomical, physiological, and molecular properties are necessary for understanding the organizational logic of neural circuits (Huang and Zeng, 2013). As phenotypic variations of neurons often span substantial parameter space, it is necessary to carry out comprehensive, quantitative, and scalable single-cell analysis to resolve the appropriate granularity of cell type definition (Zeng and Sanes, 2017). Recent advances in single-cell RNA sequencing (scRNA-seq) enable quantitative measurements of cellular transcriptome profiles at massive scale, and computational analyses reveal increasing number of “transcriptional types” and discrete as well as continuous variations (Macosko et al., 2015; Tasic et al., 2018; Zeisel et al., 2015). As neuronal phenotypes are inherently multi-modal, it is necessary to achieve single-cell analyses of orthogonal cell features toward an integrated definition of neuron types that encapsulate the issue of granularity.

Neuronal morphology has been an intuitive first-level description of cell types. In several invertebrate systems (Aso et al., 2014; Chiang et al., 2011) and the vertebrate retina (Sanes and Masland, 2015) in which neurons are relatively small and stereotyped, comprehensive and quantitative single-neuron morphometry has allowed operational and consensual definition of neuron types. Morphology-based cell catalogs in these systems have been achieved or within reach (Aso et al., 2014; Hobert et al., 2016; Seung and Sümbül, 2014), which provide a foundation for multi-modal analysis and for exploring neural circuit organization. In the mammalian brain, however, the vast diversity, large spatial span, and seemingly endless variations of neuronal shapes present unique challenges in morphological tracing and analysis (Huang and Zeng, 2013; Lichtman and Denk, 2011). Single-neuron anatomy in the mammalian brain requires overcoming several technical hurdles. The first is labeling: to systematically, reliably, sparsely, and completely label specific sets of individual neurons. The second is imaging: to achieve axon resolution imaging in brain-wide volume (Economo et al., 2016; Gong et al., 2013; Li et al., 2010). The third is cell reconstruction: to convert large image stacks into digital datasets of single-neuron morphology. The fourth is analysis: to register neuronal morphology within appropriate spatial coordinate framework, and to extract, quantify, and classify biologically relevant attributes (e.g., those relate to neural connectivity).

Here, we present a robust genetic single neuron anatomy (gSNA) platform in the mouse that overcomes some of these challenges. We combined genetic cell labeling with dual-color fluorescence micro-optical sectioning tomography (dfMOST) (Gong et al., 2016) to achieve axon resolution and brain-wide imaging and spatial registration of genetically targeted single neurons. We focused our analysis on one of the most distinctive cortical GABAergic interneurons: the axo-axonic cells (AACs) that specifically innervate the axon initial segment (AIS) of glutamatergic pyramidal neurons (PyNs) (Somogyi et al., 1982; Taniguchi et al., 2013; Woodruff et al., 2010) and likely control spike initiation. Complete reconstruction of single AACs and their precise registration along cortical laminar coordinate allowed quantitative morphological analysis in the context of input-output connectivity. We discovered that cardinal AACs consist of multiple discrete subtypes that are distinguished by highly laminar-specific soma position and dendritic and axonal arborization patterns. The laminar arrangements of AAC dendrites may allow differential recruitment by presynaptic input streams. Furthermore, the laminar stratification of AAC axon arbors correlates with the distribution of PyN subsets and the local geometry of AAC axon terminals differentially conform to the laminar features of PyN AIS, suggesting differential innervation of PyN ensembles. Our results support a hierarchical scheme of neuronal classification (Zeng and Sanes, 2017) and suggest that cardinal neuron types consist of fine-grained subtypes, which can be deduced from light microscopy and mesoscale analyses that inform input-output connectivity patterns. The gSNA platform enables scalable and comprehensive single-neuron anatomical analysis, which will provide foundational datasets for neuron type discovery and classification in the mammalian brain.

RESULTS

Establishing a gSNA Platform

Our gSNA platform consists of four components (Figure 1). The first is a method to systematically label different sets of genetically targeted individual neurons to their entirety; the second is a technology for simultaneous imaging of labeled neurons at axon resolution and all other cell body positions throughout the entire mouse brain (dfMOST) (Gong et al., 2016); the third is a procedure to completely reconstruct single neurons from brain volume image stacks; the fourth is an analysis pipeline that registers and quantifies neuronal morphology within an appropriate spatial coordinate system that reflect network connectivity. Here, we integrate genetic labeling with fMOST in the gSNA platform to analyze the morphological diversity of a well-recognized interneuron type in the cerebral cortex.

Figure 1. Schematic of the gSNA Platform Applied to the Mouse Brain.

(A) Pipeline and components of genetic single neuron anatomy (gSNA).

(B) Left: scheme of genetic and viral strategy for the labeling of axo-axonic cells (AACs). A transient CreER activity in MGE progenitors is converted to a constitutive Flp activity in mature AACs. Flp-dependent AAVs injected in specific cortical areas enables sparse and robust AAC labeling.

(C) fMOST high-resolution whole-brain imaging. Two-color imaging for the acquisition of GFP (green) channel and PI (propidium iodide, red) channel signals. PI stains brain cytoarchitecture in real time, and therefore provides each dataset with a self-registered atlas. A 488-nm wavelength laser was used for the excitation of both GFP and PI signals. Whole-brain coronal image stacks were obtained by sectioning (with a diamond knife) and imaging cycles at 1-μm z steps, guided by a motorized precision XYZ stage.

AACs were recognized as a bona fide type largely based on their unique morphology and specific innervation of PyNs at AIS (Somogyi et al., 1982). Although the precise physiological action of AACs remains be elucidated (Lu et al., 2017; Szabadics et al., 2006; Woodruff et al., 2010), the defining feature is their specialization in regulating the spike initiation of PyNs. As multiple morphological variants of AACs have been found in several cortical structures (e.g., the hippocampus [Szabo et al., 2017; Varga et al., 2014], piriform cortex, and neocortex) and in different cortical layers (DeFelipe et al., 1985; Lewis and Lund, 1990; Somogyi et al., 1982; Taniguchi et al., 2013), this raises the questions of whether the cardinal AAC type consist of multiple “subtypes,” and how AAC subgroups should be defined. We have previously captured cortical AACs through genetic fate mapping of neural progenitors of the embryonic medial ganglionic eminence (MGE) using the Nkx2.1-CreER driver line (Taniguchi et al., 2013). Conversion of transient Nkx2.1-CreER expression in MGE progenitors to a constitutive Flpase activity in AACs enabled postnatal viral targeting (He et al., 2016). By controlling CreER efficiency (i.e., tamoxifen dose) and AAV injection volume and location, we were able to achieve specific, sparse, and complete labeling of AACs in defined cortical areas (Figures 2 and S1). Here, we analyzed AACs in the medial prefrontal (mPFC), motor (MC), and somatosensory (SSC) cortex. We use the original nomenclature axo-axonic cells (AACs) (Somogyi et al., 1982) to refer to all GABAergic interneurons that innervate PyNs at AIS. Under this category, we use the term chandelier cells (ChCs) to refer to the subsets of AACs in the cerebral cortex (especially those in supragranular layers), whose axon arbors resemble the candlesticks of a chandelier light.

Figure 2. Areal and Laminar Distribution of AACs Revealed from Whole-Brain fMOST Dataset.

(A) A schematic of whole-brain coronal dataset collection (top) with an example of GFP channel (center) and PI channel (bottom) images. Scale bars: 1,000 μm.

(B) An example of the distribution of sparsely labeled AACs in mPFC. Green: AAC morphology, 100-μm max-intensity projection. Blue: cytoarchitecture revealed by PI, 5-μm max-intensity projection. Scale bar: 1,000 μm.

(C and D) Laminar distribution of L2 AACs in mPFC. Enlargement of PI channel (C) and GFP channel (D) images from the left box in (B).

(E and F) Laminar distribution of L5 AACs in mPFC. Enlargement of PI channel (E) and GFP channel (F) images from the right box in (B).

Dashed lines in (C)–(F) indicate the layer boundaries. Cortical layers were discriminated based on cell body distributions in PI channel according to the Allen Mouse Brain Reference Atlas (http://portal.brain-map.org/). Scale bars in (E) and (F): 100 μm.

Following tissue resin embedding and processing (Gong et al., 2016; Xiong et al., 2014), we used a dfMOST system to image the whole-brain samples at submicron resolution (Figure 1C; Video S1). The dual-channel capturing of neural morphology labeled by GFP and brain cytoarchitecture stained by propidium iodide (PI) (red) were achieved by using a wide-field upright epi-fluorescence microscopy with a blue laser (488 nm) for fluorescence excitation and two separate charge-coupled device (CCD) cameras for signal detection (details in STAR Methods). Importantly, the PI channel provided each brain dataset with a self-registered Nissl-like reference atlas of cell body distribution information, which allowed reliable delineation of cortical areas and layer boundaries (Figures 2, 3A, and S1). Furthermore, the image contrast in PI channel was sufficient for the reconstruction of PyN main dendrites, which were used for identifying local laminar and vertical coordinates, readjusting cell orientation, and establishing a standardized platform for comparative analysis between cells in different cortical areas (Figures 3A and 3B).

Figure 3. Single AAC Reconstructions in Cerebral Cortex.

(A) A representative AAC reconstruction and its co-registered PI channel images. Left: overlay of the reconstructed cell with its PI channel image (10-μm max intensity projection) with the original orientation. Cytoarchitecture information shows the cortical laminar organization (more details in STAR Methods). Scale bar: 50 μm. Middle: single slice of PI channel. Right: enlarged image series from the boxed area in middle panel. Arrows indicate a pyramidal neuron main dendrite extending from cell body. Scale bar: 15 μm.

(B) Rotation and alignment procedures based on reconstructed pyramidal dendrites (green). Randomly selected pyramidal dendrites near the AAC cell body were reconstructed in Neurolucida360. The vertical axis of the local cortical column was calculated by performing principal-component analysis (PCA) on the centered dendritic reconstructions. AAC reconstruction was then re-aligned in the coronal plane (XY plane) and sagittal plane (YZ plane) around the cell body based on the identified cortical column orientation.

(C) Representative AAC single-cell reconstructions in mPFC, MC, and SSC. Cortical layers in each area were indicated by dashed lines. Black: soma body. Red: dendrites. Blue: axons. The orientation of each reconstruction was re-adjusted according to the local cortical vertical axis (see more details in STAR Methods). Representative translaminar axonal and dendritic arbors in the SSC are indicated by blue and red arrows, respectively.

(D) Left: scheme of the laminar arrangement of the input and output streams of SSC, in part rooted in the laminar organization of pyramidal neuron types with distinct projection targets. Right: a schematic of representative AACs in the SSC with characteristic laminar dendritic and axonal distribution patterns. Str, striatum; Bsm, brainstem; Scd, spinal cord; SCs, superior colliculus; Pom, posterior complex of thalamus; VPM, ventral posteromedial nucleus of the thalamus; Th, thalamus; ipsi, ipsilateral; contra, contralateral.

From 11 whole-brain dfMOST datasets, we completely reconstructed 62 AACs from mPFC, MC, and SSC (Figures 3C and S2A; Table S1). As axon arbors of AACs were extremely dense and complex, all AACs were manually reconstructed. With rare exceptions (Bienvenu et al., 2012; Viney et al., 2013), previous labeling of AACs were largely carried out in brain slice preparations where axons and dendrites were severed, and thus reconstructions were mostly incomplete (Blazquez-Llorca et al., 2015; Kawaguchi and Shindou, 1998; Somogyi et al., 1982; Woodruff et al., 2010). Our dataset represents a set of complete and comprehensive AAC reconstructions in the cortex since their discovery four decades ago (Szentágothai and Arbib, 1974). The average length of AAC axons was 2.14 ± 0.79 cm (n = 62; mean ± SD), average number of axon branches was 1,369 ± 499 (n = 62; mean ± SD), and average axon branch order was 32 ± 8 (n = 62; mean ± SD). A major goal of our analysis is to define and discover AAC subtypes based on morphological features that inform connectivity, taking full advantage of the obligatory synaptic relationship between AAC axon terminals and PyN AIS. Our strategy was to examine the location and distribution of AAC cell bodies, their dendrite and axon arbor distribution, and their axon arbor geometry in the well-established coordinates of cortical laminar organization based on AAC post-synaptic targets—the PyNs (Figure 3D).

AACs Tend to Localize at the Borders between Cortical Layers

Previous studies in several species found that AACs are distributed across most if not all cortical areas and in multiple cortical layers (Lewis and Lund, 1990; Somogyi et al., 1982; Taniguchi et al., 2013), but more precise description of AAC distribution and positioning has not been reported. The cellular resolution spatial coordinate information in the dfMOST datasets allowed unambiguous and quantitative localization of AACs. Within all three areas, the largest proportion of our reconstructed AACs was located within the supragranular layers, with a major fraction at the layer 2 to layer 1 (L2/1) border (55%) and a much smaller set in L3 (5%) (Figures 2, 3C, and S1). A significant portion of AACs were found in infragranular layers, both in L5 (L5 22%) and L6 (16%). We found one AAC in L4 of SSC in our dataset. Interestingly, in most cases, AAC somata tended to localize at the border between cortical layers, with prominent apical dendrites and basal axons (Figures 2, 3C, and 3D).

AACs Elaborate Laminar-Restricted Apical and Basal Dendrites That Protrude Dendritic Spines

Almost all of the reconstructed AACs elaborated prominent apical dendrites (Figure 4). The average span of apical dendrites of L2 AACs was 85.0 μm (90% of dendrite arbors horizontally cover 85.0 ± 23.0-μm radial distance; mean ± SD; n = 61) from soma (Figures 4G and S3). In most cases (51/62; 82% of all reconstructed AACs), the apical dendrite extended within the one layer above the soma location (e.g., L1 for L2 AACs and L5 for L6 AACs). In several cases, L3 (3 cells) and L5 (4 cells) AACs extended apical dendrites all the way to the pia (Figure 3C; Videos S4 and S5). In particular, all L2 (34 AACs) and some L3 (3 cells), L5 (2 cells) AAC dendrites appeared to tightly attach to the pia with thickened apical tufts; this is in contrast to many PyN apical dendrites in L1 that do not reach near or adhere to pia surface (Figures 4A, 4B, 4F, and S3B). Interestingly, the apical but not basal dendrites of L2 ChCs sprouted filopodia-like slender dendritic spines, which were enriched in the upper half (68% in upper L1, the rest near L1/2 border) of L1 (Figures 4C–4K).

Figure 4. Characteristics of L2 AAC Dendrites.

(A) A representative L2 AAC in mPFC. 100-μm max intensity projection. Scale bar: 100 μm.

(B) Dendrites of L2 AAC. Image was enlarged from the box in (A). Scale bar: 50 μm.

(C and D) Apical (C) and main dendrites (D) were enlarged from boxes in (B). Scale bars: 30 μm (C) and 5 μm (D).

(E) Spines (arrows) on the apical dendrites were enlarged from the box in (C). Scale bar: 5 μm.

(F) Complete reconstruction of dendrites (red) and spines (black). The same cell shown in (A) and (B). Inset: enlarged from the box. Black circle: cell body. Gray lines: pia and L1/2 border. Scale bar: 50 μm.

(G) Horizontal dendritic arbor distributions of up-layer (L2 and L3) and deep-layer (L4, L5 and L6) AACs in mPFC, MC, and SSC. Data are mean ± SD.

(H) An example of heatmaps showing the density distribution patterns of a L2 AAC dendritic arbor length (left), branching nodes (middle left), terminal nodes (middle right), and spines (right). Scale bar: 200 μm.

(I) Single-cell density plots of L2 AAC dendrites (same as in H) along the cortical depth.

(J) Density plots of dendrites from 11 L2 AACs in mPFC. Different colors indicate different cells.

(K) Normalized density plots of (J) based on pia and L1/2 border positions (see more details in STAR Methods).

Black circles in (I)–(K) indicate AAC soma positions in the coordinate. Dashed lines correspond to the place of pia (top) and L1/2 border (bottom). Dark black curves in (J) and (K) are averages of all the cells. Density value was presented by ratio.

Although overall more sparse than apical dendrites, the basal dendrites of AACs show striking laminar restriction to the same layer of the cell soma (Figures 4H–4K, S3C, and S3D). For example, all L2 AACs (n = 34) restrict their basal dendrites strictly to L2 without extending to L3, while L3 AACs (n = 3) restrict their basal dendrites strictly to L3 without extending to L2 and L4 (Figures S2A and S5D). Similarly, L5 and L6 AAC basal dendrites manifest the same intralaminar restriction. Together, these results suggest that AACs elaborate their dendritic arbors in a laminar-specific and unitary pattern instead of a continuous and diffuse pattern. The polarized dendritic arborization suggests that AACs receive most of their inputs from above their cell bodies; in particular, pia-attached AAC dendrites may recruit the most superficial L1 inputs and select or modify these inputs through dendritic spines. On the other hand, the basal dendrites receive inputs strictly targeting the same layer where the cell soma is located.

AACs Elaborate Laminar-Stratified Axon Arbors, Some with Translaminar Arbors

Although the characteristic shape and exquisite specificity of AAC axons have been recognized decades ago, few if any have been reconstructed to their entirety. We found that AACs axons arborized very extensively near the cell soma (below the soma for L2 AACs and both above and below the soma for other cortical AACs; Figures 5A–5C, S4, and S5A). The average span of AAC axon arbors was 129.2 μm (90% of axon arbors horizontally cover 129.2 ± 27.5-μm radial distance; mean ± SD; n = 61). In addition to the highly predominant local arbor (i.e., intralaminar; Figure 5A), a significant fraction of L2 and L3 AAC axons (~74% of our L2 AAC reconstructions) further extended to the deeper layers (i.e., cross- and trans- laminar; Figures 3C, 3D, 5A, 5B, 5D, S2, S5A, S5D, and S5F; Videos S2 and S3). In particular, translaminar axons of L2 AACs descended through intervening layers (e.g., L3–L5A in MC or L4 in SSC) before elaborating terminal branches with presynaptic boutons (Figure 5D). This result suggests that, in addition to exerting powerful control over local PyN populations, some L2/3 AACs likely coordinate firing between local PyNs and a distant ensemble in an infragranular layer. Overall, AAC axon arbors appear to strictly conform to laminar borders instead of extending diffusely across layers, suggesting a laminar-specific and unitary pattern of axon stratification. Interestingly, we observed one L6 AAC with an inverted polarity—its dendrite extended below toward the white matter, whereas the axon extended above toward L5 (Figures 3C, S5E, and S5G).

Figure 5. Morphology and Distribution Patterns of AAC Axons in the Neocortex.

(A) A representative images of two examples of nearby intra-(left) and cross-(right) L2 AACs in mPFC. Insets are enlarged images from boxed regions showing the main axon extending from the soma (1; arrow), characteristic axon cartridge clusters, and individual boutons from different regions of the axon arbor (2, 3, and 4). Image is a projection of 100-μm image stack. Scale bars: 100 μm (low-mag image) and 10 mm (insets).

(B) A representative image containing nearby L2, L4, and L5 AACs in SSC. Enlarged L4 and L5 AACs were from the boxes in the left panel. Scale bars: 100 μm (left) and 10 μm (right). Dashed lines in (A) and (B) indicate cortical layers.

(C) Horizontal axon arbor distributions of up-layer (L2 and L3) and deep-layer (L4, L5 and L6) AACs in mPFC, MC, and SSC. Data are mean ± SD.

(D) Length density analysis of axons and dendrites from all the AACs shown in (A) and (B). Left: projection of reconstructions (dendrites in red; axons in blue). Middle: heatmap of length density distribution of dendrites (middle left) and axons (middle right). Right: length density plots of AAC dendrites and axons along cortical depth (y axis). Dashed lines indicate layer boundaries. Insets in rows 3 and 4 highlight axon branches in deep layers.

(E) An example of axon bouton reconstruction of L2 AAC in mPFC. Inset: magnified view of the boxed region.

(F) Axon cartridges that innervate PyN AIS can point upward, downward, or split from the middle.

(G and H) The numbers of synaptic boutons correlate with axon length quantified by absolute value (G) or ratio (H).

AACs Consist of Multiple Subtypes Distinguished by Dendrite-Axon Distributions That Reflect Input-Output Connectivity Patterns

The substantial variations in the location and morphology of AACs raise questions of whether they consist of anatomical “subtypes” and how subtypes can be resolved with biologically relevant properties. As morphology is a proxy to and serves the purpose of connectivity, we first adopted a connectivity-guided approach to morphology-based AAC subtyping. Our analysis was based on the premise that, at a mesoscale, establishing a synaptic connection requires the physical overlap between a presynaptic axon and its postsynaptic element within a specific anatomic location, i.e., an “anatomic parcel,” that represents the input or output component of a neural network (Ascoli and Wheeler, 2016); this tight spatial correlation often extends to the matching of fine-scale geometric features (e.g., presynaptic climbing fibers and postsynaptic Purkinje cell dendrites in the cerebellum). This obligatory correlation between pre- and post-synaptic elements, when framed in the context of circuit connectivity, provides a biologically relevant coordinate for morphological analyses.

The mesoscale correlation between pre- and post-synaptic elements is particularly identifiable and compelling for AAC and PyNs. Within the laminar architecture of the neocortex, different types of PyNs that project to distinct cortical and subcortical targets are organized, to the first approximation, into different layers, and different sources of cortical and subcortical inputs are routed through laminar streams (Harris and Shepherd, 2015) (Figure 3D). Importantly, the obligatory relationship between AAC axon terminals and PyN AIS represents a rare case where AAC axon distribution alone indicates connectivity to specific types of postsynaptic targets. Together, these provide an inherent spatial coordinate system to register AAC position and morphology in the framework of cortical input and output streams (Figure 3D). As the laminar arrangement of AAC dendrites recruit different input streams and the laminar stratification of axons mediate their output to separate PyN ensembles, we designed an AAC clustering analysis that emphasized the laminar density distribution of AAC dendritic and axonal arbors (Figure 6). We excluded L3 and L4 AACs (Figure S2A) from this analysis as there were few such examples (less than 4) in our current dataset.

Figure 6. Hierarchical Clustering of AACs Based on Cortical Laminar Density Distribution of Axons and Dendrites.

(A) Dendrogram of hierarchically clustered AACs (n = 53). KL divergences (Kullback-Leibler divergence) of normalized arbor distribution functions along cortical depth were taken as the distance metric, and furthest distance was taken as the linkage rule. See more details in STAR Methods and Figure S6 for the normalization procedures. Dashed lines correspond to the cutoff linkages of the identified eight cell clusters. Inset: silhouette analysis of the eight AAC clusters.

(B) 3D scattering plots of the eight AAC clusters from (A) based on three principal components.

(C) Axon (blue) and dendrite (red) length density distribution profiles of the eight AAC clusters. Dashed lines: cortical layer boundaries. Black circles: soma body positions. Bold lines: average of all the neurons in each cluster. Note that cell #38 in cluster 5 has apical dendrites (arrow) reading L1, a defining feature of cluster 6, but its lack of L3 axon branches (as it is located in SSC with a prominent L4) likely assigned it to cluster 5.

(D–G) Clique analysis for the identification of robust AAC clusters. Clique analysis was conducted based on hierarchical clustering with five different metrics on AAC axons: three persistent-homology-based metrics, using three different ways of measuring distance from the soma, as scalar descriptor functions defined on the neuronal processes: Euclidean, geodesic, and depth from cortical surface (“y axis”), and the length density and L-measure metrics (Scorcioni et al., 2008) defined in the text (D and E). Laplacian eigenmap embedding of hierarchical clustering for the y axis-based metric (D) and other descriptors (Figure S7A–S7E). The selection of “K” was based on silhouette analysis. Silhouette plot for K = 4 with y axis as the input metric; thickness denotes sizes of clusters; red dotted line denotes average silhouette score; larger score means better clustering (E). The relations between the five metrics were quantified by similar index (SI) and adjusted Rand index (F). Three robust AAC clusters were identified based on the clique analysis (G). The full listing of the three cliques are shown in Figure S7F.

Based on brain cytoarchitecture information of dfMOST datasets, we normalized AAC dendrite and axon density distribution to a standardized cortex template (Figure S6). Hierarchical clustering based on cortical laminar density distribution of axons and dendrites revealed eight AAC clusters grouped according to the laminar distribution of their cell body position and dendritic and axonal arborization (Figures 6A–6C). The four L2 ChC clusters correspond to intra- (cluster 4), cross- (cluster 1), and trans- (cluster 2 and cluster 3) ChC subtypes. The axon arbors of cluster 3 extend both L5 and L6 branches, but more dominantly innervate L5 (Figure S2B). Cluster 5 AACs resided in L5; their axons and dendrites were largely restricted within L5. Cluster 6 AACs resided in L5a; their axon arbors elaborated mostly within L5, but their dendrites extended to L1. Cluster 7 AACs resided at L5 and L6 border (i.e., L6a), their dendrites were restricted in L5 and L6a, and their axons arborized mainly in L6. Cluster 8 consisted of L6 AACs with intralaminar dendrite and axon arbors. These different AAC clusters likely receive different inputs and control different subsets of PyNs, and thus are distinguished by their circuit connectivity patterns. Importantly, both the dendritic and axonal arbors of AACs conform to specific cortical layers rather than extending diffusely, presumably to recruit inputs or innervate targets in those layers, respectively. This suggests that the morphological variation of AACs might be more unitary than continuous. This was particularly apparent for two broad groups of L5 AACs, one extended short, L5-restricted apical dendrite and the other extended long, L1-reaching apical dendrites (Figures 3 and S5A–S5C). We noted that this clustering method was not perfect as it assigned cell 38 to cluster 5, even though cell 38 extended apical dendrite to L1, as those characteristic to cluster 6 (Figures 6 and S5A). In addition to these eight clusters (Figure 6), we detected three L3 AACs (two in SSC, one in MC) with translaminar axon arbors and apical dendrite reaching L1 (Figures S5D and S5F; Video S4), one L4 AACs in SC (Video S6), and one inverted L6 AAC in mPFC (Figures S5E and S5G show the projection image of L6 AAC).

Hierarchical clustering based on the laminar distribution of axon density alone has a potential shortcoming: it may over-cluster or mis-cluster two identical density profiles appearing at different layer depths. Furthermore, low-dimensional projections do not always show well-separated clusters and may need other indirect evidence about clustering in the high-dimensional space such as silhouette plots. We therefore carried out a robust comparative analysis of morphological types using additional geometrical and topological characteristics of the neurons. For analyzing topological characteristics, we used a recently developed framework employing persistent homology (Li et al., 2017b) to derive a metric in the space of neuronal shapes (see STAR Methods and references). Briefly, this framework employs a descriptor function defined on the neurons, and a topological summary independent of neuronal location and orientation is derived from the descriptor function. We utilized three descriptor functions based on three different ways of measuring distances from the soma (Euclidean, geodesic, and cortical depth). In addition, we also used a community-standard metric (Scorcioni et al., 2008), employed on http://neuromorpho.org/.

We performed hierarchical clustering employing each of these metrics, varying the number of clusters. By examining the overlap between the resulting clusters (adjusted Rand index [ARI] and similarity index [SI]; Figures 6D and 6E), we concluded that the metrics carry independent information about neuronal shape. We hypothesized that if a pair of neurons appears in the same cluster across all the metrics, this provides robust evidence that those neurons belong to the same morphological type. We thus proceeded by defining a graph in which each neuron is a node, and two nodes are connected if and only if they appear in the same cluster across all five metrics considered. This procedure produced a set of disconnected cliques (fully connected clusters). The three largest cliques corresponded to three robustly identified AAC cell types that are also visible in the hierarchical clustering using only the laminar density of the axons: the intra-, cross-, and trans-L2 AAC subtypes (Figures 6G and S7). Currently, a number of AACs could not be grouped into cliques, likely due to less than enough sample size. We hypothesize that, with larger datasets, we will obtain similar robust cliques corresponding to other AAC subtypes for which evidence is provided by the hierarchical clustering shown in Figures 6D–6G.

AAC Subtypes Can Be Revealed by Axon Terminal Geometry That Correlates with That of Postsynaptic AIS

In addition to the laminar stratification of axon arbors, AAC axon terminals in different cortical layers manifested different geometric characteristics such as orientation, tortuosity, path distance, and branch order (Figures 5E–5H and 7). As strings of AAC presynaptic terminals (i.e., “cartridges”) mostly align with the AIS of postsynaptic PyNs, we hypothesized that certain geometric features of AAC terminals reflect and correlate with those of the AIS. For example, the orientations of AIS in supragranular layers of mPFC were largely vertically aligned, but deviated substantially from this columnar orientation in infragranular layers (especially in L6; Figures 7A–7C and S2B). Consistent with this postsynaptic feature, AAC axon terminals in supragranular layers were also organized in predominantly vertical and parallel orientations, each largely straight and decorated with strings of presynaptic boutons (e.g., cartridges), which together earned them the name “chandelier cell.” In infragranular layers, on the other hand, the orientation of AAC terminals varied significantly with increased tortuosity that correlated with local PyN AISs (Figures 7D–7I). Interestingly, analysis of several geometrical features of AAC terminals properly grouped AACs according to areas, laminar positions, and L2 subtypes (Figure 7J). In particular, several pairwise combinations of features classified AACs according to their areal, laminar locations, and even the three subtypes within layer 2 (Figures 7K–7O). It is notable that AAC subtypes identified by axon local geometry are consistent with those identified by analyzing the laminar distribution of dendritic and axonal arbors (Figure 6), both rooted in their connectivity to PyNs. Together, these results suggest that a connectivity-based framework of morphological analysis is informative in resolving the granularity of AAC subtypes.

Figure 7. AAC Subtypes Revealed by Axon Terminal Characteristics That Correlate with AIS.

(A) Distributions of AACs in mPFC (50 μm thick). AACs were labeled by the crossing of Nkx2.1-CreER mouse and Ai14 (LSL-tdTomato) mouse with low dose of TM induction at E18.5. Top: AACs (green) shown by the immunostaining of tdTomato. Center: cortical layers shown by the immunostaining of m2AchR. Bottom: color merged. Scale bar: 1,000 μm.

(B) AIS distributions in PrL (prelimbic cortex). Images were captured from the box in (A). Left: overlay image of AAC (green) and AIS (red). Right: immunostaining of AISs with Ankyrin-G. Insets: enlarged images. Gray lines indicate layer boundaries. Scale bars: 100 μm (low-mag) and 20 μm (insets).

(C) AIS reconstructions (purple). Insets: representative reconstructions of presynaptic AAC cartridge and postsynaptic PyN AIS pairs in L2/3, L5, and L6. Green: cartridges. Red: AISs. Scale bar: 100 μm.

(D and E) Distribution differences of AIS angles among cortical layers in mPFC (***p < 0.0001, 95% confidence level, Kruskal-Wallis test followed by Dunn’s multiple-comparisons test). Plots indicate median (full horizontal bar), mean (×), quartiles, and range. AIS data (D) and cumulative plots (E) are from the reconstructions in (C).

(F and G) The corresponding distribution differences of AAC axon terminal angles in mPFC (***p < 0.0001, 95% confidence level, Kruskal-Wallis test followed by Dunn’s multiple-comparisons test). Plots indicate median (full horizontal bar), mean (×), quartiles, and range. Axon terminal data (F) and cumulative plots (G) are extracted from all our AAC reconstructions in mPFC (Figure S2A).

(H and I) Averaged distribution differences of AAC axon terminal angles across mPFC, MC, and SSC (***p < 0.0001, 95% confidence level, Kruskal-Wallis test followed by Dunn’s multiple-comparisons test). Plots indicate median (full horizontal bar), mean (×), quartiles, and range. Axon terminal data (H) and cumulative plots (I) are extracted from all our AAC reconstructions (Figure S2A).

(J) Summary of axon terminal geometric features that separate AAC categories (cortical areas and cortical layers refer to somatic location). Green: statistically significant differences between all three pairs compared. Yellow: statistically significant differences between two of three pairs compared. Orange: statistically significant differences between one of three pairs compared. Red: no statistically significant differences.

(K and L) Areal and laminar categories of AACs separated by axon terminal geometric parameters. Parameter pairs of branch order and (K) branch tortuosity or (L) branch path length are shown. Data are mean ± SEM.

(M) Reconstructions of representative L2 AAC subtypes (L2-intra, L2-cross, and L2-trans).

(N and O) Axon terminal geometric parameters separate L2 AAC subtypes. Parameter pairs of branch path length and (N) branch fractal dimension or (O) branch tortuosity are show. Data are mean ± SEM.

(P) Schematic of inferred L2 AAC connectivity with PyNs.

DISCUSSION

As individual neurons are the basic building blocks of the nervous system, single-neuron analysis is essential to reveal the true degree of cell diversity and principles of circuit organization. Morphology is an intuitive depiction of neuron types that reflects their input-output connectivity; thus, the visualization and quantification of complete single-neuron shapes are necessary to identify and classify neuron types and deduce their anatomic relationships. However, the vast diversity, large spatial span, and vexing variations of mammalian neurons present unique challenges in cell labeling, imaging, and analysis. Recent advances in light microscopy begin to overcome the technical hurdle of submicron-resolution imaging of the entire mouse brain using either wide-field structured light illumination microscopy (i.e., MOST and fMOST) (Gong et al., 2013; Li et al., 2010) or fast-scanning two-photon microscopy (Economo et al., 2016). In particular, the dual-channel dfMOST approach allows fast and simultaneous acquisition of both neural structures and their whole-brain spatial reference at cellular resolution (Gong et al., 2016).

Another key requirement for reconstructing single neurons using light microscopy is sparse and robust labeling, and systematic labeling across neuronal populations is necessary to achieve comprehensive discovery of neuron types. Conventional transgenic approach lacks specificity and sparseness. Although viral vectors can achieve sparse labeling of distal axons (Economo et al., 2016), their limitations include (1) dense labeling of local collaterals that are difficult to reconstruct, (2) lack of specificity to local interneurons, and (3) lack of orthogonal information (e.g., molecular markers) to further restrict labeling and help interpret morphological variations in cell type identification. Our combinatorial genetic strategy overcomes these limitations. We engage multiple cell features to target subpopulations defined by gene combinations, lineage, birth time, and anatomy (He et al., 2016). We further incorporate inducible and viral methods to achieve reliable single-cell labeling (Figure 1B), which should enable “saturation screening” of morphological types or subtypes within the subpopulation. Although here we have not reached saturation screening of cortical AACs, as L4 and inverted L6 AACs were detected only once in our dataset, the approach demonstrates unprecedented specificity and comprehensiveness to a rare cortical cell type. Iterations of this labeling scheme through systematic generation of mouse driver lines (Harris et al., 2014) will enable comprehensive targeting of neuron types as has been demonstrated in genetic targeting in Drosophila (Aso et al., 2014; Jenett et al., 2012). Thus together with scRNA-seq, gSNA provides an orthogonal and scalable single-neuron analysis platform. Currently, the bottleneck of the gSNA is single-neuron reconstruction, which mostly relies on manual procedures. Future innovation in machine learning-based automatic reconstruction algorithms may increasingly overcome this limitation (Peng et al., 2015, 2017).

The goals of single-neuron anatomy are to identify and catalog cell types and, ultimately, to inform cell function through inferring connectivity. With increasing throughput in single-neuron reconstruction, a pressing issue is how to extract biologically relevant information from morphology datasets. Traditional approaches deploy a large set of geometric and topological metrics (e.g., Ascoli et al. [2008]) to quantify single-neuron morphology in isolation often without a proper spatial coordinate and circuit context; these analyses are mostly ineffective in parsing neurons into reliable and biologically informative groups. As morphology is a proxy to and serves the purpose of connectivity (Seung and Sümbül, 2014; Sümbül et al., 2014), we have adopted a connectivity-guided approach to morphological analysis. This approach is based on the premise that, although single-neuron shape by itself does not contain information about presynaptic sources and postsynaptic targets, such information can be extracted, to varying degrees, if neuron morphology can be registered and analyzed in an appropriate spatial coordinate that reflects local and/or global connectivity patterns. Indeed, the inherent polarity of dendrites and axons ensures that their distribution and geometry reflect the input source and output targets in the corresponding spatial domains, or “anatomic parcels” (Ascoli and Wheeler, 2016). Although the precise identity of input and output elements cannot be inferred from spatial location alone, anatomic parcels based on decades of classic studies provide significant information to include and exclude pre- and post-synaptic elements and thus to infer possible as well as impossible connectivity. This analysis framework is likely to recognize seemingly “subtle” morphological variations (e.g., translaminar dendrite or axon branches of AACs), which yet have significant impact on connectivity and thus cell function. In this context, the dfMOST datasets, which allow automatic registration of single-neuron morphology into proper global and local coordinates at cellular resolution within the same brain (Gong et al., 2016), is key in analysis strategies to identify and distinguish cell types and to inform connectivity. In analyzing AAC morphology, for example, the precise cell distribution information of the dfMOST dataset is crucial to derive and normalize laminar coordinates in different cortical areas, which enabled areal and laminar comparisons and inferences of input-output connectivity patterns that distinguished AAC subtypes.

A recent study suggests that cardinal GABAergic neuron types are distinguished by their input-output synaptic communication patterns encoded in transcription profiles (Paul et al., 2017). Beyond cardinal types, finer division into subtypes may be necessary to represent and explain the intricacies of neural circuit organization (Zeng and Sanes, 2017), but there is no consensus and mechanistic basis on the granularity and boundary of neuronal subtypes. Our results on cortical AACs suggest that differences in input-output connectivity, which are reflected in cell morphology, are likely a major determinant of neuronal subtypes. Differential gene expression in supragranular or infragranular AACs in the frontal cortex (Paul et al., 2017) is consistent with this interpretation. We therefore suggest that synaptic communication patterns may distinguish neuronal subtypes as well as cardinal types.

It is notable that AAC subtypes, when registered along cortical laminar coordinates, appear to manifest a degree of stereotypy and fine granularity that is similar to those of retinal bipolar cell subtypes registered upon the much finer coordinates of retinal sub-laminae (Shekhar et al., 2016). A true saturation anatomical analysis of cortical AACs will likely reveal additional subtypes. While the division of retinal bipolar subtypes is further supported by molecular, physiological, and functional evidence (Euler et al., 2014), the division of AACs subtypes based on anatomy needs to be substantiated by orthogonal datasets, such as their physiological connectivity (Lu et al., 2017) and gene expression profiles (Paul et al., 2017). On the other hand, our results suggest that high-resolution morphology dataset alone, when registered within proper spatial coordinates that reflect brain circuit organization, contain rich anatomical information on cell identity and connectivity, providing a structure basis to integrate orthogonal datasets. This analysis strategy should apply to projection neurons as dfMOST datasets contain brain-wide information on anatomical parcels that will inform the potential synaptic targets of long-range axon branches. Therefore, light microscopy-based high-throughput single-neuron anatomy will likely provide substantial information and insight on cell type diversity and mesoscale connectivity in the mammalian brain.

STAR★METHODS

Detailed methods are provided in the online version of this paper and include the following:

CONTACT FOR REAGENT AND RESOURCE SHARING

Further information and requests for resources and reagents should be directed to and will be fulfilled by the Lead Contact, Qingming Luo (qluo@mail.hust.edu.cn) or Z. Josh Huang (huangj@cshl.edu).

EXPERIMENTAL MODEL AND SUBJECT DETAILS

Experimental Animals and Low Dose TM Induction

To achieve sparse and specific targeting of AACs across neocortical areas, we crossed Nkx2.1-CreER mice (The Jackson Laboratory stock 014552) with Rosa26-loxp-stop-loxp-flpo (LSL-Flp) mice (The Jackson Laboratory stock 028584). At postnatal day 0 (P0) or day 1 (P1), we intraperitoneally induced each pup with low dose of tamoxifen (TM, 0.25 mg per pup). Tamoxifen stock solution (5mg/ml in corn oil) were prepared beforehand. Sparsely targeted AACs would express FlpO constitutively (He et al., 2016).

For immunostaining experiments, we crossed Nkx2.1-CreER mice with Rosa26-lox-stop-lox-tdTomato (Ai14) mice (The Jackson Laboratory stock 007905). To ensure embryonic day 18.5 (E18.5) TM inductions, Swiss Webster or C57B6 females (Taconic) were housed with Nkx2.1-CreER:Ai14 (ht/homo) males overnight and females were checked for vaginal plug by 9am the following morning. At E18.5, pregnant females were given oral gavage administration of TM (dose 3mg / 30 g of body weight) for sparse labeling of AACs. AACs are labeled with tdTomato. Genetic hybrids of C57B6 and Swiss Webster animals were used in these experiments. All animal breeding and surgical experiments were approved by the Institutional Animals Care and Use Committee (IACUC) of Cold Spring Harbor Laboratory or the Institutional Animal Ethics Committee of Huazhong University of Science and Technology.

METHOD DETAILS

Stereotaxic Virus Injection

Flp dependent pAAV-EF1a-fDIO-TVA-GFP (TVA: avian glycoprotein EnvA receptor) cassette was assembled and cloned using standard molecular cloning protocols with restriction enzymes from New England Biolabs. TVA-GFP (pAAV-EF1a-FLEX-GT) was a gift from Ed Callaway (Addgene plasmid # 26198). The cassette was subcloned into pAAV-EF1a-fDIO-YFP-WPRE (a gift from the Deisseroth laboratory, Stanford University) using NheI and AscI cloning sites (Fenno et al., 2014). All constructs were sequenced to ensure their fidelity and proper reversed orientation of the inserts, and packed into AAV8 viral vectors with titers ranging from 1.0 × 10¹² to 2.4 × 10¹² pfu from the UNC Vector Core (Chapel Hill, North Carolina).

For stereotaxic injection, post-weaned animals (3 to 4-week-old) were anesthetized by intraperitoneal injection with ketamine and xylazine (ketamine:100 mg/kg, xylazine: 10 mg/kg in saline), and then were fixed in a stereotaxic headframe (Kopf Instruments Model 940 series) for the identification of the coordinates of mPFC, MC and SSC areas based on the Allen Mouse Brain Reference Atlas (http://atlas.brain-map.org). Each animal received bilateral injection in mPFC, MC and SSC areas (6 injection sites per mouse). At each site, we injected 100 nL virus with Nanoliter 2010 Injector (World Precision Instruments). And we let virus express more than 21 days for strong labeling. The membrane tagged labeling by TVA-GFP fusion significantly improved the labeling of fine axon terminal. The stereotaxic coordinates are: mPFC (A/P: 1.98 mm, M/L: ± 0.5 mm; D/V: 1.5mm depth from pial surface), MC (A/P: 0.5 mm, M/L: ± 1.5 mm; D/V: 0.5 mm) and SSC (A/P: —1.5 mm, M/L: ± 3.0 mm; D/V: 0.5mm).

Immunostaining

Animals (P45-P60) were perfused with 4% PFA in PBS. The brains were removed and post-fixed overnight in the same fixative. Coronal brain slices were sectioned at 75 um thickness via vibratome. Sections were blocked with 10% normal goat serum in 0.5% Triton in PBS for an hour and then incubated overnight with primary antibodies diluted in blocking solution at room temperature. Primary antibodies used were: rabbit polyclonal RFP (1:1000, Rockland) for labeling AACs, mouse monoclonal Ankyrin-G (1:500, Neuromab) to label pyramidal axon initial segments (AIS), and rat monoclonal muscarinic Acetylcholine receptor m2 (m2AChR) (1:500, Millipore Sigma) to discriminate L3/5 and L5/6 boundaries in mPFC. Sections were subsequently washed and incubated with the appropriate fluorescently-conjugated secondary antibodies diluted in the same buffer for 3 hours at room temperature. Secondary antibodies used were: Alexa Fluor 488 goat anti-rat (1:500, Invitrogen), Alexa Fluor 594 goat anti-rabbit (1:500, Invitrogen), and Alexa Fluor 647 goat anti-mouse IgG2a (1:500, Invitrogen).

Perfusion and Whole-Brain Resin Embedding (Gang et al., 2017)

Mice were deep anesthetized by overdose of ketamine and xylazine, and then intracardially perfused with 0.01M PBS (Sigma-Aldrich Inc., St Louis, MO, USA) and 4% paraformaldehyde (PFA, Sigma-Aldrich Inc., St Louis, MO, USA). After brain dissection and about 18 hours of post-fixing in 4% PFA, brain samples were rinsed in 0.01M PBS overnight. Then samples were dehydrated in graded series of ethanol (with distilled water): 50% ethanol (2h, 3 times), 75% ethanol (2h, 1 time), 100% ethanol (2h, 2 times). After dehydration, we replaced ethanol with graded series of xylene (with pure ethanol): 50% xylene (2h, 2 times) and 100% xylene (2h the first time, and then overnight). We then infiltrated samples in graded series of Lowicryl HM20 resin (in xylene): 50% HM20 (2h), 75% HM20 (2h), 100% HM20 (2h, 2 times), 100% HM20 (2 days). After resin infiltration, samples were heat-polymerized at 50^◦Cfor 8 hours in a vacuum oven. All dehydration and infiltration procedures were treated at 4^◦C. All solutions were prepared in weight.

Note: During wide-field based dfMOST imaging, autofluorescence produced by lipofuscin in the resin-embedded brain tissue often interfered with image contrast. Swiss Webster mice, especially after 2months of age, usually express more lipofuscin compared with C57/BL6 mice. To reduce the effect of lipofuscin, all animals in this study were sacrificed around P51-P54.

Whole-Brain Dual-Color fMOST (dfMOST) Imaging

Plastic embedded brain samples were mounted on a metal base and then installed under a dual-color fluorescence micro-optical sectioning tomography (dfMOST) system for whole-brain imaging. The dfMOST system is a wide-field block-face imaging system. A blue laser (488nm) was used as the excitation light source with two separate TDI-CCD cameras for signal detection. This system runs in a stripe scanning mode (x axis) and combines with an afterward image montage to realize the centimeter-scale coronal data acquisition (Yang et al., 2015). A precision motorized XYX stage is used to conduct imaging scanning, areal expansion and ultra-thin sectioning by a diamond knife (Li et al., 2010). The high throughput and high resolution imaging of fluorescent protein labeled samples is realized with chemical sectioning (X.W. and T.Y., unpublished data). Following each scanning of one coronal plane (X-Y axes), the sample was sectioned to remove the top layer (Z axis), and then imaged again. The imaging-sectioning cycles were performed automatically with 1.0 mm Z steps until whole brain was imaged. The resin-embedded GFP fluorescence were well preserved through chemical reactivation (Xiong et al., 2014) provided by adding Na2CO3 in the imaging water bath (0.05 M, PH = 11.4).

We used a 60X water immersion objective (NA 1.0) for imaging, which provided the system with submicron resolution at 0.2 × 0.2 × 1 μm voxel sampling rate for each whole-brain dataset. High resolution and high density sampling rate greatly facilitated our cell reconstruction procedures and are especially necessary for reconstructing dense neural arborizations and fine structures (such as axon boutons and spines).

The red channel was used to capture the whole brain cytoarchitecture which was counterstained by propidium iodide (PI) (Gong et al., 2016). PI dyes were dissolved in the imaging water bath, thus stained the exposed DNAs and RNAs on the tissue surface. The staining occurred within thus was in real time. The 488 nm laser was strong enough for PI excitation. The counterstained cytoarchitecture provided a self-registered Nissl like brain atlas for the GFP channel and was used for the identification of cortical areas and layers. Furthermore, the image contrast in the PI channel was sufficient for identification and reconstruction of PyN main dendrites (Figures 3A and 3B). Weakly stained or unstained tubular cellular objectives, such as blood vessels and pyramidal main dendrites, can be seen in good contrast in PI channel.

QUANTIFICATION AND STATISTICAL ANALYSIS

Single Cell Reconstruction and Layer Boundaries Discrimination

To reconstruct sparsely labeled single ChCs from the whole-brain image datasets (~8 TB), we transformed TIFF format raw images series to LDA type (Li et al., 2017a). We then used Amira software (v 5.2.2, FEI, Mérignac Cedex, France) to load the LDA data and identify cells for initial reconstruction. We only chose cells with highly characteristic axon terminal cartridges which were true ChCs (~30% GFP-labeled neurons were not the ChC type). The areal and laminar location of selection of cells were identified based on the cytoarchitecture provided by PI staining according to Allen Mouse Brain Reference Atlas. All initial reconstructed cells were saved in SWC format.

The arborization of a complete single ChC was extremely dense: the average length of AAC axons was ~2.1cm, the average number of AAC axon branches was ~1369, and the average axon branch order was ~31. Only manual procedure was feasible to reconstruct cells with such arbor complexity. Each AAC took up to one week to complete by one person.

To ensure all AAC reconstructions were correct and complete, we carried out revisions on each initial reconstruction in Neurolucida360 software (Neurolucida, MBF Bioscience, Williston, VT). Since neurolucida 360 was not compatible with the reading of SWC format files and couldn’t hold TB-size image datasets, we transformed all the SWC files to Neurolucida ASC format using the Neuronland software (Neuromorpho.org), and we cropped smaller image stacks (GB-size) of GFP and PI channels from the whole brain datasets. The Cropping areas were based on the coordinates calculated from the initial SWC reconstructions.

Cortical layer boundaries were reconstructed in the co-registered PI channel in Neurolucida 360. Laminar positions were discriminated based on cell body distributions according to the online version of Allen Mouse Brain Atlas (http://portal.brain-map.org/). 5μm max intensity projections of PI images were used to better show the cell body distributions. Since only PFC area has relative clear L2, L3 boundaries, we did not draw L2/L3 borders for all the cells. In our analysis, the axons are separated to layer 2 and layer 3 by defining the upper half of L2/3 as layer 2, and the lower half as layer 3. L3/5 boundary was identified by the existence of sparser cell distributions and larger pyramidal cell bodies in L5. L5/6 boundary was determined based on the missing of large cell bodies and the appearance of denser and horizontal oriented cell bodies in L6.

Adjusting the Orientation AACs to the Vertical Axis of Local Cortical Column

To identify the local vertical axis of cortical depth, we randomly reconstructed a few pyramidal main dendrites near the reconstructed AAC cell body in PI channel. We took the main direction of PyN apical dendrites near the AAC cell body as the cortical column vertical axis. We first randomly reconstructed a few pyramidal apical dendrites. We then centered all the traced pyramidal dendrites, and identified their main orientation based on the vectors calculated with pyramidal dendritic vectorization by Principal Component Analysis (PCA). Using this orientation as the proxy of cortical vertical axis, we re-orientated each AAC reconstruction using the MATLAB software (Figure 3B).

Length Density Analysis

Length density analysis of AAC morphology

Length density analysis of dendrites and axons were performed using custom MATLAB routines (Yamawaki et al., 2014). Briefly, for each orientation-readjusted AAC, we set the soma center as origin of coordinate. The neuronal arbors were divided into 15 μm × 15 μm grid space in the xy plane, and the arbor length in each grid were summed covering the whole z direction. The distribution pattern in coronal plane (i.e., xy plane) was represented in heatmap. Length density profile along the cortical depth direction (i.e., y axis) were plotted to quantify the laminar distribution pattern by integrating fiber length along × direction from heat-map. Similarly, length density profiles along × axis (middle-lateral) and z axis (anterior-posterior) were plotted to quantify the horizontal distribution patterns (Figures S4C–S4F). To make easy comparison, we normalized profile by dividing the fiber total length of the cell (length ratio). Layer boundaries were also plotted in the length density figures (dashed lines). Their positions in the y axis was the average coordinates of all the contouring points covering the neuron arbor extent in × direction (Figure S6).

Normalized Length density distribution on a standard cortex template

For comparative analysis among AACs from different brain areas and samples, we normalized the laminar distribution of AAC axonal and dendritic arbors to a standard cortex template (y axis only). In the neocortex, only SSC has L4 compared with mPFC and MC, and the L6-WM (white matter) border in mPFC is usually not discernable in the coronal plane. And the thickness of the same layer in different cortical areas and even subareas can be different. To address these issues, we performed normalization based on the thickness of each layer, rather than using the distance from pia to WM. The number of laminar arbitrary units (AUs) been used for subdividing each layer was decided based on the average thickness of each layer from all cells (L1: 100.04 μm, L2/3: 180.52 μm, L5: 215.33 μm, n = 53). Here we kept the dividing size to be around 15 μm to match with the unnormalized length density analysis. Thus, the numbers of laminar AUs for dividing L1, L2/3 and L5 are 7 AUs, 12 AUs and 14 AUs respectively. According to these parameters, as shown in Figure S6, axon arbors were subdivided with different intervals for L1, L2/3 and L5. For the arbors above L1 and below L5 (L6), we used the dividing intervals of L1 and L5 respectively. Since the axons of most AACs did not innervate L4 (except one L4 AAC), we removed L4 length density data for all the AACs in SSC. Based on this method, we could get normalized length density distribution curves of dendrites and axons for each cell from all the three cortical areas.

Cluster Analysis

Based on normalized distribution of neural arbor length density along the y axis (cortical depth), 53 AACs were hierarchically clustered using a weighted KL divergence (KLD_w, symmetrized (Johnson and Sinanovic, 2001)) as the distance metric and the furthest distance as the linkage rule. A weight coefficient λ was defined as the ratio of average axon length to total axon and dendrite length across all neurons. The KLD_w matrix was calculated by multiplying the axon distribution by the length based weight l and the dendrite distribution by (1 − λ). That is KLD_w = λKLD_axon + (1 − λ)KLD_dendrite. Based on the clustering dendrogram of KL divergence, 53 AACs can be grouped to different clusters. Corresponding silhouette analysis was done based on the cutoff linkages used in the clustering

Clique Analysis

To robustly classify the AACs we did a comparative clustering study across five different metrics, to find neuronal groups that clustered together irrespective of metric utilized.

Three of the metrics were derived from topological considerations described in Li et al. (2017a, 2017b). This methodology starts by defining a “descriptor function,” which is a scalar valued function defined on the axons and dendrites of each neuron. The procedure then computes a topological signature known as the persistence diagram for each neuron based on the descriptor function. Finally, the distance between two neurons is defined by computing a suitable metric between the persistence diagrams. The persistence diagrams are by definition invariant to rigid translations and rotations, and may have further invariances. Three of the metrics were defined by using three different descriptor functions, in each case defined as a suitable distance from the soma to the point on the neuron. The three distance functions used were Euclidean distance, Geodesic distance along the neuron, and distance along the normal to the cortical sheet (we denote this the “y-axis” for brevity).

In addition, we used a metric defined by taking KL distance between the histograms created by projecting the neuronal processes onto the y axis (“length density”), and finally a community-standard metric, the L-measure (Scorcioni et al., 2008), used on neuromorpho.org.

How related are these metrics? To answer this question, we performed hierarchical clustering using each of the metrics, fixing the total number of clusters to be K. In general, the different metrics produced different sets of clusters. We compared the sets of clusters across two metrics, using the Adjusted Rand Index (ARI), and the Similarity Index (Bohland et al., 2009) (SI) defined in Bohland et al. (https://journals.plos.org/plosone/article?id=10.1371%2Fjournal.pone.0007200) to compare different parcellations of brain atlases. In each case, these indices lie between 0 and 1, with 1 corresponding to perfect correspondence between two sets of clusters. We found (Figure 6F) that both indices were generally closer to 0 than to 1, indicating that these metrics measured independent geometrical/topological characteristics of the neurons. Thus, if neurons were grouped together by all five metrics, we would gain confidence that they were robustly classified into these clusters.

To perform this robust classification, we used the following method: (i) first, we carried out hierarchical clustering using each of the metrics, with a fixed number K of clusters. (ii) We then defined an undirected graph G with each node corresponding to a neuron. The edge between two neurons is either 1 or 0 based on whether the neurons clustered together or not as described below. (iii) We then looked for disjoint cliques (in a clique, each node is connected to every other node in the clique; intuitively, a clique constitutes a set of very similar neurons). These disjoint cliques were our robust clusters.

Let the number of metrics be M ( = 5 in our case). We introduced a parameter N that controlled the edge weights of the graph G as follows: If two neurons belonged to at the same cluster for at least N of the M metrics, then we gave that edge a weight 1, otherwise we gave it a weight 0. Thus, the graph G was a function of two parameters K,N. We then looked for maximal cliques in G(K,N). For N < M, the maximal cliques in G were not in general disjoint, however for N = M the cliques can be shown to be disjoint. Consider the relation between two neurons given by an edge in G(K,M). This relation is transitive: if two pairs of neurons (N1,N2) and (N2,N3) are connected, then (N1,N2) must belong to the same cluster across all metrics, as well as neurons (N2,N3). It follows that (N1,N3) must also belong to the same cluster (of which N2 is a member). This transitivity guarantees the disjointedness of the maximal cliques: If two cliques share a vertex, then the two cliques must be identical. Thus, we considered only G(K,M) and found the disjoint maximal cliques. In our case M = 5. We selected K by examining the average silhouette scores of the clusters versus K (https://scikit-learn.org/stable/auto_examples/cluster/plot_kmeans_silhouette_analysis.html). Finally, performing clique analysis on G(K = 4, N = M = 5), we found 3 cliques with size greater than 2 (with sizes 4,6 and 8 respectively; Figures 6G and S7). These cliques were the output of our robust clustering analysis, and exemplars from each clique are showin in Figure 6G.

Calculation of Single Neuron Anatomical Features

Basic neuron morphological features of neuronal dendrites and axons were calculated using Neurolucida software. The position of cell body (area, layer) were practically identified based on the PI channel cytoarchitecture information. The distance of soma to L1/2 border were calculated based on the readjusted neuron orientation (Figure 3B) with MATLAB software. Area: brain areas that cell body stays. L1 thickness: the thickness of L1. Layer: laminar position of cell body. Soma to L1/2 border: the distance of soma center to L1/2 in micron. Soma radius: average of the distance of reconstructed contour points to the center. Dendrite Qty: the number of dendrite trees that grows out from soma. Dendrite nodes: the number of branching points of all dendrites. Dendrite ends: the number of terminal tips of dendrites. Dendrite full length: the full length of all dendrite fibers. Dendrite mean length: the mean length of all dendrite trees. Dendrite max_branch_order: max branch order of all dendrite trees. For branch order calculation, here we use centrifugal ordering, which is the basic scheme to assign branch order to a tree. Dendrite branch Qty: the number of total dendrite branches. Dendrite branch mean length: average length of all branches. Dendrite mean tortuosity: average of the tortuosity values of all dendrite branches, tortuosity is defined as [Distance along process] / [Straight line distance]. Dendrite tortuosity SD: standard deviation of the tortuosity values of all dendrite branches. Dendrite convex hull: the volume of a convex polygon by connecting the tips of the distal dendrites or axon. Axon morphological parameters are similarly defined as dendrite.

Sholl Analysis on Dendrites and Axons

We did sholl analysis on AAC dendrites and axon fiber distributions at 3D. Fiber length was used here for analysis. Sholl analysis generates a set of nested concentric spheres centered at the cell body. The smallest sphere has a radius of 5 um considering the soma radius. The spheres increase in size by a constant change in 15um, which is defined as the radius in Figures 4G and 5C. According to this spheres, many shells are constructed. Shell is the volume contained out to the given radius, but does not include the volume of any smaller shells. The fiber length in each shell was summarized. To compare different cell, we normalized fiber length as [fiber length in a shell] / [the full length for a given fiber type].

DATA AND SOFTWARE AVAILABILITY

Code Availability

All custom codes used in this study are available from the corresponding author upon reasonable request.

Data Availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

KEY RESOURCES TABLE

REAGENT or RESOURCE	SOURCE	IDENTIFIER
Antibodies
Rabbit polyclonal RFP	Rockland	Cat# 600-401-379; RRID:AB_828392
Mouse monoclonal Ankyrin-G	Neuromab	Cat# 75-146; RRID:AB_10673030
Rat monoclonal muscarinic Acetylcholine receptor m2 (m2AChR)	Millipore	Cat# Cat# AB5166; RRID:AB_91715
Alexa Fluor 488 goat anti-rat	Invitrogen	Cat#A-11006; RRID:AB_2534074
Alexa Fluor 594 goat anti-rabbit	Invitrogen	Cat# A-11037; RRID:AB_2534095
Alexa Fluor 647 goat anti-mouse IgG2a	Invitrogen	Cat#A-21241; RRID:AB_2535B10
Recombinant DNA
pAAV-EF1a-fDIO-TVA-GFP	this paper	N/A
pAAV-EF1a-FLEX-GT	Callaway Lab	Addgene plasmid # 26198
pAAV-EF1a-fDIO-YFP-WPRE	Deisseroth Lab	Fenno et al., 2014
Chemicals, Peptides, and Recombinant Proteins
Lowicryl HM20 resin	electron microscopy sciences	Cat#RT-14340
Propidium iodide (PI)	Invitrogen	Cat#P1304MP
Experimental Models: Organisms/Strains
Nkx2.1-CreER mouse	Jackson Laboratory	JAX: 014552
Rosa26-loxp-stop-loxp-fipo (LSL-Flp) mouse	Jackson Laboratory	JAX: 02B5B4
Rosa26-lox-stop-lox-tdTomato (Ai14) mouse	Jackson Laboratory	JAX: 007905
Software and Algorithms
Amira	FEI, Mérignac Cedex, France	https://www.thermofisher.com/global/en/home/industrial/electron-microscopy/electron-microscopy-instruments-workflow-solutions/3d-visualization-anaiysis-software/amira-life-sciences-biomedical.html; RRID:SCR_014305
Neurolucida360	MBF Bioscience, Williston, VT	https://www.mbfbioscience.com/neurolucida360; RRID:SCR_001775
NLMorphologyConverter	Neuronland; Neuromorpho.org	http://neuronland.org/NLMorphologyConverter/NLMorphologyConverter.html; RRID:SCR_001817

Highlights.

• An integrated platform that resolves, registers, and quantifies single-neuron morphology

• The pipeline facilitates high-resolution, scalable single neuron anatomy in mouse brain

• Cortical axo-axonic interneurons consist of multiple morphological subtypes

• AAC subtypes differ in laminar position and dendritic and axonal arborization patterns