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Classes and continua of hippocampal CA1 inhibitory neurons revealed by single-cell transcriptomics

  • Kenneth D. Harris ,

    Roles Conceptualization, Data curation, Formal analysis, Funding acquisition, Investigation, Methodology, Project administration, Software, Visualization, Writing – original draft, Writing – review & editing

    kenneth.harris@ucl.ac.uk

    Affiliations University College London Institute of Neurology, London, United Kingdom, University College London Department of Neuroscience, Physiology and Pharmacology, London, United Kingdom

  • Hannah Hochgerner,

    Roles Investigation, Writing – review & editing

    Affiliation Division of Molecular Neurobiology, Department of Medical Biochemistry and Biophysics, Karolinska Institutet, Stockholm, Sweden

  • Nathan G. Skene,

    Roles Investigation, Writing – review & editing

    Affiliations University College London Institute of Neurology, London, United Kingdom, Division of Molecular Neurobiology, Department of Medical Biochemistry and Biophysics, Karolinska Institutet, Stockholm, Sweden

  • Lorenza Magno,

    Roles Investigation, Writing – review & editing

    Affiliation University College London Wolfson Institute for Biomedical Research, London, United Kingdom

  • Linda Katona,

    Roles Investigation, Writing – review & editing

    Affiliation Department of Pharmacology, University of Oxford, Oxford, United Kingdom

  • Carolina Bengtsson Gonzales,

    Roles Investigation, Writing – review & editing

    Affiliation Division of Molecular Neurobiology, Department of Medical Biochemistry and Biophysics, Karolinska Institutet, Stockholm, Sweden

  • Peter Somogyi,

    Roles Conceptualization, Funding acquisition, Investigation, Resources, Supervision, Writing – review & editing

    Affiliation Department of Pharmacology, University of Oxford, Oxford, United Kingdom

  • Nicoletta Kessaris,

    Roles Conceptualization, Funding acquisition, Supervision, Writing – review & editing

    Affiliation University College London Wolfson Institute for Biomedical Research, London, United Kingdom

  • Sten Linnarsson,

    Roles Conceptualization, Funding acquisition, Resources, Supervision, Writing – review & editing

    Affiliation Division of Molecular Neurobiology, Department of Medical Biochemistry and Biophysics, Karolinska Institutet, Stockholm, Sweden

  • Jens Hjerling-Leffler

    Roles Conceptualization, Funding acquisition, Supervision, Writing – review & editing

    Affiliation Division of Molecular Neurobiology, Department of Medical Biochemistry and Biophysics, Karolinska Institutet, Stockholm, Sweden

Classes and continua of hippocampal CA1 inhibitory neurons revealed by single-cell transcriptomics

  • Kenneth D. Harris, 
  • Hannah Hochgerner, 
  • Nathan G. Skene, 
  • Lorenza Magno, 
  • Linda Katona, 
  • Carolina Bengtsson Gonzales, 
  • Peter Somogyi, 
  • Nicoletta Kessaris, 
  • Sten Linnarsson, 
  • Jens Hjerling-Leffler
PLOS
x

Abstract

Understanding any brain circuit will require a categorization of its constituent neurons. In hippocampal area CA1, at least 23 classes of GABAergic neuron have been proposed to date. However, this list may be incomplete; additionally, it is unclear whether discrete classes are sufficient to describe the diversity of cortical inhibitory neurons or whether continuous modes of variability are also required. We studied the transcriptomes of 3,663 CA1 inhibitory cells, revealing 10 major GABAergic groups that divided into 49 fine-scale clusters. All previously described and several novel cell classes were identified, with three previously described classes unexpectedly found to be identical. A division into discrete classes, however, was not sufficient to describe the diversity of these cells, as continuous variation also occurred between and within classes. Latent factor analysis revealed that a single continuous variable could predict the expression levels of several genes, which correlated similarly with it across multiple cell types. Analysis of the genes correlating with this variable suggested it reflects a range from metabolically highly active faster-spiking cells that proximally target pyramidal cells to slower-spiking cells targeting distal dendrites or interneurons. These results elucidate the complexity of inhibitory neurons in one of the simplest cortical structures and show that characterizing these cells requires continuous modes of variation as well as discrete cell classes.

Author summary

Single-cell RNA sequencing allows scientists to count the number of copies of each gene expressed in multiple individually isolated cells. Because different cell types express genes in different amounts, “clusters” of cells with similar expression patterns are likely to correspond to different cell types. As well as discrete classes, however, cells also show continuous variation in gene expression. To study the relationship between cell classes and continua in a well-understood brain system, we applied new analysis methods to a dataset of inhibitory interneurons from area CA1 of the mouse hippocampus. Thanks to decades of intensive work, at least 23 classes of CA1 interneurons have been previously defined. We were able to identify them all with our transcriptomic clusters but unexpectedly found three to be identical. Because the connectivity of these cells has already been established, we were also able to identify the primary mode of continuous variation in these cells, which related to their axon target location. This in-depth understanding of the relatively simple cortical circuit of CA1 not only clarifies the cellular composition of this important brain structure but also will form a solid foundation for understanding more complex structures, such as the isocortex.

Introduction

Cortical circuits are composed of highly diverse neurons, and a clear definition of cortical cell types is essential for the explanation of their contribution to network activity patterns and behavior. Cortical neuronal diversity is strongest amongst GABAergic neurons. In hippocampal area CA1—one of the architecturally simplest cortical structures—GABAergic neurons have been divided so far into at least 23 classes of distinct connectivity, firing patterns, and molecular content [16]. A complete categorization of CA1 inhibitory neurons would provide not only essential information to understand the computational mechanisms of the hippocampus but also a canonical example to inform studies of more complex structures, such as six-layered isocortex.

CA1 GABAergic neurons have been divided into six major groups based on connectivity and expression patterns of currently used molecular markers. Parvalbumin (PVALB)-positive neurons (including basket, bistratified, and axo-axonic cells) target pyramidal cells’ somata, proximal dendrites, or axon initial segments, firing fast spikes that lead to strong and rapid suppression of activity [7,8]. Somatostatin (SST)-positive oriens/lacunosum-moleculare (O-LM) cells target pyramidal cell distal dendrites and exhibit slower firing patterns [9]. GABAergic long-range projection cells send information to distal targets and comprise many subtypes, including SST-positive hippocamposeptal cells; NOS1-positive backprojection cells targeting dentate gyrus and CA3; and several classes of hippocamposubicular cells, including trilaminar, radiatum-retrohippocampal, and PENK-positive neurons [1014]. Cholecystokinin (CCK)-positive interneurons are a diverse class characterized by asynchronous neurotransmitter release [15,16] that have been divided into at least five subtypes targeting different points along the somadendritic axis of pyramidal cells [1721]. Neurogliaform and Ivy cells release GABA diffusely from dense local axons and can mediate volume transmission as well as conventional synapses [22,23]. Interneuron-selective (I-S) interneurons comprise at least three subtypes specifically targeting other inhibitory neurons and expressing one or both of Vasoactive intestinal polypeptite (VIP) and calretinin (CALB2) [2,2426]. Finally, additional rare types, such as large SST/NOS1 cells [27], have been described at a molecular level, but their axonal targets and relationship to other subtypes is unclear.

This already complex picture likely underestimates the intricacy of CA1 inhibitory neurons. Currently defined classes likely divide into several further subtypes, and additional neuronal classes likely remain to be found (e.g., [28]). Furthermore, it is unclear whether a categorization into discrete classes is even sufficient to describe the diversity of cortical inhibitory neurons [29,30]. For example, several CCK interneuron classes have been described, targeting pyramidal cells at multiple locations ranging from their somata to distal dendrites, and the molecular profile and spiking phenotype of these cells correlates with their synaptic target location, with fast-spiking cells more likely to target proximal segments of pyramidal neurons [18,19,21]. Do such cells represent discrete classes with sharp interclass boundaries, or do they represent points along a continuum? Finally, while a cell’s large-scale axonal and dendritic structure likely remains fixed throughout life, both gene expression and electrophysiological properties can be modified by factors such as neuronal activity [3134]. To what extent is the observed molecular diversity of interneurons consistent with activity-dependent modulation of gene expression?

Single-cell RNA sequencing (scRNA-seq)—which can read out the expression levels of all genes in large numbers of individual cells—provides a powerful opportunity to address these questions. This method has successfully identified the major cell classes in several brain regions [3546]. Nevertheless, identifying fine cortical cell classes has not been straightforward because of both incomplete prior information on the underlying cell types and complicating factors, such as potential continuous variability within these classes. The large body of prior work on CA1 interneurons provides a valuable opportunity to identify transcriptomic clusters with known cell types in an important cortical circuit, enabling confident identification of known and novel classes and investigation of questions such as continuous variability.

Here, we describe a transcriptomic analysis of 3,663 inhibitory neurons from mouse CA1. This analysis revealed 49 clusters, of which we could identify 41 with previously described cell types, with the remaining 8 representing putative novel cell types. All previously described CA1 GABAergic classes could be identified in our database, but our results unexpectedly suggest that three of them are identical. The larger number of clusters occurring in our transcriptomic analysis reflected several previously unappreciated subtypes of existing classes and tiling of continua by multiple clusters. Our data suggest a common genetic continuum exists between and within classes, from faster-firing cells targeting principal cell somata and proximal dendrites, to slower-firing cells targeting distal dendrites or interneurons. Several classes previously described as discrete represent ranges along this continuum of gene expression.

Results

Data collection and identification of inhibitory cells

We collected cells from six Slc32a1-Cre;R26R-tdTomato mice, three of age p60 and three of age p27. Cells were procured using enzymatic digestion and manual dissociation [46], and data were analyzed using the 10X Genomics “cellranger” pipeline, which uses unique molecular identifiers (UMIs) to produce an absolute integer quantification of each gene in each cell. The great majority of cells (4,572/6,971 cells total; 3,283/3,663 high-quality interneurons) came from the older animals. Because we observed no major difference in interneuron classes between ages, data were pooled between them (S1 Fig). Fluorescence-activated cell sorting (FACS) yielded an enriched but not completely pure population of GABAergic neurons. A first-round clustering (using the method described below) was therefore run on the 5,940 cells passing quality control, identifying 3,663 GABAergic neurons (as judged by the expression of genes Gad1 and Slc32a1).

Cluster analysis

We analyzed the data using a suite of four novel algorithms derived from a probabilistic model of RNA distributions. All four methods were based on the observation that RNA counts within a homogeneous population can be approximated using a negative binomial distribution (see Methods, [47,48]). The negative binomial distribution accurately models the high variance of transcriptomic read counts (S2A and S2B Fig). As a consequence, algorithms based on this distribution weight the presence or absence of a gene more than its numerical expression level—for example, this distribution treats read counts of 0 and 10 as more dissimilar than read counts of 500 and 1,000 (S2C Fig).

The algorithm we used for clustering was termed ProMMT (Probabilistic Mixture Modeling for Transcriptomics). This algorithm fits gene expression in each cluster k by a multivariate negative binomial distribution with cluster-specific mean μk. The mean expression levels of only a small subset of genes are allowed to vary between clusters (150 for the current analysis; S3 Fig); these genes are selected automatically by the algorithm by maximum likelihood methods. The use of such “sparse” methods is essential for probabilistic classification of high-dimensional data [49], and the genes selected represent those most informative for cluster differentiation. The number of clusters was chosen automatically using the Bayesian Information Criterion (BIC) [50]. The ProMMT algorithm also provides a natural measure of the distinctness of each cluster, which we term the isolation metric (see Methods).

The ProMMT algorithm divided CA1 interneurons into 49 clusters (Fig 1). We named the clusters using a multilevel scheme after genes that are strongly expressed at different hierarchical levels; for example, the cluster Calb2.Vip.Nos1 belongs to a first-level group characterized by strong expression of Calb2 (indicating I-S interneurons); a second-level group Calb2.Vip; and a third-level group distinguished from other Calb2.Vip cells by stronger expression of Nos1. This naming scheme was based on the results of hierarchical cluster analysis of cluster means, using a distance metric based on the negative binomial model (Methods; Fig 1).

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Fig 1. The ProMMT algorithm split CA1 GABAergic neurons into 49 clusters.

Dendrogram (left) shows a hierarchical cluster analysis of these classes. Table shows class names (chosen hierarchically according to strongly expressed genes), number of cells per class, isolation metric of each class (higher for distinct classes), the mean value of latent variable analysis for cells in this class, and the biological cell type identified from its gene expression pattern. Asterisks indicate hypothesized novel classes. Right, bar chart showing log expression of 25 selected genes for all cells in the class. Note the expression pattern of Lhx6, which suggests a developmental origin in medial ganglionic eminence for clusters Cacna2d1.Lhx6.Vwa5a and above. CGE, caudal ganglionic eminence; I-S/IS, interneuron-selective; MGE, medial ganglionic eminence; NGF, neurogliaform cell; O-Bi, Oriens-Bistratified; O-LM, oriens/lacunosum-moleculare; ProMMT, Probabilistic Mixture Modeling for Transcriptomics; slm, stratum lacunosum-moleculare; so, stratum oriens; sp, stratum pyramidale; sr, stratum radiatum.

https://doi.org/10.1371/journal.pbio.2006387.g001

Data visualization

To visualize cell classes in two dimensions, we modified the t-stochastic neighbor embedding (tSNE) algorithm [51] for data with negative binomial variability, terming this approach nbtSNE (negative binomial tSNE). In conventional tSNE, the similarity between data points is defined by their Euclidean distance, which corresponds to conditional probabilities under a Gaussian distribution. We obtained greater separation of clusters and a closer correspondence to known cell types by replacing the Gaussian distribution with the same negative binomial distribution used in our clustering algorithm (see Methods; S4 Fig).

The nbtSNE maps revealed that cells were arranged in 10 major “continents” (Fig 2). The way expression of a single gene differed between classes could be conveniently visualized on these maps by adjusting the symbol size for each cell according to that gene’s expression level. Consistent with previous transcriptomic analyses, we found that classes were rarely, if ever, identified by single genes but rather by combinatorial expression patterns. Thanks to the extensive literature on CA1 interneurons, 25 genes together sufficed to identify the main continents with known cell classes (Fig 3), and it was also possible to identify nearly all the finer subclasses using additional genes specific to each class (S1 Text).

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Fig 2. Two-dimensional visualization of expression patterns using nbtSNE algorithm, which places cells of similar expression close together.

Each symbol represents a cell, with different color/glyph combinations representing different cell classes (legend, right). Grey boxes and numbers refer to the “continents” mentioned in the text and subsequent figures. nbtSNE, negative binomial t-stochastic neighbor embedding; O-LM, oriens/lacunosum-moleculare.

https://doi.org/10.1371/journal.pbio.2006387.g002

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Fig 3. Expression levels of 25 selected genes that together allow identification of major cell classes.

Each subplot shows an nbtSNE map of all cells, with marker size indicating log-expression level of the gene named above the plot. Similar maps for all genes can be found online at http://linnarssonlab.org/ca1/.

https://doi.org/10.1371/journal.pbio.2006387.g003

Identification of cell types

Previous work has extensively characterized the connectivity, physiology, and firing patterns of CA1 inhibitory neurons, and these cellular properties have been related to the expression of large numbers of marker genes. We next sought to identify our transcriptomic clusters with previously defined cell types, taking advantage of the “Rosetta stone” provided by this extensive prior research. Explaining how the identifications were made requires an extensive discussion of the previous literature, which is presented in full as S1 Text, online. Here, we briefly summarize the major subtypes identified (summarized in Fig 4).

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Fig 4. Inferred circuit diagram of identified GABAergic cell types.

The identification of transcriptomic clusters with known cell classes is described in full in S1 Text. Laminar locations and connections between each class are derived from previous literature. CGE, caudal ganglionic eminence; IS, interneuron-selective MGE, medial ganglionic eminence; NGF, neurogliaform cell; O-Bi, Oriens-Bistratified; O-LM, oriens/lacunosum-moleculare; R-LM, Radiatum/lacunosum-moleculare.

https://doi.org/10.1371/journal.pbio.2006387.g004

Continent 1 was identified with the Sst-positive hippocamposeptal and O-LM cells of stratum oriens (so). These cells all expressed Sst and Grm1, and were further divided into two Npy+/Ngf+ clusters identified as hippocamposeptal neurons [52] and three Pnoc+/Reln+/Npy− clusters identified with O-LM cells [9]. In addition, continent 1 contains a previously undescribed subclass positive for Sst, Npy, and Reln.

Continent 2 was identified as basket and bistratified cells. These were all positive for Tac1 (the precursor to the neuropeptide Substance P), as well as Satb1 and Erbb4, but were negative for Grm1. They were divided into two Pvalb+/Sst− clusters identified with basket cells, two Pvalb+/Sst+/Npy+ clusters identified with bistratified cells (Klausberger et al., 2004), and three Pvalb− clusters identified with Oriens-Bistratified (O-Bi) cells [53].

Continent 3 was identified as axo-axonic cells because of their expression of Pvalb but not Satb1 [54]. This continent’s three clusters were Tac1 negative but positive for other markers, including Snca, Pthlh, and C1ql1, which have also been associated with axo-axonic cells in isocortex [43,44]. We note that this dichotomy of Pvalb interneurons into Tac1-positive and -negative subclasses is likely homologous to previous observations in isocortex [55].

Continent 4 was identified as Ivy cells and medial ganglionic eminence (MGE)-derived neurogliaform cells. These cells expressed Cacna2d1, which we propose as a unique identifier of hippocampal neurogliaform/ivy cells, as well as Lhx6 and Nos1 [56]. They were divided into a Reln+ cluster identified with MGE-derived neurogliaform cells and a Reln−/Vwa5a+ cluster identified with Ivy cells [23]. This continent is homologous to the isocortical Igtp class defined by Tasic and colleagues [44], which we hypothesize may represent isocortical neurogliaform cells of MGE origin; this hypothesis could be confirmed using fate mapping.

Continent 5 was identified as caudal ganglionic eminence (CGE)-derived neurogliaform cells. Its three clusters contained Cacna2d1 and many other genes in common with those of continent 4, but lacked Lhx6 and Nos1 [56]. Similar to isocortical putative neurogliaform cells, this continent expressed Ndnf and contained a distinct subtype positive for Cxcl14 [44]. As with continent 4, continent 5 mainly expressed Reln but also contained a small Reln-negative cluster, which we suggest forms a rare and novel class of CGE-derived ivy cell.

Continent 6 was identified with Sst-negative long-range projection interneurons. It divided into two distinct clusters, both of which were strongly positive for Ntng1. The first strongly expressed Chrm2 but lacked Sst and Pvalb, identifying them as trilaminar cells [12,57]. The second subgroup lacked most classical molecular markers; this fact, together with their inferred laminar location at the stratum radiatum / stratum lacunosum-moleculare (sr/slm) border, identified them as putative radiatum-retrohippocampal neurons that project to the retrosplenial cortex [12,58].

Continents 7 and 8 were identified as what are traditionally called Cck interneurons. This term is somewhat unfortunate: while these cells indeed strongly express Cck, many other inhibitory classes express Cck at lower levels, including even Pvalb+ basket cells [59]. Continents 7 and 8 cells comprised 13 highly diverse clusters but shared strong expression of Cnr1, Sncg, Trp53i11, and several other novel genes. Continent 8 is distinguished by expression of Cxcl14, which localizes these cells to the sr/slm border. This continent comprised a continuum ranging from soma-targeting basket cells, identified by their Slc17a8 (vGlut3) expression, to dendrite-targeting cells, identified by expression of Calb1 or Reln [19,21]. Continent 7, lacking Cxcl14, was identified as Cck cells of other layers and contained multiple subtypes characterized by the familiar markers Calb1, Vip, and Slc17a8 [21] as well novel markers such as Sema5a and Calca. Associated with continent 8 were several apparently novel subtypes: a rare and distinct group positive for both Scl17a8 and Calb1 and marked nearly exclusively by Lypd1; a Ntng1+/Ndnf+ subgroup related to cells of continent 6; and a group strongly expressing both Vip and Cxcl14, which therefore likely corresponds to a novel Vip+/Cck+ interneuron at the sr/slm border.

Continent 9 was identified as I-S interneurons. Its eight clusters fell into three groups: Calb2+/Vip− neurons identified as IS-1 cells, Calb2−/Vip+ neurons identified as IS-2 cells, and Calb2+/Vip+ neurons identified as IS-3 cells [2,24,26,60]. All expressed Penk [61]. These cells contained at least two novel subgroups: an IS-3 subtype positive for Nos1 and Myl1, homologous to the Vip Mybpc2 class defined in isocortex [44], and a rare subclass of IS-1 cells positive for Igfbp6.

Continent 10 contained a single highly distinct cluster located in an “island” off continent 1. It contained cells strongly positive for Sst and Nos1 [27], whose expression pattern is consistent with that of both backprojection cells [13] and PENK-positive projection cells [10], suggesting that these three previously identified classes reflect a single cell type.

Comparison with isocortical classes

Our finding of 49 clusters in a sample of 3,663 CA1 cells contrasts with a previous study of isocortical area V1 (primary visual cortex), which found 23 clusters from a sample of 761 inhibitory neurons [44]. One can imagine three reasons for the greater number of clusters found in the present study: the larger sample size used here may have resulted in our resolving more clusters, the use of a different clustering algorithm may have allowed the current study to reveal finer cell types, or area CA1 might genuinely contain more diverse inhibitory neurons than isocortex. To address these questions, we performed two analyses. First, we applied our clustering algorithm to the data of Tasic and colleagues (2016), and second we reanalyzed subsamples of the data of both the current study and of Tasic and colleagues (2016) to see how the number of clusters found varies with cell count and with sequencing depth.

Applying the ProMMT algorithm to the Tasic dataset yielded 30 clusters (S5A and S5B Fig). The cluster assignments almost completely overlapped as far as top-level groupings but showed some more subtle distinctions in finer-level clusters (S5C Fig). We examined three of these novel classes’ differences in more depth, to ask whether the finer distinctions found by the ProMMT algorithm could correspond to genuine biological cell classes. The most notable of these was cluster 11, which contained neurons that had previously been assigned to the neurogliaform clusters Ndnf Cxcl14, Ndnf Car4, but lacked common neurogliaform markers such as Lamp5 and Gabrd. Instead, cells in these clusters expressed Calb2 and Penk but not Vip, suggesting cells homologous to hippocampal IS-1 cells and potentially matching the Vip-negative I-S layer 1 “single-bouquet cells” (SBCs) described by Jiang and colleagues [62,63]. To test whether cluster 11 indeed corresponds to SBCs, we took advantage of a Patch-seq study [64] that contrasted gene expression in anatomically identified layer 1 SBCs and neurogliaform cells (S5D Fig). We found that the genes that Cadwell and colleagues had reported as distinguishing SBCs from neurogliaform cells indeed occurred in almost entirely nonoverlapping populations of cells; furthermore, these populations closely matched the ProMMT clusters identified with SBCs and neurogliaform cells. Examination of two further subdivisions found by the ProMMT algorithm again revealed genes uniquely expressed in nonoverlapping subpopulations of the Sst Cbln4 and Vip Parm1 clusters (S6 Fig). We conclude that the larger number of clusters identified by the ProMMT algorithm at least in part results from its ability to distinguish subtle variations in gene expression between related cell types.

To ask whether the greater number of clusters found in the current study might in part arise from its larger sample size, we reran the cluster analysis on randomly selected subsets of cells from our dataset. We found a strong linear increase in the number of clusters found with increasing sample size (S7A Fig). To investigate what effect sequencing depth may have had, we resampled our dataset to simulate lower read counts for the same cells, and again found an approximately linear increase in the number of identified clusters with read count (S7B and S7C Fig). We performed similar analyses on Tasic and colleagues’ data and obtained similar results (S7D and S7E Fig).

We therefore conclude that the larger number of clusters found by the current study is more likely to reflect a combination of larger sample size and more sensitive clustering algorithms than a greater number of biological cell types in CA1 than in V1. Furthermore, we expect that an even larger sample size or greater sequencing depth would have revealed yet more, finely distinguished cell types.

Continuous variation between and within cell classes

Although the major continents of the expression map were clearly separated, clusters within these continents often appeared to blend into each other continuously. This suggests continuous gradation in gene expression patterns: while our probabilistic mixture model will group cells from a common negative binomial distribution into a single cluster, it will tile cells of continuously graded mean expression into multiple clusters.

Although visualization methods such as nbtSNE can suggest whether classes are discrete or continuously separated, they are not sufficient to confirm the suggestion. Such methods exhibit local optima, raising the possibility that apparent continuity only occurs for particular initialization conditions. Furthermore, as nbtSNE is based on a subset of genes, it is conceivable that discrete/continuous patterns occur only for this subset.

To confirm the apparent continuity or discreteness of these groups, we therefore employed a novel method of negative binomial discriminant analysis that is independent of nbtSNE and considers all genes. Given a pair of cell classes, this method compares how close each cell’s whole-genome expression pattern is to each class, using a cross-validated likelihood ratio statistic. For two classes identified as basket and axo-axonic cells, the histogram of likelihood ratios was clearly bimodal (Fig 5A, top), indicating that every cell exhibited a much stronger fit to its own class than to the other, and confirming the discrete separation of these classes. A second example of clusters identified with Ivy and MGE-neurogliaform cells, however, showed different behavior (Fig 5A, middle): a unimodal likelihood ratio histogram indicated that the two clusters ran smoothly into each other, tiling a continuum of gene expression patterns. The bimodality of the likelihood ratio can be captured by a d’ statistic, which for these two examples was 7.2 and 1.5, respectively. Perhaps ironically, the degree to which two neighboring classes are discrete or continuous was itself a continuous variable. For example, Slc17a8-expressing Cxcl14/Cck neurons showed largely continuous overlap with their neighboring Cck/Cxcl14 cells, but with some small indication of bimodality, characterized by a d’ of 3.1 (Fig 5A, bottom). We conclude that while truly discrete cluster separations do exist, the dataset is not fully described as a set of discrete classes, and that many clusters tile continuous dimensions (Fig 5B).

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Fig 5. Analysis of discrete versus continuous variation by negative binomial discriminant analysis.

(A) Histogram of log-likelihood ratios for three example cluster pairs, measuring how much better each cell’s whole-genome expression pattern is explained by one or the other cluster. The top histogram (basket versus axo-axonic cells) is clearly bimodal, indicating discrete separation. The bottom two histograms (ivy versus MGE-neurogliaform cells; two subclasses of Cck/Cxcl14 cells) show substantial overlap, indicating continuous variation between clusters. The degree of bimodality is captured by the d’ statistic above each plot. (B) Pseudocolor matrix showing continuity of each pair of clusters, as assessed by d’ statistic. White means strongly bimodal; darker colors indicate continuity.

https://doi.org/10.1371/journal.pbio.2006387.g005

Latent factor analysis reveals a common mode of variation across all cell types that correlates with axon target location

The existence of continuous variation in gene expression suggests that cluster analysis is not giving a complete picture of neuronal gene expression patterns. To further study the biological significance of continuously varying gene expression, we therefore applied a complementary method, latent factor analysis. Cluster analysis can be viewed as an attempt to summarize the expression of all genes using only a single discrete label per cell (the cell’s cluster identity); the value this label takes for each cell is not directly observed but is “latent” and inferred from the data. Latent factor analysis also attempts to predict the expression of all genes using only a single variable (the “latent factor”), but now with a continuous rather than discrete distribution. As with cluster analysis, the latent factor is not directly observed but is inferred for each cell. Latent factor analysis operates without knowledge of cluster identity and therefore requires that the same rules be used to predict gene expression from the latent factor for cells of all types. Clearly, one should expect neither method to precisely predict the expression of all genes from a single variable, but the rules of cellular organization they reveal may provide important biological information.

As expected, latent factor analysis produced a complementary view to cluster analysis (Fig 6A). Knowing a cell’s cluster identity did not suffice to predict its latent factor value, and vice versa. For example, the ranges of latent factor values for cells in the clusters identified with Cck and Pvalb basket cells overlapped. Nevertheless, the range of possible latent factor values was not identical between clusters, and the mean latent factor value of each cluster differed in a manner that had a clear biological interpretation.

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Fig 6. Latent factor analysis reveals a common mode of continuous variation that is consistent across cell types and correlates with axon target location.

(A) Latent factor analysis assigns a single number to each cell via a search for the factor values that best predict expression of multiple genes. Mean factor values within each cluster differ systematically in a way that correlates with the identified cell class’s axon target location. Each point represents a cell, with the x-coordinate showing latent factor value and y-coordinate showing cluster, sorted by mean latent factor value. (B) Continuous gradient of latent factor values across continent 8 (top; symbol size denotes latent factor value). Largest values are found in western Slc17a8-expressing neurons identified with soma-targeting Cck basket cells; smallest values are found in eastern Calb1-expressing neurons identified with dendrite-targeting Cck cells. (C) Correlation of latent factor values with expression of six example genes. Symbols as in (A); blue, continent 2 (basket/bistratified), green, continent 8 (Cck/Cxcl14). (D) Correlations of genes with the latent factor are preserved across cell classes. X-axis: correlation of gene with latent factor in continent 2; y-axis, correlation in continent 8; Spearman’s ρ = 0.58, p < 10−100. Inset, Spearman ρ values for all pairs of continents, p < 10−100 in each case. AU, arbitrary units.

https://doi.org/10.1371/journal.pbio.2006387.g006

The mean latent factor value of each cluster correlated with the axon target location of the corresponding cell type (Fig 6A). The clusters showing largest mean latent factor values were identified with soma-targeting basket cells (both Pvalb and Cck expressing) and with axo-axonic cells. Lower values of the latent factor were found in clusters identified with dendrite-targeting Cck cells and with bistratified, Ivy, and hippocamposeptal cells, which target pyramidal cells’ proximal dendrites [14,23]. Still lower values of the latent factor were found in clusters identified with neurogliaform and O-LM cells, which target pyramidal distal dendrites. The lowest values of all were found in clusters identified with cells synapsing on inhibitory interneurons: the IS cells of continent 9 and the Sst/Penk/Nos1 cells of continent 10, whose local targets are Pvalb cells [10].

While mean values of the latent factor differed between continents, there was also substantial variability within cells of a single continent. For example, a gradient of latent factor values was seen within continent 8 (identified with Cck-positive neurons at the sr/slm border), with larger values in the west smoothly transitioning to smaller values in the east (Fig 6B). Comparison of gene expression patterns in continent 8 to previous work again suggested that this gradient in latent factor values correlates with axon target location. Indeed, immunohistochemistry has demonstrated that CCK-positive cells expressing SLC17A8 (expressed in western continent 8) project to the pyramidal layer [21], while those expressing CALB1 (expressed in the east) target pyramidal cell dendrites [3,18,65]. The cannabinoid receptor Cnr1, which is more strongly expressed in soma-targeting neurons [66,67], was also more strongly expressed in western cells with larger latent factor values.

As expected, the expression levels of many individual genes correlated with the latent factor; furthermore, the directions of these correlations were consistent, even within distantly related cell types. We investigated the relationships of genes to the latent factor by focusing initially on the Pvalb- and Cck-expressing cells of continents 2 and 8 (Fig 6C). Most genes correlated similarly with the latent factor in both classes. For example, the Na+/K+ pump Atp1b1 and the GABA synthesis enzyme Gad1 correlated positively with the latent factor for multiple cell types, while 6330403K07Rik, a gene of unknown function, correlated negatively. Some genes’ expression levels depended on both cell type and latent factor value. For example, the ion channel Kcnc1 (which enables rapid action potential repolarization in fast-spiking cells) correlated positively with the latent factor in both Pvalb and Cck cells, but its expression was stronger in Pvalb cells, even for the same latent factor value. Other genes showed correlations with the latent factor, but only within the specific classes that expressed them. For example, expression of Pvalb correlated with the latent factor within cells of continent 2, but the gene was essentially absent from cells of continent 8; conversely, Cnr1 expression correlated with the latent factor in continent 8 but was essentially absent in cells of continent 2. Thus, the latent factor value is not alone sufficient to predict a cell’s gene expression pattern but provides a summary of continuous gradation in the expression of multiple genes in multiple cell types.

The relationship of genes to latent factor values was statistically similar across cell types. To demonstrate this, we computed the Spearman correlation of each gene’s expression level with the latent factor, separately, within cells of each continent (S1 Table). As expected from the scatterplots (Fig 6C), the correlation coefficients for Atp1b1, Gad1, and 6330403K07Rik were similar between continents 2 and 8 (Fig 6D). Also as expected, Pvalb and Cnr1 showed strong positive correlations with the latent factor within the continent where these genes were expressed, but correlations close to zero within the continent where they were barely expressed. In general, the correlation coefficients of genes with the latent factor were preserved between continents 2 and 8 (Fig 6D; Spearman rank correlation ρ = 0.58, p < 10−100). A similar relationship was found across all continents (Fig 6D, inset; p < 10−100 in each case), although cells of continents 9 and 10 showed less similarity than continents 1–8. Furthermore, similar results were obtained when analyzing isocortical data, most notably in isocortical Pvalb cells (S8 Fig).

In summary, the expression of many genes correlates with a single continuous variable, the latent factor value assigned to each cell. While this latent factor does not provide a complete summary of a cell’s gene expression pattern, the direction and strength of the correlation of individual genes to the latent factor is largely preserved across cell types. Furthermore, while a cell’s latent factor value was not simply a function of its cell class, mean latent factor values differed between clusters, being largest for clusters identified with cell types whose axons target pyramidal somata or axon initial segments and smallest for clusters identified with cell types targeting pyramidal distal dendrites or interneurons.

Biological significance of genes correlating with the latent factor

The above results suggest that the expression of a large set of genes is modulated in a largely consistent way across multiple cell types in a manner that correlate with their axonal targets. What biological functions might these genes serve? While one might certainly expect structural genes be differentially expressed between soma- and dendrite-targeting interneurons, these cells also differ in their physiology. Indeed, Pvalb-expressing basket cells are known for their fast-spiking phenotype, which produces rapid, powerful perisomatic inhibition and is mediated by a set of rapidly acting ion channels and synaptic proteins, including Kcnc1, Kcna1, Scn1a, Scn8a, and Syt2 [8]. Although most other interneurons show regular-spiking phenotype, CCK-expressing basket cells with a fast-spiking phenotype have also been reported [18,20]. We therefore hypothesized that genes responsible for the fast-spiking phenotype might be positively correlated with the latent factor, because of increased expression in soma-targeting cells of all classes.

Consistent with this hypothesis, genes associated with fast-spiking phenotype (Kcnc1, Kcna1, Scn1a, Scn8a, Syt2) were amongst the genes most positively correlated with the latent factor in both Pvalb and Cck basket cells (Fig 6D). However, this positive correlation was not restricted to these cell types: in an ordering of the correlations of all genes with the latent factor (taking into account cells of all types), these genes ranked in the 99.9th, 98.3rd, 99.5th, 98.9th, and 95th percentiles, respectively (S1 Table).

Other gene families positively correlated with the latent factor included genes associated with mitochondria (e.g., mt-Cytb), ion exchange and metabolism (e.g., Atp1b1; Slc24a2), GABA synthesis and transport (e.g., Gad1, Slc6a1), vesicular release (e.g., Syp, Sv2a, Cplx2, Vamp1), and fast ionotropic glutamate and GABA receptors (e.g., Gria1, Gabra1) as well as GABAB receptors (e.g., Gabbr1, Gabbr2, Kcnj3, Kctd12). The genes correlating negatively with the latent factor were less familiar but included Atp1b2, a second isoform of the Na+/K+ pump; Fxyd6, which modulates its activity; Nrsn1, whose translation is suppressed after learning [68], as well as many neuropeptides (e.g., Sst, Vip, Cartpt, Tac2, Penk, Crh; exceptional neuropeptides such as Cck showed positive correlation). Genes associated with neurofilaments and intermediate filaments (e.g., Nefh, Nefl, Krt73) tended to show positive weights, while genes associated with actin processing (e.g., Gap43, Stmn1, Tmsb10) tended to show negative weights. Many other genes of as yet unknown function correlated positively and negatively with the latent factor (for example, 6330403K07Rik). Relating the latent factor correlations of each gene to their gene ontology (GO) annotations (which are not granular enough to list annotations such as fast-spiking physiology) suggested that negatively correlated genes tended to be associated with translation and ribosomes, while positively correlated genes were associated with diverse functions, including transcription, signal transduction, ion transport, and vesicular function and with cellular compartments, including mitochondria, axons, and dendrites (S2 Table).

We therefore suggest that cells with large values of the latent factor not only target more proximal components of pyramidal cells but also express genes enabling a faster spiking firing pattern, more synaptic vesicles, and larger amounts of GABA release; receipt of stronger excitatory and inhibitory inputs; and faster metabolism. These are all characteristics of Pvalb-expressing fast-spiking interneurons [8]; however, a similar continuum was observed within all cell types, suggesting that these genes are commonly regulated in all CA1 interneurons.

The fact that the latent factor differs systematically between cells with different axonal targets suggests that this property is in good measure fixed, as it seems unlikely that neurons would make major changes to their axonal targets in adulthood. Nevertheless, interneuronal gene expression can be modulated by activity, and some of the genes that were most strongly correlated with the latent factor (Pvalb, Kcna1) are amongst those with activity-dependent modulation [3134,69].

To investigate whether the genes correlated with the latent factor might also be partially modulated by neuronal activity, we correlated each gene’s latent factor score with that gene’s modulation by in vivo light exposure after dark housing, using data from three classes of visual cortical interneurons (made available by Mardinly and colleagues [33]). We observed a moderate relationship of latent factor weighting to activity modulation in Sst neurons (r = 0.26; p < 10−12; S9 Fig), suggesting that activity-dependent modulation of Sst cells may cause them to move along the continuum of latent factor values. A weaker but still significant correlation was observed for Pvalb neurons (r = 0.11; p < 0.002), whereas no significant relationship was found for Vip neurons (p = 0.17). These data therefore suggest that a portion of the continuous variability of gene expression observed in CA1 interneurons may arise from activity-dependent modulation but that such modulation is unlikely to be a full explanation for the genetic continua revealed by latent factor analysis.

Histological confirmation of transcriptomic predictions

The transcriptomic classification we derived makes a large number of predictions for the combinatorial expression patterns of familiar and novel molecular markers in distinct CA1 interneuron types. To verify our transcriptomic classification, we set out to test some of these predictions using traditional methods of molecular histology.

Our first tests regarded the very distinct Sst.Nos1 cluster of continent 10. This cluster’s expression pattern matched three previously reported rare hippocampal inhibitory cell types: large SST-immunopositive cells that are intensely immunoreactive for NOS1 throughout the cytoplasm, revealing their full dendrites [27]; PENK-positive projection cells [10]; and strongly NADPH diaphorase-labeled (i.e., NOS1-positive) backprojection cells [13]. We therefore hypothesized that these cell types, previously regarded as separate, may in fact be identical. To test this hypothesis, we performed a series of triple and quadruple immunoreactions, focusing on the intensely NOS1-positive neurons (n = 3 mice, n = 70 cells: 39% in so/alveus; 10% in stratum pyramidale (sp); 27% in sr; 24% at the sr/slm border). Similar to previously reported PENK-projection, backprojection, and SST/NOS1 cells [10,13,27]—but unlike SST-positive O-LM cells [9]—these neurons all showed spiny or sparsely spiny dendrites. As expected from the Sst.Nos1 cluster, we found that they were all SST/NPY double positive (n = 20/20) and were virtually all weakly positive for CHRM2 (n = 36/38) and GRM1 (n = 17/17) in the somatodendritic plasma membrane, strongly positive for PCP4 (n = 19/21) in the cytoplasm and nucleus, and strongly positive for PENK (n = 35/42) in the Golgi apparatus and granules in the soma and proximal dendrites (Fig 7). By contrast, the more numerous moderately NOS1-positive cells (which include many interneuron types such as ivy, MGE-neurogliaform, and a subset of IS-3 neurons) were mostly immunonegative for CHRM2, PCP4, and PENK, although some were positive for GRM1. Our results are therefore consistent with the hypothesis that all three previously reported classes correspond to the Sst1.Nos1 cluster.

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Fig 7. Immunohistochemical characterization of intensely NOS1-positive neurons.

(A) A large multipolar neuron in stratum pyramidale is strongly SST and NPY positive in the somatic Golgi apparatus and weakly positive for CHRM2 in the somatodendritic plasma membrane (maximum intensity projection, z stack, height 11 μm; inset, maximum intensity projection of three optical slices, z stack height 2 μm). A smaller, more weakly NOS1-positive cell (double arrow) in the lower left is immunonegative for the other molecules; a second NPY-positive cell (arrow) adjoining the NOS1+ neuron is immunonegative for the other three molecules. (B) A NOS1-positive cell and another NOS1-immunonegative cell (asterisk) at the border of stratum radiatum and lacunosum-moleculare are both positive for GRM1 in the plasma membrane and PENK in the Golgi apparatus and in granules, but only the NOS1+ cell is immunopositive for CHRM2 (maximum intensity projection, z stack, height 10 μm). (C) An intensely NOS1-positive cell in stratum radiatum is also positive for PCP4 in the cytoplasm and nucleus and for PENK in the Golgi apparatus and in granules (maximum intensity projection, z stack, height 15 μm).

https://doi.org/10.1371/journal.pbio.2006387.g007

A second prediction of our classification was the expression of Npy in multiple subclasses of Cck cell, most notably the Slc17a8- and Calb1-expressing clusters of continent 8. This was unexpected, as NPY (at least at the protein level) has instead been traditionally associated with SST-expressing neurons and ivy/neurogliaform cells (Fuentealba et al., 2008a; Katona et al., 2014). Nevertheless, no studies to our knowledge have yet examined immunohistochemically whether the neuropeptides NPY and CCK can be colocalized in the same interneurons. We therefore tested this by double immunohistochemistry in sr and slm (Fig 8A, n = 3 mice). Consistent with our predictions, 119 out of 162 (74% ± 6%) of the cells immunopositive for pro-CCK were also positive for NPY (an additional 73 cells were positive for NPY only, which, according to our identifications, should represent neurogliaform and radiatum-retrohippocampal cells). A subset (176 cells) of NPY and/or pro-CCK immunopositive neurons were further tested for CALB1 in triple immunoreactions. As expected, nearly all CALB1-positive neurons were pro-CCK positive (89% ± 2%), and CALB1 immunoreactivity was seen in a subset of the cells containing both pro-CCK and NPY (27% ± 3%). Additional triple immunohistochemistry for NPY, pro-CCK, and SLC17A8 (VGLUT3) revealed triple positive cells in sr and particularly at the sr/slm border, as predicted by the class Cck.Cxcl14.Slc17a8 (Fig 8B). Because of the low level of somatic immunoreactivity for SLC17A8 (which, as a vesicular transporter, is primarily trafficked to axon terminals), we could not count these cells reliably; however, of the cells that were unambiguously immunopositive for SLC17A8, in a majority we detected NPY. Additional analysis combining double in situ hybridization for Slc17a8 and Npy with immunohistochemistry for pro-CCK (Fig 8C, n = 3 mice) confirmed that the great majority of Slc17a8-expressing cells were also positive for Npy and pro-CCK (84% ± 3%). As predicted by our identifications, the converse was not true: a substantial population of Npy/pro-CCK double-positive cells (57% ± 7% of the total) did not show detectable Slc17a8, which we identify with dendrite-targeting neurons in the east of continent 8.

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Fig 8. Confirmation of predicted colocalization of NPY and pro-CCK.

(A) Interneurons at the sr/slm border immunopositive for both NPY and pro-CCK (cells 1 and 2), one of which (cell 1) is also immunopositive for CALB1. A third neuron is positive only for pro-CCK and CALB1 (cell 3). (B) Interneurons at the sr/slm border immunopositive for NPY (cells 1–3), pro-CCK (cells 2 and 4), and SLC17A8 (VGLUT3, cell 2). Note SLC17A8-positive terminals targeting unlabeled cells (arrows). (A, B) Both NPY and pro-CCK are detected in the Golgi apparatus and endoplasmic reticulum surrounding cell nuclei; in addition, some axons are also immunopositive for NPY (see arrow in (A); average intensity projections, z stacks, height 6.3 μm and 10.4 μm, respectively). (C) Combined double in situ hybridization and immunohistochemistry shows that nearly all Slc17a8-expressing cells also express Npy and are immunopositive for pro-CCK (arrows), but some Npy/pro-CCK cells do not express Slc17a8 (arrowheads). Scale bars: 10 μm (A, B), 50 μm (C). sr/slm, stratum radiatum and stratum lacunosum-moleculare.

https://doi.org/10.1371/journal.pbio.2006387.g008

Several cell types in our classification expressed Cxcl14, a gene whose expression pattern in the Allen Brain Atlas shows localization largely at the sr/slm border. The Cxcl14-positive population includes all clusters of continent 8, which express Cck and contain subclusters expressing Npy, Calb1, Reln, and Vip; a subtype of CGE-derived neurogliaform cell that expresses Reln and Npy but lacks Nos1 and expresses Kit at most weakly; as well as IS-1, IS-2, and radiatum-retrohippocampal cells. However, as all Cxcl14-positive clusters lacked Lhx6, we conclude they should be distinct from all MGE-derived neurons, including MGE-derived neurogliaform cells.

To test these predictions, we performed in situ hybridization for Cxcl14 simultaneously with in situ hybridization or immunohistochemistry to detect Reln, Npy, CALB1, CCK, PVALB, Sst, Nos1, and Kit (n = 3 mice; Fig 9). In addition, we combined fluorescent in situ hybridization for Cxcl14 with immunohistochemistry for yellow fluorescent protein (YFP) in Lhx6-Cre/R26R-YFP mice, which allows identification of developmental origin by marking MGE-derived interneurons (Fogarty et al., 2007). The results of these experiments were consistent with our hypotheses. We found that within CA1, Cxcl14-expressing cells were primarily located at the sr/slm border (71% ± 3%), although a subpopulation of cells were also found in other layers. We found no overlap of Cxcl14 with YFP in the Lhx6-Cre/R26R-YFP mouse, confirming the CGE origin of Cxcl14-expressing neurons (Fig 9A). The majority of Cxcl14-positive cells expressed Reln (72% ± 4%), accounting for 42% ± 9% of Reln-expressing neurons (substantial populations of Reln+/Cxcl14− cells located in so and slm likely represent O-LM and MGE-neurogliaform cells, respectively (Fig 9B). Indeed, although less than half of Reln cells were located at the R-LM border (44% ± 1%), the great majority of Reln+/Cxcl14+ cells were found there (88% ± 6%). Consistent with the expected properties of continent 8 cells, a large fraction of the Cxcl14 population were immunoreactive for pro-CCK (62% ± 6%; Fig 9C), while substantial minorities were positive for CALB1 (29% ± 2%; Fig 9D) or Npy (25% ± 5%; Fig 9E). However, as expected from the lack of Cxcl14 in MGE-derived neurogliaform and IS-3 cells, we observed no overlap of Cxcl14 with Nos1 (0 out of 209 cells; Fig 9F) and very weak overlap with Kit, which is primarily expressed in clusters Cacna2d1.Ndnf.Npy and Cacna2d1.Ndnf.Rgs10, associated with the Cxcl14-negative CGE-neurogliaform population (1 of 264 cells, respectively, from all mice; Fig 9G).

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Fig 9. Analysis of Cxcl14 co-expression patterns confirms predicted properties Cck.Cxcl14 cells.

(A) Cxcl14-expressing cells are CGE derived: in situ hybridization for Cxcl14 combined with immunohistochemistry for YFP in the Lhx6-Cre/R26R-YFP mouse yields no double labeling. (B) Double in situ hybridization for Cxcl14 and Reln marks a population of neurons located primarily at the sr/slm border. Note Reln expression without Cxcl14 in so and slm, likely reflecting O-LM and neurogliaform cells. (C–E) Subsets of the Cxcl14-positive neurons are positive for pro-CCK or CALB1 (in situ hybridization plus immunohistochemistry), or Npy (double in situ hybridization). (F, G) No overlap was seen of Cxcl14 with Nos1 or Kit. In all panels, arrowheads indicate double-expressing neurons. Scale bars: 200 μm (A), 100 μm (B–G). b, sr/slm border region; O-LM, oriens/lacunosum-moleculare; slm, stratum lacunosum-moleculare; sm, stratum moleculare of the dentate gyrus; so, stratum oriens; sp, stratum pyramidale; sr, stratum radiatum; sr/slm, stratum radiatum and stratum lacunosum-moleculare; YFP, yellow fluorescent protein.

https://doi.org/10.1371/journal.pbio.2006387.g009

The cluster Cck.Cxcl14.Vip presented a puzzle, because Cxcl14 is located primarily at the sr/slm border, whereas immunohistochemistry in rat has localized CCK/VIP basket cells to sp [24]. Because Cxcl14 expression can sometimes also be found in sp, we tested whether this cluster reflects sp cells by combining in situ hybridization for Cxcl14 with immunohistochemistry against VIP in mouse CA1 (Fig 10). This revealed frequent co-expression at the sr/slm border (8% ± 1% Cxcl14 cells positive for Vip; 23% ± 1% Vip cells positive for Cxcl14) but very few Cxcl14 cells in sp, and essentially no double labeling (1 of 147 Vip cells in sp was weakly labeled for Cxcl14). We therefore conclude that this cluster indeed represents a novel cell type located at the sr/slm border, expressing Cck, Vip, and Cxcl14.

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Fig 10. Overlap of Cxcl14 and Vip.

The class Cck.Cxcl14.Vip represented a puzzle: Vip/Cck cells had previously been reported in sp, but Cxcl14 is detected primarily at the sr/slm border, although exceptional cells can be detected in sp also. (A) Double fluorescent in situ hybridization images reveal that the vast majority of cells co-expressing Cxcl14 and Vip were found at the sr/slm border, confirming the location of this novel class. (B) Zoom into rectangles 1 and 2. Arrowheads: double-expressing cells. b, sr/slm border region; slm, stratum lacunosum-moleculare; so, stratum oriens; sp, stratum pyramidale; sr, stratum radiatum; sr/slm, stratum radiatum and stratum lacunosum-moleculare.

https://doi.org/10.1371/journal.pbio.2006387.g010

Discussion

The molecular architecture of CA1 interneurons has been intensively studied over the last decades, leading to the identification of 23 inhibitory classes. Our transcriptomic data showed a remarkable correspondence to this previous work, with all previously described classes identified in our database. Our analysis also revealed a continuous mode of variability common across multiple cell types, eight hypothesized novel classes, as well as additional molecular subdivisions of previously described cell types.

Surprisingly, these data suggest that three previously described CA1 cell groups in fact represent a single cell class, a fact previously overlooked because of the limited combinations of molecules tested in prior work. The Sst.Nos1 class is strongly positive for Nos1 and also expresses Sst, Npy, Chrm2, Pcp4, and Penk, but unlike Penk-positive I-S cells of continent 9, it lacks Vip. This class is homologous to the “Int1” and “Sst Chodl” classes defined in isocortex, which have been identified with long-range projecting sleep-active neurons [44,46,70,71]. The three previously described classes identified with Sst.Nos1 are PENK-immunopositive neurons with projections to subiculum, which were shown to be VIP negative, but not tested for SST or NOS1 (Fuentealba et al., 2008b); the NADPH diaphorase-labeled (i.e., strongly NOS1-positive) axons reported by Sik and colleagues (1994) as projecting to CA3 and dentate, but not tested for SST or PENK; and the SST/NOS1 cells identified by Jinno and Kosaka (2004) in mouse, which were not tested for long-range projections or for PENK. While it remains possible that a larger transcriptomic sample of these rare neurons would reveal subclasses, our present data suggest that Sst.Nos1 cells are a homogeneous population: the nbtSNE algorithm, BIC criterion, and further manual exploration failed to reveal any finer distinctions. We therefore suggest that they constitute a class of inhibitory neurons with diverse long-range projection targets. Interestingly, the targets of PENK-positive projection cells are most commonly PVALB-positive interneurons, unlike conventional IS cells, which preferentially target SST cells [10]. As these cells are identified as sleep active, this fact may provide an important clue to the mechanisms underlying sleep in cortical circuits.

The match between our transcriptomic analysis and previous immunohistochemical work (primarily in rat) is so close that it is simpler to describe the few areas of disagreement than the many areas of agreement. First, ACTN2 has been used as a neurogliaform marker in rat [72] but was almost completely absent from any cell type of our database. We suggest this reflects a species difference, as previous attempts with multiple ACTN2 antibodies have been unsuccessful in mouse (J. H.-L., unpublished observations), and Actn2 labeling is not detectable in the Allen atlas [73]. Second, we observed Calb2 in a subset of putative O-LM cells; these Calb2-expressing neurons typically also expressed Calb1. Such O-LM cells have not been described in rat [9], but CALB2/SST neurons have been observed in mouse isocortex [44,74]. A third inconsistency regards NCALD, which in rat was reported not to overlap with PVALB, SST, or NPY [75], but did so in our data. Finally, it has previously been reported that a subset of O-LM cells show Htr3a expression [76]. In our data, we observed at most weak expression of Htr3a in Sst cells, and the cells showing it belonged to clusters identified as hippocamposeptal rather than O-LM cells.

Our analysis revealed several rare and presumably novel cell groups, although we cannot exclude that some of these were inadvertently included from neighboring areas such as subiculum (S10 Fig). Sst.Npy.Serpine2 and Sst.Npy.Mgat4c, which simultaneously expressed Sst, Npy, and Reln, fit the expected expression pattern of neither O-LM nor hippocamposeptal cells; Sst.Erbb4.Rgs10 is a distinct group related to Pvalb basket and bistratified cells; Cck.Lypd1 formed a rare and highly distinct class expressing Cck, Slc17a8, and Calb1; Ntng1.Synpr showed an expression pattern with features of both sr/slm Cck neurons and projection cells; and Cck.Cxcl14.Vip represents a cell class strongly positive for both Cck and Vip located at the sr/slm border that appears to be a pyramidal- rather than interneuron-targeting class. The analysis also revealed subdivisions of known types, such as the division of IS-3 cells into Nos1-positive and -negative groups, and the division of CGE-NGF cells into Car4- and Cxcl14-expressing subtypes. Finally, our data suggested that with more cells or deeper sequencing, even rarer types are likely to be found, as subsetting analysis showed a linear increase in the number of clusters with cell count and read depth, with little sign of saturation as yet. The data appeared to contain several novel cell types not containing enough cells to overcome the algorithm’s parsimony penalty, such as a small group of cells with features of both basket and axo-axonic cells located off the coast of continent 3; such cells have indeed been rarely encountered by quantitative electron microscopic analysis of synaptic targets in the rat (P. S., unpublished observations).

Latent factor analysis revealed a common continuum of gene expression across the database, suggesting a large “module” of genes that are coregulated in multiple types of hippocampal interneuron. The latent factor differed between clusters, and clusters with larger latent factor values were identified with interneuron types targeting pyramidal cell somas or proximal dendrites (such as Pvalb or Cck/Slc17a8 expressing basket cells), while those with low mean values were identified with interneurons targeting pyramidal distal dendrites (such as Sst or Cck/Calb1 expressing dendrite-targeting cells) or targeting other interneurons. Subtler differences in latent factor were found within clusters, suggesting that a similar continuum exists within cells of a single type. Genes positively correlated with the latent factor are associated with fast-spiking phenotype, presynaptic function, GABA release, and metabolism. Consistent with this expression pattern, perisomatic inhibitory cells show fast-spiking phenotypes and deliver powerful, accurately timed inhibition [8], but interneurons targeting distal dendrites show slower-spiking patterns; presumably because distal inputs are subject to passive dendritic filtering, their presynaptic vesicle release does not need to be so accurately timed. I-S cells had the lowest mean values of the latent factor, consistent with their small axonal trees and metabolic machinery [77]. The stronger expression of many neuropeptides in cells of low latent factor suggests that these slower, distal-targeting interneurons may also rely more heavily on neuropeptide signaling, for which slow firing rates support outputs transduced by slower G-protein–coupled receptors. Interestingly, a study conducted independently of the present work identified enriched expression of a gene module similar to our latent factor in isocortical Pvalb neurons [43] and suggested it is controlled by the transcription factor PGC-1α [78,79]. Our results suggest that Cck-expressing basket cells have a similar expression pattern and that, more generally, expression of this module correlates with a neuron’s axonal target location.

Several novel genes correlating with the factor appear to be interesting candidates for future research, such as Trp53i11, Yjefn3, and Rgs10, associated with faster-spiking Cck cells; Zcchc12 and 6330403K07Rik, both associated with slower-firing cells of all classes; and Fxyd6, associated with slow spiking, which may modulate ion exchange. Intriguingly, genes for neurofilaments and other intermediate filaments were positively correlated with the latent factor, while genes involved in actin processing were negatively correlated; we hypothesize that this might reflect a different cytoskeletal organization required for somatic- and dendritic-targeting neurons.

The question of how many cell classes a given neural circuit contains is often asked of transcriptomic analyses, but we argue this question will not have a clearly defined answer. For example, our data indicate no sharp dividing line between ivy cells and MGE-derived neurogliaform cells. Yet cells at the two ends of the continuum are clearly different: not only do their gene expression patterns differ substantially, but their different axonal targets indicate different roles in circuit function [23]. In statistics, multiple criteria can be used to define how many clusters should be assigned to a dataset; a common approach (which is used by the ProMMT algorithm) is to consider a cluster indivisible if within-cluster fluctuations cannot be distinguished from random noise. Using this criterion, the number of clusters of CA1 interneurons increased with the number of cells and read depth analyzed, showing no sign of saturation in the current dataset. Furthermore, we observed several apparent rare classes that were too small to be assigned their own clusters at present, together with further subtle gradations within currently assigned clusters. The fact that we observed more clusters in CA1 than the 23 previously identified in isocortex [44] should therefore not be taken as implying that CA1 is a more complex circuit but simply that our larger sample size and different clustering algorithm were able to detect finer distinctions. Indeed, our data suggest that while the divisions between the 10 major “continents” are unambiguous, the organization of gene expression within these continents is complex and subtle, and likely far more detailed than characterized by our present 49 clusters. An understanding of this multiscale variability in gene expression in CA1 interneurons will be a key tool to understanding the function of this circuit.

Methods

scRNA-seq

Animals.

Slc32a1 (vesicular GABA transporter)-Cre BAC transgenic mice [80] were crossed with a tdTomato reporter line to generate mice with fluorescently labeled inhibitory neurons. Both the Slc32a1-Cre and tdTomato mouse lines were of mixed B6 and CD1 backgrounds. Three of these mice were used for both the p28 and p63 cohorts; both males and females were used at each age. All experimental procedures followed the guidelines and recommendations of Swedish animal protection legislation and were approved by the local ethical committee for experiments on laboratory animals (Stockholms Norra Djurförsöksetiska nämnd, Sweden; N282/14). The raw data are available on GEO under accession number GSE99888, and a gene expression matrix together with results of clustering, latent factor analysis, and nbtSNE are available at https://figshare.com/articles/Transcriptomic_analysis_of_CA1_inhibitory_interneurons/6198656. An online viewer for expression maps (cf. Fig 3) is available at http://linnarssonlab.org/ca1/.

Single-cell suspension and FACS.

Dissection and single cell dissociation were carried out as described before (Marques et al. 2016), with slight alterations for p63 animals, for which NMDG-HEPES–based solution was used in all steps to enable better recovery of the aged cells (Tanaka, 2008). The NMDG-HEPES–based cutting solution contained 93 mM NMDG, 2.5 mM KCl, 1.2 mM NaH2PO4, 30 mM NaHCO3, 20 mM HEPES, 25 mM glucose, 5 mM sodium ascorbate, 2 mM thiourea, 3 mM sodium pyruvate, 10 mM MgSO4*7H2O, 0.5 mM CACl2*2H2O, and 12 mM N-acetyl-L-cysteine; it was adjusted to pH 7.4 with 10N HCl. Mice were humanely killed by an overdose of Isoflurane and Ketamine/Xylazine, followed by transcardial perfusion through the left ventricle with artificial cerebrospinal fluid (aCSF) equilibrated in 95% O2 5% CO2 before use. The brains were removed and CA1 was microdissected from 300 μm vibratome sections. Single-cell suspensions were prepared using Papain (Worthington) with 30 min enzymatic digestion, followed by manual trituration with fire-polished Pasteur pipettes. The albumin density gradient was only performed for the p63 samples. On a BD FACSAria II, tdTomato-positive cells were sorted into oxygenated aCSF at 4 °C, concentrated, inspected for viability, and counted.

To assess the accuracy of our dissection, we studied the gene expression patterns of simultaneously collected pyramidal cells using previously published genetic criteria (S10 Fig). No cells exhibited expression patterns consistent with CA2 or CA3 [35], but a fraction of these cells (62 of 357 total excitatory neurons) expressed genes seen in a region stretching from the dorsomedial lip of CA1 to the subiculum. Although this result is consistent with dissection of only CA1 interneurons, we also cannot rule out the presence of a small number of atypical interneuron classes located at the dorsomedial lip, or of inclusion of some subicular interneurons.

10X Chromium mRNA-seq.

Sorted suspensions were added to 10X Chromium RT mix, aiming at 2,500 cells recovered per experiment. Downstream cDNA synthesis (14 PCR cycles) and library preparation were carried out as instructed by the manufacturer (10X Genomics Chromium Single Cell Kit Version 1). Libraries were sequenced on the Illumina HiSeq2500 to an average depth of 112,000 reads per cell (raw), yielding on average 3,600 distinct molecules and 1,700 genes per cell. Demultiplexed samples were aligned to the reference genome and converted to mRNA molecule counts using the “cellranger” pipeline version 1.1, provided by the manufacturer.

Normalization.

Prior to many analyses (clustering, latent factor analysis, and nbtSNE), the expression vectors for each cell were normalized, so that each cell’s total RNA expression became equal to the total cellular RNA count averaged over all cells in the database. However, scatterplots of expression (Fig 6C) show unnormalized values.

Quality control.

Cells showing abnormally high values of nuclear noncoding RNAs (Meg3, Malat1, Snhg11) or mitochondrial genes were discarded, as this can signify cell lysis. Cells were discarded if the summed normalized expression of these genes exceeded a threshold of 600.

Immunohistochemistry (Oxford)

Six adult (20 wk old) male C57BL/6J mice (Charles River, Oxford, UK) were perfusion fixed following anesthesia and tissue preparation for immunofluorescence (Katona et al., 2014) and analysis using wide-field epifluorescence microscopy [21] was performed as described. The following primary antibodies were used: anti-calbindin (goat, Fronteir Inst, Af104); anti-pro-CCK (rabbit, 1:2,000, Somogyi et al., 2004); anti-metabotropic glutamate receptor 1a (GRM1, rabbit, 1:1,000; guinea pig, 1:500; gifts from Prof. M. Watanabe, Frontier Institute); anti-muscarinic acetylcholine receptor 2 (CHRM2, rat, 1:400, EMD Millipore Corporation, MAB367); anti-NOS1 (rabbit, 1:1,000, EMD Millipore Corporation, AB5380; mouse, 1:1,000, Sigma-Aldrich, N2280); anti-NPY (mouse, 1:5,000, Abcam, #ab112473); anti-Purkinje cell protein 4 (PCP4, rabbit, 1:500, Santa Cruz Biotechnology, sc-74816); anti-pre-pro-enkephalin (PENK, guinea pig, 1:1,000, gift from Takahiro Furuta, Kyoto University, Japan; rabbit, 1:5,000, LifeSpan Biosciences, LS-C23084); anti-SST (sheep, 1:500, Fitzgerald Industries International, CR2056SP); anti-VGLUT3 (guinea pig, Somogyi et al 2004). Secondary antibodies were raised in donkey against immunoglobulin G of the species of origin of the primary antibodies and conjugated to Violet 421 (1:250); DyLight405 (1:250); Alexa 488 (1:1,000); cyanine 3 (1:400); Alexa 647 (1:250); cyanine 5 (Cy5, 1:250). With the exception of donkey‐antimouse‐Alexa488 purchased from Invitrogen, all secondary antibodies were purchased from Stratech.

For cell counting, image stacks (212 × 212 μm area; 512 × 512 pixels; z stack height on average 12 μm) were acquired using LSM 710/AxioImager.Z1 (Carl Zeiss) laser scanning confocal microscope equipped with Plan-Apochromat 40×/1.3 Oil DIC M27 objective and controlled using ZEN (2008 v5.0 Black, Carl Zeiss). In a second set of sections, images were taken using Leitz DM RB (Leica) epifluorescence microscope equipped with PL Fluotar 40×/0.5 objective. Counting was performed either using ImageJ (v1.50b, Cell Counter plugin) on the confocal image stacks or OPENLAB software for the epifluorescence documentation. For the CCK counts, numbers were pooled from two separate reactions testing for a given combination of primary antibodies (n = 3 mice each reaction, 2–3 sections each mouse) and reported as average values ± standard deviation. For the testing of intensely nNOS-positive neurons, cells were selected using Leitz DM RB (Leica) epifluorescence microscope equipped with PL Fluotar 40×/0.5 objective. Cells were pooled from three separate reactions testing for a given combination of primary antibodies (n = 3 mice each reaction, 2 sections each mouse) and reported as pooled data. Image processing was performed using ZEN (2012 Blue, Carl Zeiss), ImageJ (v1.51m, open source), Inkscape (0.92, open source), and Photoshop (CS5, Adobe).

In situ hybridization (UCL)

Wild-type (C57BL/6/CBA) male and female adult (p30) mice and Lhx6-CreTg transgenic mice were perfusion-fixed, as previously described (Rubin et al., 2010), followed by immersion fixation overnight in 4% paraformaldehyde. Fixed samples were cryoprotected by overnight immersion in 20% sucrose, embedded in optimal cutting temperature (OCT) compound (Tissue Tek, Raymond Lamb Ltd Medical Supplies, Eastbourne, UK), and frozen on dry ice. 30 μm cryosections were collected in DEPC-treated PBS and double in situ hybridization was carried out as described (Rubin et al., 2010). Probes used included either a Cxcl14-(digoxgenin)DIG RNA probe in combination with Reln-(fluorescein)FITC; Npy-FITC, Sst-FITC, or Vip-FITC probes; or a Cxcl14-FITC probe with Nos1-DIG, Kit-DIG, Scl17a8-DIG, or Pvalb-DIG probes. DIG-labeled probes were detected with an anti-DIG-alkaline phosphatase (AP)-conjugated antibody followed by application of a Fast Red (Sigma) substrate. The first reaction was stopped by washing 3 × 10 min in PBS, and the sections were incubated with an anti-FITC-Peroxidase (POD)-conjugated antibody (1:1,500—Roche) overnight. The POD signal was developed by incubating the sections with Tyramide-FITC:amplification buffer (1:100, TSA-Plus, Perkin Elmer) for 10 min at room temperature. For immunohistochemistry after in situ hybridization, the following antibodies were used: anti-Calbindin (rabbit, 1:1,000, Swant, Bellinzona, Switzerland); anti-pro-CCK (rabbit, 1:2,000, Somogyi et al., 2004); anti-GFP (chicken, 1:500, Aves Labs). All sections were counterstained with Hoechst 33258 dye (Sigma, 1,000-fold dilution) and mounted with Dako Fluorescence Mounting Medium (DAKO).

For cell counts, images (at least two sections per mouse) were acquired on an epifluorescence microscope (Zeiss) with a 10× objective. Several images spanning the entire hippocampal CA1 were stitched using Microsoft Image Composite Editor. Cells were counted manually in the CA1 area, including sr and slm, and in a subregion spanning 100 μm across the border between sr and slm, where most Cxcl14-positive cells are located. Confocal images (z stack height on average 25 μm, 2 μm spacing) were taken on a Leica confocal microscope under a 10× objective and processed for contrast and brightness enhancement with Photoshop (CS5, Adobe). A final composite was generated in Adobe Illustrator (CS5, Adobe).

Cluster analysis

Code for cluster analysis and all other algorithms can be found at https://github.com/cortex-lab/Transcriptomics.

Sparse mixture model.

The ProMMT algorithm performs cluster analysis by modeling molecular counts by a mixture of sparse multivariate negative binomial distributions. Specifically, let x represent the Ngenes-dimensional vector summarizing the expression of all genes in a single cell. We model the probability distribution of x with a mixture model: (1)

Here, k denotes a cell class, p(x|k) denotes the probability that a cell in this class will have expression vector x, and the “class prior” πk represents the fraction of cells belonging to this class. To model p(x|k), we use the following distribution family: (2)

In this family, the distribution of all genes is modelled as conditionally independent within a class. The within-class distribution of each gene g depends on a single parameter μg,k (the mean level of the gene in that class). Furthermore, the distributions of only a subset S of genes are allowed to vary between classes, while the remainder are constrained to have a class-independent distribution with mean μg,0. Taking S to have a fixed and small size NS ensures a “sparse model,” which can be fit robustly in high dimensions from only a small number of cells. Note that while the set S could in principle vary between classes, we have found that using a single set S for all classes provides good results.

Negative binomial distribution.

To model the variability of each gene within a class, we use a negative binomial distribution. The negative binomial distribution is a model of count data with greater variance than the Poisson distribution and is frequently used as a model for gene expression levels [47,48]. The negative binomial is specified by two parameters, r and p, and has distribution (3)

This distribution has mean , and for fixed r, the maximum likelihood estimate of parameter p is , where μ is the sample mean. For fixed r, the standard deviation of this distribution scales asymptotically linearly with its mean: . In contrast, the Poisson distribution has a smaller standard deviation, which scales with the square root of the mean.

We verified that a negative binomial with fixed r is appropriate for scRNA-seq data by considering a relatively homogeneous class (CA1 pyramidal cells; S2A Fig; data from Zeisel et al [46]). This analysis confirmed that the negative binomial with r = 2 accurately modelled the relationship of standard deviation to mean in these data. The “wide” shape of the negative binomial distribution (S2B Fig) has a consequence that the absolute expression levels of a gene matters much less than whether the gene is expressed at all. Indeed, examining the symmetrized Kullback-Leibler divergence of negative binomials with different means (S2C Fig)—an indication of the penalty paid for misestimating the mean expression level—indicates that a much smaller penalty is paid for fitting a mean of 500 to a distribution whose actual mean is 1,000, than for fitting a mean of 10 to a distribution whose actual mean is 0.

EM algorithm.

To fit the model, we fix r = 2 and fit the parameters S, μ, and π by maximum likelihood. Because maximum likelihood fitting involves a sum over (unknown) class assignments, we use a standard Expectation-Maximization (EM) algorithm [81,82]. We define zc,k to be the expected value of an indicator variable taking the value 1 if cell c belongs to class k:

The algorithm alternates between an E step, where zc,k is computed using the current values of the parameters S and μ, and an M step, where S and μ are optimized according to the current values of zc,k.

E-step.

The E step is straightforward. Observe that

The constant term includes the contributions of all genes not in S, as well as the binomial coefficient from Eq 3, none of which depend on the value of k and therefore do not affect the result.

One can compute zc,k from this using Bayes’ theorem; in practice, however, we found that when the set S contains a reasonable number of genes (approximately 100 or more), all values of zc,k are close to 0 or 1, so there is little to lose by employing a much faster “hard EM” algorithm, in which, for all cells c, only a single winning kc has with all others 0.

M-step.

In the M-step, we are given zc,k and must find the set S of genes that are allowed to differ between classes, and their class means μg,k, by maximum likelihood. Although one might expect finding S to pose an intractable combinatorial optimization problem, it can in fact be solved quickly and exactly. The derivation below is for a hard EM algorithm; the soft case can be derived easily but requires substantially more computation time, without a noticeable increase in performance.

We first define a quantity L0 to be the log likelihood of the data under a model in which S = ∅, so all the expression of each gene g is determined by its grand mean μg,0, independent of cluster assignments. Observe that where represents the gain in log likelihood obtained when the distribution of gene g is allowed to vary between classes. To compute the optimal value of the set S, we note that the values of Yg are independent of each other. Thus, the optimal set S is simply the Ns genes with the largest values of Yg.

The maximum likelihood estimates of the negative binomial parameters pg,k are given by , where μg,k denotes the average expression of genes g for the cells currently assigned to cluster k, and μg,0 is the mean expression of gene g for all cells in the database. Because the negative binomial distribution can give zero likelihoods if any μg,k = 0, we use a regularized mean estimate: where Nk denotes the number of cells in cluster k, and the regularization parameters take the values A = 10−4, B = 1.

Finally, we compute the priors πk as the fraction of cells c with kc = k, as is standard in EM.

BIC penalty.

To automatically choose the number of clusters, we employed the BIC method [50], which for our model takes the form of a penalty per cluster added to the log likelihood.

Cluster splitting.

As is typical for cluster analysis, the likelihood function has multiple local maxima, and steps must be taken to ensure the algorithm does not become trapped in a suboptimal position. To do this, we use a heuristic that splits clusters that are poorly fit by a negative binomial distribution. The full clustering method consists of a divisive approach that alternates such splits with EM runs that then re-optimize the parameters.

For each cluster k, the splitting heuristic searches for genes g whose likelihood would be substantially increased if the cluster was split in two, according to whether the expression of gene g is above a threshold Θg. Note that after splitting, the amount by which the log likelihood gain Yg changes can be written as

Here, pg represents the maximum-likelihood parameter for gene g in the cluster under consideration, represents this parameter computed only for cells with xg < Θg, and represents this parameter for cells with xg ≥ Θg. The only values of Θ for which a split need be considered correspond to the expression levels of cells in the cluster, and ΔYg can therefore be rapidly computed for all g and Θ using cumulative summation, with computational cost linear in the size of the expression matrix.

Full algorithm.

The full algorithm consists of repeatedly alternating the EM algorithm with cluster splitting and merging operations to escape from local maxima. The algorithm is initialized by assigning all cells to a single cluster.

On each iteration, all clusters are first split in two using the splitting heuristic. Specifically, for each cluster, ΔYg is computed for all g and Θ, and the optimal split points Θg are found for each gene. The 10 genes giving top values of are found. For each of them, the cluster is split, an EM algorithm run to convergence on the resulting cluster pair, and the split providing the highest increase in likelihood is kept. Once all clusters have been split, they are combined to produce a dataset with twice the original number of clusters, and the EM algorithm is run, to allow points to be reassigned between the split clusters.

The iteration ends with a round of cluster pruning. For each cluster, we compute the deletion loss: the decrease in log likelihood that would occur if all points in the cluster were reassigned to their second-best matching cluster. If this loss does not outweigh the BIC penalty, the cluster’s points are so reassigned, and EM is run on the full dataset. This process continues until no cluster’s deletion loss is smaller than the BIC penalty.

The algorithm is run for a set number of iterations (50 in the current case) and the final result corresponds to the clustering that gave the highest score.

Isolation metric

To measure how well separated each cluster is from its neighbors, we define an isolation metric equal to the deletion loss (described in the previous section), divided by Nklog(2), where Nk is the number of cells assigned to cluster k. This has an information-theoretic interpretation, as the number of additional bits that would be required to communicate the gene expression pattern of a cell in cluster k, using a code defined by the probability model if cluster k were deleted.

Hierarchical cluster clustering

Each cluster produced by the EM algorithm is specified by a mean expression vector. To understand the relationship between these cluster means, we applied a clustering method to the clusters themselves. This was achieved using Ward’s method, with a distance matrix given by the K-L divergence between cluster means, weighted by the number of cells per cluster.

nbtSNE algorithm

To visualize the locations of the cells, we derived a variant of the tSNE algorithm [51] appropriate for data following a negative binomial distribution.

Stochastic neighbor embedding algorithms such as tSNE start by converting Euclidean distances between pairs of high-dimensional vectors xi into conditional probabilities according to a Gaussian distribution: . The tSNE algorithm then adjusts the locations of low-dimensional representation yi in order to minimize the K-L divergence of a symmetrized pj|i, with a t-distribution on the yi.

The Gaussian distribution, however, is not the most appropriate choice for transcriptomic data. We found that we obtained better results using the same negative binomial distribution as in the ProMMT algorithm: where excluding a binomial coefficient that cancels when computing pj|i. The sum runs over the set of genes g that were chosen by the ProMMT algorithm.

In the original tSNE algorithm, variations in distance between the points xi are overcome by adjusting the variance for each point i to achieve constant perplexity of the symmetrized conditional distributions. We took the same approach, finding a scale factor λi for each cell i to ensure that the scaled symmetrized distribution had a fixed perplexity of 15. This computation and the implementation K-L minimization was achieved using Laurens van der Maaten’s drtoolbox (https://lvdmaaten.github.io/drtoolbox/). The algorithm was initialized by placing all points on a unit circle, with angular position determined by their parent cluster, linearly ordered by the hierarchical cluster clustering.

For comparison, we ran four other methods of tSNE analysis (S4 Fig) using either all genes or the 150 genes found by ProMMT, and either a Euclidean metric or a Euclidean metric after log(1+x) transformation. Perplexity of 15 was again used and initialization was the same as before. Using all genes gave results that were difficult to interpret, particularly for log-transformed data, which we ascribe the noise arising from the large number of weakly expressed genes in the database. Using the gene subset provided more interpretable results, and combining the gene subset with log(1+x) transformation yielded results similar to nbtSNE, while a Euclidean metric yielded a less clear distinction of isolated classes such as Cck.Lypd1 and Sst.Nos1. We conclude that the alignment of nbtSNE to the probability distribution of RNA counts allows the algorithm to take into account differences between weakly expressed genes, and that a log(1+x) transformation approximates this probability distribution. We also conclude that gene subsetting prevents noise from the large number of genes that do not differ between classes from swamping the signal, and that this is particularly important with algorithms sensitive to changes in weakly expressed genes. We suggest that nbtSNE provides a principled probabilistic method for choosing the transformation and gene subset required for informative tSNE analysis.

Negative binomial discriminant analysis

To investigate whether a pair of clusters were discretely separated or tiled a continuum we developed a method of cross-validated negative binomial discriminant analysis. This analysis assesses the separation of two clusters k1 and k2 by computing the log likelihood ratio for each cell to belong to the two clusters. It is simple to show that this ratio for a cell c is given by

The sum runs over all genes g in the database, not just the set S found by the ProMMT algorithm.

The degree to which clusters k1 and k2 are discrete is visible by the bimodality of the histogram of Δc, which can be quantified using a d’ statistic, , where μi and σi represent the mean and standard deviation of Δc for cells arising in cluster i. In this analysis, it is essential that the ratios Δc are computed on a separate “test set” of cells to the “training set” used to estimate pg,k, otherwise even a random division of a single homogeneous cluster would give an apparently bimodal histogram because of overfitting.

Latent factor analysis

To model continuous variation between cells, we used a negative binomial latent factor model. The model is parametrized by two matrices, W and F of size Ngenes × Nfactors and Nfactors × Ncells. The distribution of each cell follows a negative binomial distribution with mean μgc = r exp(f Wgf Ffc):

This corresponds to the natural parameterization of the negative binomial, p = 1 / (1 + exp(f Wgf Ffc)). As usual, we take a fixed value of r = 2. For the analysis described in this study, we use only a single latent factor, but add a second column to F of all ones to allow the mean expression level to vary between genes.

Given a dataset xgc, we fit the matrices W and F by maximum likelihood. As the negative binomial distribution with fixed r belongs to the exponential family, we can use the simple alternating method of Collins and colleagues [83]. Note that we do not require a sparse algorithm because (unlike in clustering), the number of parameters is fixed. However, to avoid instability, only genes that have reasonable expression levels in the database are kept (genes are included if at least 10 cells express at least 5 copies of the RNA), and a quadratic regularization penalty −50[|W|2 + |F|2] is added to the log likelihood.

To relate the correlations of each gene with the latent factor to their GO categories (S2 Table), we used the MGI mouse GO database (downloaded 2 April 2018), accessed via MATLAB’s bioinformatics toolbox. An enrichment score was computed for each GO term by summing the Spearman rank correlations of gene expression with the latent factor, over all genes annotated with that term.

Supporting information

S1 Fig. No major difference was observed in cell type distribution between the four samples collected.

Each plot shows the location of all cells collected in a sample on the nbtSNE plots. Top row: mice of age p60; bottom row, age p27. Statistical testing of homogeneity of cluster IDs between mice yielded a weakly significant overall result (p = 3 × 10−5; χ2 test), but post hoc analysis (individual 2×2 contingency tables, Bonferroni corrected) did not identify any clusters with individually significant differences between mice. We suspect that the weakly significant difference might reflect slightly differential dissection of layers in the four samples. nbtSNE, negative binomial t-stochastic neighbor embedding.

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S2 Fig. Detected RNA counts can be fit by a negative binomial distribution.

(A) Standard deviation versus mean expression in a population of CA1 pyramidal cells (Zeisel et al. 2015). Each point represents a single gene. Red curve shows prediction of negative binomial distribution with r = 2. (B) Example negative binomial probability distribution. Low probability is assigned to very small counts, but for larger counts, there is no strong dependence on precise count value. (C) Symmetrized Kullback-Liebler divergence between two negative binomial distributions, as a function of their mean values. High values (indicating poor fit) are obtained when one mean is close to zero, and the other is large; when both means are far from zero, their precise values do not have a major effect.

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S3 Fig. Pseudocolor representation showing mean expression levels of the 150 genes selected by the ProMMT algorithm in each cluster (unnormalized, log scale).

ProMMT, Probabilistic Mixture Modeling for Transcriptomics.

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S4 Fig. Four alternative methods of tSNE analysis.

Left columns show results when all genes are used; right columns show results with the 150 genes selected by ProMMT. Top row shows a Euclidean metric; bottom row shows Euclidean metric after log(1+x) transformation. All methods were initialized from the same starting point as nbtSNE. Of the four methods, only the log(1+x) transformed data with gene subset gave comparable results to nbtSNE. This indicates that the primary effect of the negative binomial distribution is to downweight differences in expression between strongly expressed genes, similarly to the log(1+x) transformation, and that gene subsetting produces more interpretable results whether or not transformation is used. nbtSNE, negative binomial t-stochastic neighbor embedding; ProMMT, Probabilistic Mixture Modeling for Transcriptomics; tSNE, t-stochastic neighbor embedding.

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S5 Fig. Analysis of isocortical interneurons.

(A) nbtSNE algorithm applied to 761 interneurons of mouse V1, from Tasic and colleagues (2016). Symbols indicate 23 clusters assigned by Tasic and colleagues. (B) Same data, with symbols representing 30 clusters assigned by ProMMT algorithm. (C) Confusion matrix relating cluster assignments made by the two algorithms. Right; cell classes identified with ProMMT clusters (black), and genes used to make the identification (red: expressed, blue: not expressed). (D) Reprint of figure from Cadwell and colleagues (2016) showing expression of selected genes in layer 1 SBCs and eNGCs. (E) Scatterplot matrix showing expression of these genes in Tasic and colleagues’ data support the identification of SBCs made by ProMMT algorithm. eNGC, elongated neurogliaform cell; nbtSNE, negative binomial t-stochastic neighbor embedding; ProMMT, Probabilistic Mixture Modeling for Transcriptomics; SBC, single-bouquet cell.

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S6 Fig. Additional cluster divisions found by the ProMMT algorithm in the data of Tasic and colleagues (2016).

Left and right panels show scatterplot matrices for sets of genes with near-exclusive expression in further subdivisions of the Vip Parm1 and Sst Cbln4 clusters. Red and green points indicate which subcluster the cell was placed in by the ProMMT algorithm. ProMMT, Probabilistic Mixture Modeling for Transcriptomics.

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S7 Fig. Number of detected clusters increases linearly with cell count and read depth.

(A) To investigate how the number of detected clusters might change with the number of cells analyzed, we reclustered random subsets of different numbers of cells. The number of clusters identified increased with cell count. (B) To investigate how the number of detected clusters might change with read depth, we resampled reads independently for each cell and gene, following a binomial distribution with probability between 0 and 1. Again, cluster count increased linearly with read depth; although a marginally sublinear trend was potentially visible, this was not statistically significant (p > 0.05, power-law regression). (C) Expected gene count (i.e., mean number of genes with expression >0, averaged over cells in a class), computed as a function of the binomial probability. Color scheme indicated below. (D,E) Similar analysis as (A,B) for the data of Tasic and colleagues (2016).

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S8 Fig. Latent factor analysis of isocortical interneurons yields similar results to analysis in CA1.

(A) Mean latent factor values differ between cell classes (cf. Fig 6A). Each point represents a cell; x-axis shows latent factor value; y-axis shows original cluster assignments. (B) Correlations of genes with the latent factor for isocortical Pvalb cells (y-axis) are similar to those of their CA1 counterparts (x-axis; cf. Fig 6D).

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S9 Fig. Activity-dependent modulation of gene expression partially matches variation along genetic latent factor.

Each panel represents a cell type analyzed by Mardinly and colleagues (2016). Within each panel, every point represents a gene, and the y-axis value shows the log ratio of its expression level after 7.5 h of light exposure, compared to dark housing, in the corresponding subtype of visual cortical interneurons. The x-axis value shows that gene’s latent factor weighting as determined from our CA1 data. Blue line shows linear regression fit, which was strongest for Sst neurons (r = 0.25; p < 10−12), weaker but significant for Pvalb neurons (r = 0.11; p < 0.002), and insignificant for Vip neurons (r = 0.05, p = 0.17). Only genes of strong mean expression were analyzed (>5,000 normalized reads). A small number of example genes of particular interest are highlighted with red text.

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S10 Fig. Analysis of simultaneously collected pyramidal cells.

The main group of cells exhibited a continuous gradation of gene expression, consistent with previous reports of graded expression of genes such as Wfs1 and Dcn between dorsal and ventral CA1. No cells were identified as CA2 or CA3, as we did not detect populations consistently expressing genes such as Cacng5, Sostdc1, S100b, Ccdc3, Iyd, or Coch. However, three small clusters together containing 62 of the total 357 excitatory neurons were identified as either occurring at the dorsomedial lip of stratum oriens or subiculum, because of their expression of genes such as Tshz2, Tle4, Lxn, and Car10, whose Allen atlas expression patterns are shown at bottom.

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S1 Table. Contains correlation coefficients and significance p-values of a set of example genes correlated with the latent factor.

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S2 Table. Contains a list of gene ontology terms most correlated with the latent factor.

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S1 Text. Contains the in-depth reasoning behind the identifications of our transcriptomic clusters with known cell classes.

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Acknowledgments

We thank T. Viney, A. Joshi, G. Unal, and B. Bekkouche for discussions and comments on the manuscript.

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