Pathway and Gene Set Overdispersion Analysis (PAGODA)

To characterize significant aspects of transcriptional heterogeneity in a scRNA-seq dataset, PAGODA relies on a series of statistical and computational steps (Fig. 1). First, the measurement properties of each cell, such as effective sequencing depth, drop-out rate and amplification noise are estimated using a previously described mixture model approach²⁷ with minor enhancements (Step 1, Fig. 1). Using these models, the observed expression variance of each gene is renormalized based on the genome-wide variance expectation at the appropriate expression magnitude (Step 2). Batch correction is also performed at this stage. The resulting residual variance, modeled by the χ² statistic, effectively distinguishes subpopulation-specific genes (Supplementary Notes 1,2), and determines the contribution of each gene to the subsequent PCA calculations.

PAGODA then examines an extensive panel of gene sets to identify those showing a statistically significant excess of coordinated variability (Step 3). The gene sets include annotated pathways, such as Gene Ontology (GO) categories, as well as clusters of transcriptionally-correlated genes found within a given dataset (de novo gene sets). The later allows PAGODA to detect aspects of transcriptional heterogeneity driven by processes that are not represented in the pathway annotation. The prevalent transcriptional signature of each gene set is captured by its first principal component (PC), using weighted PCA to adjust for technical noise contributions. If the amount of variance explained by the first PC of a given gene set is significantly higher than expected (Step 4, correcting for multiple hypotheses), the gene set is said to be overdispersed, and is included in the subsequent analysis.

The PC of each overdispersed gene set separates cells along a certain axis (PC scores). Many PCs will show very similar patterns, either because the same genes drive them, or because multiple biological processes distinguish the same subsets of cells. To provide a non-redundant view of the transcriptional heterogeneity within the dataset, PCs from significantly overdispersed gene sets are clustered, and those with similar gene loadings or cell separation patterns are combined to form a single 'aspect' of heterogeneity (Step 5, Supplementary Fig. 1). The resulting major aspects of transcriptional heterogeneity can be explored numerically or through an interactive web browser interface²⁸ (Step 6). As we illustrate below, examination of individual aspects and their relationships to each other can provide insights and functional clues not apparent from the most prominent cell classification. Finally, if upon further interpretation one or more aspects of transcriptional heterogeneity are determined to be extraneous to the biological context, PAGODA provides an option to control explicitly for such aspects (Step 7).

PAGODA captures alternative annotations of individual cells

To illustrate PAGODA on a complex cell population, we re-examined scRNA-seq data for 3,005 cells from the mouse cortex and hippocampus from a recent publication by Zeisel et al.⁹. This extensive dataset covers a variety of cell types, some of which exhibit very distinct expression signatures. Zeisel et al. also introduced a novel heterogeneity analysis method called BackSPIN⁹ that performs recursive partitioning. Applying PAGODA revealed nine major aspects of heterogeneity that distinguish the seven top-level classes and two lower-level subpopulations identified by BackSPIN (Fig. 2). The functional interpretation of the identified aspects is evident from the identity of overdispersed GO categories. The most significant aspect separates oligodendrocytes, the most numerous cell type in the dataset, which are easily distinguished by strong overdispersion of myelination-related pathways. Similarly, overdispersion of immune, vascular, and muscle-associated GO-annotated gene sets identify microglia, vascular endothelial, and mural subpopulations respectively. Other cell types, such as ependymal cells, or different types of neurons are distinguished by de novo gene set signatures, with most overdispersed genes revealing their identity (e.g. Gad1, Tbr1, Gabra5).

We noted that aspects distinguishing many of the cell types appear to overlap, most frequently with the myelination signature. For instance, a subset of 35 cells exhibits prominent expression of both immune response genes characteristic of microglia as well as genes responsible for myelin sheath (Fig. 2). Similarly, myelin-associated expression signature is observed for a subset of vascular cells, astrocytes, pyramidal neurons and interneurons. These hybrid signatures most likely correspond to cases in which two cells of different cell types were captured together (see Supplementary Fig. 2 for the analysis of cell type co-occurrence frequencies). The occurrence and functional interpretation of such ambiguous cases where a given cell exhibits multiple alternative signatures are apparent from PAGODA analysis. In contrast, BackSPIN, as well as other partitioning methods, would need to classify such cells based on one of the signatures or isolate them as a separate class without exposing their relationship to other groups.

We further evaluated PAGODA performance by re-analyzing datasets that were used to present alternative methods of heterogeneity analysis^8,11,29, recovering previously identified subpopulations and identifying additional biologically-relevant features (Supplementary Note 3). In particular, PAGODA’s ability to associate with a given cell multiple, potentially independent aspects of transcriptional heterogeneity, allows one to focus on biologically-relevant subpopulations that may be distinguished by relatively subtle transcriptional variation. For instance, in reanalyzing data for mouse CD4⁺ T that was used to present an elegant GP-LVM approach by Buettner et al¹¹, PAGODA successfully recovered Il4ra-Il24 response and a closely aligned glycolysis aspect in addition to a prominent mitosis-associated signature, without requiring explicit correction steps. Furthermore, PAGODA revealed a prominent subpopulation of cells exhibiting an expression signature typical of dendritic cells that was not previously observed.

PAGODA reveals multiple aspects of heterogeneity in mouse NPCs

As heterogeneity amongst NPCs may influence downstream neural diversity, we performed Smart-Seq³⁰ on 65 NPCs isolated from the cerebral cortex of 13.5-day embryonic mouse brain. The most significant aspect of heterogeneity identified by PAGODA within the isolated NPCs reflects gradual induction of the genes associated with neuronal maturation and growth (Fig. 3a, top aspect). Approximately half of the cells express Dcx, Sox11, and other known markers of neuronal maturation, with the most mature subset expressing genes involved in neuronal maturation and growth cones (Neurod6, Gap43). Such cells maintain expression of some progenitor markers (e.g., vimentin) and therefore likely represent developing, committed neurons. In contrast, the set of early NPCs exhibits strong M- and S-phase signatures that are absent from the more mature NPCs, as well as up-regulation of genes characteristic of early progenitor state³¹ (Sox2, Notch2, Hes1) captured by the “negative regulation of neuronal differentiation” and “neural tube development” GO categories.

Maturation of neuronal progenitors is closely tied to the spatial organization of the developing cortex³². We used spatial expression patterns³³ of genes differentially expressed between the early and maturing NPCs to reconstruct the most likely spatial distribution of these cells within the mouse brain (Fig. 3b, Online Methods). As expected, we found early NPCs localize close to ventricular zone (VZ). We also used in situ RNA-FISH (Online Methods) to examine two genes, Rpa1 and Nnd, of unknown relationship to the embryonic cerebral cortex (Fig. 3c). Consistent with their predicted pattern, Rpa1 was most prominent in proliferative regions. Ndn localized in the post-mitotic regions (especially the cortical plate), as well as rare cells within the subventricular zone (SVZ, Supplementary Fig. 3).

An additional subset of NPCs was distinguished by expression of Eomes, Neurod1, and other genes localized to the SVZ region and thought to distinguish basal progenitors^31,34. The Eomes signature mark cells that express intermediate levels of genes associated with neuronal maturation as well as a subset of mature NPCs and subset of early NPCs undergoing DNA replication, likely representing neuronally-committed NPCs maturing in the SVZ, and dividing basal NPCs, respectively. These dividing cells express notch signaling genes (Dll1, Notch2, Mfng) concurrently with Eomes and therefore likely represent nascent basal progenitors³¹.

Two other aspects cut across the main NPC maturation axis. The first is driven by prominent expression of Ndn (Fig. 3a). Ndn, initially noted for high expression in mature neurons³⁵, has also been shown to be expressed in the VZ³⁶, and to restrict both proliferation and apoptosis rates in NPCs^36–38. In combination with RNAscope analyses (Supplementary Fig. 3), we found Ndn to be expressed within a subset of NPCs, approximately a quarter of which exhibit pronounced mitotic signatures and are likely localized in the SVZ. The second cross-cutting aspect is coordinated expression of Dlx homeodomain transcription factors. Dlx genes mark tangentially-migrating NPCs, which originate in the ganglionic eminence (GE) and migrate to the cortical areas, giving rise to the GABAergic neurons^39,40. The Dlx-positive cells express other markers of tangentially migrating NPCs, most notably Sp9 and Sp8 transcription factors⁴¹. Indeed, spatial localization of these cells was predicted to be in the GE region, where tangentially-migrating NPCs are expected to originate (Fig. 3b). In agreement with earlier observations of such NPCs undergoing mitosis in the cortical VZ/SVZ areas, two of ten Dlx-positive NPCs were captured in S-phase and one in M-phase.

To illustrate the methodological advantage of PAGODA, we re-examined our NPC data using alternative analysis methods, including PCA, ICA, tSNE^12,17, GP-LVM¹⁶, and BackSPIN⁹ (Supplementary Figs. 4,5). While none of the methods were able to recover all of the identified subpopulations, BackSPIN provided the most compelling results, capturing heterogeneity involving expression of Dlx and Prdx4/Mest. However, the reported clustering grouped only some of the cells associated with each signature, illustrating limitations of partitioning-based interpretation in a complex biological context.

Isolation and single-cell RNA-seq of mouse neural progenitor cells (NPC) and astrocytes (ASC)s

Single NPCs were isolated from C57BL/6J embryonic day 13.5 cortices for RNA-sequencing. Timed-pregnant mice were sacrificed by deep anesthesia followed by cervical dislocation. The embryos were quickly removed and cortical hemispheres were isolated, ganglionic eminences removed, and all pups brains were pooled. All animal protocols were approved by the Institutional Animal Care and Use Committee at The Scripps Research Institute (La Jolla, CA) and conform to the National Institutes of Health guidelines.

Single cells were isolated by gentle trituration in ice-cold phosphate buffered saline containing 2 mM EGTA (PBSE) using P1000 tips with decreasing bore diameter. Cells were then filtered through a 40 uM nylon cell strainer and stained with propidium iodide (PI), a live-dead stain, and fluorescence activated single cell sorting (FACS) was performed selecting for PI negative cells. Samples remained on ice throughout the process and total processing time from cervical dislocation to sorting was limited to 2 hours. Single cells were sorted directly into cell lysis buffer provided in the Clontech SMARTer® Ultra™ Low RNA Kit for Illumina® Sequencing (cat # 634936), and sequencing libraries were generated using the manufacturer’s protocol. Resulting libraries were sequenced on the Illumina® HiSeq™ 2000 sequencing platform.

Gene validation using in situ hybridization with RNA-scope

Mouse E13.5 embryos were removed from timed pregnant mice and prepared according to RNAscope instructions for paraffin embedded tissue. RNAscope probes (Advanced Cell Diagnostics) were designed by the manufacturer (Cat. # : GINS2 435891, RPA1 435911) and sections were processed using RNAscope 2.0 High Definition Reagent Kit - BROWN (Cat. #:310035) according to the manufacturer’s instructions. Sections were imaged on a Ziess Axioimager at 20× magnification.

Previously published single-cell RNA-seq data

For the mixture of cultured human neuronal progenitor cells (NPCs) and primary cortical samples from Pollen et al²⁹, SRA files for each study were downloaded from the Sequence Read Archive (http://www.ncbi.nlm.nih.gov/sra) and converted to FASTQ format using the SRA toolkit (v2.3.5). FASTQ files were aligned to the human reference genome (hg19) using Tophat (v2.0.10) with Bowtie2 (v2.1.0) and Samtools (v0.1.19). Gene expression counts were quantified using HTSeq (v0.5.4). Read counts for the Th2 data by Buettner et al¹¹ were downloaded from the supplementary site (http://github.com/PMBio/scLVM/blob/master/data/Tcell/data_Tcells.Rdata). Read (or UMI) count matrices for other two datasets were downloaded from GEO: GSE60361 for Zeisel et al⁹; GSE59739 for Usoskin et al⁸.

Evaluating overdispersion of individual genes

For each gene, the approach estimates the ratio of observed to expected expression variance and the statistical significance of the observed deviation from the expected value. To illustrate the rationale, we start with a Poisson approximation. Let $c_g^i$ be the number of reads observed for a gene g in a cell i. If such reads follow a Poisson distribution with the mean μ_g and variance ν_g (both equal to some Poisson rate λ_g), then Fisher’s index of dispersion $D_g=\sum _{i=1}^k{(c_g^i-{\mu }_g)}^2/{\nu }_g$ follows ${\chi }_{k-1}^2$ distribution⁴³. While for the Poisson case ν_g = μ_g, for negative binomial process, ν_g = μ_g + (μ_g)²/θ, where θ is the size parameter. As θ decreases from very high values where the negative binomial is well approximated by a Poisson, D_g diverges from ${\chi }_{k-1}^2$. Analytical adjustments of D_g based on the negative binomial moments can improve χ² approximation⁴⁴. For more accurate approximation we used a numeric correction of the χ² degrees of freedom, depending on the magnitude of θ, so that $D_g~{\chi }_{f(\theta )}^2$ (Supplementary Note 2, Figure SN2.2).

To account for the possibility of drop-out events, weighted sample variance estimates were used, so that: $D_g=\sum _{\mathit{\text{cell i}}}\lfloor w_g^i{(c_g^i-{\mu }_g^i)}^2\rfloor /[{\mu }_g^i+{({\mu }_g^i)}^2/{\theta }_i(e_g)]~{\chi }_{k_g}^2$, where $w_g^i$ is the probability that the measurement in a cell i was not a drop-out event based on the error model for cell i, and $k_g=\sum _{i=1}^k{w}_g^{i}f({\theta }_i(e_g))$ is the effective degrees of freedom for the gene g. ${\mu }_g^i=e_g{\alpha }_i$, where e_g is the expected expression magnitude of a gene g across the measured cells.

Since negative binomial (or NB/Poisson mixture) models do not fully capture the variability trends observed in the real scRNA-seq measurements, D_g estimates for the real data can systematically deviate from 1. To adjust for this non-centrality, we normalized D_g by its transcriptome-wide expectation value $D_g^e$, where $D_g^e$ models the transcriptome-wide dependency of D_g on gene expression magnitude. $D_g^e$ estimates were obtained using a general additive model (GAM, fit using the mgcv R package) as a smooth function of gene expression magnitude e_g. To improve smoothness, the GAM fit was performed on the corresponding squared coefficient of residual variance (D_g/E_g)². The fit is performed on all of the genes. The P value of overdispersion for a gene g was then be calculated as $P_g^{od}=F_{{\chi }_{k_g}^2}(k_g{D}_g/D_g^e)$, where $F_{{\chi }_k^2}$ is CDF of χ² distribution with k degrees of freedom.

To improve stability of the estimates with respect to outliers, a Winsorization procedure⁴⁵ was applied to the read count matrix prior to the variance evaluation described above. To ensure that the outliers are trimmed in a manner independent of the total cell coverage, the Winsorization procedure was applied to the FPM matrix (i.e. normalizing counts by the library size), that were then translated back into the integer counts. A trim value of 3 was used for all datasets (i.e. observations from the three highest and tree lowest cells for each gene were Winsorized).