Detecting heterogeneity in single-cell RNA-Seq data by non-negative matrix factorization

Datasets

Five scRNA-Seq datasets are used in this study. For the first four datasets that don’t have UMI, normalized fragments per kilo-base per million reads (FPKM) is calculated and used as input to the clustering methods. For the last dataset (iPSC) where UMI technique is adopted, we used the author provided “molecule counts” as the input.

Mouse lung epithelial cells

scRNA-Seq data were retrieved from the original 201 samples of lung distal epithelial cells of embryonic mouse (GSE52583) (Treutlein et al., 2014). The original dataset contains cells collected from four time points: E14.5, E16.5, E18.5 and AT2. After filtering (the procedure is detailed in the “Sample and Gene Filtering” section below), 201 single-cell samples and 4,594 genes are used in downstream analysis. The closest pair of groups, which consists of 45 cells from E14.5 and 27 cells from E16.5 was used for unsupervised clustering comparison.

Mouse HSCs and MPP1s

scRNA-Seq data were extracted from mouse hematopoietic stem cells (HSCs) and early multipotent progenitors (MPP1s). The data were pre-processed into the format of a FPKM expression profile (Table S1), which include 59 HSCs and 53 MPP1 single cells. After filtering, 95 samples and 2,887 genes were used in downstream analysis.

Glioblastoma

scRNA-Seq data were retrieved from the original 875 samples of glioblastoma tumor cells in 5 patients (MGH26, MGH28, MGH29, MGH30, and MGH31), along with population and cell line controls (GSE57872) (Patel et al., 2014). After filtering, 419 single-cell samples and 6,996 genes were used in downstream analysis. The closest pair of groups, which consists of 80 cells from patient MGH29 and 73 cells from MGH31 was used for unsupervised clustering comparison.

Mouse bone marrow

scRNA-Seq data were extracted from mouse macrophage DC progenitors (MDPs), common DC progenitors (CDPs), and Pre-DCs (GSE60781) (Schlitzer et al., 2015). We used the FPKM table provided by the authors. After filtering, 242 single-cell samples and 5,489 genes are used in downstream analysis. The closest pair of groups, which consists of 59 MDPs and 89 CDPs was used for the unsupervised clustering comparison.

Human induced pluripotent stem cell lines

scRNA-Seq data were extracted from induced pluripotent stem cell lines of three Yoruba individuals. On each individual three technical replicates were performed. A total of 5 bp random sequence UMI were attached to the transcripts in order to avoid amplification bias. We used the molecule counts provided by the authors. After filtering, 864 single-cell samples and 9,750 genes are used in downstream analysis. The closest pair of groups, which consists of 288 cells from individual NA19098 and 288 cells from individual NA19239 was used for the unsupervised clustering comparison.

Single-cell RNA-Seq analysis

Normalization of counts

We used reads per kilo base per million (FPKM) to represent the gene expression level, where the length of each gene was calculated by UCSC RefSeq annotation table, by concatenating all the exons. We normalized the data using DESeq2.

Sample and gene filtering

Samples expressing housekeeping genes with geometric average FPKM lower than 4 were deemed abnormal and removed. Genes that were not expressed at all in over 70% of the cells were removed.

Closest pair identification

The closest pair of groups among the samples is defined as the pair that has the smallest distance between the two groups’ centroids, on the 2-dimentional correlation t-SNE plot. The correlation t-SNE is the t-SNE method (Van der Maaten & Hinton, 2008) performed on the correlation distance between two samples x and y: ${\displaystyle d_c\left(x,y\right)=1-cor\left(x,y\right).}$

Non-negative matrix factorization (NMF)

We used the R-package implementation of NMF (Gaujoux & Seoighe, 2010) to perform NMF analysis. NMF is mathematically approximated by: A ≈ WH, where A (n by m) is the matrix representing the scRNA-Seq profile in this report, W is a slim weight matrix (n by k, where n ≫ k), H is a wide matrix (k by m, where m ≫ k), and all three of them are non-negative (Brunet et al., 2004). The column vectors in W are called meta-genes, which are higher-level abstraction of the original gene expression pattern. For gene i, the loadings are the k values in W at row i. We used the method “brunet” to solve the approximation of A, which employs the multiplicative iterative algorithm described by the following rules: ${\displaystyle H_{au}\leftarrow H_{au}\frac{\sum _i\frac{W_{ia}{V}_{iu}}{{\left(WH\right)}_{iu}}}{\sum _k{W}_{ka}}}$ ${\displaystyle W_{ia}\leftarrow W_{ia}\frac{\sum _u\frac{H_{au}{A}_{iu}}{{\left(WH\right)}_{iu}}}{\sum _v{H}_{av}}.}$

The initialization of H_au and W_ia was generated as random seed matrices drawn from a uniform distribution within the same range as the entries in the matrix A. Since the starting matrices were randomized, we conducted an average of 30 simulations for each NMF run to obtain the consensus clustering results. We used Kullback–Leibler divergence (KL-divergence) as the distance function, as it has significantly better performance theorized in Yang et al. (2011). The clustering results of all possible k’s (usually ranging from 2 to 5, as higher k values require exponentially more time to run) were listed and k was chosen when the best cophenetic correlation coefficient is achieved, as proposed in Brunet et al. (2004).

Other packages used for detecting significant or important genes

DE methods for bulk-level RNA-Seq: we used two most popular bulk-level RNA-Seq methods: DESeq2 and edgeR, to compare on the results of DE genes.

DE methods for scRNA-Seq: three methods were investigated, with default settings of the packages: (1) Monocle: this is a versatile method (V 1.0.0) that performs differential expression analysis between cell types or states, moreover places cells in order according to their progression through processes such as cell differentiation (Trapnell et al., 2014); (2) SCDE: this package (V 1.2.1) implemented in R is based on Bayesian method, where the individual genes were modeled explicitly as a mixture of the dropout and amplification events by the Poisson model and negative binomial model (Kharchenko, Silberstein & Scadden, 2014); (3) MAST: this method (V 1.0.1) implemented in R was originally used to detected DE genes in qPCR results of single cells. We selected the 500 genes with the lowest likelihood ratio test p-value using Hurdle Model provided by the package, as recommended by the authors (McDavid et al., 2013).

Additionally, we experimented if introducing t-SNE, a dimension reduction method that was recently successfully applied to scRNA-Seq, would improve the results of NMF. We used the C+ + accelerated R-package Rtsne (V 0.10), based on the original C+ + implementation (Van der Maaten, 2013).

Module detection package

We used Functional Epigenetic Modules (FEM) R package (Jiao, Widschwendter & Teschendorff, 2014) for module detection. FEM utilizes an expansion algorithm based on the z-score of the expression level, by using a list of seed genes as the starting point. It selects the top modules based on p-values calculated by a Monte Carlo method.

We modified the source code of the FEM package and changed the process of the seed gene selection. Instead of selecting the seed genes based on the z-score of the expression level, we directly plugged in a list of genes as the seed genes, which were generated from each of the compared method for important gene detection.

Measuring the performance of unsupervised clustering methods

Pair-wise Rand measure for clustering between the test and the reference is defined by ${\displaystyle R=\frac{TP+TN}{TP+FP+FN+TN}}$ in which the four quantities TP, FP, FN, and TN are cardinals of the four sets of pairs. T/F means true/false based on the reference, and P/N means positive/negative results from the test. Specifically, a positive result (P) refers to a pair of samples clustered in the same group by the tested method; a true positive (TP) or true negative (TN) result represents the case where the agreements between the test and the reference clustering is reached (Rand, 1971).

Modularity detection and pathway analysis

We used Functional Epigenetic Modules (FEM) package (Jiao, Widschwendter & Teschendorff, 2014) implemented in R for module detection. FEM utilizes SpinGlass algorithm (Reichardt & Bornholdt, 2006) based on the z-score of the expression level, by using a list of seed genes as the starting points. It selects the top modules based on p-values calculated from a Monte Carlo method. We modified the source code of the package to allow seed genes generated from other methods (NMF, DESeq2, edgeR, SCDE, MAST and Monocle) that detect significant or important genes. In each case, we used top 500 most important genes as the seeds for FEM. We next compared biological meanings of the resulting modules by Gene Ontology (GO) or Kyoto Encyclopedia of Genes and Genomes (KEGG) pathway enrichment analysis, implemented as DAVID Web Service in R (Huang, Sherman & Lempicki, 2008; Huang, Sherman & Lempicki, 2009).

Data and code availability

The Glioblastoma, mouse lung distal epithelial, mouse bone marrow, and human induced pluripotent stem cell lines datasets are downloaded from Gene Expression Omnibus (GEO) repository with accession codes GSE57872, GSE52583, GSE60781, and GSE77288, respectively. The code used for the package NMFEM can be found at https://github.com/lanagarmire/NMFEM, and https://github.com/lanagarmire/NMFEM_extra.

NMF accurately clusters scRNA-Seq data among similar populations

We first assess NMF’s accuracy in unsupervised clustering compared to two other commonly used methods: K-means and hierarchical clustering (Hclust) algorithms. For generality, different distance metric and linkage variations of Hcust clustering were explored, including the combinations of Euclidean Distance & Complete Linkage (Euclidean + Complete), Euclidean Distance & Ward Linkage (Euclidean + Ward), and Correlation Metric & Complete Linkage (Correlation + Complete). To draw unbiased conclusions, we tested these clustering methods on five datasets, including a mouse embryonic lung epithelial dataset (Treutlein et al., 2014), a mouse hematopoietic stem cell (HSC) and multipotent progenitor (MPP) cell dataset (Table S1), a human glioblastoma dataset (Patel et al., 2014), a mouse bone marrow dendritic cells dataset (Schlitzer et al., 2015), and lastly a human induced pluripotent stem cell (iPSC) dataset with unique molecular identifier (UMI) counts (Tung et al., 2016). A good clustering method should be able to separate groups that are most similar, therefore we selected the closet two groups in each dataset (Methods).

As shown in Fig. 2, NMF consistently achieves the highest performance among all methods compared, as measured by the Rand Index measure (Methods). Indeed, despite the high level of similarity between each pair of groups, NMF achieves an average Rand measure of 0.88 among the five datasets. In particular, it has an impressive Rand measure of 0.95 in the mouse embryonic lung epithelial dataset (Fig. 2A) and almost 1.00 in the UMI iPSC dataset (Fig. 2E). In contrast, K-means and the three variations of hierarchical clustering (Euclidean + Complete, Euclidean + Ward, and Correlation + Complete) all have significantly (p-value < 0.05) lower averaged Rand measures of 0.66, 0.52, 0.66, and 0.52, respectively (Fig. 2). Most of the wrongly clustered samples by K-means are located between the two clusters in the Euclidean space (Fig. S1A ). And hierarchical clustering methods can be heavily affected by individual outliers (Figs. S1B– S1D).

t-SNE is a commonly used dimension reduction method that exaggerates the differences between populations (Van der Maaten & Hinton, 2008), and was previously used in combination with other clustering methods on scRNA-Seq data (Van der Maaten & Hinton, 2008; Bushati et al., 2011; Junker et al., 2014). Therefore, we investigated the effect of t-SNE preprocessing on NMF and other compared methods next. Interestingly, NMF performs significantly worse after t-SNE preprocessing (Fig. 2). We speculate that the more significant decrease in accuracy by NMF is attributed to the fact that NMF is not a distance-based method, and the reduction of features after t-SNE interferes with NMF’s ability to conduct component decomposition more drastically than other methods.

NMF discovers biologically meaningful genes to separate subpopulations

One major advantage of NMF over many other unsupervised clustering methods such as K-means, is its ability to simultaneously identify genes that are characteristic to each subpopulations. We use the discriminative metric called D-score, based the previous rank-2 discriminant NMF implementation (Jia et al., 2015). Briefly, D-score is a non-negative number, and the more positive a gene’s D-score is, the more unique this gene is expressed in a subpopulation (Methods). We ranked the top genes in NMF by D-score in the descending order, and sought prior literature reports to validate the utilities of NMF empirically.

For the top ranked NMF genes differentiating E14.5 and E16.5 (Treutlein et al., 2014), we found biological evidence to support their functions. For example, Mal, T-Cell Differentiation Protein 2 (Mal2) ranked 2nd by NMF, was noted to be involved in the dynamic circuit of early lung development (Ye, Liu & Wu, 2012). Another gene Surfactant Associated 2 (Sfta2) ranked 4th by NMF, was recently identified as an expression QTL (eQTL) gene during early lung development (George et al., 2016). Additionally, we examined top genes differentiating the subsets of AT1 vs. AT2 samples as reported originally (Treutlein et al., 2014). Impressively, the four genes Hopx, Ager, Egfl6, and Sftpc which were marker genes reported in the original report, have ranks of 1st, 12th, 23rd and 27th among the top genes according to NMF.

Similarly, in the HSC vs. MPP1 dataset, many of the top-ranked genes were previously noted as either differentially expressed between the two types of cells or characteristic to one of the two types. For example, Cysteine Rich Protein 1 (Crip1), ranked 2nd by NMF D-score, is found to be expressed lower in Hdac3 knock-out cells undergoing HSC and MPP differentiation (Summers et al., 2013). Regulator of G-Protein Signaling 2 (Rgs2), ranked 3rd by NMF, was noted to be differentially expressed in HSCs (Phillips et al., 2000; Li & Akashi, 2003; Park et al., 2003). SKI-Like Proto-Oncogene (Skil), ranked 8th by NMF, was shown to play important roles in hematopoietic development (Pearson-White et al., 1995).

For the MGH29 and MGH31 glioblastoma patient data (Patel et al., 2014), although we could not obtain definite clinical subtypes based on the original paper, we did observe that many top genes identified had previously been related to various types of cancers. For example, Chromosome 8 Open Reading Frame 4 (C8orf4), ranked 9th by NMF, was identified as “Thyroid cancer 1 (TC1)” (Panebianco et al., 2015; Zhang et al., 2015; Zhu et al., 2015; Huang et al., 2016). Epidermal Growth Factor Receptor (EGFR), a gene ranked 31st by NMF, has elevated expression from MGH29 to MGH31. EGFR is a well-known growth factor receptor noted for its critical role on cell division control. Moreover, three top genes EZR (ranked 12th), TUBB (ranked 27th), and RDX (ranked 36th), were shown to be involved in organization and regulation of morphological characteristics of breast cancer cells including cell shape and membrane to membrane docking (Kopp et al., 2016).

Comparison of important genes from NMF and other methods

To further understand the patterns recognized by NMF, we compared the top ranked genes identified by NMF with the those by other recent scRNA-Seq analysis methods, including Monocle (Trapnell et al., 2014), MAST (McDavid et al., 2013) as well as SCDE (Kharchenko, Silberstein & Scadden, 2014) (Treutlein et al., 2014). In addition, we included DESeq2 and edgeR, two differential expression (DE) methods commonly used in bulk RNA-Seq analysis.

We compared the different methods using MA plots to analyze the mouse embryonic lung epithelial cells dataset (E14.5 and E16.5, Fig. 3). For fair-comparison, we highlighted the top 500 genes identified by each method in blue. Since the global gene expression levels are reduced from E14.5 to E16.5, all methods detect mainly down-regulated genes. The specific genes identified by these methods however vary greatly (Fig. 3, Figs. S2 and S3), but NMF is most different from other methods, based on its unique mathematical formulation. Unlike other methods that are prone to lowly expressed genes, NMF tends to select genes that have intermediate expression levels (Figs. S3). Indeed, 90% of selected genes have log FPKM between 2.32 and 4.66. Other methods, on the other hand, select more genes with lower expression levels. Specifically, SCDE, MAST, DESeq2, edgeR and Monocle have 56%, 45%, 31%, 27% and 18% genes below FPKM = 1, respectively. The same pattern has been observed in the HSC vs. MPP, glioblastoma, and bone marrow dataset (Figs. S4A–S4C). Lowly expressed genes usually have relatively higher levels of noise (Brennecke et al., 2013), evident by comparing the CV2 levels between genes selected by different methods (Fig.  S5), and their apparent differential expression may be less reliable.

We further tested whether such intermediately expressed genes identified by NMF are robust and unlikely a result of random sampling. We performed additional runs with each run deliberately dropping one sample from the dataset. The results show that the top 500 genes have over 95% probability to re-appear in this top 500 list, compared to less than 2% probability for any other non-top genes (Fig. S6). The reason that NMF tends to avoid lowly expressed genes is that D-score considers absolute expression level of a gene, rather than the relative expression level (see ‘Methods’). The lower its expression level, the less likely a gene is selected as a feature gene by NMF. On the other hand, very highly expressed genes are more likely to be expressed across all cells. They do not generate large differences in their meta-gene loadings, and will not achieve high D-score as well.

Modularity detection with NMF based framework

We next asked if the important genes detected by NMF convey unique and meaningful biological functions. Previously, a community detection method based on SpinGlass algorithm named FEM has been reported to detect functional modules on protein-protein interaction (PPI) networks (Jiao, Widschwendter & Teschendorff, 2014). Inspired by this approach, we used the 500 top genes selected by NMF as seed genes, and ran vertex-initialized SpinGlass models on the PPI network. Modified from FEM, here each vertex (gene) is weighted by t-statistics measuring the expression level (rather than DNA methylation) changes. In order to assess the robustness of the method, we performed random permutations on the data and calculated the p-value for each module. The top four modules for mouse embryonic lung epithelial cells dataset are shown in Fig. 4. We conducted the same procedure on HSC vs. MPP1, glioblastoma, and bone marrow datasets (Figs. S4D–S4F).

Consistent with the down-regulating trend of all genes from E14.5 to E16.5 (Fig.  3), these top four modules exhibit strong down-regulation as well. Five hub genes are identified: Rad21, Atf3, Polr2j, Tecr and Rpl37, among which Tecr and Rpl37 are in the same module. These modules are involved in chromosome structural maintenance (seed Rad21), transcription activation (seed Atf3), RNA polymerase (seed Polr2j), and ribosome component and various enzyme coding genes (Tecr and Rpl37). The fact that the top modules are all related to transcription and translation is interesting, as it explains the observed global gene expression down-regulation observed earlier (Fig. 3).