2.1 Loading in the count matrix

Our first task is to load the count matrices into memory. One matrix was generated for each plate of cells used in the study. In each matrix, each row represents an endogenous gene or a spike-in transcript, and each column represents a cell. Subsequently, the count in each entry of the matrix represents the number of reads mapped to a particular gene/transcript in a particular cell.

unzip("E-MTAB-5522.processed.1.zip")

# Reading in the count tables for each of the two plates.
plate1 <- read.delim("counts_Calero_20160113.tsv", 
    header=TRUE, row.names=1, check.names=FALSE)
plate2 <- read.delim("counts_Calero_20160325.tsv", 
    header=TRUE, row.names=1, check.names=FALSE)

gene.lengths <- plate1$Length # First column is the gene length.
plate1 <- as.matrix(plate1[,-1]) # Discarding gene length (as it is not a cell).
plate2 <- as.matrix(plate2[,-1])
rbind(Plate1=dim(plate1), Plate2=dim(plate2))

##         [,1] [,2]
## Plate1 46703   96
## Plate2 46703   96

We combine the two matrices into a single object for further processing. This is done after verifying that the genes are in the same order between the two matrices.

stopifnot(identical(rownames(plate1), rownames(plate2)))
all.counts <- cbind(plate1, plate2)

For convenience, the count matrix is stored in a SingleCellExperiment object from the SingleCellExperiment package. This allows different types of row- and column-level metadata to be stored alongside the counts for synchronized manipulation throughout the workflow.

library(SingleCellExperiment)
sce <- SingleCellExperiment(list(counts=all.counts))
rowData(sce)$GeneLength <- gene.lengths
sce

## class: SingleCellExperiment 
## dim: 46703 192 
## metadata(0):
## assays(1): counts
## rownames(46703): ENSMUSG00000102693 ENSMUSG00000064842 ... SIRV7
##   CBFB-MYH11-mcherry
## rowData names(1): GeneLength
## colnames(192): SLX-9555.N701_S502.C89V9ANXX.s_1.r_1
##   SLX-9555.N701_S503.C89V9ANXX.s_1.r_1 ...
##   SLX-11312.N712_S508.H5H5YBBXX.s_8.r_1
##   SLX-11312.N712_S517.H5H5YBBXX.s_8.r_1
## colData names(0):
## reducedDimNames(0):
## spikeNames(0):

We identify the rows corresponding to ERCC spike-in transcripts from the row names. We store this information in the SingleCellExperiment object for future use. This is necessary as spike-ins require special treatment in downstream steps such as normalization.

isSpike(sce, "ERCC") <- grepl("^ERCC", rownames(sce))
summary(isSpike(sce, "ERCC"))

##    Mode   FALSE    TRUE 
## logical   46611      92

This dataset is slightly unusual in that it contains information from another set of spike-in transcripts, the Spike-In RNA Variants (SIRV) set. For simplicity, we will only use the ERCC spike-ins in this analysis. Thus, we must remove the rows corresponding to the SIRV transcripts prior to further analysis, which can be done simply by subsetting the SingleCellExperiment object.

is.sirv <- grepl("^SIRV", rownames(sce))
sce <- sce[!is.sirv,] 
summary(is.sirv)

##    Mode   FALSE    TRUE 
## logical   46696       7

Comments from Aaron:

• Some feature-counting tools will report mapping statistics in the count matrix (e.g., the number of unaligned or unassigned reads). While these values can be useful for quality control, they would be misleading if treated as gene expression values. Thus, they should be removed (or at least moved to the colData) prior to further analyses.
• Be aware of using the ^ERCC regular expression for human data where the row names of the count matrix are gene symbols. An ERCC gene family actually exists in human annotation, so this would result in incorrect identification of genes as spike-in transcripts. This problem can be avoided by publishing count matrices with standard identifiers (e.g., Ensembl, Entrez).

2.2 Incorporating cell-based annotation

We load in the metadata for each library/cell from the sdrf.txt file. It is important to check that the rows of the metadata table are in the same order as the columns of the count matrix. Otherwise, incorrect metadata will be assigned to each cell.

metadata <- read.delim("E-MTAB-5522.sdrf.txt", check.names=FALSE, header=TRUE)
m <- match(colnames(sce), metadata[["Source Name"]]) # Enforcing identical order.
stopifnot(all(!is.na(m))) # Checking that nothing's missing.
metadata <- metadata[m,]
head(colnames(metadata))

## [1] "Source Name"                "Comment[ENA_SAMPLE]"       
## [3] "Comment[BioSD_SAMPLE]"      "Characteristics[organism]" 
## [5] "Characteristics[cell line]" "Characteristics[cell type]"

We only retain relevant metadata fields to avoid storing unnecessary information in the colData of the SingleCellExperiment object. In particular, we keep the plate of origin (i.e., block) and phenotype of each cell. The second field is relevant as all of the cells contain a CBFB-MYH11 oncogene, but the expression of this oncogene is only induced in a subset of the cells.

colData(sce)$Plate <- factor(metadata[["Factor Value[block]"]])
pheno <- metadata[["Factor Value[phenotype]"]]
levels(pheno) <- c("induced", "control")
colData(sce)$Oncogene <- pheno
table(colData(sce)$Oncogene, colData(sce)$Plate)

##          
##           20160113 20160325
##   induced       48       48
##   control       48       48

2.3 Incorporating gene-based annotation

Feature-counting tools typically report genes in terms of standard identifiers from Ensembl or Entrez. These identifiers are used as they are unambiguous and highly stable. However, they are difficult to interpret compared to the gene symbols which are more commonly used in the literature. Given the Ensembl identifiers, we obtain the corresponding gene symbols using annotation packages like org.Mm.eg.db.

library(org.Mm.eg.db)
symb <- mapIds(org.Mm.eg.db, keys=rownames(sce), keytype="ENSEMBL", column="SYMBOL")
rowData(sce)$ENSEMBL <- rownames(sce)
rowData(sce)$SYMBOL <- symb
head(rowData(sce))

## DataFrame with 6 rows and 3 columns
##   GeneLength            ENSEMBL      SYMBOL
##    <integer>        <character> <character>
## 1       1070 ENSMUSG00000102693          NA
## 2        110 ENSMUSG00000064842          NA
## 3       6094 ENSMUSG00000051951        Xkr4
## 4        480 ENSMUSG00000102851          NA
## 5       2819 ENSMUSG00000103377          NA
## 6       2233 ENSMUSG00000104017          NA

It is often desirable to rename the row names of sce to the gene symbols, as these are easier to interpret. However, this requires some work to account for missing and duplicate symbols. The code below will replace missing symbols with the Ensembl identifier and concatenate duplicated symbols with the (unique) Ensembl identifiers.

new.names <- rowData(sce)$SYMBOL
missing.name <- is.na(new.names)
new.names[missing.name] <- rowData(sce)$ENSEMBL[missing.name]
dup.name <- new.names %in% new.names[duplicated(new.names)]
new.names[dup.name] <- paste0(new.names, "_", rowData(sce)$ENSEMBL)[dup.name]
rownames(sce) <- new.names
head(rownames(sce))

## [1] "ENSMUSG00000102693" "ENSMUSG00000064842" "Xkr4"              
## [4] "ENSMUSG00000102851" "ENSMUSG00000103377" "ENSMUSG00000104017"

We also determine the chromosomal location for each gene using the TxDb.Mmusculus.UCSC.mm10.ensGene package. This will be useful later as several quality control metrics will be computed from rows corresponding to mitochondrial genes.

library(TxDb.Mmusculus.UCSC.mm10.ensGene)
location <- mapIds(TxDb.Mmusculus.UCSC.mm10.ensGene, keys=rowData(sce)$ENSEMBL, 
    column="CDSCHROM", keytype="GENEID")
rowData(sce)$CHR <- location
summary(location=="chrM")

##    Mode   FALSE    TRUE    NA's 
## logical   22428      13   24255

Alternatively, annotation from BioMart resources can be directly added to the object using the getBMFeatureAnnos function from scater. This may be more convenient than the approach shown above, but depends on an available internet connection to the BioMart databases.

3.1 Defining the quality control metrics

Low-quality cells need to be removed to ensure that technical effects do not distort downstream analysis results. We use several quality control (QC) metrics:

• The library size is defined as the total sum of counts across all features, i.e., genes and spike-in transcripts. Cells with small library sizes are of low quality as the RNA has not been efficiently captured (i.e., converted into cDNA and amplified) during library preparation.
• The number of expressed features in each cell is defined as the number of features with non-zero counts for that cell. Any cell with very few expressed genes is likely to be of poor quality as the diverse transcript population has not been successfully captured.
• The proportion of reads mapped to spike-in transcripts is calculated relative to the library size for each cell. High proportions are indicative of poor-quality cells, where endogenous RNA has been lost during processing (e.g., due to cell lysis or RNA degradation). The same amount of spike-in RNA to each cell, so an enrichment in spike-in counts is symptomatic of loss of endogenous RNA.
• In the absence of spike-in transcripts, the proportion of reads mapped to genes in the mitochondrial genome can also be used. High proportions are indicative of poor-quality cells (Islam et al. 2014; Ilicic et al. 2016), possibly because of loss of cytoplasmic RNA from perforated cells. The reasoning is that mitochondria are larger than individual transcript molecules and less likely to escape through tears in the cell membrane.

For each cell, we calculate these quality control metrics using the calculateQCMetrics function from the scater package (McCarthy et al. 2017). These are stored in the row- and column-wise metadata of the SingleCellExperiment for future reference.

library(scater)
mito <- which(rowData(sce)$CHR=="chrM")
sce <- calculateQCMetrics(sce, feature_controls=list(Mt=mito))
head(colnames(colData(sce)), 10)

##  [1] "Plate"                          "Oncogene"                      
##  [3] "is_cell_control"                "total_features_by_counts"      
##  [5] "log10_total_features_by_counts" "total_counts"                  
##  [7] "log10_total_counts"             "pct_counts_in_top_50_features" 
##  [9] "pct_counts_in_top_100_features" "pct_counts_in_top_200_features"

The distributions of these metrics are shown in Figure 1, stratified by oncogene induction status and plate of origin. The aim is to remove putative low-quality cells that have low library sizes, low numbers of expressed features, and high spike-in (or mitochondrial) proportions.

sce$PlateOnco <- paste0(sce$Oncogene, ".", sce$Plate)
multiplot(
    plotColData(sce, y="total_counts", x="PlateOnco"),
    plotColData(sce, y="total_features", x="PlateOnco"),
    plotColData(sce, y="pct_counts_ERCC", x="PlateOnco"),
    plotColData(sce, y="pct_counts_Mt", x="PlateOnco"),
    cols=2)

Figure 1: Distributions of various QC metrics for all cells in the 416B dataset
This includes the library sizes, number of expressed genes, and proportion of reads mapped to spike-in transcripts or mitochondrial genes.

It is also valuable to examine how the QC metrics behave with respect to each other (Figure 2). Generally, they will be in rough agreement, i.e., cells with low total counts will also have low numbers of expressed features and high ERCC/mitochondrial proportions. Clear discrepancies may correspond to technical differences between batches of cells (see below) or genuine biological differences in RNA content.

par(mfrow=c(1,3))
plot(sce$total_features, sce$total_counts/1e6, xlab="Number of expressed genes",
    ylab="Library size (millions)")
plot(sce$total_features, sce$pct_counts_ERCC, xlab="Number of expressed genes",
    ylab="ERCC proportion (%)")
plot(sce$total_features, sce$pct_counts_Mt, xlab="Number of expressed genes",
    ylab="Mitochondrial proportion (%)")

Figure 2: Behaviour of each QC metric compared to the total number of expressed features
Each point represents a cell in the 416B dataset.

3.2 Identifying outliers for each metric

Picking a threshold for these metrics is not straightforward as their absolute values depend on the experimental protocol. For example, sequencing to greater depth will lead to more reads and more expressed features, regardless of the quality of the cells. Similarly, using more spike-in RNA in the protocol will result in higher spike-in proportions. To obtain an adaptive threshold, we assume that most of the dataset consists of high-quality cells, and identify cells that are outliers for the various QC metrics.

Outliers are defined based on the median absolute deviation (MADs) from the median value of each metric across all cells. We remove cells with log-library sizes that are more than 3 MADs below the median log-library size. A log-transformation improves resolution at small values, especially when the MAD of the raw values is comparable to or greater than the median. We also remove cells where the log-transformed number of expressed genes is 3 MADs below the median value.

libsize.drop <- isOutlier(sce$total_counts, nmads=3, type="lower", 
    log=TRUE, batch=sce$PlateOnco)
feature.drop <- isOutlier(sce$total_features, nmads=3, type="lower", 
    log=TRUE, batch=sce$PlateOnco)

The batch= argument ensures that outliers are identified within each level of the specified plate/oncogene factor. This allows isOutlier() to accommodate systematic differences in the QC metrics across plates (Figure 1), which can arise due to technical differences in processing (e.g., differences in sequencing depth) rather than any changes in quality. The same reasoning applies to the oncogene induction status, where induced cells may have naturally fewer expressed genes for biological reasons. Failing to account for these systematic differences would inflate the MAD estimate and compromise the removal of low-quality cells.

We identify outliers for the proportion-based metrics in a similar manner. Here, no transformation is required as we are identifying large outliers, for which the distinction should be fairly clear on the raw scale. We do not need to use the mitochondrial proportions as we already have the spike-in proportions (which serve a similar purpose) for this dataset. This avoids potential issues arising from genuine differences in mitochondrial content between cell types that may confound outlier identification.

spike.drop <- isOutlier(sce$pct_counts_ERCC, nmads=3, type="higher",
    batch=sce$PlateOnco)

Subsetting by column will retain only the high-quality cells that pass each filter described above. We examine the number of cells removed by each filter as well as the total number of retained cells. Removal of a substantial proportion of cells (> 10%) may be indicative of an overall issue with data quality.

keep <- !(libsize.drop | feature.drop | spike.drop)
data.frame(ByLibSize=sum(libsize.drop), ByFeature=sum(feature.drop),
    BySpike=sum(spike.drop), Remaining=sum(keep))

##   ByLibSize ByFeature BySpike Remaining
## 1         5         4       6       183

We then subset the SingleCellExperiment object to retain only the putative high-quality cells. We also save the original object to file for later use.

sce$PassQC <- keep
saveRDS(sce, file="416B_preQC.rds")
sce <- sce[,keep]
dim(sce)

## [1] 46696   183

Comments from Aaron:

• See this section for a more detailed discussion of the assumptions underlying the outlier-based detection of low-quality cells.

5.1 Inspecting the most highly expressed genes

We examine the identities of the most highly expressed genes (Figure 4). This should generally be dominated by constitutively expressed transcripts, such as those for ribosomal or mitochondrial proteins. The presence of other classes of features may be cause for concern if they are not consistent with expected biology. For example, a top set containing many spike-in transcripts suggests that too much spike-in RNA was added during library preparation, while the absence of ribosomal proteins and/or the presence of their pseudogenes are indicative of suboptimal alignment.

fontsize <- theme(axis.text=element_text(size=12), axis.title=element_text(size=16))
plotQC(sce, type = "highest-expression", n=50) + fontsize

Figure 4: Percentage of total counts assigned to the top 50 most highly-abundant features in the 416B dataset
For each feature, each bar represents the percentage assigned to that feature for a single cell, while the circle represents the average across all cells. Bars are coloured by the total number of expressed features in each cell, while circles are coloured according to whether the feature is labelled as a control feature.

5.2 Filtering out low-abundance genes

Low-abundance genes are problematic as zero or near-zero counts do not contain much information for reliable statistical inference (Bourgon, Gentleman, and Huber 2010). These genes typically do not provide enough evidence to reject the null hypothesis during testing, yet they still increase the severity of the multiple testing correction. In addition, the discreteness of the counts may interfere with statistical procedures, e.g., by compromising the accuracy of continuous approximations. Thus, low-abundance genes are often removed in many RNA-seq analysis pipelines before the application of downstream methods.

The “optimal” choice of filtering strategy depends on the downstream application. A more aggressive filter is usually required to remove discreteness (e.g., for normalization) compared to that required for removing underpowered tests. For hypothesis testing, the filter statistic should also be independent of the test statistic under the null hypothesis. Thus, we (or the relevant function) will filter at each step as needed, rather than applying a single filter for the entire analysis.

Several metrics can be used to define low-abundance genes. The most obvious is the average count for each gene, computed across all cells in the dataset. We calculate this using the calcAverage() function, which also performs some adjustment for library size differences between cells. We typically observe a peak of moderately expressed genes following a plateau of lowly expressed genes (Figure 5).

ave.counts <- calcAverage(sce, use_size_factors=FALSE)
hist(log10(ave.counts), breaks=100, main="", col="grey80", 
    xlab=expression(Log[10]~"average count"))

Figure 5: Histogram of log-average counts for all genes in the 416B dataset

A minimum threshold can be applied to this value to filter out genes that are lowly expressed. The example below demonstrates how we could remove genes with average counts less than 1. The number of TRUE values in demo.keep corresponds to the number of retained rows/genes after filtering.

demo.keep <- ave.counts >= 1
filtered.sce <- sce[demo.keep,]
summary(demo.keep)

##    Mode   FALSE    TRUE 
## logical   33490   13206

We also examine the number of cells that express each gene. This is closely related to the average count for most genes, as expression in many cells will result in a higher average (Figure 6). Genes expressed in very few cells are often uninteresting as they are driven by amplification artifacts (though they may also also arise from rare populations). We could then remove genes that are expressed in fewer than n cells.

num.cells <- nexprs(sce, byrow=TRUE)
smoothScatter(log10(ave.counts), num.cells, ylab="Number of cells", 
    xlab=expression(Log[10]~"average count"))

Figure 6: The number of cells expressing each gene in the 416B dataset, plotted against the log-average count
Intensity of colour corresponds to the number of genes at any given location.

As mentioned above, we will apply these filters at each step rather than applying them globally by subsetting sce. This ensures that the most appropriate filter is used in each application. Nonetheless, we remove genes that are not expressed in any cell to reduce computational work in downstream steps. Such genes provide no information and would be removed by any filtering strategy.

to.keep <- num.cells > 0
sce <- sce[to.keep,]
summary(to.keep)

##    Mode   FALSE    TRUE 
## logical   22833   23863

6.1 Using the deconvolution method to deal with zero counts

Read counts are subject to differences in capture efficiency and sequencing depth between cells (Stegle, Teichmann, and Marioni 2015). Normalization is required to eliminate these cell-specific biases prior to downstream quantitative analyses. This is often done by assuming that most genes are not differentially expressed (DE) between cells. Any systematic difference in count size across the non-DE majority of genes between two cells is assumed to represent bias and is removed by scaling. More specifically, “size factors” are calculated that represent the extent to which counts should be scaled in each library.

Size factors can be computed with several different approaches, e.g., using the estimateSizeFactorsFromMatrix function in the DESeq2 package (Anders and Huber 2010; Love, Huber, and Anders 2014), or with the calcNormFactors function (Robinson and Oshlack 2010) in the edgeR package. However, single-cell data can be problematic for these bulk data-based methods due to the dominance of low and zero counts. To overcome this, we pool counts from many cells to increase the count size for accurate size factor estimation (Lun, Bach, and Marioni 2016). Pool-based size factors are then “deconvolved” into cell-based factors for cell-specific normalization.

sce <- computeSumFactors(sce)
summary(sizeFactors(sce))

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##  0.3416  0.7229  0.9245  1.0000  1.1483  3.5925

The size factors are well-correlated with the library sizes for all cells (Figure 7). This suggests that most of the systematic differences between cells are driven by differences in capture efficiency or sequencing depth. Any DE between cells would yield a non-linear trend between the total count and size factor, and/or increased scatter around the trend. We observe some evidence of this after oncogene induction, where the size factors after induction are systematically lower. This is consistent with composition biases (Robinson and Oshlack 2010) introduced by upregulation of genes after induction.

plot(sce$total_counts/1e6, sizeFactors(sce), log="xy",
    xlab="Library size (millions)", ylab="Size factor",
    col=c("red", "black")[sce$Oncogene], pch=16)
legend("bottomright", col=c("red", "black"), pch=16, cex=1.2,
    legend=levels(sce$Oncogene))

Figure 7: Size factors from deconvolution, plotted against library sizes for all cells in the 416B dataset
Axes are shown on a log-scale. Wild-type cells are shown in black and oncogene-induced cells are shown in red.

Comments from Aaron:

• While the deconvolution approach is robust to the high frequency of zeroes in scRNA-seq data, it will eventually fail if too many counts are zero. This manifests as negative size factors, which are obviously nonsensical. To avoid this, the computeSumFactors function will automatically remove low-abundance genes prior to the calculation of size factors. Genes with a library size-adjusted average count below a specified threshold (min.mean) are ignored.
  • For read count data, the default value of 1 is usually satisfactory. For UMI data, counts are lower so a threshold of 0.1 is recommended.
  • While the library size-adjusted average is not entirely independent of the bias (Bourgon, Gentleman, and Huber 2010), this is a better filter statistic than the sample mean count. The latter would enrich for genes that are upregulated in cells with large library sizes, resulting in inflated size factor estimates for those cells.
• Cell-based QC should always be performed prior to normalization, to remove cells with very low numbers of expressed genes. If this is not done, the computeSumFactors function may yield negative size factors for low-quality cells.
• The sizes argument can be used to specify the number of pool sizes to use to compute the size factors. More sizes yields more precise estimates at the cost of some computational time and memory. In general, sizes should not be below 20 cells, to ensure that there are sufficient non-zero expression values in each pool. We also recommend that the total number of cells should be at least 100 for effective pooling.
• For highly heterogeneous datasets, it is advisable to perform a rough clustering of the cells. This can be done with the quickCluster function and the results passed to computeSumFactors via the cluster argument. Cells in each cluster are normalized separately, and the size factors are rescaled to be comparable across clusters. This avoids the need to assume that most genes are non-DE across the entire population - only a non-DE majority is required between pairs of clusters. We demonstrate this approach later with a larger dataset, as there are not enough cells in the 416B dataset.

6.2 Computing separate size factors for spike-in transcripts

Size factors computed from the counts for endogenous genes are usually not appropriate for normalizing the counts for spike-in transcripts. Consider an experiment without library quantification, i.e., the amount of cDNA from each library is not equalized prior to pooling and multiplexed sequencing. Here, cells containing more RNA have greater counts for endogenous genes and thus larger size factors to scale down those counts. However, the same amount of spike-in RNA is added to each cell during library preparation. This means that the counts for spike-in transcripts are not subject to the effects of RNA content. Attempting to normalize the spike-in counts with the gene-based size factors will lead to over-normalization and incorrect quantification of expression. Similar reasoning applies in cases where library quantification is performed. For a constant total amount of cDNA, any increases in endogenous RNA content will suppress the coverage of spike-in transcripts. As a result, the bias in the spike-in counts will be opposite to that captured by the gene-based size factor.

To ensure normalization is performed correctly, we compute a separate set of size factors for the spike-in set. For each cell, the spike-in-specific size factor is defined as the total count across all transcripts in the spike-in set. This assumes that none of the spike-in transcripts are differentially expressed, which is reasonable given that the same amount and composition of spike-in RNA should have been added to each cell (Lun et al. 2017). (See below for a more detailed discussion on spike-in normalization.) These size factors are stored in a separate field of the SingleCellExperiment object by setting general.use=FALSE in computeSpikeFactors. This ensures that they will only be used with the spike-in transcripts but not the endogenous genes.

sce <- computeSpikeFactors(sce, type="ERCC", general.use=FALSE)

6.3 Applying the size factors to normalize gene expression

The count data are used to compute normalized log-expression values for use in downstream analyses. Each value is defined as the log₂-ratio of each count to the size factor for the corresponding cell, after adding a prior count of 1 to avoid undefined values at zero counts. Division by the size factor ensures that any cell-specific biases are removed. If spike-in-specific size factors are present in sce, they will be automatically applied to normalize the spike-in transcripts separately from the endogenous genes.

sce <- normalize(sce)

The log-transformation is useful as it means that any differences in the values directly represent log₂-fold changes in expression between cells. This is usually more relevant than the absolute differences in coverage, which need to be interpreted in the context of the overall abundance. The log-transformation also provides some measure of variance stabilization (Law et al. 2014), so that high-abundance genes with large variances do not dominate downstream analyses. The computed values are stored as an "logcounts" matrix in addition to the other assay elements.

7.1 Fitting a trend to the spike-in variances

Variability in the observed expression values across genes can be driven by genuine biological heterogeneity or uninteresting technical noise. To distinguish between these two possibiltiies, we need to model the technical component of the variance of the expression values for each gene. We do so using the set of spike-in transcripts, which were added in the same quantity to each cell. Thus, the spike-in transcripts should exhibit no biological variability, i.e., any variance in their counts should be technical in origin.

We use the trendVar() function to fit a mean-dependent trend to the variances of the log-expression values for the spike-in transcripts. We set block= to block on the plate of origin for each cell, to ensure that technical differences between plates do not inflate the variances. Given the mean abundance of a gene, the fitted value of the trend is then used as an estimate of the technical component for that gene. The biological component of the variance is finally calculated by subtracting the technical component from the total variance of each gene with the decomposeVar function.

var.fit <- trendVar(sce, parametric=TRUE, block=sce$Plate,
    loess.args=list(span=0.3))
var.out <- decomposeVar(sce, var.fit)
head(var.out)

## DataFrame with 6 rows and 6 columns
##                                   mean              total
##                              <numeric>          <numeric>
## ENSMUSG00000103377 0.00801037877839526 0.0117416958615873
## ENSMUSG00000103147  0.0344865345591075 0.0716382020605793
## ENSMUSG00000103161 0.00521187224764422  0.004971239574775
## ENSMUSG00000102331  0.0185051179446466 0.0323577082946858
## ENSMUSG00000102948  0.0591783482173367 0.0886595415581617
## Rp1                 0.0972805805064885  0.454538935512767
##                                    bio               tech            p.value
##                              <numeric>          <numeric>          <numeric>
## ENSMUSG00000103377 -0.0237346026365764 0.0354762984981637                  1
## ENSMUSG00000103147 -0.0811139104461332  0.152752112506713  0.999999999993329
## ENSMUSG00000103161 -0.0181138443394628 0.0230850839142378                  1
## ENSMUSG00000102331  -0.049601656974152 0.0819593652688378  0.999999999998749
## ENSMUSG00000102948  -0.173456540044603  0.262116081602765                  1
## Rp1                 0.0236757758027058  0.430863159710061 0.0345090750415943
##                                  FDR
##                            <numeric>
## ENSMUSG00000103377                 1
## ENSMUSG00000103147                 1
## ENSMUSG00000103161                 1
## ENSMUSG00000102331                 1
## ENSMUSG00000102948                 1
## Rp1                0.150289201925332

We visually inspect the trend to confirm that it corresponds to the spike-in variances (Figure 8)). The wave-like shape is typical of the mean-variance trend for log-expression values. A linear increase in the variance is observed as the mean increases from zero, as larger variances are possible when the counts increase. At very high abundances, the effect of sampling noise decreases due to the law of large numbers, resulting in a decrease in the variance.

plot(var.out$mean, var.out$total, pch=16, cex=0.6, xlab="Mean log-expression", 
    ylab="Variance of log-expression")
curve(var.fit$trend(x), col="dodgerblue", lwd=2, add=TRUE)
cur.spike <- isSpike(sce)
points(var.out$mean[cur.spike], var.out$total[cur.spike], col="red", pch=16)

Figure 8: Variance of normalized log-expression values for each gene in the 416B dataset, plotted against the mean log-expression
The blue line represents the mean-dependent trend fitted to the variances of the spike-in transcripts (red).

We check the distribution of expression values for the genes with the largest biological components. This ensures that the variance estimate is not driven by one or two outlier cells (Figure 9).

chosen.genes <- order(var.out$bio, decreasing=TRUE)[1:10]
plotExpression(sce, features=rownames(var.out)[chosen.genes]) + fontsize

Figure 9: Violin plots of normalized log-expression values for the top 10 genes with the largest biological components in the 416B dataset
Each point represents the log-expression value in a single cell.

7.2 Choosing the parameters of the trend fit

In practice, trend fitting is complicated by the small number of spike-in transcripts and the uneven distribution of their abundances. For low numbers of cells, these issues are exacerbated by the low precision of the variance estimates. Thus, some tuning of trend parameters such as span may be required to achieve a suitable fit - see ?trendVar for more details. Setting parametric=TRUE is especially useful for modelling the expected wave-like shape of the mean-variance relationship. (This is not the default setting as it is not robust for arbitrary trend shapes.)

The trendVar function will also automatically filter out low-abundance genes prior to trend fitting. This ensures that low-abundance genes do not interfere with the fit due to discreteness, which biases the estimate of variability of the variances around the trend; or due to the frequency of low-abundance genes, which reduces the sensitivity of span-based smoothing algorithms at higher abundances. The internal choice of filtering strategy involves a number of considerations:

• Filtering uses the average of log-expression values rather than the (library size-adjusted) average count. The mean log-expression is independent of the variance estimate in a linear modelling framework (Bourgon, Gentleman, and Huber 2010), which ensures that the filter does not introduce spurious trends in the variances at the filter boundary.
• The filter threshold is specified with the min.mean argument in trendVar. We use the default threshold of 0.1 (min.mean) based on the appearance of discrete patterns in the variance estimates for simulated Poisson-distributed counts. Lower thresholds of 0.001-0.01 may be more suitable for very sparse data, e.g., from droplet-based protocols.
• The filter used in trendVar is not applied in decomposeVar by default. Retention of all genes ensures that weak biological signal from rare subpopulations is not discarded. To apply the filter in decomposeVar, users should set subset.row=rowMeans(logcounts(sce)) > 0.1 in the function call.

Finally, users can set use.spikes=FALSE to fit a trend to the variances of the endogenous genes in the absence of spike-in transcripts. This requires some care in interpretation of the results, which will be discussed later.

Comments from Aaron:

• Negative biological components are often obtained from decomposeVar. These are intuitively meaningless as it is impossible for a gene to have total variance below technical noise. Nonetheless, such values occur due to imprecise estimation of the total variance, especially for low numbers of cells.
• decomposeVar also yields p-values that can be used to define HVGs at a specific threshold for the false discovery rate (FDR). We will discuss this in more detail later, as formal detection of HVGs is not necessary for feature selection during data exploration.

11.1 Defining cell clusters from expression data

The denoised log-expression values are used to cluster cells into putative subpopulations. Specifically, we perform hierarchical clustering on the Euclidean distances between cells, using Ward’s criterion to minimize the total variance within each cluster. This yields a dendrogram that groups together cells with similar expression patterns across the chosen genes.

pcs <- reducedDim(sce, "PCA")
my.dist <- dist(pcs)
my.tree <- hclust(my.dist, method="ward.D2")

Clusters are explicitly defined by applying a dynamic tree cut (Langfelder, Zhang, and Horvath 2008) to the dendrogram. This exploits the shape of the branches in the dendrogram to refine the cluster definitions, and is more appropriate than cutree for complex dendrograms. Greater control of the empirical clusters can be obtained by manually specifying cutHeight in cutreeDynamic. We also set minClusterSize to a lower value than the default of 20, to avoid spurious aggregation of distant small clusters.

library(dynamicTreeCut)
my.clusters <- unname(cutreeDynamic(my.tree, distM=as.matrix(my.dist), 
    minClusterSize=10, verbose=0))

We examine the distribution of cells in each cluster with respect to known factors. Each cluster is comprised of cells from both batches, indicating that the clustering is not driven by a batch effect. Differences in the composition of each cluster are observed with respect to Oncogene, consistent with a biological effect of oncogene induction.

table(my.clusters, sce$Plate)

##            
## my.clusters 20160113 20160325
##           1       40       39
##           2       19       19
##           3       14       12
##           4       12       14
##           5        6        8

table(my.clusters, sce$Oncogene)

##            
## my.clusters induced control
##           1      79       0
##           2       0      38
##           3       0      26
##           4       0      26
##           5      14       0

We visualize the cluster assignments for all cells on the t-SNE plot in Figure 13. Adjacent cells are generally assigned to the same cluster, indicating that the clustering procedure was applied correctly.

sce$cluster <- factor(my.clusters)
plotTSNE(sce, run_args=list(use_dimred="PCA", perplexity=20, 
    rand_seed=200), colour_by="cluster") + fontsize

Figure 13: t-SNE plot of the denoised PCs of the 416B dataset
Each point represents a cell and is coloured according to the cluster identity to which it was assigned.

We check the separatedness of the clusters using the silhouette width (Figure 14). Cells with large positive silhouette widths are closer to other cells in the same cluster than to cells in different clusters. Conversely, cells with negative widths are closer to other clusters than to other cells in the cluster to which it was assigned. Each cluster would ideally contain many cells with large positive widths, indicating that it is well-separated from other clusters.

library(cluster)
clust.col <- scater:::.get_palette("tableau10medium") # hidden scater colours
sil <- silhouette(my.clusters, dist = my.dist)
sil.cols <- clust.col[ifelse(sil[,3] > 0, sil[,1], sil[,2])]
sil.cols <- sil.cols[order(-sil[,1], sil[,3])]
plot(sil, main = paste(length(unique(my.clusters)), "clusters"), 
    border=sil.cols, col=sil.cols, do.col.sort=FALSE) 

Figure 14: Barplot of silhouette widths for cells in each cluster
Each cluster is assigned a colour and cells with positive widths are coloured according to the colour of its assigned cluster. Any cell with a negative width is coloured according to the colour of the cluster that it is closest to. The average width for all cells in each cluster is shown, along with the average width for all cells in the dataset.

Most cells in in Figure 14 have small positive widths, representing weak separation between clusters in the 416B dataset. This may be symptomatic of over-clustering where clusters that are clearly defined on oncogene induction status are further split into subsets that are less well separated. The silhouette width can be used to gauge the optimal parameter values (e.g., cut height, number of clusters) that maximize the separation between clusters. For example, we could vary the cut height or splitting depth in cutreeDynamic to maximize the average silhouette width across all cells. Nonetheless, we will proceed with the current clustering scheme in my.clusters, which provides reasonable partitions for further characterization of heterogeneity.

Comments from Aaron:

• An alternative clustering strategy is to use a matrix of distances derived from correlations (e.g., as in quickCluster). This is more robust to noise and normalization errors, but is also less sensitive to subtle changes in the expression profiles.
• Both Ward’s criterion and complete linkage yield spherical, compact clusters. In particular, complete linkage favours the formation of clusters with the same diameter. This may be desirable in some cases but is less appropriate when subpopulations differ in their variance. Thus, we typically use Ward’s criterion for our initial clustering. Of course, it is simple (and recommended) to try other approaches provided that some assessment is performed, e.g., using the silhouette width.

11.2 Detecting marker genes between clusters

Once putative subpopulations are identified by clustering, we can identify marker genes for each cluster using the findMarkers function. This fits a linear model to the log-expression values for each gene using limma (Ritchie et al. 2015). The aim is to test for DE in each cluster compared to the others while blocking on uninteresting factors such as the plate of origin in design. The top DE genes are likely to be good candidate markers as they can effectively distinguish between cells in different clusters.

markers <- findMarkers(sce, my.clusters, block=sce$Plate)

For each cluster, the DE results of the relevant comparisons are consolidated into a single output table. This allows a set of marker genes to be easily defined by taking the top DE genes from each pairwise comparison between clusters. For example, to construct a marker set for cluster 1 from the top 10 genes of each comparison, one would filter marker.set to retain rows with Top less than or equal to 10. Other statistics are also reported for each gene, including the adjusted p-values (see below) and the log-fold changes relative to every other cluster.

marker.set <- markers[["1"]]
head(marker.set, 10)

## DataFrame with 10 rows and 6 columns
##             Top                  FDR           logFC.2           logFC.3
##       <integer>            <numeric>         <numeric>         <numeric>
## Aurkb         1  5.7638412198846e-33 -7.38736272933879 -6.75497329818331
## Tk1           1 9.61602859914994e-29 -4.88938260194308  -7.6726728600925
## Cdca8         1  9.3336100611373e-23 -6.95561973369242 -5.26318440208277
## Myh11         1 7.72591419170216e-22  4.40782364901204   4.3664017090546
## Ccna2         2 4.19565578321792e-32  -7.4070487345862 -7.23242529096501
## Rrm2          2 2.30486427788651e-26 -5.47876989143603 -7.96605564594272
## Cks1b         2 2.68544148101752e-18 -6.78334738720281   -6.020564371456
## Pirb          2 1.36988637558453e-15  5.21806533636566  5.18529493496878
## Ube2c         3 6.56635312984242e-28 -7.84909846487951 -4.30861252389314
## Pclaf         3 2.34916599505947e-26 -5.63808422406845 -7.67117998682273
##                 logFC.4             logFC.5
##               <numeric>           <numeric>
## Aurkb  -2.3013261083864   -6.41735160332462
## Tk1   -3.86403644009469   -4.24172385898634
## Cdca8 -2.51714896902757   -7.26824410188525
## Myh11  4.40568678169596     0.9387643805397
## Ccna2 -2.78261375473849   -7.31965669537105
## Rrm2  -3.47077716641592   -4.95579772214588
## Cks1b -4.60349671465141   -6.40480503325219
## Pirb   5.84975802713357 -0.0110358172874627
## Ube2c -2.10642020313117   -6.67791590516897
## Pclaf -2.81249908761293    -5.2901842158707

We save the list of candidate marker genes for further examination.

write.table(marker.set, file="416B_marker_1.tsv", sep="\t", 
    quote=FALSE, row.names=FALSE)

We visualize the expression profiles of the top candidates to verify that the DE signature is robust (Figure 15). Most of the top markers have strong and consistent up- or downregulation in cells of cluster 1 compared to some or all of the other clusters. A cursory examination of the heatmap indicates that cluster 1 contains oncogene-induced cells with strong downregulation of DNA replication and cell cycle genes. This is consistent with the potential induction of senescence as an anti-tumorigenic response (Wajapeyee et al. 2010). A more comprehensive investigation of the function of these markers can be performed with gene set enrichment analyses, e.g., using kegga or goana from limma.

top.markers <- rownames(marker.set)[marker.set$Top <= 10]
plotHeatmap(sce, features=top.markers, columns=order(sce$cluster), 
    colour_columns_by=c("cluster", "Plate", "Oncogene"),
    cluster_cols=FALSE, center=TRUE, symmetric=TRUE, zlim=c(-5, 5)) 

Figure 15: Heatmap of mean-centred and normalized log-expression values for the top set of markers for cluster 1 in the 416B dataset
Column colours represent the cluster to which each cell is assigned, the plate of origin or the oncogene induction status of each cell, as indicated by the legend.

Many of the markers in Figure 15 are not uniquely up- or downregulated in the chosen cluster. Testing for unique DE tends to be too stringent as it overlooks important genes that are expressed in two or more clusters. For example, in a mixed population of CD4⁺-only, CD8⁺-only, double-positive and double-negative T cells, neither Cd4 or Cd8 would be detected as subpopulation-specific markers because each gene is expressed in two subpopulations. With our approach, both of these genes will be picked up as candidate markers as they will be DE between at least one pair of subpopulations. A combination of markers can then be chosen to characterize a subpopulation, which is more flexible than trying to find uniquely DE genes.

We strongly recommend selecting some markers for use in validation studies with an independent replicate population of cells. The aim is to identify a corresponding subset of cells that express the upregulated markers and do not express the downregulated markers. Ideally, a different technique for quantifying expression would also be used during validation, e.g., fluorescent in situ hybridisation or quantitative PCR. This confirms that the subpopulation genuinely exists and is not an artifact of scRNA-seq or the computational analysis.

Comments from Aaron:

• By setting direction="up", findMarkers will only return genes that are upregulated in each cluster compared to the others. This is convenient in highly heterogeneous populations to focus on genes that can immediately identify each cluster. While lack of expression may also be informative, it is less useful for positive identification.
• findMarkers can also be directed to find genes that are DE between the chosen cluster and all other clusters. This should be done by setting pval.type="all", which defines the p-value for each gene as the maximum value across all pairwise comparisons involving the chosen cluster. Combined with direction="up", this can be used to identify unique markers for each cluster. However, this is sensitive to overclustering, as unique marker genes will no longer exist if a cluster is split into two smaller subclusters.
• It must be stressed that the (adjusted) p-values computed here cannot be properly interpreted as measures of significance. This is because the clusters have been empirically identified from the data. limma does not account for the uncertainty of clustering, which means that the p-values are much lower than they should be. This is not a concern in other analyses where the groups are pre-defined.
• The overlapExprs function may also be useful here, to prioritize candidates where there is clear separation between the distributions of expression values of different clusters. This differs from findMarkers, which is primarily concerned with the log-fold changes in average expression between clusters.