Seurat part 3 – Data normalization and PCA

Now that we have performed our initial Cell level QC, and removed potential outliers, we can go ahead and normalize the data. By default, Seurat implements a global-scaling normalization method “LogNormalize” that normalizes the gene expression measurements for each cell by the total expression, multiplies this by a scale factor (10,000 by default), and log-transforms the result.

pbmc <- NormalizeData(object = pbmc, normalization.method = "LogNormalize", 
    scale.factor = 10000)

Seurat calculates highly variable genes and focuses on these for downstream analysis. FindVariableGenes calculates the average expression and dispersion for each gene, places these genes into bins, and then calculates a z-score for dispersion within each bin. This helps control for the relationship between variability and average expression. This function is unchanged from (Macosko et al.), but new methods for variable gene expression identification are coming soon. We suggest that users set these parameters to mark visual outliers on the dispersion plot, but the exact parameter settings may vary based on the data type, heterogeneity in the sample, and normalization strategy. The parameters here identify ~2,000 variable genes, and represent typical parameter settings for UMI data that is normalized to a total of 1e4 molecules.

pbmc <- FindVariableGenes(object = pbmc, mean.function = ExpMean, dispersion.function = LogVMR, 
    x.low.cutoff = 0.0125, x.high.cutoff = 3, y.cutoff = 0.5)

length(x = pbmc@var.genes)

The single cell dataset likely contains ‘uninteresting’ sources of variation. This could include not only technical noise, but batch effects, or even biological sources of variation (cell cycle stage). As suggested in Buettner et al, NBT, 2015, regressing these signals out of the analysis can improve downstream dimensionality reduction and clustering. To mitigate the effect of these signals, Seurat constructs linear models to predict gene expression based on user-defined variables. The scaled z-scored residuals of these models are stored in the slot, and are used for dimensionality reduction and clustering.

We can regress out cell-cell variation in gene expression driven by batch (if applicable), cell alignment rate (as provided by Drop-seq tools for Drop-seq data), the number of detected molecules, and mitochondrial gene expression. For cycling cells, we can also learn a ‘cell-cycle’ score and regress this out as well. In this simple example here for post-mitotic blood cells, we regress on the number of detected molecules per cell as well as the percentage mitochondrial gene content.

Seurat v2.0 implements this regression as part of the data scaling process. This is achieved through the argument in ScaleData.

pbmc <- ScaleData(object = pbmc, = c("nUMI", "percent.mito"))

Next we perform PCA on the scaled data. By default, the genes in object@var.genes are used as input, but can be defined using pc.genes. We have typically found that running dimensionality reduction on highly variable genes can improve performance. However, with UMI data – particularly after regressing out technical variables, we often see that PCA returns similar (albeit slower) results when run on much larger subsets of genes, including the whole transcriptome.

Here we are printing the first 5 PCAs and the 5 representative genes in each PCA.

pbmc <- RunPCA(object = pbmc, pc.genes = pbmc@var.genes, do.print = TRUE, pcs.print = 1:5, 
    genes.print = 5)

Seurat provides several useful ways of visualizing both cells and genes that define the PCA, including PrintPCAVizPCAPCAPlot, and PCHeatmap

# Examine and visualize PCA results a few different ways
PrintPCA(object = pbmc, pcs.print = 1:5, genes.print = 5, use.full = FALSE)

VizPCA(object = pbmc, pcs.use = 1:2)
PCAPlot(object = pbmc, dim.1 = 1, dim.2 = 2)
# ProjectPCA scores each gene in the dataset (including genes not included
# in the PCA) based on their correlation with the calculated components.
# Though we don't use this further here, it can be used to identify markers
# that are strongly correlated with cellular heterogeneity, but may not have
# passed through variable gene selection.  The results of the projected PCA
# can be explored by setting use.full=T in the functions above
pbmc <- ProjectPCA(object = pbmc, do.print = FALSE)

In particular PCHeatmap allows for easy exploration of the primary sources of heterogeneity in a dataset, and can be useful when trying to decide which PCs to include for further downstream analyses. Both cells and genes are ordered according to their PCA scores. Setting cells.use to a number plots the ‘extreme’ cells on both ends of the spectrum, which dramatically speeds plotting for large datasets. Though clearly a supervised analysis, we find this to be a valuable tool for exploring correlated gene sets.

PCHeatmap(object = pbmc, pc.use = 1, cells.use = 500, do.balanced = TRUE, label.columns = FALSE)
PCHeatmap(object = pbmc, pc.use = 1:12, cells.use = 500, do.balanced = TRUE, 
    label.columns = FALSE, use.full = FALSE)

To overcome the extensive technical noise in any single gene for scRNA-seq data, Seurat clusters cells based on their PCA scores, with each PC essentially representing a ‘metagene’ that combines information across a correlated gene set. Determining how many PCs to include downstream is therefore an important step.

In Macosko et al, we implemented a resampling test inspired by the jackStraw procedure. We randomly permute a subset of the data (1% by default) and rerun PCA, constructing a ‘null distribution’ of gene scores, and repeat this procedure. We identify ‘significant’ PCs as those who have a strong enrichment of low p-value genes.

# NOTE: This process can take a long time for big datasets, comment out for
# expediency.  More approximate techniques such as those implemented in
# PCElbowPlot() can be used to reduce computation time
pbmc <- JackStraw(object = pbmc, num.replicate = 100, do.print = FALSE)

The JackStrawPlot function provides a visualization tool for comparing the distribution of p-values for each PC with a uniform distribution (dashed line). ‘Significant’ PCs will show a strong enrichment of genes with low p-values (solid curve above the dashed line). In this case it appears that PCs 1-10 are significant.

JackStrawPlot(object = pbmc, PCs = 1:12)

A more ad hoc method for determining which PCs to use is to look at a plot of the standard deviations of the principle components and draw your cutoff where there is a clear elbow in the graph. This can be done with PCElbowPlot. In this example, it looks like the elbow would fall around PC 9.

PCElbowPlot(object = pbmc)

PC selection – identifying the true dimensionality of a dataset – is an important step for Seurat, but can be challenging/uncertain for the user. We therefore suggest these three approaches to consider. The first is more supervised, exploring PCs to determine relevant sources of heterogeneity, and could be used in conjunction with GSEA for example. The second implements a statistical test based on a random null model, but is time-consuming for large datasets, and may not return a clear PC cutoff. The third is a heuristic that is commonly used, and can be calculated instantly. In this example, all three approaches yielded similar results, but we might have been justified in choosing anything between PC 7-10 as a cutoff. We followed the jackStraw here, admittedly buoyed by seeing the PCHeatmap returning interpretable signals (including canonical dendritic cell markers) throughout these PCs. Though the results are only subtly affected by small shifts in this cutoff, we strongly suggest to always explore the PCs you choose to include downstream.