• Motivation
• Biases
  • Depth bias
  • Composition bias
  • Mean-variance correlation
• Normalisation strategies
• Feature Selection

• We derive biological insights downstream by comparing cells against each other.

• But the UMI count differences makes it harder to compare cells.

• Why do total transcript molecules (UMI counts) detected between cells differ?

  • Biological:
    • Cell subtype differences - size and transcriptional activity, variation in gene expression
  • Technical: scRNA data is inherently noisy
    • Low mRNA content per cell
    • cell-to-cell differences in mRNA capture efficiency
    • Variable sequencing depth
    • PCR amplification efficiency

Normalization reduces technical differences so that differences between cells are not technical but biological, allowing meaningful comparison of expression profiles between cells.

Depth bias: Read differences between cells

Simple library size normalization accounts for the depth bias

• Few genes contribute to most read counts
• In this example, the total read counts are the same across the cells
• Gene 1 contributes 80% of reads in cell2, leaving other genes with fewer read counts.

• Library size normalization can not correct composition bias.

Mean and variance of raw counts for genes are correlated

More highly expressed genes tend to look more variable because larger numbers result in higher variance

A gene expressed at a low level tends to have a low variance across cells:

var(c(2,4,2,4,2,4,2,4)) = 1.14

A gene with the same proportional differences between cells, but expressed at a higher level will have higher variance:

var(c(20,40,20,40,20,40,20,40)) = 114.29

If we take the logs of the expression values, the variances are the same for both genes:

var(log(c(2,4,2,4,2,4,2,4))) = 0.14

var(log(c(20,40,20,40,20,40,20,40))) = 0.14

This “variable stabilising transformation” helps to remove the correlation between mean and variance

Normalization has two steps

1. Scaling
   • Calculate size factors or normalization factors that represents the relative depth bias in each cell
   • Scale the counts for each gene in each cell by dividing the raw counts with cell specific size factor
2. Transformation: Transform the data after scaling
   • Per million (e.g. CPM)
   • log2 (e.g. Deconvolution)
   • Pearson residuals (eg. sctransform)

CPM: convert raw counts to counts-per-million (CPM)

• for each cell
• by dividing counts by the library size then multiplying by 1.000.000.
• does not address compositional bias caused by highly expressed genes that are also differentially expressed between cells.

DESeq’s size factor

• For each gene, compute geometric mean across cells
• For each cell
  • compute for each gene the ratio of its expression to its geometric mean,
  • derive the cell’s size factor as the median ratio across genes.
• Not suitable for sparse scRNA-seq data as the geometric mean is computed on non-zero values only.

“This procedure omits the need for heuristic steps including pseudocount addition or log-transformation and improves common downstream analytical tasks such as variable gene selection, dimensional reduction, and differential expression. We named this method sctransform.”

Steps:

1. Estimate size factors using a regularized negative binomial regression model

2. Scale the counts by dividing the raw counts with the estimated size factors

3. Apply a variance stabilizing transformation to the scaled counts by calculating Pearson residuals from the negative binomial regression model

Pearson residual = (Observed value – Expected value) / √(Expected variance)

If a gene has exactly the expression level we’d expect based on the model → residual = 0

If a gene is expressed higher than expected → positive residual

If a gene is expressed lower than expected → negative residual

These residuals become our normalised values and they’re useful for several reasons:

• Standardized scale: All genes end up on the same scale regardless of their expression level

• Variance stabilization: Unlike raw counts, these residuals have roughly the same variance across all expression levels. The transformation ensures that genes with different expression levels can be compared fairly – the variance no longer depends on the mean expression level.

• Interpretation: Positive residuals mean higher-than-expected expression; negative means lower-than-expected. A residual of +2 means “this gene is expressed about 2 standard deviations higher than expected”.

Really Useful Website:

https://biostatsquid.com/sctransform-simple-explanation/

By default these are used for downstream dimensionality reduction and clustering (although in most cases you can change this)

• Which genes should we use for downstream analysis?

Select genes which capture biologically-meaningful variation, while reducing the number of genes which only contribute to technical noise

• We get different total counts for each cell due to technical factors (depth bias)
• A simplistic library size normalisation (e.g. CPM) removes a large part of this bias
• However, composition bias causes spurious differences between cells
• Early methods developed for bulk RNA-seq are not appropriate for sparse scRNA- seq data.
• The SCTransform method uses a regularized negative binomial regression model to estimate size factors, and applies a variance stabilizing transformation to the scaled counts.
• This accounts for both sequencing depth (library size) and gene-specific effects simultaneously.