Normalization (RNA-seq)

Reads/Fragments Per Kilobase per Million mapped reads. This method normalizes for both sequencing depth and gene length in a single step.

• RPKM: Used for single-end reads
• FPKM: Used for paired-end reads (counts fragments, not reads)
• Limitation: The sum of normalized counts differs between samples, making cross-sample comparisons problematic
• Origin: Pioneered by Mortazavi et al. (2008) for RNA-seq quantification

Transcripts Per Million normalizes for gene length first, then for sequencing depth, ensuring the sum of all TPMs in a sample equals one million.

• Order matters: Gene-length normalization precedes depth normalization
• Advantage over RPKM: TPM values represent the proportion of transcripts from a given gene, making them directly comparable across samples
• Interpretation: A TPM of 100 means 100 out of every 1 million RNA molecules originate from that gene
• Commonly used in expression atlases like GTEx and TCGA

A robust scaling normalization implemented in the edgeR package that estimates sample-specific scale factors rather than transforming raw counts.

• Mechanism: Computes a weighted trimmed mean of log expression ratios between each sample and a reference
• Trimming: Excludes the most highly expressed genes (30% by default) and those with extreme log-ratios (5% by default)
• Assumption: Most genes are not differentially expressed between conditions
• Output: Scale factors used as offsets in the negative binomial model, preserving raw integer counts

The default normalization method in DESeq2 that computes size factors using the median of gene-wise ratios relative to a pseudo-reference sample.

• Step 1: For each gene, compute the geometric mean across all samples to create a synthetic reference
• Step 2: For each sample, calculate the ratio of each gene's count to the reference
• Step 3: The sample's size factor is the median of all these ratios
• Robustness: The median is insensitive to outlier genes with extreme expression
• Integration: Size factors enter the generalized linear model as an offset term

A distribution-matching technique that forces all samples to have identical empirical distributions of expression values.

• Process: Ranks genes within each sample, then replaces each value with the mean of values at the same rank across all samples
• Effect: Eliminates any global differences in distribution shape, making samples directly comparable
• Use case: Common in microarray analysis and sometimes applied to RNA-seq after log-transformation
• Caution: Can introduce artifacts if the underlying distributions truly differ between biological conditions
• Implementation: Available in the limma package for transformed count data

A simple scaling method that divides each gene's count by the 75th percentile of its sample's non-zero count distribution.

• Rationale: The upper quartile is less influenced by a few extremely highly expressed genes than the total count
• Calculation: Size factor = upper quartile of counts (excluding zeros) for a sample
• Comparison: More robust than total-count normalization (CPM) but less sophisticated than TMM or DESeq2
• Origin: Proposed by Bullard et al. (2010) as an improvement over global scaling
• Use: Available in edgeR as method="upperquartile"

The total number of mapped reads per sample varies between runs. Normalization adjusts for this disparity because a sample with 20 million reads will naturally have higher raw counts than one with 10 million, even if biological expression is identical. Without correction, sequencing depth becomes a confounding variable, making samples incomparable and skewing differential expression results toward false positives in deeper-sequenced libraries.

Longer transcripts generate more RNA-seq fragments than shorter ones at the same expression level. This gene length bias is a technical artifact that must be corrected for within-sample comparisons (e.g., ranking genes by expression) using metrics like RPKM, FPKM, or TPM. However, for between-sample differential expression, methods like DESeq2 and edgeR use raw counts with offsets, as gene length cancels out when comparing the same gene across conditions.

A few highly expressed genes can consume a disproportionate fraction of the library, artificially suppressing counts for all other genes. Trimmed Mean of M-values (TMM) normalization in edgeR and Relative Log Expression (RLE) in DESeq2 address this by computing robust scaling factors. These methods assume most genes are not differentially expressed and exclude extreme outliers, providing a more accurate effective library size than raw total counts.

CPM is the simplest normalization: raw counts divided by total library size, multiplied by one million. While intuitive, it fails to correct for RNA composition bias and is sensitive to outliers. Its primary utility is as a filtering threshold—genes with very low CPM across all samples are removed before differential testing because they lack sufficient signal for statistical inference and only contribute noise to multiple testing correction.

TPM is a two-step normalization: first divide read counts by gene length (in kilobases) to get Reads Per Kilobase (RPK), then scale all RPK values by their sum per million. This ensures the sum of all TPMs in a sample equals one million, making transcript proportions directly comparable across samples. TPM is the gold standard for within-sample comparisons and visualization, but raw counts remain essential for statistical modeling.

VST is a mathematical transformation applied to normalized counts that renders the variance approximately independent of the mean. This is critical for exploratory techniques like Principal Component Analysis (PCA) and hierarchical clustering, which assume homoskedasticity. DESeq2 implements a blind VST that ignores experimental design, preventing the introduction of artificial clustering while making count data suitable for distance-based visualization methods.