Counts Per Million (CPM)

CPM transforms raw read counts by dividing each gene's count by the total mapped reads in the sample and multiplying by one million. This accounts for varying library sizes between samples, where one sample may have 20 million reads and another 50 million. Without this correction, a gene with 100 reads would appear 2.5x more expressed in the deeper sample purely due to technical bias. CPM places all samples on a comparable scale.

The calculation is straightforward:

CPM = (Gene Count / Total Mapped Reads) * 10^6

• Gene Count: Raw number of reads mapping to a gene
• Total Mapped Reads: Library size for that sample
• 10^6: Scaling factor for interpretability

A CPM of 1 means that for every million reads sequenced, one read mapped to that gene. This linear scaling preserves the relative proportions of counts within a sample.

CPM is the standard metric for defining expressed vs. unexpressed genes. A common threshold is a CPM > 1 in at least n samples (where n is the smallest group size). Genes below this threshold are considered noise and removed before differential expression testing. This filtering reduces the multiple testing burden and improves statistical power by eliminating genes with insufficient data for reliable dispersion estimation.

CPM does not account for gene length. A 5kb gene and a 1kb gene expressed at the same biological level will produce different raw counts because longer transcripts generate more fragments. Consequently, CPM values cannot be directly compared between different genes within the same sample. For within-sample comparisons, use Transcripts Per Million (TPM) or Reads Per Kilobase Million (RPKM). CPM is valid only for comparing the same gene across samples.

CPM is the input to more sophisticated normalization methods like the Trimmed Mean of M-values (TMM) used in edgeR. The TMM algorithm:

• Calculates CPM for all genes
• Trims extreme log-ratios and high-expression genes
• Computes a weighted mean of the remaining M-values
• Derives sample-specific scaling factors

These factors are then applied to the raw library sizes to produce effective library sizes for downstream analysis.

A typical RNA-seq workflow positions CPM as the first normalization step:

1. Raw counts from alignment/quantification
2. CPM calculation for initial exploration
3. Low-expression filtering using CPM thresholds
4. TMM/RLE normalization for effective library size
5. Differential expression with DESeq2/edgeR

CPM is also used to generate log-CPM values for visualization (e.g., heatmaps, PCA plots) after adding a small prior count to avoid log(0).

An alternative normalization unit that addresses a key limitation of CPM. While CPM only corrects for sequencing depth, TPM first normalizes for gene length and then for depth. This produces a metric where the sum of all TPMs in a sample equals one million, allowing for direct comparison of transcript proportions across samples. For differential expression analysis, TPM is generally preferred over CPM because it accounts for the fact that longer genes generate more reads.

The median of ratios method used by DESeq2 is a more sophisticated approach than CPM. It computes a size factor for each sample by taking the median ratio of each gene's count to its geometric mean across all samples. This method is robust to outlier genes and compositional biases, making it the standard for differential expression testing. CPM is often used as a preliminary filtering metric before applying DESeq2's normalization.

The normalization method implemented in edgeR, TMM calculates scale factors by computing a weighted trimmed mean of log expression ratios between samples. It trims away genes with extreme expression and high variability before estimating the normalization factor. Like DESeq2's method, TMM is more robust than CPM for between-sample normalization, as it accounts for the fact that a minority of highly expressed genes can dominate total read counts.

The voom (variance modeling at the observational level) method transforms raw count data into log-counts per million (logCPM) with associated precision weights. This bridges the gap between RNA-seq count data and the limma linear modeling framework originally designed for microarrays. The transformation estimates the mean-variance relationship of the log-counts, allowing established linear modeling tools to be applied to sequencing data with proper statistical rigor.

CPM normalization does not correct for batch effects—systematic non-biological variation introduced by processing samples in different groups, on different days, or by different technicians. Tools like ComBat-seq use negative binomial regression to adjust for known batch covariates while preserving count data properties. Failing to correct for batch effects can lead to spurious differential expression calls, even when using properly normalized data.

In single-cell RNA-seq analysis, CPM is often calculated after pseudobulk aggregation—summing counts from individual cells grouped by sample and cell type. This creates synthetic bulk profiles that can be analyzed with established tools like DESeq2 and edgeR. Pseudobulk methods avoid the inflated false positive rates of single-cell-level differential testing while preserving the biological replicates necessary for valid statistical inference.