RNA-Seq Volcano Plot: Differential Gene Expression

Experiment Design

Replicates per group (n) 4

log₂ fold-change cutoff 1.0

FDR threshold (BH α) 0.05

Show non-significant genes

Results (2,000 genes tested)

Upregulated

Downregulated

True positive rate

Observed FDR

BH-adjusted p cutoff

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Legend

Significant, upregulated Significant, downregulated Not significant True positive (ground truth)

How it works

Each of 2,000 simulated genes gets a baseline expression level and, for ~15% of them, a real ("ground truth") log₂ fold-change between a control and treatment condition. n independent replicate measurements per group are drawn with per-gene biological noise that shrinks as baseline expression rises — the same mean–variance trend real RNA-seq count data shows (low-count genes are noisier).

For every gene a Welch two-sample t-test is computed from the simulated replicates:

t = (x̄_B − x̄_A) / √(s²_A/n_A + s²_B/n_B)
ν  = (s²_A/n_A + s²_B/n_B)² / [ (s²_A/n_A)²/(n_A−1) + (s²_B/n_B)²/(n_B−1) ]
p  = I_{ν/(ν+t²)}(ν/2, 1/2)   (regularized incomplete beta — exact two-tailed t p-value)

Testing 2,000 genes at once means some will look "significant" by chance alone. The Benjamini-Hochberg procedure controls the false discovery rate: sort all p-values ascending, find the largest rank i where p₍ᵢ₎ ≤ (i/m)·α, and call every gene at or below that rank significant.

Replicates (n) — more replicates shrink the standard error, raising statistical power to detect real effects.
log₂FC cutoff — the volcano plot's horizontal "no small effects" gate; a gene must clear both the fold-change and FDR bars to be called.
FDR threshold (α) — the accepted rate of false discoveries among everything called significant; raising it calls more genes but admits more false positives.
True positive rate / observed FDR — because this simulation knows which genes were truly perturbed, it can score itself: TPR = correctly-called ÷ all true DE genes; observed FDR = false calls ÷ all calls.

Real pipelines (DESeq2, edgeR) go further — modelling counts as negative-binomial and sharing variance information across genes (empirical Bayes shrinkage) — but the fold-change / significance / multiple-testing logic visualised here is exactly the core of every RNA-seq differential expression analysis.

log₂ fold-change → −log₁₀(p) → mean expression →

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RNA-Seq Volcano Plot: Differential Gene Expression Analysis