Differential Expression from Counts: Dispersion, Fit and Shrinkage
Sequencing gives counts, not measurements, and counts carry a mean-variance relationship that a normal model gets wrong. This stop fits a count model, borrows information across genes to estimate dispersion, and reads the result honestly.
What a learner can do afterwards
- Explain why read counts need a negative binomial rather than a normal or Poisson model
- Say what library-size normalisation corrects and what composition effects it cannot fix
- Interpret shrunken fold changes and explain why low-count genes move the most
1 · Read
You treat sequencing output as counts, not measurements. Two samples differ in total reads, and replicates vary far more than coin flip sampling predicts. A normal model gets this wrong, and a Poisson model underfits the extra variance.
You scale counts before you compare anything. A sample sequenced twice as deeply shows roughly twice the counts for every gene, so size factors rescale using the bulk of moderately expressed genes. But scaling has limits: a few huge transcripts can distort every share, and then the constant majority assumption breaks. Diagnostic plots show when count distributions warp after scaling; suspect composition effects and distrust comparisons until the failure is fixed.
You see a tenfold rise built from three reads versus zero and feel excited. Then you check the counts and the uncertainty, and the excitement fades. The pipeline models counts with a negative binomial, borrows strength across genes to estimate dispersion, and shrinks your flimsy fold change toward zero.
You read shrunken fold changes as conservative statements of what the data support. Strongly expressed genes barely move, while low count genes move the most because their raw estimates carry the least information. A shrunken value near zero with wide uncertainty means no trustworthy evidence of change.
You scale for depth, you model counts with a negative binomial plus borrowed dispersion, and you trust shrunken changes over raw ratios.
More to read
16.1 Regulation of Gene Expression
Cells regulate genes at every step from chromatin packing to protein breakdown, but transcription control dominates. Transcription factors bind enhancers and promoters to switch genes on or off in each cell type. Measuring those activity differences across conditions is the goal of differential expression analysis. Older microarrays measured expression through probe hybridization, while RNA sequencing counts the molecules directly. Counts bring statistical headaches. Two samples differ in total reads, and biological replicates vary far more than coin flip sampling predicts, so honest analysis needs models built for noisy count data.
17.1 Biotechnology
Sequencing instruments count fragments, and those counts depend on depth as well as biology. A sample sequenced twice as deeply shows roughly twice the counts for every gene, so raw counts must be scaled before any comparison. Size factor normalisation performs this scaling using the bulk of moderately expressed genes. Scaling has limits. If one condition switches on a handful of extremely abundant transcripts, they consume a large share of reads and depress everything else. Standard size factors assume most genes stay constant, and that assumption breaks under massive compositional shifts. Diagnostic plots of count distributions catch the failure before it corrupts the results.
16.7 Cancer and Gene Regulation
Cancer shows why careful expression analysis matters. Tumours misregulate growth genes, silence repair genes, and reactivate programs that healthy adult cells keep shut. A naive fold change on low counts can scream tenfold up from three reads versus zero, which is pure noise dressed as discovery. Modern pipelines therefore model counts with a negative binomial, estimate per gene dispersion by borrowing strength across genes, and shrink fold changes toward zero. Strongly expressed genes barely move, while flimsy low count estimates collapse. The published number is then a conservative statement of what the data actually support.
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2 · Watch
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Where it sits
Learn first
Nothing; this is a starting point.
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.