The Molecule That Was Counted Twice

Bioinformatics Insight Series · No. 15

The Molecule That Was Counted Twice

Unique molecular identifiers are supposed to turn PCR copies back into molecules. What they actually deliver depends on how you collapse them — and on how many molecules you had to begin with.

By Kanna Nandakumar, PhD · Zetobit LLC

A variant appears at 0.4% allele frequency in a cell-free DNA panel. Fourteen reads carry the alternate allele out of thirty-five hundred at the position. The question that decides whether this result reaches a report is deceptively simple: how many molecules does fourteen reads represent?

If the answer is fourteen, the call is plausible. If the answer is one — one original fragment amplified fourteen times during library prep — the call is an artifact wearing the costume of evidence. Read counts cannot distinguish these cases. This is the problem unique molecular identifiers were built to solve, and the reason nearly every low-frequency assay now carries them.

UMIs work by tagging each starting fragment with a random barcode before amplification.¹ All PCR descendants of that fragment inherit the same tag. Group the reads by tag, collapse each group into a single consensus, and the amplification is undone: you are back to counting molecules. The logic is clean, and when the assay is well built the gains are real — error rates drop by orders of magnitude, and variants below 1% become tractable.²

The trouble is that every step in that sentence hides an assumption, and the assumptions fail in ways that are quiet rather than loud.

Grouping is not free

Reads with the same tag are assumed to descend from the same molecule. Two things break this. First, tags collide: with a barcode space of N and a fragment count approaching N, distinct molecules will occasionally draw the same tag by chance, and if they also share a start coordinate they will be merged. This is why serious designs pair the UMI with the fragment's mapping position rather than trusting the tag alone.³ Second, tags mutate: sequencing and PCR errors within the barcode itself split one true family into several apparent ones, which inflates the molecule count and, more insidiously, strands single reads in families of size one where no consensus can be formed.

Tools handle this by clustering tags within an edit distance rather than requiring exact matches. UMI-tools' directional method — which merges a lower-count neighbor into a higher-count one when the counts differ by roughly the ratio expected from amplification — measurably outperforms naive exact-match grouping.³ The choice of grouping method is not a detail. It sets the denominator for every downstream frequency you report.

The comforting arithmetic of UMIs — tag, collapse, count — assumes the molecule you are trying to count made it into the library at all.

Collapse thresholds trade sensitivity for specificity, explicitly

Once families are formed, you must decide which ones you trust. A family of one read carries no internal evidence: there is nothing to compare it against, so an error in that read is indistinguishable from a true variant. A family of three or five, where every member agrees, is strong evidence — the same base error would have had to occur independently in each PCR product, which is vanishingly unlikely.

Duplex approaches push this further by tagging both strands of the original duplex separately and requiring agreement between the two strand families.⁴ Because most polymerase and oxidative damage artifacts affect one strand only, requiring both strands to agree removes an entire artifact class. The reported error rates are extraordinary — but so is the cost, because a duplex consensus requires that both strands of the same original molecule be sampled, sequenced, and survive filtering.

Every threshold you raise discards molecules. Requiring family size ≥3 might discard half your families. Requiring duplex support might discard eighty percent. Those discarded molecules were your sensitivity.

The threshold is a dial, not a setting. Raising the minimum family size suppresses more error but retains fewer molecules. The curves are schematic; their exact shape is assay-specific and must be measured on your own control material, not assumed. Note that the axis is not linear in cost: duplex consensus demands substantially deeper sequencing to reach the same molecule count.

The ceiling nobody set

Here is the part that surprises people. Suppose you sequence deeply enough that every original molecule is captured many times over, cluster tags perfectly, and require duplex support. Your assay is now nearly error-free. It still cannot detect a variant present on fewer than roughly one molecule.

Cell-free DNA is the sharpest illustration. In healthy plasma, a milliliter typically yields on the order of a few thousand genome equivalents, though the range across individuals and disease states is wide.⁵ At 0.01% allele frequency — one variant molecule per ten thousand genome equivalents — a few milliliters of plasma may contain only a handful of variant molecules, or none at all. When it is none, the failure is not detection; the molecule was never in the tube. Sampling is Poisson, and no amount of sequencing recovers a molecule that was never drawn.⁶

This is why input mass belongs on the same page of the validation report as sequencing depth, and why "we sequenced to 50,000×" answers a question nobody asked if the library was built from twelve nanograms. Depth buys you confidence about molecules you have. Input buys you the molecules.

What to check before you trust a number

When reviewing a UMI-based result — your own or a vendor's — four questions separate a real limit of detection from a marketed one. What was the DNA input mass, converted to genome equivalents? What fraction of input molecules survived conversion into the library and became recoverable families? What was the family-size distribution, not its mean? And was the grouping method position-aware and error-tolerant, or exact-match?

A pipeline that reports thirty-five hundred reads at a position and a pipeline that reports thirty-five hundred molecules at that position are making claims that differ by orders of magnitude in strength. The barcodes do not enforce the distinction. The analyst does.

References

1. Kivioja T, Vähärautio A, Karlsson K, et al. Counting absolute numbers of molecules using unique molecular identifiers. Nature Methods. 2011;9(1):72–74.
2. Newman AM, Lovejoy AF, Klass DM, et al. Integrated digital error suppression for improved detection of circulating tumor DNA. Nature Biotechnology. 2016;34(5):547–555.
3. Smith T, Heger A, Sudbery I. UMI-tools: modeling sequencing errors in Unique Molecular Identifiers to improve quantification accuracy. Genome Research. 2017;27(3):491–499.
4. Schmitt MW, Kennedy SR, Salk JJ, et al. Detection of ultra-rare mutations by next-generation sequencing. PNAS. 2012;109(36):14508–14513.
5. Meddeb R, Dache ZAA, Thezenas S, et al. Quantifying circulating cell-free DNA in humans. Scientific Reports. 2019;9:5220.
6. Kennedy SR, Schmitt MW, Fox EJ, et al. Detecting ultralow-frequency mutations by Duplex Sequencing. Nature Protocols. 2014;9(11):2586–2606.