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Rare-Variant Data and Inference · Tutorial 404 of 989

Sequencing Errors That Mimic Rare Variants

Learn to distinguish evidence for a true rare allele from error, contamination, or PCR amplification, and to interpret replicate results cautiously.

Intermediate 12 min read

What You'll Learn

  • Model alternate reads expected from a specified base-calling error rate
  • Interpret an error-model tail probability without treating it as the probability that a call is false
  • Recognize how contaminating DNA can produce low-frequency alleles
  • Use molecule families and read counts to identify PCR-driven inflation
  • Compare independent preparations while accounting for sampling variability

Why a Few Alternate Reads Need an Explanation

At a rare-variant site, even a small number of reads carrying an alternate base can look important. But a small alternate-read count can arise when the true DNA carries the reference base: base-calling mistakes may substitute the alternate base, contaminating DNA may contribute it, or PCR may amplify one error or one molecule into many reads. These mechanisms matter because many rare-variant calls are supported by only a few observations, and technical artifacts can therefore resemble genuine low-frequency alleles.

The key is to ask what the observations represent. A read is a sequenced output, not necessarily an independent DNA molecule. Several reads can descend from the same original molecule, especially after PCR. Evidence is stronger when alternate observations occur on multiple independent molecules and persist in separately prepared material, and weaker when they show a pattern expected from a specific technical mechanism.

Definition: A sequencing artifact is a technical observation that resembles a variant but does not reflect the target DNA sequence in the sample being studied. A base-calling error is an incorrectly assigned base in a read; contamination is unintended DNA from another source in the sample or library; and a PCR artifact is a misleading signal produced or amplified during polymerase chain reaction. These mechanisms can coexist.

Base-Calling Errors as a Probability Model

Suppose the true sequence at a site is the reference base. Let \(q\) be the probability that one read from a distinct, independently sampled original DNA molecule is called as the particular alternate base. If there are \(n\) such reads, and each has the same error probability \(q\) independently of the others, the number of alternate calls \(X\) follows a binomial model:

$$ X\sim\operatorname{Binomial}(n,q), \qquad P(X=j)={n\choose j}q^j(1-q)^{n-j}. $$

This is an error-only model: it assumes the DNA is truly reference at the site and that the specified error probability applies to each observation. In practice, \(q\) should represent the chance of a call to this particular alternate base, not automatically the total probability of any mismatched base. It may depend on the base substitution, sequence context, read quality, and sequencing process. If reads are PCR duplicates, errors are correlated, or error rates differ across reads, the simple binomial model may not be adequate.

Worked Example: Four Alternate Reads Under an Error Model

In a hypothetical sample, 40 independent original molecules are read at a site believed to be reference. Suppose the estimated probability that any one molecule is called as this specific alternate base is \(q=0.005\). Four alternate calls are observed. How surprising is that count under the error-only model?

Check the model. The calculation assumes a true reference genotype at the site, a common per-observation alternate-call probability of 0.005, and independence across the 40 molecules. Here, “independent molecules” is essential: 40 reads copied from a much smaller number of PCR templates would not satisfy the assumption merely because there are 40 read records.

Under the model, \(X\sim\operatorname{Binomial}(40,0.005)\). The relevant probability is the chance of four or more alternate calls:

$$ P(X\ge 4)=\sum_{j=4}^{40}{40\choose j}(0.005)^j(0.995)^{40-j} \approx 4.947\times 10^{-5}. $$

Thus, if the stated error-only model were correct, the probability of at least four alternate calls is about 0.00004947, or 0.004947%. This is a small tail probability under that model, but it is not the probability that the call is false. The model omits other explanations, such as contamination, and its conclusion depends on the assumed error rate and independence.

Read-level patterns help assess whether the assumed model is plausible. For example, alternate calls concentrated in low-quality reads, at a particular read position, or on only one sequencing orientation can be consistent with technical error. Support distributed across high-quality reads and independent molecules is more reassuring, though it does not by itself prove that the allele is real. A striking tail probability from an overly optimistic error model should not be mistaken for strong evidence if that model fails to represent the data-generation process.

Contamination Can Introduce Genuine Alternate Bases

Contamination differs from a base-calling error: the alternate base may be correctly read, but it comes from DNA that is not the intended sample. A small contribution from another individual can produce a low alternate fraction at sites where that source carries an allele absent from the intended sample. A useful first calculation relates the contaminating fraction to the expected alternate fraction.

For example, suppose a fraction \(c\) of DNA molecules comes from a contaminating donor who is heterozygous at a site, while the intended sample is reference homozygous. If the DNA molecules contribute equally and there is no allele-specific amplification, the donor contributes half alternate-bearing molecules. The expected alternate fraction is therefore \(c/2\). This simple relationship is conditional on those assumptions; other donor genotypes or unequal amplification give different expectations.

Worked Example: A Low-Frequency Allele From Contaminating DNA

In a hypothetical sequencing run, the intended sample is believed to be reference homozygous at a site. A possible contaminating donor is heterozygous there. Suppose the donor contributes 2% of the DNA molecules, and 200 independent molecules are observed. The sample has two alternate molecules.

Check the assumptions. Assume the contamination fraction is a fraction of molecules, the donor is truly heterozygous, and the two donor alleles contribute equally. Also assume there is no allele-specific amplification. Under these conditions, the expected alternate fraction from contamination is \(0.02/2=0.01\).

The expected alternate count is:

$$ 200(0.01)=2 \text{ alternate molecules}. $$

The observed count, two of 200, is exactly the count expected on average under this contamination scenario. It is therefore not, by itself, evidence that the intended sample carries the variant. A practical diagnostic is to ask whether other alleles known to be present in the suspected donor also appear at compatible low fractions in the sample. Evidence across multiple donor-informative sites is more informative than one matching site, although it still requires attention to sampling and laboratory records.

Contamination can be introduced at different stages, so comparisons among samples and controls processed together can be informative. A low-frequency allele in a sample that also appears in a negative control, or at a similar fraction in several samples sharing a likely source, raises concern. Conversely, not seeing an allele in a control does not guarantee that the sample is uncontaminated: the contaminant may be sparse, and its alleles may not be observed at every site.

PCR Can Inflate the Apparent Number of Supporting Reads

PCR produces many copies from a limited set of starting molecules. If an error occurs during amplification, copies descended from the error-containing product can make the erroneous base appear repeatedly. Even without a new error, many reads can arise from one original molecule. Consequently, the raw alternate-read fraction can differ substantially from the fraction among distinct starting molecules.

Molecular identifiers, when used and reliably assigned before amplification, can help group reads by their likely original molecule. They do not make every family infallible: an error early in amplification can dominate a family, and errors during identifier assignment or grouping can also mislead. The useful question is not simply whether many reads agree, but whether independent molecules support the allele and whether the family-level evidence is coherent.

Worked Example: Many Reads From One Alternate Molecule Family

In a hypothetical library, 48 reads cover a site. Eighteen carry the alternate base and 30 carry the reference base. After grouping by molecular identifier, all 18 alternate reads belong to one family; the reference reads belong to ten other families, with three reads in each. A separately prepared library has zero alternate families among 12 observed molecules.

Check what is counted. Assume the identifiers correctly group descendants of original molecules. The raw read-level alternate fraction is:

$$ \frac{18}{48}=0.375=37.5\%. $$

But the family-level fraction is:

$$ \frac{1}{1+10}=\frac{1}{11}\approx 0.0909=9.09\%. $$

The 18 alternate reads are not 18 independent confirmations: they represent one observed molecule family. This pattern is consistent with read-count inflation by amplification, but it does not establish that the one alternate molecule is erroneous. In the independent library, if the true molecule-level alternate fraction were \(1/11\), the probability of observing zero alternate molecules in 12 is \((10/11)^{12}\approx 0.318\). Thus, this replicate result alone would not be surprising under that low fraction and does not rule out a genuine low-level allele.

If the intended interpretation were a germline heterozygous genotype with equal sampling of the two alleles, a family fraction of 1/11 would be far from the expected one-half and would warrant investigation. Allelic imbalance, low input, or other sampling effects could also matter. The appropriate conclusion is that the read count exaggerates the number of independent observations and the call needs further evidence, not that PCR has been proven to create the alternate base.

Replicates: What They Can and Cannot Establish

A replicate is most useful when it is genuinely independent for the technical question being asked. Resequencing the same amplified library can check some sequencing-stage behavior, but it does not independently test an error introduced before or during that library’s amplification. Preparing a new library from a separate aliquot tests more of the process; an independent extraction can test still earlier steps. The design should therefore be stated before interpreting agreement or disagreement.

Replicate comparisons also depend on the biological model. A germline heterozygote, a low-level mosaic allele, and a contaminating allele imply different expected fractions. A variant absent from one replicate may be inconsistent with a well-sampled germline heterozygote yet plausible when the expected fraction is low and the number of independent molecules is small.

Worked Example: A Discordant Independent Replicate

Two hypothetical libraries are prepared independently from separate sample aliquots. Each yields 60 independent molecules at a site. The first has eight alternate molecules and the second has none. Consider whether the observations fit a germline heterozygote model, assuming equal allele sampling and no allele-specific loss.

Check the assumptions. Under this specified model, each independent molecule has probability \(0.5\) of carrying the alternate allele. For the second library, the probability of zero alternate molecules is:

$$ P(X=0)={60\choose 0}(0.5)^0(0.5)^{60} =2^{-60}\approx 8.674\times 10^{-19}. $$

Zero of 60 is extraordinarily unlikely under the stated equal-sampling heterozygote model. The discordance therefore argues against interpreting these observations as a straightforward, well-sampled germline heterozygote. It does not identify the cause: possibilities include an artifact in the first preparation, allele dropout, or a biological state with a lower alternate fraction than a conventional germline heterozygote. If the true fraction were low, zero observations could be more plausible. Replicate discordance is diagnostic evidence to investigate, not a standalone label for the mechanism.

A Practical Diagnostic Sequence

A disciplined review separates three questions: are the reads technically credible, are the observations independent, and does the signal recur in material that was prepared independently? The sequence below keeps those questions distinct.

1
Specify the claim and the error model.
State whether the claim concerns a germline genotype, a low-level allele, or another target. If using a binomial error calculation, define the specific alternate-call probability, the number of independent observations, and the assumptions that justify them.
2
Inspect read-level support.
Review base-call quality and whether alternate observations are concentrated in particular read positions or orientations. Treat these as clues about error, not as individually decisive tests.
3
Count independent molecules where possible.
Compare raw alternate reads with molecule-family support. A large read count from one family is not equivalent to the same count spread across independent molecules.
4
Compare appropriate controls and replicates.
Check whether plausible donor alleles appear in the sample, and whether the call recurs after an independently prepared library or extraction. Interpret a negative replicate in light of the expected allele fraction and the number of molecules examined.

Common Mistake and Why This Matters

Common mistake: “Four alternate reads have a very small probability under the sequencing-error model, so the variant must be real.” The reasoning overlooks the model’s conditions. The tail probability only describes alternate calls under the particular assumed error rate, independence, and true-reference null. It does not account for contamination or PCR dependence, and it is not the probability that the call is false.

Correction: Treat the error-model calculation as one diagnostic component. Ask whether its assumptions fit the observations, determine how many independent molecules support the allele, and compare controls and independent preparations. A low-frequency call can be technically suspicious even when a simple error-only probability is small; conversely, one negative replicate does not automatically disprove an allele when few molecules were sampled.

Reliable distinction among artifacts matters because false rare-variant calls can distort interpretation and subsequent analyses. The goal is not to declare every low-count observation false, but to match the strength of the conclusion to the evidence: read quality, molecular independence, plausible contaminant patterns, and reproducibility all contribute. These checks address base-calling, contamination, and PCR; other technical explanations require their own diagnostics.

Check Your Understanding

Answer each question by stating the relevant model or assumption as well as your conclusion.

  1. Under what assumptions does the number of alternate calls follow a binomial distribution with parameters \(n\) and \(q\)?
  2. Why does a small error-model tail probability not equal the probability that a rare-variant call is false?
  3. A heterozygous contaminating donor contributes 4% of DNA molecules to a reference-homozygous sample. Under equal allele contribution, what alternate fraction is expected from that donor at the site?
  4. Why should 20 alternate reads from one molecule family not be treated as 20 independent observations?
  5. What does a negative independent replicate tell you, and why does its interpretation depend on the expected allele fraction and molecule count?
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