Peak Calling and Enrichment Interpretation

What a Peak Call Represents

A peak caller identifies genomic intervals where reads from a ChIP-seq or ATAC-seq experiment are more concentrated than expected under a specified background model. A peak is therefore a statistical call about enrichment, not a direct measurement of biological importance, regulatory function, or causal effect. The result depends on the read data, the background estimate, the caller’s model, and the thresholds used.

As in the earlier material on input controls and background in ChIP-seq, an input or other suitable control can help represent nonspecific signal and technical background. A caller may compare a candidate interval with a control, with nearby genomic background, or with both. These choices matter: a region can appear enriched relative to one background definition and not another. ChIP-seq and ATAC-seq also differ in the biological signal they capture, but both require a procedure to distinguish local read enrichment from background.

Definition: A peak call is a genomic interval that passes a caller’s specified criteria for enrichment over its estimated background. A peak score is a numerical summary assigned by the caller; its meaning depends on the score definition. A threshold is a decision rule, such as requiring an adjusted p-value below a chosen level, that determines which candidate intervals are reported.

Most callers first represent mapped reads or fragments as counts or a local coverage pattern. They then estimate background, identify candidate enriched regions, calculate a score or significance measure, and apply thresholds. The details vary. Some callers are designed for sharp, localized enrichment; others accommodate broad enrichment extending over a larger region. There is no single peak score or threshold that has the same interpretation in every software package.

A Count-Based Model for Enrichment

A simple model makes the logic of a peak test explicit. Let \(Y_T\) and \(Y_C\) be the read counts in one genomic window for the target assay and its control. Let \(s_T\) and \(s_C\) represent their effective sequencing exposures, such as library-depth scaling factors. Under a simple independent Poisson model,

Y_T \sim \operatorname{Poisson}(s_T\lambda_T), \qquad Y_C \sim \operatorname{Poisson}(s_C\lambda_C).

Here \(\lambda_T\) and \(\lambda_C\) are the underlying per-exposure rates in the window. A basic null hypothesis is \(H_0:\lambda_T=\lambda_C\); enrichment corresponds to the one-sided alternative \(H_a:\lambda_T>\lambda_C\). This model assumes that, conditional on the rates and exposures, counts are independent and that the Poisson variance equals the mean. Real sequencing data can depart from these assumptions, so this model illustrates the test’s logic rather than describing every caller.

When the two rates are equal, conditioning on the total count removes the unknown common rate. The target count then has a binomial distribution whose success probability depends on the exposures.

Y_T \mid (Y_T+Y_C=m), H_0 \sim \operatorname{Binomial}\left(m,\frac{s_T}{s_T+s_C}\right).

For equal exposures, this probability is \(1/2\). If the target count is unusually large under this conditional null distribution, the window shows evidence of enrichment. In practice, callers may use more elaborate local backgrounds, adjust for control depth, model fragment properties, or account for different region shapes. A local background can be important because read density varies across the genome; comparing every window with one genome-wide average may be misleading.

Derivation: If \(Y_T\) and \(Y_C\) are independent Poisson counts with means \(s_T\lambda\) and \(s_C\lambda\) under \(H_0\), their joint probability at counts \(y_T,y_C\), conditional on their sum \(m\), is proportional to \((s_T\lambda)^{y_T}(s_C\lambda)^{y_C}/(y_T!y_C!)\). Since \(y_C=m-y_T\), the factors involving \(\lambda\) are constant across possible \(y_T\). Normalizing the remaining terms gives the binomial probability with success probability \(s_T/(s_T+s_C)\). Thus, an excess target count can be tested without estimating the shared rate for that window.

Worked Examples: Counts, Scores, and Region Width

Worked Example: Testing a Candidate Window

Suppose a hypothetical target library and control have equal effective exposure. In a 1-kilobase window, the target has 40 reads and the control has 10. Calculate the target-to-control enrichment ratio and the one-sided conditional p-value under the equal-rate null.

The observed count ratio is \(40/10=4.00\), so the target count is four times the control count in this window. Under \(H_0\), the total is \(m=40+10=50\), and the target count has a \(\operatorname{Binomial}(50,0.5)\) distribution. The one-sided p-value is

P(Y_T\geq 40\mid Y_T+Y_C=50,H_0) = \sum_{k=40}^{50}{50\choose k}(0.5)^{50} \approx 1.20\times 10^{-5}.

This is strong evidence against equal rates for this one window under the stated model. The ratio of 4.00 describes the observed enrichment magnitude; the p-value describes how unusual a count at least this large would be under the null. Neither calculation alone establishes that the region has a biological function. Because a genome-wide analysis tests many windows, a small raw p-value must also be assessed in the context of multiple testing.

Worked Example: Applying a Score Threshold

A hypothetical caller reports two candidate peaks. Peak A has \(p=10^{-8}\), \(q=0.002\), and fold enrichment 3.5. Peak B has \(p=10^{-6}\), \(q=0.08\), and fold enrichment 12. Suppose the analysis requires \(q<0.05\) and fold enrichment of at least 2. Which peaks pass?

Peak A’s transformed significance score, if the caller reports \(-\log_{10}(p)\), is \(-\log_{10}(10^{-8})=8\). Its adjusted value satisfies \(0.002<0.05\), and its fold enrichment satisfies \(3.5\geq2\), so it passes both criteria.

Peak B’s corresponding transformed score is \(-\log_{10}(10^{-6})=6\). Its fold enrichment passes because \(12\geq2\), but its adjusted value does not because \(0.08\not<0.05\). It therefore fails the combined rule. Its larger fold enrichment does not override the adjusted-significance requirement. These criteria are analysis choices, not universal biological cutoffs.

A q-value is an adjusted measure used when testing many candidates; it is not the probability that a particular peak is false. Under appropriate assumptions for the adjustment procedure, a threshold such as \(q<0.05\) is used to control the expected false discovery proportion among reported calls. The exact interpretation depends on the adjustment method and its assumptions.

Worked Example: A Broad Region With Modest Enrichment

Consider a hypothetical 10-kilobase region divided into ten 1-kilobase bins. Each bin has 24 target reads and 20 control reads, with equal exposure. The total counts are 240 and 200, giving a pooled ratio of \(240/200=1.20\). In an individual bin, the log count ratio is \(\log(24/20)=0.1823\), and a simple Poisson approximation gives its standard error as

SE\{\log(Y_T/Y_C)\} \approx \sqrt{\frac{1}{24}+\frac{1}{20}} =0.3028.

The individual-bin standardized contrast is \(0.1823/0.3028=0.602\), which is weak evidence in a single bin. If counts are pooled across the ten bins and treated as independent Poisson counts, the approximate standard error becomes

\sqrt{\frac{1}{240}+\frac{1}{200}}=0.09574, \qquad \frac{\log(1.20)}{0.09574} =\frac{0.1823}{0.09574} \approx 1.904.

The pooled contrast is more compelling than the contrast in any one bin because the modest elevation is consistent across the region. However, it is not automatically a reliable broad peak: neighboring bins may be dependent, the background may vary across the region, and a genome-wide adjustment may weaken the evidence. This example illustrates why region width and enrichment strength should be examined together rather than interpreting a long interval as strong simply because it covers many bases.

Interpreting Scores and Thresholds

Peak callers commonly report several kinds of quantities. Their names can be similar across tools even when their formulas differ, so interpretation should start with the software’s definition.

Quantity	What it summarizes	What it does not establish
Fold enrichment	Target signal relative to an estimated background, on a ratio scale	That the enrichment is statistically significant or biologically functional
p-value	Evidence against a specified null model for a candidate	The probability that the null is true, or the chance that the peak is false
Adjusted p-value or q-value	Evidence after accounting for a set of multiple tests, under a chosen procedure	A guarantee that each reported region is a true peak
Transformed score	A rescaling, such as \(-\log_{10}(p)\), of another quantity	A directly comparable score across callers or analyses unless definitions match

A threshold converts a continuous score into a reported set. A stringent adjusted-p-value threshold can reduce weak calls but may omit real, low-count enrichment. A permissive threshold can increase sensitivity while also admitting more background fluctuations. Fold-enrichment cutoffs add an effect-size requirement, but a fixed cutoff may not suit every assay, region type, or scientific aim.

The p-values of nearby windows are not generally independent: adjacent windows can share reads or reflect the same underlying region. Multiple-testing procedures differ in how they handle dependence, and the number of tested candidates can depend on the caller’s candidate-generation and windowing rules. Therefore, report the caller, its background and scoring choices, and the thresholds used rather than presenting a peak list as if it were independent of analysis settings.

Diagnosing Weak or Excessively Broad Peak Sets

A weak peak set may contain few calls, low enrichment ratios, or calls that barely pass the selected threshold. Possible explanations include genuinely sparse signal, limited read depth, an unsuitable background estimate, or an overly stringent rule. Conversely, a large set of low-score calls can reflect a permissive threshold or a background model that does not represent local variation. The peak list alone cannot distinguish these explanations.

Broad calls require particular care. Some chromatin signals genuinely extend over wide regions, while a caller can also produce an overly broad interval by joining nearby enriched segments across gaps or by using permissive boundaries. Inspect whether enrichment is coherent across the reported interval, whether boundaries depend strongly on merging settings, and whether the width is plausible for the assay and target. A long region with only a small average excess should not be described as a strong, sharply localized peak.

Check the score definition. Confirm whether a reported score is a raw p-value, adjusted value, fold change, or transformed quantity.
Compare strength and significance. A large ratio can be uncertain when counts are sparse; a small ratio can be statistically detectable with abundant counts.
Inspect the background comparison. An inappropriate or poorly matched background can generate apparent enrichment or conceal it.
Assess sensitivity to thresholds and width settings. A peak set that changes dramatically under small changes may be unstable; the chosen settings should be justified in context.
Check assumptions and mapping limitations. Count dependence, overdispersion, and ambiguous read placement can make a simple count model unreliable.

These checks diagnose peak-call interpretation, not a substitute for a full sequencing-library quality assessment. Nor does a peak call by itself compare conditions or establish regulatory causation. Those are distinct questions that require methods suited to the relevant data and design.

Common Mistake

Common mistake: “This peak has the largest fold enrichment, so it is the strongest and most reliable call.” A large ratio can arise from a very small denominator and few total reads, making the estimate unstable. Conversely, a modest ratio supported by many observations may yield stronger statistical evidence. Correction: interpret enrichment magnitude, count support, background model, adjusted significance, and region width together. None of these alone is a complete measure of biological importance.

Check Your Understanding

Answer each question, then compare with the worked solutions below.

With equal target and control exposures, a window has 30 target reads and 20 control reads. What is its observed count ratio, and what is the target-count distribution under the equal-rate null conditional on the total?
A caller reports \(p=0.001\) and \(-\log_{10}(p)=3\). Explain what the transformed score means and name one conclusion it does not support.
A candidate has fold enrichment 8 but \(q=0.12\). Does it pass a rule requiring \(q<0.05\)? Why does its large fold enrichment not change the answer?
Give two possible reasons for a peak set to contain unusually broad regions, and one diagnostic for distinguishing a coherent broad signal from an over-merged call.
Why should a caller’s raw p-values not be interpreted as though each genomic window were an isolated, prespecified test?

Solutions. (1) The ratio is \(30/20=1.50\). The total is 50, so under equal exposures and the equal-rate null, the conditional target count follows \(\operatorname{Binomial}(50,0.5)\). (2) The score is \(-\log_{10}(0.001)=3\); it expresses the p-value on a transformed scale. It does not give the probability that the null is true or prove biological function. (3) No. Since \(0.12\not<0.05\), it fails the adjusted-value requirement; the fold enrichment is a separate measure and cannot replace that rule. (4) Broad regions may reflect genuinely extended enrichment or permissive merging of nearby segments. Check whether enrichment is coherent across the interval and whether its width changes sharply when merging settings change. (5) Many genomic candidates are tested, and nearby windows can be dependent. Interpretation must account for multiple testing and the caller’s candidate-generation procedure rather than treating each raw p-value as the result of a single isolated test.