1 A peak is evidence, not yet a named concentration
Metabolomics studies small molecules; lipidomics concentrates on lipids and their structural diversity. Targeted assays measure a specified panel using a defined analytical method. Untargeted workflows discover and quantify features. In the liquid-chromatography/mass-spectrometry examples here, a feature is characterized by mass-to-charge ratio (m/z), retention time, and supporting spectra. Retention time records when a compound elutes from the column; m/z describes an ion, not a unique molecular identity.
One molecule can produce several features through isotopes, adducts, or fragments. An adduct is an ion formed by association with another species, such as a proton or sodium ion; these forms can have different m/z values for the same underlying molecule. Conversely, unresolved compounds can contribute to one signal. Counting feature rows differs from counting identified molecules. Other platforms, including NMR, need their own measurement description.
Keep a feature identifier separate from its candidate name and identification evidence. Report whether a match uses an authentic standard, spectral evidence, or a weaker annotation. The Metabolomics Standards Initiative paper makes identification and analytical reporting explicit. An attractive pathway name is not a substitute for that evidence.
For lipids, the reported structural resolution matters. In the LIPID MAPS shorthand hierarchy, PC identifies a lipid class and PC 34:1 gives a sum composition: total chain carbons and a double-bond-equivalent count at that reporting level. It does not specify individual chains or double-bond positions. PC 16:0_18:1 adds chain information; the underscore leaves their positions unspecified. Even chain-level evidence need not locate a double bond. Match the name’s resolution to the evidence. Across-study labels at sum-composition level need not identify one fully resolved molecule.
2 Separate concentration from response
In a local linear working model, let an analyte signal be
I_i=k_i C_i+b_i+\epsilon_i.
C_i is concentration; k_i represents response/recovery in that specimen and run; b_i is background; and \epsilon_i is residual error. A 50% larger response factor can create a 50% larger signal at unchanged concentration. This is a local working model over a usable range, not a guarantee of linear response everywhere.
The controls have different roles:
Control
What it helps assess
Blank
Background, carryover, and signals introduced by processing
Internal standard
Response/recovery relative to a known added substance; the addition stage determines which steps it tracks
Calibration series
The response–concentration relationship over a defined range and matrix
Repeated pooled QC
Drift and repeatability of a common material through the run
These controls add measurement information. They do not increase the number of independently sampled people. A pooled QC also does not reveal each person’s underlying concentration.
An isotope-labeled internal standard can track some common multiplicative effects when it behaves appropriately for the analyte. A class-level standard need not correct every lipid’s response equally. A calibration curve also has a domain: extrapolating below its quantification range is an additional assumption. Metabolite-reporting recommendations describe standards and documentation of analytical effects.
For a synthetic example, let concentration be 10 in both groups and the internal-standard concentration be 2. The response factors are 1 in group 0 and 1.5 in group 1, shared by the analyte and standard within each group. Predict the raw-signal contrast and the analyte-to-standard ratios before reading the calculation.
Ignoring background and error, the analyte and standard equations are I_i=k_iC_i and S_i=k_i^{\mathrm{std}}C_{\mathrm{std}}. Dividing gives
In the toy, the response factors match within each specimen, so their ratio is 1. Raw signals 10 and 15 become ratios 10/2=5 and 15/3=5. Multiplying by the standard concentration 2 recovers concentration 10. If the standard instead has response factor 1 in both groups, its signals are 2 and 2 and the ratios become 5 and 7.5: the artifact remains. A stable but non-unit response ratio needs calibration too.
Background prevents this simple cancellation unless it is adequately handled. A normalized peak area supports a concentration claim only after validating the response relationship, calibration, and usable range.
3 Run order can mimic biology
If all cases are injected after all controls, biological group and instrument drift can be confounded. Randomized or balanced acquisition and regular QC injections create information for distinguishing them. Technical correction after a fully confounded run cannot supply the unobserved comparison without additional assumptions.
This deterministic toy has no group effect on concentration. A monotone run effect creates a raw signal difference. A perfectly representative QC curve removes it by construction. This illustrates a requirement, not a recommended real-world drift algorithm.
Figure 1: A deliberately confounded acquisition order. Dots are specimen signals and crosses are exact synthetic QC signals. Dividing by the known QC trend cancels this multiplicative drift; the result relies on the same drift affecting QC and specimens.
The toy uses the exact factor \exp(0.015t) at injection position t, so division recovers 10 by construction. QC measurements provide additional reference information. Successful correction assumes their drift transfers to the biological specimens; a trend in pooled material alone does not uniquely determine the specimens’ technical trend.
A real QC fit is estimated. It needs coverage across run order, appropriate material, checks for feature-specific behavior, and assessment of fitting uncertainty. Interpolation between controls and extrapolation beyond the last control make different demands. Outcome-guided choices that maximize group separation undermine this diagnostic purpose. Preserve the fitted reference and processing version with the data.
4 Define absence, non-detection, and quantification limits
A recorded zero can encode a true absence, an integration failure, a value below detection, or a software placeholder. A detection limit concerns distinguishing signal from background under a specified criterion. A quantification limit concerns estimating an amount with acceptable performance under the method’s criterion. A signal can be detected yet fall outside the validated quantification range. Document flags, units, and limits rather than converting all such records into the same number.
For an analyte with missing values, choose the target explicitly: detection probability under the assay protocol; concentration in a specified population; or a mean measured response among detected specimens. These require different data and assumptions. For a known lower threshold, the unobserved concentration distribution is still not identified nonparametrically from detected values alone. See the censoring example in Proteomics: from measured evidence to an estimand and Missingness, selection, and the observed-data target.
5 From a feature table to an inferential target
For a positive calibrated concentration, define Y as its prespecified log2 representation. A difference of conditional means or a population-standardized contrast is a meaningful target when its units and population are specified. For a normalized peak feature, the corresponding target concerns that response representation. The statistical machinery may be shared while the biological interpretation differs.
A sum of lipid signals is not automatically a total molar concentration. If two lipids have response factors 1 and 10, moving a fixed total concentration of 2 from the first lipid to the second changes total signal from 2 to 20. The class total in molar units stays fixed. Overlapping annotations or several adducts can also double-count evidence.
A lipid-class target needs a membership rule, a quantity to sum, and compatible units. A pathway analysis also needs mapping uncertainty and the tested family recorded. Filtering weak signals changes that family; collapsing peaks after observing their group effects introduces selection. Narrow statistical intervals quantify sampling uncertainty for the defined feature; they do not resolve uncertain molecular identity.
Flexible nuisance regression can adjust a well-defined measured-outcome contrast for covariates under support and inference conditions. It cannot resolve unknown molecular identity, perfectly confounded acquisition, or nonidentified below-limit values. Name these measurement limitations separately from estimation uncertainty.
6 A practical audit
Retain specimen, person, extraction, plate, and injection IDs; feature keys and annotation confidence; standards, blanks, and QC positions; units and calibration range; detection/quantification flags; and each normalization or drift correction. Check group overlap across acquisition conditions. Plot missingness and QC behavior before testing. Then use Differential expression and abundance and Multiple testing when the tests are not independent for the prespecified feature family.
7 Exercises
The checkpoint is this assay specialization’s completion target. Additional practice is optional. Try the checkpoint before opening its hint or solution.
Checkpoint · MET-01 — Separate a molecular quantity from its assay response
Task type: Computation and diagnosis.
Both groups have concentration 10. Their response factors are 1 and 1.5. An internal standard at concentration 2 shares the factors. Calculate raw signals and ratios. Then explain what fails if the standard has factor 1 in both groups. State what PC 34:1 leaves unresolved and why all controls injected first is a design issue.
Ready to continue when: you can connect response correction, identification resolution, and acquisition design to the scope of a group contrast.
Transfer: Can a narrower confidence interval compensate for uncertain molecular identity?
Hint
Write the analyte and standard response equations separately before dividing.
Solution outline — open after trying
Raw signals are 10 and 15; shared-response standard signals are 2 and 3, giving ratios 5 and 5. With unmatched standard signals 2 and 2, the ratios become 5 and 7.5. The signal artifact remains. PC 34:1 reports a sum composition rather than complete chain/position structure. Confounded run order prevents a direct separation of group and drift without additional information or assumptions.
Additional practice (optional)
Add a nonzero background to the internal-standard example and identify when simple division fails.
Propose a balanced run order with blanks and QC samples; distinguish the independent biological denominator from injection count.
Define a lipid-class total on a calibrated molar scale and on an arbitrary signal scale. Explain why the targets differ.
---title: "Metabolomics and lipidomics: features, identities, and scales"subtitle: "From peak response to a defensible molecular comparison"guide-status: "Available"---**Before reading:** The [Understanding an omics dataset](understanding-omics-data.qmd) page, logarithms, and [Preprocessing and the quantity being estimated](preprocessing-and-estimands.qmd).## A peak is evidence, not yet a named concentrationMetabolomics studies small molecules; lipidomics concentrates on lipids and their structural diversity. Targeted assays measure a specified panel using a defined analytical method. Untargeted workflows discover and quantify features. In the liquid-chromatography/mass-spectrometry examples here, a feature is characterized by mass-to-charge ratio ($m/z$), retention time, and supporting spectra. Retention time records when a compound elutes from the column; $m/z$ describes an ion, not a unique molecular identity.One molecule can produce several features through isotopes, adducts, or fragments. An **adduct** is an ion formed by association with another species, such as a proton or sodium ion; these forms can have different $m/z$ values for the same underlying molecule. Conversely, unresolved compounds can contribute to one signal. Counting feature rows differs from counting identified molecules. Other platforms, including NMR, need their own measurement description.Keep a feature identifier separate from its candidate name and identification evidence. Report whether a match uses an authentic standard, spectral evidence, or a weaker annotation. The [Metabolomics Standards Initiative paper](https://doi.org/10.1007/s11306-007-0082-2) makes identification and analytical reporting explicit. An attractive pathway name is not a substitute for that evidence.For lipids, the reported structural resolution matters. In the [LIPID MAPS shorthand hierarchy](https://www.lipidmaps.org/databases/shorthand/overview), PC identifies a lipid class and PC 34:1 gives a sum composition: total chain carbons and a double-bond-equivalent count at that reporting level. It does not specify individual chains or double-bond positions. PC 16:0_18:1 adds chain information; the underscore leaves their positions unspecified. Even chain-level evidence need not locate a double bond. Match the name's resolution to the evidence. Across-study labels at sum-composition level need not identify one fully resolved molecule.## Separate concentration from responseIn a local linear working model, let an analyte signal be$$I_i=k_i C_i+b_i+\epsilon_i.$$$C_i$ is concentration; $k_i$ represents response/recovery in that specimen and run; $b_i$ is background; and $\epsilon_i$ is residual error. A 50% larger response factor can create a 50% larger signal at unchanged concentration. This is a local working model over a usable range, not a guarantee of linear response everywhere.The controls have different roles:::: {.table-responsive}| Control | What it helps assess ||---|---|| Blank | Background, carryover, and signals introduced by processing || Internal standard | Response/recovery relative to a known added substance; the addition stage determines which steps it tracks || Calibration series | The response–concentration relationship over a defined range and matrix || Repeated pooled QC | Drift and repeatability of a common material through the run |:::These controls add measurement information. They do not increase the number of independently sampled people. A pooled QC also does not reveal each person's underlying concentration.An isotope-labeled internal standard can track some common multiplicative effects when it behaves appropriately for the analyte. A class-level standard need not correct every lipid's response equally. A calibration curve also has a domain: extrapolating below its quantification range is an additional assumption. [Metabolite-reporting recommendations](https://pmc.ncbi.nlm.nih.gov/articles/PMC3226225/) describe standards and documentation of analytical effects.<span id="fig-metabolite-response"></span>For a **synthetic** example, let concentration be 10 in both groups and the internal-standard concentration be 2. The response factors are 1 in group 0 and 1.5 in group 1, shared by the analyte and standard within each group. Predict the raw-signal contrast and the analyte-to-standard ratios before reading the calculation.Ignoring background and error, the analyte and standard equations are $I_i=k_iC_i$ and $S_i=k_i^{\mathrm{std}}C_{\mathrm{std}}$. Dividing gives$$\frac{I_i}{S_i}=\frac{k_i}{k_i^{\mathrm{std}}}\frac{C_i}{C_{\mathrm{std}}}.$$In the toy, the response factors match within each specimen, so their ratio is 1. Raw signals 10 and 15 become ratios $10/2=5$ and $15/3=5$. Multiplying by the standard concentration 2 recovers concentration 10. If the standard instead has response factor 1 in both groups, its signals are 2 and 2 and the ratios become 5 and 7.5: the artifact remains. A stable but non-unit response ratio needs calibration too.Background prevents this simple cancellation unless it is adequately handled. A normalized peak area supports a concentration claim only after validating the response relationship, calibration, and usable range.## Run order can mimic biologyIf all cases are injected after all controls, biological group and instrument drift can be confounded. Randomized or balanced acquisition and regular QC injections create information for distinguishing them. Technical correction after a fully confounded run cannot supply the unobserved comparison without additional assumptions.This **deterministic toy** has no group effect on concentration. A monotone run effect creates a raw signal difference. A perfectly representative QC curve removes it by construction. This illustrates a requirement, not a recommended real-world drift algorithm.```{r}#| label: fig-metabolite-drift#| fig-height: 5.5#| fig-cap: "A deliberately confounded acquisition order. Dots are specimen signals and crosses are exact synthetic QC signals. Dividing by the known QC trend cancels this multiplicative drift; the result relies on the same drift affecting QC and specimens."#| fig-alt: "The upper panel shows rising specimen and QC signals over run order; the lower panel shows constant corrected signal despite group changes halfway through."run <-1:40; group <-as.integer(run >20)drift <-exp(0.015* run)raw <-10* drift; qc_run <-seq(1, 40, by =3)qc <-10*exp(0.015* qc_run)par(mfrow =c(2, 1), mar =c(4, 4, 1, 1))plot(run, raw, pch =16, col =c("#2F80C8", "#D55E00")[group +1],xlab ="Injection order", ylab ="Raw signal")points(qc_run, qc, pch =4, cex =1.4)legend("topleft", c("Group 0", "Group 1", "Pooled QC"),pch =c(16, 16, 4), col =c("#2F80C8", "#D55E00", "black"), bty ="n")plot(run, raw / drift, pch =16, ylim =c(9, 11),col =c("#2F80C8", "#D55E00")[group +1],xlab ="Injection order", ylab ="Corrected signal")```The toy uses the exact factor $\exp(0.015t)$ at injection position $t$, so division recovers 10 by construction. QC measurements provide additional reference information. Successful correction assumes their drift transfers to the biological specimens; a trend in pooled material alone does not uniquely determine the specimens' technical trend.A real QC fit is estimated. It needs coverage across run order, appropriate material, checks for feature-specific behavior, and assessment of fitting uncertainty. Interpolation between controls and extrapolation beyond the last control make different demands. Outcome-guided choices that maximize group separation undermine this diagnostic purpose. Preserve the fitted reference and processing version with the data.## Define absence, non-detection, and quantification limitsA recorded zero can encode a true absence, an integration failure, a value below detection, or a software placeholder. A **detection limit** concerns distinguishing signal from background under a specified criterion. A **quantification limit** concerns estimating an amount with acceptable performance under the method's criterion. A signal can be detected yet fall outside the validated quantification range. Document flags, units, and limits rather than converting all such records into the same number.For an analyte with missing values, choose the target explicitly: detection probability under the assay protocol; concentration in a specified population; or a mean measured response among detected specimens. These require different data and assumptions. For a known lower threshold, the unobserved concentration distribution is still not identified nonparametrically from detected values alone. See the censoring example in [Proteomics: from measured evidence to an estimand](proteomics.qmd#missing-signals-do-not-have-a-single-explanation) and [Missingness, selection, and the observed-data target](../questions-and-design/missingness-and-selection.qmd).## From a feature table to an inferential targetFor a positive calibrated concentration, define $Y$ as its prespecified log2 representation. A difference of conditional means or a population-standardized contrast is a meaningful target when its units and population are specified. For a normalized peak feature, the corresponding target concerns that response representation. The statistical machinery may be shared while the biological interpretation differs.A sum of lipid signals is not automatically a total molar concentration. If two lipids have response factors 1 and 10, moving a fixed total concentration of 2 from the first lipid to the second changes total signal from 2 to 20. The class total in molar units stays fixed. Overlapping annotations or several adducts can also double-count evidence.A lipid-class target needs a membership rule, a quantity to sum, and compatible units. A pathway analysis also needs mapping uncertainty and the tested family recorded. Filtering weak signals changes that family; collapsing peaks after observing their group effects introduces selection. Narrow statistical intervals quantify sampling uncertainty for the defined feature; they do not resolve uncertain molecular identity.Flexible nuisance regression can adjust a well-defined measured-outcome contrast for covariates under support and inference conditions. It cannot resolve unknown molecular identity, perfectly confounded acquisition, or nonidentified below-limit values. Name these measurement limitations separately from estimation uncertainty.## A practical auditRetain specimen, person, extraction, plate, and injection IDs; feature keys and annotation confidence; standards, blanks, and QC positions; units and calibration range; detection/quantification flags; and each normalization or drift correction. Check group overlap across acquisition conditions. Plot missingness and QC behavior before testing. Then use [Differential expression and abundance](../analysis-problems/differential-expression-and-abundance.qmd) and [Multiple testing when the tests are not independent](../analysis-problems/multiple-testing.qmd) for the prespecified feature family.## ExercisesThe checkpoint is this assay specialization's completion target. Additional practice is optional. Try the checkpoint before opening its hint or solution.::: {#checkpoint-met-01 .checkpoint}### Checkpoint · MET-01 — Separate a molecular quantity from its assay response {.unnumbered}**Task type:** Computation and diagnosis.Both groups have concentration 10. Their response factors are 1 and 1.5. An internal standard at concentration 2 shares the factors. Calculate raw signals and ratios. Then explain what fails if the standard has factor 1 in both groups. State what PC 34:1 leaves unresolved and why all controls injected first is a design issue.**Ready to continue when:** you can connect response correction, identification resolution, and acquisition design to the scope of a group contrast.**Transfer:** Can a narrower confidence interval compensate for uncertain molecular identity?<details class="checkpoint-help"><summary>Hint</summary>Write the analyte and standard response equations separately before dividing.</details><details class="checkpoint-help"><summary>Solution outline — open after trying</summary>Raw signals are 10 and 15; shared-response standard signals are 2 and 3, giving ratios 5 and 5. With unmatched standard signals 2 and 2, the ratios become 5 and 7.5. The signal artifact remains. PC 34:1 reports a sum composition rather than complete chain/position structure. Confounded run order prevents a direct separation of group and drift without additional information or assumptions.</details>:::### Additional practice (optional) {.unnumbered}1. Add a nonzero background to the internal-standard example and identify when simple division fails.2. Propose a balanced run order with blanks and QC samples; distinguish the independent biological denominator from injection count.3. Define a lipid-class total on a calibrated molar scale and on an arbitrary signal scale. Explain why the targets differ.## Reading- Sumner et al., [minimum reporting standards](https://doi.org/10.1007/s11306-007-0082-2): analytical metadata and identification.- Fernie et al., [recommendations for reporting metabolite data](https://pmc.ncbi.nlm.nih.gov/articles/PMC3226225/): analytical evidence and standards.- [LIPID MAPS shorthand hierarchy](https://www.lipidmaps.org/databases/shorthand/overview): match structural claims to measurement resolution.<span id="continue-through-the-collection"></span>
