Linear Regression Fitting For Chromatography

linear-regression-fitting-for-chromatography

Summary

Fit a linear regression model to retention time (RT) data extracted from liquid chromatography–mass spectrometry (LC-MS) runs using calibrant peptides (e.g., iRT standards) to quantify the linearity of RT behavior and validate chromatographic reproducibility. This skill produces an R-squared value that measures how well the fitted model explains variance in observed retention times.

When to use

Apply this skill when you have extracted retention times at peak maxima (rtFittedAPEX) from extracted-ion chromatograms (XICs) of known internal RT calibrants (e.g., 11 iRT peptides with annotated iRTscore values), and you want to assess whether your LC-MS chromatographic system behaves predictably and linearly across the mass range. Use this as a quality-control step after raw data extraction and chromatogram fitting to validate instrumental performance.

When NOT to use

• Input chromatograms contain fewer than 4–5 calibrant peptides; linear regression requires sufficient degrees of freedom and a wide dynamic range of iRTscore values to be statistically meaningful.
• Calibrant peptides show evidence of co-elution, peak overlap, or poor XIC signal-to-noise; the extracted rtFittedAPEX values will be biased and invalidate the model.
• The LC-MS system is known to operate in non-linear RT regions (e.g., very early or very late in the gradient), where a linear model is mechanistically inappropriate.

Inputs

• rawrr::rawrrChromatogram object (extracted ion chromatograms for calibrant peptides)
• vector of observed retention times (rtFittedAPEX, in minutes)
• vector of reference iRT calibration scores (iRTscore, unitless or in relative RT units)

Outputs

• linear regression model object (lm class in R)
• R-squared value (coefficient of determination, 0–1 range)
• fitted slope and intercept coefficients
• predicted retention times for validation set

How to apply

Extract RT values at the maximum of intensity traces for all calibrant peptide XICs using rawrr::readChromatogram() with 10 ppm mass tolerance and 'xic' filter type. Fit an intercept-free or intercept-enabled linear model lm(rtFittedAPEX ~ iRTscore) using the observed RTs and their corresponding reference iRT scores. Report the R-squared value from the model summary: values > 0.99 indicate highly linear RT behavior characteristic of well-functioning Orbitrap systems. The fitted model slope and intercept can also be used to transform future observed RTs to predicted retention indices for target compound identification.

Related tools

• rawrr (R package used to extract chromatogram data and read Thermo Orbitrap raw files; provides readChromatogram() and readFileHeader() functions to obtain RT values and instrument metadata) — https://github.com/fgcz/rawrr
• RawFileReader (.NET assembly wrapped by rawrr that provides low-level binary access to Thermo Scientific .raw file contents) — https://github.com/thermofisherlsms/RawFileReader
• R base lm() (Standard R function used to fit linear regression models to RT data and iRT calibration scores)

Examples

C <- rawrr::readChromatogram(rawfile, mass = iRTmz, tol = 10, type = 'xic', filter = 'ms'); lm_fit <- lm(rtFittedAPEX ~ iRTscore, data = data.frame(rtFittedAPEX = observed_rts, iRTscore = irt_scores)); summary(lm_fit)$r.squared

Evaluation signals

• R-squared value is ≥ 0.9999 (as reported in the article for iRT regression on well-functioning Q Exactive HF), indicating that the linear model explains >99.99% of variance in observed RTs.
• Residuals of the fitted model are normally distributed and homoscedastic (checked via plot(lm_object) diagnostics); systematic patterns in residuals suggest non-linearity or outliers.
• Fitted RTs computed from the model (predict(lm_object)) match observed rtFittedAPEX values with mean absolute error <0.5 min (or proportionally < 2% of gradient time).
• All 11 iRT calibrant peptides (or minimum of 5 peptides across wide iRTscore range) are included in the model fit; no calibrants are excluded as outliers without documented justification.

Limitations

• The skill assumes that rtFittedAPEX values from chromatogram peak-fitting are accurate; poor peak shape or baseline noise will propagate error into the regression.
• Linear regression can mask localized non-linearity; RT behavior may be linear in one region (e.g., iRTscore 10–80) but non-linear at extremes. Inspect residuals and consider polynomial or spline fits if R-squared is unexpectedly low (<0.99).
• On Windows systems, the rawrr::readChromatogram() function requires the decimal symbol to be configured as '.' (period) in system locale settings; failure to do so causes data extraction errors.
• The skill is specific to Thermo Scientific Orbitrap .raw files (as wrapped by RawFileReader); adaptation to other instrument formats (Waters, Bruker, Sciex) would require different data-reading libraries.

Evidence

• [other] construct a linear regression model lm(rtFittedAPEX ~ iRTscore) using annotated iRT reference scores and report R-squared value: "Fit intensity traces stored in rawrrChromatogram objects to extract retention times at maximum intensity (rtFittedAPEX). Construct a linear regression model lm(rtFittedAPEX ~ iRTscore) using"
• [other] Extract ion chromatograms using readChromatogram with 10 ppm tolerance: "Extract precursor m/z values and retention times for known iRT peptide standards using rawrr::readChromatogram() with mass tolerance 10 ppm and XIC filter."
• [other] R-squared of 0.9999 indicates highly linear RT behavior: "R-squared of 0.9999 for iRT regression indicating highly linear RT behavior"
• [other] Extract RTs at maximum of fitted intensity traces and fit linear model: "we extract the RTs at the maximum of the fitted intensity traces stored in the rawrrChromatogram object and fit a linear model"
• [readme] rawrr wraps RawFileReader .NET assembly functionality: "rawrr wraps the functionality of the RawFileReader .NET assembly"