Mixed-Effects Statistical Model for Comparative LC−MS Proteomics Studies

Abstract

Comparing a protein's concentrations across two or more treatments is the focus of many proteomics studies. A frequent source of measurements for these comparisons is a mass spectrometry (MS) analysis of a protein's peptide ions separated by liquid chromatography (LC) following its enzymatic digestion. Alas, LC-MS identification and quantification of equimolar peptides can vary significantly due to their unequal digestion, separation, and ionization. This unequal measurability of peptides, the largest source of LC-MS nuisance variation, stymies confident comparison of a protein's concentration across treatments. Our objective is to introduce a mixed-effects statistical model for comparative LC-MS proteomics studies. We describe LC-MS peptide abundance with a linear model featuring pivotal terms that account for unequal peptide LC-MS measurability. We advance fitting this model to an often incomplete LC-MS data set with REstricted Maximum Likelihood (REML) estimation, producing estimates of model goodness-of-fit, treatment effects, standard errors, confidence intervals, and protein relative concentrations. We illustrate the model with an experiment featuring a known dilution series of a filamentous ascomycete fungus Trichoderma reesei protein mixture. For 781 of the 1546 T. reesei proteins with sufficient data coverage, the fitted mixed-effects models capably described the LC-MS measurements. The LC-MS measurability terms effectively accounted for this major source of uncertainty. Ninety percent of the relative concentration estimates were within 0.5-fold of the true relative concentrations. Akin to the common ratio method, this model also produced biased estimates, albeit less biased. Bias decreased significantly, both absolutely and relative to the ratio method, as the number of observed peptides per protein increased. Mixed-effects statistical modeling offers a flexible, well-established methodology for comparative proteomics studies integrating common experimental designs with LC-MS sample processing plans. It favorably accounts for the unequal LC-MS measurability of peptides and produces informative quantitative comparisons of a protein's concentration across treatments with objective measures of uncertainties.

Development and Evaluation of Normalization Methods for Label-free Relative Quantification of Endogenous Peptides

“…Detecting Differential Expression-Mixed-effects statistical modeling has previously been used to estimate relative protein concentrations where each peptide is modeled and summarized to global relative protein abundances (38,39). Mixedeffects modeling was used to compare the fraction of differentially expressed peaks detected using DeCyder-, Regr-, and RegrRun-normalized data.…”

Peptide-level Robust Ridge Regression Improves Estimation, Sensitivity, and Specificity in Data-dependent Quantitative Label-free Shotgun Proteomics

“…Benchmark Peptide-based Model-We start from the peptidebased linear regression models as proposed by Daly et al (39) Clough et al (22) and Karpievitch et al (40), of which we have independently proven their superior performance compared to summarizationbased workflows (21). In general, the following model is proposed: (1) ridge regression, which leads to shrunken yet more stable log 2 fold change (FC) estimates, (2) Empirical Bayes estimation of the variance, which further stabilizes variance estimators, and (3) M-estimation with Huber weights, which reduces the impact of outlying peptide intensities.…”

Impact of the omic technologies for understanding the modes of action of biological control agents against plant pathogens

“…Labeling procedures quantify changes of protein abundance between samples and at the same time detect post-translational modifications (Otto et al 2012;Wöhlbrand et al 2013). Efficient label-free protocols for relative quantification based on LC-MS methods are available (Otto et al 2012), and a statistical model for comparative proteomics studies has been optimized on T. reesei data (Daly et al 2008). High throughput analyses of proteomes are nowadays possible thanks to new mass spectrometers that permit sequencing of thousands of protein reads, and association with the specific protein that originated each peptide in the mixtures (Helsens et al 2010) can be made using powerful bioinformatic tools for protein identification (Mesuere et al 2012).…”

“…However, there still exist different technical challenges and limitations since protein separation and analysis are inherently skill-based and are difficult to automate. The bias has decreased significantly as the numbers of observed peptides per protein have increased (Daly et al 2008), highlighting advantages of large proteomic data developed with the gel-free technologies. However, large and expensive proteomic facilities, sophisticated bioinformatics analyses and robust statistical tools are required for the new proteomic technologies.…”