ProMix: Enhancing Protein Quantification through Experimental Design and Statistical Normalization

Abstract

Isobaric labelling of biospecimens followed by mass spectrometry has become the method of choice for large-scale, untargeted, quantitative proteomic profiling. However, subtle variation in experimental conditions can amplify sample variability and introduce systematic biases. Motivated by the challenges and opportunities arose in a recent proteogenomic study, we developed ProMix, a flexible analytical framework designed to improve protein normalization by leveraging two key experimental design features: (1) the inclusion of an additional reference sample to serve as an internal standard, and (2) the incorporation of replicates of each specimen. ProMix can utilize either or both features. Through applications to both simulated and real datasets, we demonstrate the improved performance of ProMix and highlight the advantages of the enhanced experimental design strategies.

Graphical Abstract

Introduction

Multiplexed quantitative mass spectrometry (MS)-based proteomics approaches, such as Tandem Mass-Tag (TMT) and multiplexed isobaric tags for relative and absolute quantitation (iTRAQ), enable comprehensive and multifaceted interrogation of the proteomes in biofluid, tissues and cells^1,2. Offering reliable data quality at scalable throughput, these approaches have been widely adopted in large-scale clinical and proteogenomic studies^3-5.

A key component of TMT is the use of isobaric tags (or “channels”), that share identical overall masses but differ in isotopic composition. A typical MS experiment (hereafter referred to as a “block”) analyzes multiple samples as a mixture, with peptides from each sample labeled with a distinct isobaric tag (Figure 1A) and profiled by MS2 or MS3. As detailed in the Dataset section, a block may consist of data from multiple MS/MS acquisitions. Current TMT reagents support the multiplexing of up to 18 samples per mixture. In the ideal setting, a given peptide from all samples appears as a single peak in the MS1 spectrum. Upon fragmentation, the reporter ions unique to each tag become distinguishable, allowing quantification of peptides across samples based on their intensities in the MS2 or MS3 spectra (Figure 1B). In multi-block studies, a common reference sample is typically included in each mixture to serve as an internal standard, facilitating data integration across blocks. Peptide and protein identification can be performed using either data-dependent acquisition (DDA) or data-independent acquisition (DIA), with quantification supported by various software tools, including Proteome Discover⁶, MaxQuant⁷, Sage⁸, OpenMS⁹ and FragPipe¹⁰.

Figure 1. Experimental design and data representation of the proteomics study of lung tissues from GTEx.

(A) TMT10plex labeling was used to profile peptides from lung specimens (${\mathrm{S}}_1,\dots ,{\mathrm{S}}_8$) and two references (Q: lung-specific reference, ${\mathrm{S}}_0$: mega-pool) across 36 blocks. Each specimen was analyzed in two blocks; ${\mathrm{S}}_2$ in Blocks 1 and R illustrates replicates. (B) TMT-LC-MS platform generated spectra for protein identification and quantification. (C) Protein abundance $Y_{gk}$ is defined as the log₂ ratio of sample intensity to the tissue-specific reference (Q) in the same block and serves as input for both PQN and ProMix.

An essential goal of proteomic studies is to compare protein abundance across samples from different conditions or treatment groups. However, stochastic variation in protein measurements complicates such comparisons, necessitating normalization at the protein level. Two major sources of measurement error are of particular concern. First, the total amount of peptide input can vary across samples, introducing unknown scaling factors. This can be corrected by sample-wise normalization methods, such as adjusting to a fixed total or median protein intensity, or setting the median log-ratios relative to the reference channel to zero^11-13. Second, in studies with multiple blocks, additional technical variation, referred to here as block effects, arises from fluctuations in instrument performance, stochastic precursor ion selection, and variation in reference sample input. Block effects not only increase the variability of individual measurements but also induce correlations among channels within the same block. Notably, block effects cannot be estimated or corrected without replicates or additional assumptions, and ignoring them can bias downstream analyses.

TMT-LC-MS has become the method of choice for proteogenomic studies of nonplasma tissues, which aim to elucidate the genetic basis of protein variation^4,14,15. A core analysis in this field is the detection of protein quantitative trait loci (pQTLs) — genetic variants statistically associated with protein abundance. Unlike differential expression studies that compare a few predefined conditions, pQTL analyses test each protein against hundreds (cis-pQTLs) to millions (trans-pQTLs) of variants. Designing balanced blocks across all genotypes is infeasible. Additionally, protein abundance traits are highly polygenic in natural populations, with individual variants explaining only a small fraction of the total variation. With a sample size of over 50,000, a plasma-based study revealed that more than 80% of the 2922 proteins had at least one pQTL¹⁶; however, achieving such a large sample size is rarely feasible in tissue- or disease-specific studies. Thus, pQTL analyses place particularly strong demands on protein normalization strategies. Most published pQTL studies^17-20 have adopted a method, called probability quotient normalization (PQN)¹¹, which adjusts for sample-specific variation but does not correct for block effects.

This study addresses these challenges through both analytic and experimental design enhancements. We introduce ProMix, a flexible and scalable normalization framework tailored for proteogenomic studies that simultaneously corrects for sample-specific variation and block effects. ProMix leverages two practical design strategies: (1) including a second reference in each block and (2) incorporating replicates across blocks. In the second part of the paper, we evaluate the impact of these design strategies on normalization performance. Using both simulated and real datasets, we show that ProMix, combined with these design features, substantially improves protein quantification accuracy and consistency. ProMix is implemented in R, is compatible with a wide range of upstream quantification pipelines, and produces normalized data ready for downstream analyses such as pQTL mapping. ProMix is publicly available at https://github.com/tanglab/ProxMix.

Experimental Section

ProMix Model and Method

ProMix takes as its input relative protein abundance, calculated as the log₂ ratio of a protein in a sample relative to the reference measured in the same block. Hereafter, we refer to this quantity as “abundance.” In each block, the abundance data are represented as a matrix, with rows corresponding to proteins and columns to samples. For clarity, we use “specimen” to denote biological tissues and reserve “sample” for single biological or technical replicates. Data from all blocks are then combined to form the input matrix, $Y_{gk}$, where $g=1,\dots ,G$ indexes proteins quantified across all blocks and $k=1,\dots ,K$ indexes samples (Figure 1). We note that, since not all proteins are detected in all samples and blocks, the matrix the matrix $Y_{gk}$ typically contains a substantial proportion of missing data. For convenience, we define $l_k\in \{0,1,\dots ,L\}$ to map a sample $k$ to its corresponding specimen, $l$, such that samples $k$ and $k^{\prime }$ are replicates from a same biospecimen if $l_k=l_{k^{\prime }}$. Likewise, we define $r_k\in \{1,2,\dots ,R\}$ to map a sample to its block.

Using these notations, ProMix model the abundance with a linear mixed model:

$$Y_{gk}={\mu }_g+{\alpha }_k+b_{g{r}_k}+{\gamma }_{g{l}_k}+e_{gk}.$$ (1)

A summary of model parameters is provided in Table 1. Brief, ${\mu }_g$ is the global mean deviation, across all samples, from the reference for protein $g$. The term ${\alpha }_k$ captures sample-specific deviations, adjusting for variation in total peptide input. The term, $b_{g{r}_k}$, is the block effects for protein, $g$, modeled as a random effect: $b_{g{r}_k}\sim \mathrm{N}(0,{\varphi }_g)$. In the special case of ${\varphi }_g=0$, $b_{g{r}_k}=0$ for all blocks, specifying a protein with no block effects. The term ${\gamma }_{g{l}_k}$ represents the specimen effect of protein $g$ in specimen $l_k$ and is the variable of primary interest. The estimates, ${\widehat{\gamma }}_{g{l}_k}$, are used as the normalized protein abundances. Finally, $e_{gk}\sim \mathrm{N}(0,{\sigma }_g^2)$ is the residual error. Together, the parameters in the model are $\Omega ={({\mu }_g,{\alpha }_k,{\gamma }_{gl},{\varphi }_g,{\sigma }_g^2)}_{1\le g\le G,1\le k\le K,0\le l\le L}$, as summarized in Table 1.

Table 1.

Summary of parameters in ProMix, Model (1). The interpretation of variable indices is as follow: G: number of proteins; L: number of specimens; K: number of samples; R: number of blocks.

Variable	Interpretation	Shared across	Index: {range}	Fixed/Random effects
$Y_{gk}$	Observed abundance of protein $g$ in sample $k$.	None. Individual data point.	$g:\{1:G\}$ $k:\{1:K\}$	NA
${\mu }_g$	Mean abundance; protein-specific	All measurements on a protein	$g:\{1:G\}$	Fixed
${\alpha }_k$	Sample effects	All proteins in a sample (channel)	$k:\{1:K\}$	Fixed
${\gamma }_{gl}$	Specimen effects; protein-specific	All replicates of a biospecimen	$g:\{1:G\}$ $l:\{1:L\}$	Fixed
$b_{g{r}_k}$	Block effects; protein-specific. $b_{g{r}_k}\sim \mathrm{N}(0,{\varphi }_g)$	All channels in a block	$g:\{1:G\}$ $r_k:\{1:R\}$	Random
$e_{gk}$	Residual error, $e_{gk}\sim \mathrm{N}(0,{\sigma }_g^2)$	None.	$g:\{1:G\}$ $k:\{1:K\}$	Random

Simultaneous estimation of all parameters is computationally intensive. We therefore developed an efficient coordinate-wise descent algorithm²¹ for ProMix, detailed in Supporting Information S1.

PQN

As a benchmark, we compare ProMix with probability quotient normalization (PQN), a widely used normalization procedure in proteogenomic analysis ¹¹. PQN normalizes across samples by setting the median log₂ ratio of each sample relative to the reference to zero:

$$Y_{gk}^{\text{PQN}}=Y_{gk}-{\text{median}}_{1\le g\le G}\left(Y_{gk}\right),1\le k\le K.$$ (2)

Note that the initial estimate of ${\alpha }_k$ computed in the first iteration of ProMix (Step 2.1 in Supporting Information S1) is equivalent to the PQN normalization constant. While the median is typically computed across all non-missing proteins in each sample, the probability of missing in multiplexed MS-based experiments depends on true abundance, total abundance in the block, and stochastic ion selection. To mitigate the influence of such variability, we recommend computing the median over a curated subset of common proteins, as explained below in data analyses.

Evaluation Criteria

We evaluated the normalized abundances ${\widehat{\gamma }}_{g{l}_k}$ (ProMix) and $Y_{gk}^{\text{PQN}}$ (PQN) using three metrics.

Root mean of squared error (RMSE).

For simulated data, where true values are known, RMSE for each protein is computed as $\sqrt{\frac{1}{L}{\sum }_{l=1}^L{\left({\widehat{\gamma }}_{gl}-{\gamma }_{gl}\right)}^2}$. Mean abundance is centered as zero for each protein and for both ProMix and PQN, as this quantity is not informative for downstream analysis.

Replication-RMSE (repRMSE) and ProMix-LOO.

An alternative measure of precision is the RMSE between replicates, as this quantity should be reduced after the adjustment of sample effects and block effects. Because repRMSE does not require the knowledge of the true abundance, it can be used to evaluate normalization methods for both simulated and real datasets.

However, directly comparing repRMSE between ProMix and PQN gives ProMix an unfair advantage as ProMix uses the replicate information. In other words, the model may underestimate the residual errors. To correct for this, we develop a leave-one-out approach (ProMix-LOO), where one sample per block is omitted during model fitting. Estimated block effects are then used to calculate specimen effects in the held-out samples. repRMSE is computed only on replicate pairs involving held-out samples.

Coefficient of Variation (CV).

CV quantifies the standardized dispersion between replicate samples. We calculate geometric CV, which is appropriate for log-transformed data²². For each protein, the CV is computed within each specimen using its replicates, and the median CV across all specimens is used as the protein-level CV. This protein-level CV serves as a metric for comparing normalization methods.

Datasets

This section describes the datasets used in this manuscript, focusing on the TMT experimental design, as it is most relevant for the proposed method. Additional details about each dataset are provided in Supporting Information S2.

GTEx-Lung (TMT-LC-MS3)

This real-world proteogenomic dataset was used to compare normalization approaches.

Experimental design.

Fang et al. (2025) quantified protein abundance in 144 lung tissues from the Genotype-Tissue-Expression Project (GTEx)²³. The study consists of 36 TMT10plex blocks. Each block contains eight samples from distinct donors, one tissue-specific reference (pooled lung peptides) and one mega-pool reference (a mix of 201 specimens from 32 tissue sites used in a previous study)²⁴. Replicates of each biospecimen was assayed in two different blocks (Figure 1A). Details about the GTEx project and biospecimen collection can be found in previous publications^24,25.

MS acquisition and protein quantification.

Raw data were acquired in data-dependent (DDA) mode, using high-resolution LC-MS/MS followed by synchronous precursor selection (SPS)-MS3-based quantification²⁶. Protein identification and quantification were performed using MSFragger and Philosopher^27-29. Abundances were computed as log₂ ratios relative to the tissue-specific reference. A total of 9,063 proteins were detected in at least one of the 288 lung samples, with a 23% missing rate.

Protein normalization analyses.

Normalized protein abundances were computed using both ProMix and PQN. For PQN, sample-level normalization followed Model (2), and specimen-level abundance was the mean of its replicates. To reduce the impact of stochastic missingness, the PQN constants or ProMix sample effects (${\widehat{\alpha }}_k$) were calculated using a subset 4,173 proteins with reference intensity >20 and no missing values in the mega-pool reference.

Simulated Data

We generated simulated data mirroring the GTEx-Lung design to evaluate normalization methods when true abundance and all sources of variation were known. This dataset also enabled us to evaluate the benefits of experimental design strategies.

Simulation setting.

We simulated 144 biospecimens across 36 blocks, each containing two replicates and two references. Abundances for 8,000 proteins were drawn from Model (1), with block, sample, specimen, and residual effects sampled from distributions matching empirical estimates from GTEx-Lung. The median proportions of variance attributable to block, donor, sample, and random measurement errors were 0.07, 0.45, 0.16 and 0.23, respectively (Figure S1). For 403 proteins, block effects were set to zero; for these proteins the block effects in ProMix were unnecessary. This simulation procedure was extended to generate a second simulated dataset, used to investigate the impact of protein normalization on pQTL mapping (Supporting Information S3).

Protein normalization analyses.

We applied both ProMix and PQN to the simulated data. Since true abundances were known, we used RMSE to quantify normalization accuracy and assess the benefits of design features such as a second reference and replicate inclusion. We also validated repRMSE as a proxy for RMSE in real datasets. Finally, we compared normalization strategies based on their ability to identify cis-pQTLs.

HapMap-LCL (TMT-LC-MS2)

To demonstrate broader applicability, we analyzed a second dataset originally generated by Wu et al. (2013), which quantified protein abundance in lymphoblastoid cell lines (LCLs) from the International HapMap Project (HapMap) ^4,30.

This dataset comprised 95 LCLs measured across 51 TMT6plex blocks. Replicate numbers varied from 2 to 5 per LCL (Supporting Information S2). Each block included a single reference sample derived from the peptide mixture of cell line GM12878. Protein abundance was computed as the median log2 ratio of all peptides mapping to each gene. Proteins with missing rates less than 40% across all samples were retained for normalization using PQN and ProMix.

Results and Discussion

We analyzed three datasets, two real and one simulated, to address two key questions. First, we evaluated the statistical efficiency of normalization methods in estimating protein abundance across biospecimens, comparing ProMix to PQN, the most widely used normalization method in proteogenomics. Second, we assessed the benefits of including a second reference sample in each block and incorporating specimen-level replicates.

Statistical efficiency of Normalization Methods on Simulated Data

As the core goal of ProMix was to reduce bias and variability in the protein quantification, we first compared the statistical efficiency of ProMix and PQN using simulated data. Because the true protein abundances were known, we quantified estimation accuracy RMSE, measuring the distance between the true and the estimated abundance across all specimens for each protein. Both PQN and ProMix reduced RMSE compared to simple averaging of replicate measurements without normalization, underscoring the necessity of normalization (Figure 2A-B).

Figure 2. Comparison of normalization methods using simulated data.

(A-B) QQ-plot of root mean of squared error (RMSE) across specimens for each protein, comparing ProMix and PQN (y-axis) to simple averaging of replicates (x-axis, “Before normalization”). (A) Block effects are absent. (B) Block effects are present. (C-D) Scatter plot comparing replication root mean of squared errors (repRMSE) computed from specimen replicates, using PQN (x-axis) or ProMix-LOO normalization (y-axis). (C) Block effects are absent. (D) Block effects are present.

To compare the two methods in greater detail, we stratified proteins by the presence or absence of simulated block effects. In the absence of block effects, PQN was the more parsimonious model and ProMix was expected to suffer a small loss of efficiency for estimating the unnecessary block effects parameters. However, this loss of efficiency was negligible: PQN achieved lower RMSE for 54% of proteins, while ProMix performed better for the remaining 46% (Figure 2A). In contrast, when block effects were presented, ProMix substantially outperformed PQN, achieving lower RMSE in 93% of proteins (two-sided Wilcoxon test $p<1\times {10}^{-56}$; Figure 2B).

We also compared the two methods using repRMSE, a metric that does not rely on knowledge of true abundance. When block effects were present, ProMix-LOO outperformed PQN for 91% of proteins (Figure 2D). The two methods performed similarly when block effects were absent (Figure 2C). Furthermore, the reduction in repRMSE achieved by ProMix-LOO correlated strongly with reductions in RMSE ($r^2=0.65,p<2\times {10}^{-16}$; Figure S2A), confirming that repRMSE is a reliable proxy for normalization performance in real data. In contrast, ProMix without LOO appeared to reduce repRMSE without reducing RMSE in the absence of block effects, indicating overfitting (Figure S2B). Together, these results suggest repRMSE, computed via ProMix-LOO, can be used as diagnostic criterion for evaluating normalization methods and experimental designs, when true protein abundance is unknown.

Normalization Performance in GTEx-Lung Data

In the GTEx-Lung data, 9,063 proteins were quantified in at least one specimen, of which 7,842 proteins were observed in at least 72 (i.e. 50% of the 144) specimens. Without replicates, only 7088 proteins would have met this threshold. A median of 6,937.5 proteins were quantified per sample, and 4,231 proteins were quantified across all 288 samples. Missingness patterns were correlated within blocks (Figure S3). We applied ProMix to 7,762 proteins that were quantified in at least 7 of the 36 blocks and had a minimum of 10 replicate pairs. Compared to PQN, ProMix-LOO achieved lower repRMSE for 7,233 (93%) proteins and lower CV for 7108 (92%) proteins (Figure 3A). The median intraclass correlation, representing the proportion of stochastic variance attributable to block effects, was 0.27, with 25% and 75% percentiles of 0.19 and 0.35, respectively (Figure 3B). These values indicate that block effects constitute a non-negligible source of technical variation in this data.

Figure 3. Normalization performance in GTEx-Lung data.

(A) Comparison of PQN (x-axis) and ProMix with leave-one-out (y-axis) based on replication root mean of squared error (repRMSE) between replicates across 7,762 proteins. (B) Histogram of the estimated intraclass correlations.

Impact of Normalization on pQTL mapping

To evaluate the downstream impact of improved normalization, we used a second simulated data (Supporting Information S3). In proteins with strong block effects, ProMix outperformed PQN by enabling more accurate detection of pQTLs (Supporting Information S3, Table S1). In the real GTEx-Lung data, ProMix normalization identified 251 pQTLs at a false discovery rate (FDR) < 0.1, compared to 216 using PQN. These results highlight the critical importance of robust and accurate normalization for downstream analyses.

General applicability of ProMix to Other Proteomic Datasets

The normalization approach implemented in ProMix is applicable to protein abundance data generated from multiplexed studies and allows users to choose upstream workflow most appropriate for their own study. To assess the broader applicability of ProMix, we analyzed a publicly available dataset generated by Wu et al., which employed a different protein database and quantification pipeline⁴. In this dataset, the median intraclass correlation was 0.54, indicating even greater block-driven variation than in the GTEx-Lung data. ProMix-LOO again outperformed PQN, achieving lower repRMSE and CV for 89% and 99% of proteins, respectively. The median CV across proteins was 0.035 for ProMix and 0.056 for PQN (Figures S4B and S5).

Evaluation of Experimental Design Features

We next used simulated data to examine the value of two experimental design features: replicates and inclusion of a second reference per block. The design employed in the GTEx-Lung study, which incorporated two replicates for each specimen and a second reference sample in each block, is referred to as the “Full design.” We compared this design to three alternatives:

1. SingleRef: replicates included, but only one reference sample in each block.

2. NoRep: no replicates, but two reference samples in each block.

3. SingleRef+NoRep: no replicates and only one reference sample, representing typical current practice and serving as a baseline.

Under the SingleRef design, the ProMix model remains fully identifiable. However, Model (1) is over-specified for the other two alternative designs. For NoRep, we used a reduced ProMix model estimating block effects from reference samples alone. For SingleRef+NoRep, block and specimen effects are not separately identifiable, so we applied PQN.

The results are shown in Figure 4, which compares the RMSE of three alternative designs (y-axis) to that of Full design (x-axis). When block effects were absent, SingleRef and Full designs performed similarly and both outperformed the two designs without replicates (Figure 4A). This is expected, as repeated measurements drive most of the performance gain in the absence of block effects. When block effects were present, both replicates and a second reference sample contributed to improved accuracy (Figure 4B). Notably, the SingleRef design achieved performance nearly equivalent to the Full design, suggesting that block effects can be estimated from replicates alone. However, when replicates are infeasible due to specimen limitations, a second reference provides an efficient alternative, with minimal additional blocks (<6%) under current TMT18plex configurations.

Figure 4. Impact of experimental designs on normalization using simulated data.

QQ-plot of root mean of squared error (RMSE) comparing four experimental designs: Full (two references + replicates), SingleRef (one reference + replicates), NoRep (two references, no replicates), and SingleRef+NoRep (single-reference design without replicates). Full design (x-axis) is used as the benchmark. (A) Block effects are absent. (B) Block effects are present.

Reducing experiment-driven variability is essential in multiplex proteomic studies, as it introduces undesirable correlation structures within blocks (Figures 3B and S5B). We have shown that both design features considered here, replicates and additional references, enable estimation and correction of block effects during the normalization step. We note that these two augmented experimental features offer additional benefits unrelated to normalization. In the GTEx-Lung study, the primary motivation for including replicates was to increase proteome coverage and to reduce missingness, while the primary motivation for including a second reference was to facilitate comparisons with a prior study²⁴.

While ProMix effectively reducing block effects, it may inadvertently remove true biological variation when block effects are confounded with biological covariates. In pQTL studies, for example, this may happen if genotype is correlated with TMT-sets. Although complete balance across all variants is impractical, the risk of confounding can be mitigated by balancing or randomizing TMT assignment by characteristics of the specimen, such as donor’s age, sex, genetic ancestry and disease status.

Limitation and Future Scope

Our analyses of GTEx-Lung and HapMap-LCL datasets revealed that block effects vary across proteins (Figures 3B and S5B). Simulated data confirmed that repRMSE from ProMix-LOO provides a useful diagnostic for assessing the need for ProMix (Figure S2A). In GTEx-Lung, PQN yielded lower repRMSE than ProMix-LOO for ~6% of proteins, possibly reflecting low block-to-block variability or poor estimation of block effects. For such proteins, an extension of ProMix can choose to shrink block effects to zero, which amounts to using PQN for these proteins. In some cases, poor performance stemmed from missing data in entire experiments, numerical instability, or outlier influence. Future work could improve estimation by modeling the distribution of block effects, either via Bayesian priors or empirical Bayes strategies similar to those used for RNA-seq dispersion modeling ³¹. Finally, the linear mixed model framework underlying ProMix offers flexibility for accommodating emerging technological innovations in multiplexed proteomics³².

Conclusions and Outlook

This study introduces and evaluates ProMix, a protein normalization approach that leverages two practical experimental design features: the inclusion of replicates and the incorporation of a second reference sample in each block. Enhancing the consistency of protein quantification across experimental blocks while reducing sampling variability is especially critical in studies where biological variation is subtle relative to technical noise.

ProMix shares conceptual similarities with existing methods such as limma^33,34 and MSstatsTMT¹², in that all three methods employ linear mixed models. However, limma and MSstatsTMT have been designed primarily for detecting differential protein abundance across pre-specified conditions under a split-plot design, where subjects within a condition are treated as exchangeable, and individual effects are modeled as random effects but not directly estimated. In contrast, proteogenomic studies aim to quantify subject-level protein abundance and test its association with thousands of genetic variants, often requiring adjustment for covariates such as age, sex, and ancestry. ProMix addresses these requirements by explicitly estimating individual-level abundance while modeling block effects, enabling more accurate normalization in multiplexed proteomic datasets. ProMix integrates seamlessly with existing protein quantification workflows, and the resulting normalized protein abundances are suitable as quantitative phenotype inputs for downstream proteogenomic analyses.

Supplementary Material

Computational algorithm of ProMix; additional details of datasets analyzed; simulation and results on a pQTL analysis; description of simulated mass-spectrometry protein quantification data; confirmation that repRMSE informs RMSE; missing patterns in GTEx-Lung data; QQ-plot comparing CVs of ProMix and PQN on two real datasets; and normalization of a second multiplex proteomics data (PDF).

ABBREVIATION

MS

mass spectrometry

TMT

tandem mass tag

iTRAQ

isobaric tags for relative and absolute quantitation

LC

liquid chromatography

DDA

data-dependent acquisition

DIA

data-independent acquisition

SPS

synchronous precursor selection

PQN

probability quotient normalization

GTEx

Genotype-Tissue Expression

RMSE

root mean of squared errors

LOO

leave-one-out

pQTL

protein quantitative trait loci

FDR

false discovery rate

CV

coefficient of variation

Data Availability

The GTEx lung data is available at PRIDE (Accession ID: PXD059303). The PSM data of Wu et al. (2013) was downloaded at http://www.peptideatlas.org/PASS/PASS00230[. Source codes and scripts are available at https://github.com/tanglab/ProxMix.