Analyzing mass spectrometry data with limpa
Background
limpa assumes that label-free proteomics profiling has been performed on a series of biological samples, and that peptide quantifications have been obtained for each sample (Luo et al 2023). limma reads the peptide or peptide-precursor data from popular software tools such as DIA-NN (https://github.com/vdemichev/DiaNN) (Demichev et al 2020), Spectronaut (https://staging.biognosys.com/software/spectronaut/) or MaxQuant (Tyanova et al 2016). In each case, the peptide quantifications are read into a wide-format (peptide by sample) matrix of log-intensities. The only other information required to start a limpa analysis is a vector specifying the protein or protein-group membership of each peptide.
Peptide quantifications typically include missing values for some samples, which cause considerable problems for downstream analyses. The missing values can’t just be ignored, because they occur more often at low intensities, and missing value imputation also introduces biases and problems. limpa uses statistical models developed by Li & Smyth (2023) to evaluate how much information can be recovered from the missing values, quantifying the overall missing value “mechanism” into a detection probability curve (DPC). limpa uses the DPC, together with a Bayesian model, to summarize the peptide quantifications into protein-level quantifications and to undertake limma-based differential expression analyses (Li 2024, Ritchie et al 2015).
How to get help
Any questions about limpa can be sent to the Bioconductor support forum.
How to cite
Li M, Cobbold SA, Smyth GK (2025). Quantification and differential analysis of mass spectrometry proteomics data with probabilistic recovery of information from missing values. bioRxiv 2025/651125. doi:10.1101/2025.04.28.651125
Quick start
If y.peptide is a matrix of peptide-level
log2-intensities (including NAs), protein.id is a vector of
protein IDs, and design is a design matrix, then the
following code will quantify complete log2-expression for the proteins
without missing values and will conduct a differential expression
analysis defined by the design matrix.
library(limpa)
dpcfit <- dpc(y.peptide)
y.protein <- dpcQuant(y.peptide, protein.id, dpc=dpcfit)
fit <- dpcDE(y.protein, design)
fit <- eBayes(fit)
topTable(fit)Example analysis
Real proteomics datasets are too large to analyze in this vignette, but we can demonstrate a complete reproducible analysis using a small simulated data. First, generate the dataset:
Loading required package: limmaThe dataset is stored as a limma EList object, with components
E (log2-expression), genes (feature
annotation) and targets (sample annotation). The simulation
function can generate any number of peptides or proteins but, by
default, the dataset has 100 peptides belonging to 25 proteins and the
samples are in two groups with \(n=5\)
replicates in each group. About 40% of the expression values are
missing.
[1] 100 10 Protein DEStatus
Peptide001 Protein01 NotDE
Peptide002 Protein01 NotDE
Peptide003 Protein01 NotDE
Peptide004 Protein01 NotDE
Peptide005 Protein02 NotDE
Peptide006 Protein02 NotDE
1 2
5 5 [1] 0.389Next we estimate the intercept and slope of the detection probability curve, which relates the probability of detection to the underlying peptide expression level on the logit scale.
1 peptides are completely missing in all samples. beta0 beta1
-3.8185 0.7455 
Then we use the DPC to quantify the protein log2-expression values, using the DPC to represent the missing values.
Estimating hyperparameters ...Quantifying proteins ...Proteins: 25 Peptides: 100There are no longer any missing values, and the samples now cluster
into groups. The plotMDSUsingSEs() function is similar to
plotMDS() in the limma package, but takes account of the
standard errors generated by dpcQuant().
> Group <- factor(y.peptide$targets$Group)
> Group.color <- Group
> levels(Group.color) <- c("blue","red")
> plotMDSUsingSEs(y.protein, pch=16, col=as.character(Group.color))
Finally, we conduct a differential expression analysis using the
limma package. The dpcDE function calls limma’s
voomaLmFit function, which was specially developed for use
with limpa. voomaLmFit computes precision weights, in a
similar way to voom for RNA-seq, but instead of using count
sizes it use the quantification precisions from dpcQuant.
The plot shows how dpcDE predicts the protein-wise
variances from the quantification uncertainties and expression
levels.
Protein DEStatus NPeptides PropObs logFC AveExpr t
Protein23 Protein23 Up 4 0.950 0.9339 9.244 4.8083
Protein24 Protein24 Down 4 0.975 -0.8071 9.330 -4.0091
Protein22 Protein22 Up 4 1.000 0.6810 8.912 3.9458
Protein08 Protein08 Up 4 0.450 0.6313 4.728 2.3289
Protein13 Protein13 NotDE 4 0.650 -0.5068 5.976 -2.2627
Protein07 Protein07 NotDE 4 0.425 0.4689 4.285 1.7542
Protein11 Protein11 NotDE 4 0.650 0.3455 5.189 1.3688
Protein21 Protein21 NotDE 4 0.850 0.2861 8.486 1.4679
Protein10 Protein10 NotDE 4 0.375 0.2369 4.850 0.9797
Protein03 Protein03 Down 4 0.250 -0.2145 2.724 -0.8672
P.Value adj.P.Val B
Protein23 3.026e-06 7.566e-05 4.1967
Protein24 8.659e-05 9.230e-04 1.0706
Protein22 1.108e-04 9.230e-04 0.7351
Protein08 2.088e-02 1.238e-01 -3.6447
Protein13 2.475e-02 1.238e-01 -3.9470
Protein07 8.097e-02 3.374e-01 -4.7688
Protein11 1.726e-01 5.395e-01 -5.3940
Protein21 1.437e-01 5.134e-01 -5.5073
Protein10 3.284e-01 8.872e-01 -5.8837
Protein03 3.869e-01 8.872e-01 -5.9559This small dataset has five truly DE proteins. Four of the give are top-ranked in the DE results. The other DE protein is ranked 10th in the DE results and does not achieve statistical significant because it had only 17% detected observations and, hence, a high quantification uncertainty.
To view the log-expression values for the top DE protein, together with standard errors:
Quantification without protein summaries
For some applications, it is desirable to complete and impute the peptide-level intensities without summarizing them at the protein level. This is can done in limpa by
y.peptide.complete <- dpcImpute(y.peptide, dpc=dpcfit)Sesssion information
R version 4.5.2 (2025-10-31)
Platform: x86_64-pc-linux-gnu
Running under: Ubuntu 24.04.3 LTS
Matrix products: default
BLAS: /usr/lib/x86_64-linux-gnu/openblas-pthread/libblas.so.3
LAPACK: /usr/lib/x86_64-linux-gnu/openblas-pthread/libopenblasp-r0.3.26.so; LAPACK version 3.12.0
locale:
[1] LC_CTYPE=en_US.UTF-8 LC_NUMERIC=C
[3] LC_TIME=en_US.UTF-8 LC_COLLATE=C
[5] LC_MONETARY=en_US.UTF-8 LC_MESSAGES=en_US.UTF-8
[7] LC_PAPER=en_US.UTF-8 LC_NAME=C
[9] LC_ADDRESS=C LC_TELEPHONE=C
[11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C
time zone: Etc/UTC
tzcode source: system (glibc)
attached base packages:
[1] stats graphics grDevices utils datasets methods base
other attached packages:
[1] limpa_1.2.1 limma_3.66.0 BiocStyle_2.38.0
loaded via a namespace (and not attached):
[1] digest_0.6.38 R6_2.6.1 fastmap_1.2.0
[4] xfun_0.54 maketools_1.3.2 cachem_1.1.0
[7] knitr_1.50 htmltools_0.5.8.1 rmarkdown_2.30
[10] buildtools_1.0.0 lifecycle_1.0.4 cli_3.6.5
[13] sass_0.4.10 data.table_1.17.8 jquerylib_0.1.4
[16] statmod_1.5.1 compiler_4.5.2 sys_3.4.3
[19] tools_4.5.2 evaluate_1.0.5 bslib_0.9.0
[22] yaml_2.3.10 BiocManager_1.30.27 jsonlite_2.0.0
[25] rlang_1.1.6 Data input
The limpa pipeline starts with a matrix of peptide precursor
intensities (rows for peptides and columns for samples) and a character
vector of protein IDs. The input data can be conveniently supplied as a
limma EList object, but a plain numeric matrix containing the
log-intensities is also acceptable. Non-detected peptides should be
entered as NA.
limpa includes the functions readDIANN(),
readSpectronaut(), readFragPipe() and
readMaxQuant(), which read peptide or peptide-precursor
level data output by the popular mass spectrometry quantification tools
DIA-NN, Spectronaut, FragPipe, and MaxQuant respectively. In each case,
limpa directly reads files output by those tools without any need for
prior processing by the analyst.
The readDIANN() function reads the main DIA-NN “Report”
file, and it supports either the tab-delimited text format written by
DIA-NN version 1 or the Apache Parquet format used by DIA-NN version 2.
For example,
will read a Report.tsv file written by DIA-NN v1 from
the current working directory, and
will read a Report.parquet file written by DIA-NN v2.
The format can be specified explicity but, by default, is detected
automatically from the Report file name.
The readDIANN() function also includes the option to
filter peptide-precursors based on Q-values. While limpa is robust to
different filtering choices, we recommend the following settings for
data searched with match-between-run (MBR):
> y.peptide <- readDIANN("Report.tsv",
+ q.columns = c("Q.Value","Lib.Q.Value","Lib.PG.Q.Value"),
+ q.cutoffs = 0.01)and the following settings if searched without MBR:
> y.peptide <- readDIANN("Report.tsv",
+ q.columns = c("Q.Value","Global.Q.Value","Global.PG.Q.Value"),
+ q.cutoffs = 0.01)These settings follow suggestions from Thierry Nordmann (Max Planck Institute of Biochemistry).
After reading in the data, it is common to filter out non-proteotypic peptides by
and to filter out compound protein groups (protein groups mapped to two or more protein IDs) by
These filtering steps are not required by limpa but help with downstream interpretation of the results.
Protein groups can also be filtered by number of peptides, typically to remove proteins with only one detected precursor:
This step is entirely optional. We generally recommend that users
keep all proteins in order to retain maximum information. The
dpcQuant() function will still quantify complete data even
for proteins with just one peptide.
Note that peptides do not need to be filtered based on the proportion of detected or missing values. limpa can process peptides correctly even if the number of detections is small.
The detection probability curve
Missing values for some peptides in some samples has complicated the
analysis of MS proteomics data. Peptides with very low expression values
are frequently not detected, but peptides at high expression levels may
also be undetected for a variety of reasons that are not completely
understood or easily predictable, for example ambiguity of their elution
profile with that of other peptides. If y is the true
expression level of a particular peptide in a particular sample (on the
log2 scale), then limpa assumes that the probability of detection is
given by \[P(D | y) = F(\beta_0 + \beta_1
y)\] where \(D\) indicates
detection, \(\beta_0\) and \(\beta_1\) are the intercept and slope of
the DPC and \(F\) is the logistic
function, given by plogis in R. This probability
relationship is called the detection probability curve (DPC) in limpa.
The slope \(\beta_1\) measures how
dependent the missing value process is on the underlying expression
level. A slope of zero would means completely random missing values,
while very large slopes correspond to left censoring. The DPC allows
limpa to recover information in a probabilistic manner from the missing
values. The larger the slope, the more information there is to recover.
We typically find \(\beta_1\) values
between about 0.7 and 1 to be representative of real MS data.
The DPC is difficult to estimate because y is only
observed for detected peptides, and the detected values are a biased
representation of the complete values that in principle might have been
observed had the missing value mechanism not operated. limpa uses a
mathematical exponential tilting argument to represent the DPC in terms
of observed values only, which provides a means to estimate the DPC from
real data. The DPC slope \(\beta_1\) is
nevertheless often under-estimated if the variability of each peptide is
large.
Quantification
limpa uses the DPC, together with a Bayesian model, to estimate the expression level of each protein in each sample. It fits an additive model \[\mu_{ij} = \gamma_i + \delta_j\] to the peptide log-intensities for each protein, where \(\mu_{ij}\) is the expected log-expression of peptide \(j\) in sample \(i\), \(\gamma_i\) is the log-expression level of the protein in sample \(i\) and \(\delta_j\) is the baseline effect for peptide \(j\). A sum-to-zero constraint is applied to the peptide effects \(\delta_j\) so that the protein expression \(\gamma_i\) represents the average log-expression of the peptides in sample \(i\). The log-likelihood consists of squared residuals for each observed peptide value and the log probability of being missing for each non-detected peptide value. A multivariate normal prior is also applied to the protein log-expression values, where the prior is estimated from the global data for all proteins. DPC-Quant maximizes the log-posterior with respect to the \(\gamma_i\)s and \(\delta_j\)s, and the final \(\gamma_i\)s become the protein quantifications. DPC-Quant also returns the posterior standard error with which each log-expression value is estimated.
Quantifying every row: protein-level data or post-translational modifications
For some proteomics applications, we want to undertake quantification
and differential expression analysis for every row of data instead of
summarizing multiple rows into proteins. This can arise in the study of
post-translational modifications, where rows correspond to distinct
modifications. It can also arise when the analyst only has access to
data such as LFQ values that has already been summarized at the protein
level, including missing values. To impute and quantify on a rowwise
base, use the dpcImpute function instead of
dpcQuant. The input is similar as for dpcQuant
except there is no need to specify protein IDs.
Differential expression
Finally, the protein log2-expression values and associated
uncertainties are passed to the voomaLmFitWithImputation
function, which computes precision weights for each observation and fits
proteinwise linear models. voomaLmFitWithImputation
combines features from the voomaLmFit and
voomLmFit functions in the limma and edgeR packages. It
uses both protein expression and the quantification standard errors to
predict the protein-wise variances and, hence, to construct precision
weights for downstream linear modelling. This allows the uncertainty
associated with missing values imputation to be propagated through to
the differential expression analysis.
voomaLmFitWithImputation also gives special consideration
to instances where all the expression values for a particular protein
are imputed for one or more treatment conditions, ensuring robust
differential expression analyses even for proteins with only a small
proportion of detected peptides.
limpa’s dpcDE function is a wrapper function, passing
the appropriate standard errors from dpcQuant to
voomaLmFitWithImputation. The limpa package is fully
compatible with limma analysis pipelines, allowing any complex
experimental design and other downstream tasks such as the gene ontology
or pathway analysis. The dpcDE() function accepts any
argument that voomaLmFitWithImputation (or
voomaLmFit) does. For example,
dpcDE(y.protein, design, sample.weights=TRUE) can be used
to downweight outlier samples. Or
dpc(y.protein, design, block=subject) could be used to
model the correlation between repeated observations on the same
subject.
Very large datasets
dpcQuant() will be relatively slow, taking several
hours, for very large datasets with thousands of samples. For large
datasets, very fast imputation at the row level can be done by
imputeByExpTilt(), although this method does not provide
standard errors to quantify precision.
Funding
The limpa project was supported by Chan Zuckerberg Initiative EOSS grant 2021-237445, by Melbourne Research and CSL Translational Data Science Scholarships to ML, and by NHMRC Investigator Grant 2025645 to GS.
Cited references
Demichev V, Messner CB, Vernardis SI, Lilley KS, Ralser M (2020). DIA-NN: neural networks and interference correction enable deep proteome coverage in high throughput. Nature Methods 17(1), 41-44.
Li M, Smyth GK (2023). Neither random nor censored: estimating intensity-dependent probabilities for missing values in label-free proteomics. Bioinformatics 39(5), btad200. doi:10.1093/bioinformatics/btad200
Li M, Cobbold SA, Smyth GK (2025). Quantification and differential analysis of mass spectrometry proteomics data with probabilistic recovery of information from missing values. bioRxiv 2025/651125. doi:10.1101/2025.04.28.651125
Li M (2024). Linear Models and Empirical Bayes Methods for Mass Spectrometry-based Proteomics Data. PhD Thesis, University of Melbourne. http://hdl.handle.net/11343/351600
Lou R, Cao Y, Li S, Lang X, Li Y, Zhang Y, Shui W (2023). Benchmarking commonly used software suites and analysis workflows for DIA proteomics and phosphoproteomics. Nature Communications 14(1), 94.
Ritchie ME, Phipson B, Wu D, Hu Y, Law CW, Shi W, Smyth GK (2015). limma powers differential expression analyses for RNA-sequencing and microarray studies. Nucleic Acids Research 43, e47. doi:10.1093/nar/gkv007
Tyanova S, Temu T, Cox J (2016). The MaxQuant computational platform for mass spectrometry-based shotgun proteomics. Nature Protocols 11, 2301-2319.
- Background
- How to get help
- How to cite
- Quick start
- Example analysis
- Quantification without protein summaries
- Sesssion information
- Data input
- The detection probability curve
- Quantification
- Quantifying every row: protein-level data or post-translational modifications
- Differential expression
- Very large datasets
- Funding
- Cited references