Contents

1 Purpose

This vignette demonstrates how two conditions, e.g., treatment vs. control, can be compared and the differences statistically tested. We use simulated protein abundances of an LFQ experiment with two treatment groups (A, B) and a control group (Ctrl). After first examining the data using QC plots and then normalizing the data, we compare each treatment group with the control. The output of the comparison is the difference in the mean intensities for quantified proteins (log2 fold-change) in each group, along with statistical parameters such as degrees of freedom, standard errors, p-value and the FDR.

2 Simulated protein abundances

library(prolfqua)

sim_lfq_data_protein_config() simulates protein abundances in long format, one row per protein and sample, and returns them together with a matching AnalysisConfiguration. To read your own data, see the article Importing your data.

xx <- prolfqua::sim_lfq_data_protein_config(Nprot = 100, weight_missing = 0.5)
xx
## $data
## # A tibble: 1,200 × 8
##    sample sampleName group_ isotopeLabel protein_Id  abundance qValue nrPeptides
##    <chr>  <chr>      <chr>  <chr>        <chr>           <dbl>  <dbl>      <dbl>
##  1 A_V1   A_V1       A      light        0EfVhX~3967      20.4      0          2
##  2 A_V1   A_V1       A      light        0YSKpy~2865      NA       NA         NA
##  3 A_V1   A_V1       A      light        0m5WN4~6025      16.4      0          7
##  4 A_V1   A_V1       A      light        3QLHfm~8938      23.0      0          1
##  5 A_V1   A_V1       A      light        3QYop0~7543      23.1      0          7
##  6 A_V1   A_V1       A      light        76k03k~7094      25.5      0          4
##  7 A_V1   A_V1       A      light        7QuTub~1867      18.4      0          4
##  8 A_V1   A_V1       A      light        7cbcrd~7351      27.1      0          2
##  9 A_V1   A_V1       A      light        7soopj~5352      19.5      0          2
## 10 A_V1   A_V1       A      light        7zeekV~7127      20.6      0          8
## # ℹ 1,190 more rows
## 
## $config
## <AnalysisConfiguration>
##   Public:
##     annotation_vars: function () 
##     bin_resp: 
##     clone: function (deep = FALSE) 
##     factor_depth: 1
##     factor_keys: function () 
##     factor_keys_depth: function () 
##     factors: list
##     file_name: sample
##     get_response: function () 
##     hierarchy: list
##     hierarchy_depth: 1
##     hierarchy_keys: function () 
##     hierarchy_keys_depth: function (names = TRUE) 
##     id_vars: function () 
##     ident_q_value: qValue
##     ident_score: 
##     is_response_transformed: FALSE
##     isotope_label: isotopeLabel
##     min_peptides_protein: 2
##     norm_value: NULL
##     nr_children: nrPeptides
##     opt_mz: 
##     opt_rt: 
##     opt_se: 
##     pattern_contaminants: NULL
##     pattern_decoys: NULL
##     pop_response: function () 
##     sample_name: sampleName
##     sep: ~
##     set_response: function (col_name) 
##     value_vars: function () 
##     work_intensity: abundance

Create the LFQData class instance and remove zero or very small intensities, which most quantification software reports for missing values.

lfqdata <- prolfqua::LFQData$new(xx$data, xx$config)
lfqdata$remove_small_intensities()
lfqdata$factors()
## # A tibble: 12 × 3
##    sample  sampleName group_
##    <chr>   <chr>      <chr> 
##  1 A_V1    A_V1       A     
##  2 A_V2    A_V2       A     
##  3 A_V3    A_V3       A     
##  4 A_V4    A_V4       A     
##  5 B_V1    B_V1       B     
##  6 B_V2    B_V2       B     
##  7 B_V3    B_V3       B     
##  8 B_V4    B_V4       B     
##  9 Ctrl_V1 Ctrl_V1    Ctrl  
## 10 Ctrl_V2 Ctrl_V2    Ctrl  
## 11 Ctrl_V3 Ctrl_V3    Ctrl  
## 12 Ctrl_V4 Ctrl_V4    Ctrl

You can always convert the data into wide format.

lfqdata$data_wide()$data[1:3,1:7]
## # A tibble: 3 × 7
##   protein_Id  isotopeLabel  A_V1  A_V2  A_V3  A_V4  B_V1
##   <chr>       <chr>        <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 0EfVhX~3967 light         20.4  23.8  22.3  21.5  NA  
## 2 0YSKpy~2865 light         NA    17.7  16.7  17.7  18.2
## 3 0m5WN4~6025 light         16.4  NA    NA    18.2  24.3

2.1 Visualization of not normalized data

After this first setting up of the analysis we show now how to normalize the proteins and the effect of normalization. Furthermore we use some functions to visualize the missing values in our data.

lfqplotter <- lfqdata$get_Plotter()
density_nn <- lfqplotter$intensity_distribution_density()

2.1.1 Visualization of missing data

lfqplotter$na_heatmap()
Heatmap of missing protein intensities, black - missing, white - present

Figure 1: Heatmap of missing protein intensities, black - missing, white - present

lfqdata$get_Summariser()$plot_missingness_per_group()
# of proteins with 0,1,...N missing values

Figure 2: # of proteins with 0,1,…N missing values

lfqplotter$missigness_histogram()
Intensity distribution of proteins depending on # of missing values

Figure 3: Intensity distribution of proteins depending on # of missing values

2.1.2 Computing standard deviations, mean and CV.

Other important statistics such as coefficient of variation, means and standard deviations can be easily calculated using the get_Stats function and visualized with a violin plot.

stats <- lfqdata$get_Stats()
stats$violin()
Violin plots of CVs in the different groups and among all groups

Figure 4: Violin plots of CVs in the different groups and among all groups

prolfqua::table_facade( stats$stats_quantiles()$wide, paste0("quantile of ",stats$stat ))

Table 1: quantile of CV
probs A B Ctrl All
0.10 2.121145 1.445998 1.499604 3.416437
0.25 2.603169 2.734033 2.135081 4.316819
0.50 3.860492 3.487257 3.744767 5.077622
0.75 5.552086 5.449944 5.701197 7.229931
0.90 7.745671 6.931290 8.396967 10.211265 
stats$density_median()
Distribution of CV's for top 50% and bottom 50% proteins by intensity.

Figure 5: Distribution of CV’s for top 50% and bottom 50% proteins by intensity

2.2 Normalize protein intensities and show diagnostic plots

We normalize the data by \(\log_2\) transforming and then \(z-scaling\).

lt <- lfqdata$get_Transformer()
transformed <- lt$log2()$robscale()$lfq
transformed$is_transformed()
## [1] TRUE
pl <- transformed$get_Plotter()
density_norm <- pl$intensity_distribution_density()
gridExtra::grid.arrange(density_nn, density_norm)
Distribution of intensities before and after normalization.

Figure 6: Distribution of intensities before and after normalization

pl$pairs_smooth()
Scatterplot matrix

Figure 7: Scatterplot matrix

## NULL
p <- pl$heatmap_cor()
p
Heatmap, Rows - proteins, Columns - samples

Figure 8: Heatmap, Rows - proteins, Columns - samples

3 Fit the model and compute contrasts

We compare each treatment group with the control. build_contrast_analysis() fits one model per protein and computes the contrasts in one call. We use the method lm_impute: a linear model per protein, with the protein variances moderated by the empirical Bayes method so that proteins with few observations borrow strength from all proteins. Proteins without observations in one group are refitted with the missing values set to the limit of detection (LOD). The article Filling the gaps uses these models to complete the data for heatmaps and PCA. The vignette All modelling methods at a glance lists the other methods.

contr_spec <- c(
  "AvsC" = "group_A - group_Ctrl",
  "BvsC" = "group_B - group_Ctrl"
)
fa <- build_contrast_analysis(transformed, "~ group_", contr_spec, method = "lm_impute")
contrdf <- fa$get_contrasts()

The column estimate_type tells how each estimate was obtained: observed from the measured intensities, lod_imputed from the refit at the LOD.

dplyr::count(contrdf, contrast, estimate_type)
## # A tibble: 4 × 3
##   contrast estimate_type     n
##   <chr>    <chr>         <int>
## 1 AvsC     lod_imputed       7
## 2 AvsC     observed         93
## 3 BvsC     lod_imputed       7
## 4 BvsC     observed         93
plotter <- fa$get_Plotter()
plotter$volcano()$FDR
Volcano plots of the two contrasts.

Figure 9: Volcano plots of the two contrasts

plotter$ma_plot()
MA plot showing the dependency of mean abundance with respect to the difference

Figure 10: MA plot showing the dependency of mean abundance with respect to the difference

The proteins with FDR < 0.1 in at least one contrast:

sig <- dplyr::filter(contrdf, FDR < 0.1)
signif <- transformed$get_copy()
signif$set_data(signif$data_long() |> dplyr::filter(protein_Id %in% sig$protein_Id))
hmSig <- signif$get_Plotter()$heatmap()
hmSig
Heatmap of the proteins with FDR < 0.1 in at least one contrast

Figure 11: Heatmap of the proteins with FDR < 0.1 in at least one contrast

myProteinIDS <- head(unique(contrdf$protein_Id), 3)
dplyr::filter(contrdf, protein_Id %in% myProteinIDS)
## # A tibble: 6 × 16
##   modelName estimate_type protein_Id  contrast    diff avgAbd
##   <chr>     <chr>         <chr>       <chr>      <dbl>  <dbl>
## 1 lm_impute observed      0EfVhX~3967 AvsC      0.0808   4.43
## 2 lm_impute observed      0YSKpy~2865 AvsC      0.0192   4.16
## 3 lm_impute observed      0m5WN4~6025 AvsC     -0.225    4.23
## 4 lm_impute observed      0EfVhX~3967 BvsC     -0.119    4.33
## 5 lm_impute observed      0YSKpy~2865 BvsC     -0.0640   4.11
## 6 lm_impute observed      0m5WN4~6025 BvsC      0.162    4.42
## # ℹ 10 more variables: std.error.unmoderated <dbl>, df.unmoderated <dbl>,
## #   std.error <dbl>, statistic <dbl>, df <dbl>, p.value <dbl>, conf.low <dbl>,
## #   conf.high <dbl>, sigma <dbl>, FDR <dbl>

Protein and contrast pairs that lm_impute could not estimate, if any:

fa$get_missing()
## # A tibble: 0 × 2
## # ℹ 2 variables: protein_Id <chr>, contrast <chr>

4 Gene Set Enrichment Analysis (GSEA)

After computing contrasts, proteins can be ranked by log2 fold change or t-statistic and subjected to gene set enrichment analysis. The typical workflow is:

  1. Extract UniProt IDs from the contrast results using prolfqua::get_uniprot_id_from_fasta_header()
  2. Map UniProt IDs to Entrez Gene IDs using AnnotationDbi::mapIds() with a species-specific annotation package
  3. Create a named ranked list (statistic values named by gene IDs)
  4. Run GSEA using clusterProfiler::gseGO() or clusterProfiler::gseKEGG()

For details see:

The prolfqua package is described in (Wolski et al. 2023).

5 Session Info

sessionInfo()
## R version 4.6.1 (2026-06-24)
## Platform: x86_64-pc-linux-gnu
## Running under: Ubuntu 24.04.5 LTS
## 
## Matrix products: default
## BLAS:   /home/biocbuild/bbs-3.24-bioc/R/lib/libRblas.so 
## LAPACK: /usr/lib/x86_64-linux-gnu/lapack/liblapack.so.3.12.0  LAPACK version 3.12.0
## 
## locale:
##  [1] LC_CTYPE=en_US.UTF-8       LC_NUMERIC=C              
##  [3] LC_TIME=en_GB              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: America/New_York
## tzcode source: system (glibc)
## 
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods   base     
## 
## other attached packages:
## [1] prolfqua_0.99.8  dplyr_1.2.1      BiocStyle_2.41.0
## 
## loaded via a namespace (and not attached):
##   [1] Rdpack_2.6.6           gridExtra_2.3.1        sandwich_3.1-3        
##   [4] rlang_1.3.0            magrittr_2.0.5         clue_0.3-68           
##   [7] GetoptLong_1.1.1       multcomp_1.4-32        otel_0.2.0            
##  [10] matrixStats_1.5.0      compiler_4.6.1         mgcv_1.9-5            
##  [13] png_0.1-9              vctrs_0.7.3            pkgconfig_2.0.3       
##  [16] shape_1.4.6.1          crayon_1.5.3           fastmap_1.2.0         
##  [19] magick_2.9.1           backports_1.5.1        labeling_0.4.3        
##  [22] utf8_1.2.6             promises_1.5.0         rmarkdown_2.32        
##  [25] nloptr_2.2.1           UpSetR_1.4.1           tinytex_0.61          
##  [28] purrr_1.2.2            xfun_0.62              glmnet_5.2            
##  [31] jomo_2.7-6             logistf_1.26.1         cachem_1.1.0          
##  [34] jsonlite_2.0.0         progress_1.2.3         later_1.4.8           
##  [37] pan_2.0                prettyunits_1.2.0      broom_1.0.13          
##  [40] parallel_4.6.1         cluster_2.1.8.3        R6_2.6.1              
##  [43] stringi_1.8.9          bslib_0.12.0           RColorBrewer_1.1-3    
##  [46] limma_3.99.4           boot_1.3-32            rpart_4.1.27          
##  [49] jquerylib_0.1.4        estimability_2.0.0     Rcpp_1.1.2            
##  [52] bookdown_0.48          iterators_1.0.14       knitr_1.52            
##  [55] zoo_1.9-1              IRanges_2.47.5         httpuv_1.6.17         
##  [58] Matrix_1.7-6           splines_4.6.1          nnet_7.3-21           
##  [61] tidyselect_1.2.1       dichromat_2.0-1        yaml_2.3.12           
##  [64] doParallel_1.0.17      codetools_0.2-20       lattice_0.23-1        
##  [67] tibble_3.3.1           plyr_1.8.9             shiny_1.14.0          
##  [70] withr_3.0.3            S7_0.2.2               coda_0.19-4.1         
##  [73] evaluate_1.0.5         survival_3.8-12        circlize_0.4.18       
##  [76] pillar_1.11.1          BiocManager_1.30.27    mice_3.19.0           
##  [79] KernSmooth_2.23-27     foreach_1.5.2          stats4_4.6.1          
##  [82] reformulas_0.4.4       plotly_4.12.1          generics_0.1.4        
##  [85] hms_1.1.4              S4Vectors_0.51.10      ggplot2_4.0.3         
##  [88] scales_1.4.0           minqa_1.2.8            xtable_1.8-8          
##  [91] glue_1.8.1             emmeans_2.0.4          tools_4.6.1           
##  [94] data.table_1.18.6.1    lme4_2.1-0             forcats_1.0.1         
##  [97] mvtnorm_1.4-2          Cairo_1.7-0            grid_4.6.1            
## [100] tidyr_1.3.2            crosstalk_1.2.2        rbibutils_2.4.1       
## [103] colorspace_2.1-4       nlme_3.1-172           formula.tools_1.7.1   
## [106] cli_3.6.6              viridisLite_0.4.3      ComplexHeatmap_2.29.0 
## [109] gtable_0.3.6           sass_0.4.10            digest_0.6.39         
## [112] operator.tools_1.6.3.1 BiocGenerics_0.59.12   ggrepel_0.9.8         
## [115] TH.data_1.1-5          htmlwidgets_1.6.4      rjson_0.2.23          
## [118] farver_2.1.2           htmltools_0.5.9        lifecycle_1.0.5       
## [121] httr_1.4.9             mime_0.13              GlobalOptions_0.1.4   
## [124] mitml_0.4-5            statmod_1.5.2          MASS_7.3-66

References

Wolski, Witold E., Paolo Nanni, Jonas Grossmann, Maria d’Errico, Ralph Schlapbach, and Christian Panse. 2023. “prolfqua: A Comprehensive R-Package for Proteomics Differential Expression Analysis.” Journal of Proteome Research 22 (4): 1092–1104. https://doi.org/10.1021/acs.jproteome.2c00441.