Introduction

Differential-expression analysis identifies proteins that change between pairs of conditions. When an experiment contains three or more ordered conditions, Pattern Profiler addresses a complementary question: which proteins follow the same expression pattern across the complete experiment? Proteins that increase, decrease, peak, or recover together may participate in related biological processes even when their absolute abundances differ.

pattern_profiler_analysis() uses fuzzy c-means clustering, implemented with the Mfuzz package (Kumar and Futschik, 2007). Unlike hard clustering, fuzzy clustering does not force every protein into a single group. Instead, it assigns a membership value between 0 and 1 to every protein–cluster pair. High membership indicates a clear match to a pattern, whereas intermediate membership identifies proteins with more ambiguous profiles.

This vignette shows how to select proteins, choose the number of clusters, interpret memberships and expression profiles, and save the results for later use.

Setup and example data

Pattern Profiler is included in NADIA, while Mfuzz and its clustering dependencies are optional. The following commands install the required packages if they are not already available.

if (!requireNamespace("BiocManager", quietly = TRUE))
  install.packages("BiocManager")

BiocManager::install(c("NADIA", "Mfuzz", "Biobase"))
install.packages("e1071")

We use nadia_dia, the example DIA proteomics dataset distributed with NADIA. The data are first processed to obtain both the intensity assays and the differential-expression results required by Pattern Profiler.

library(NADIA)
data(nadia_dia)

res <- process_proteomics(nadia_dia, verbose = FALSE)

The processed experiment contains three ordered conditions (A, B, and D), each represented by four samples. Replicates are retained during protein quantification and are aggregated only when the condition-level profiles are constructed.

design_table <- as.data.frame(SummarizedExperiment::colData(res$se_proc))
design_table <- as.data.frame(table(Condition = design_table$Condition))
names(design_table)[2] <- "Samples"

knitr::kable(
  design_table,
  caption = "Number of samples available for each condition."
)

Pattern Profiler is most informative when the conditions have a meaningful order, such as time points, doses, or disease stages. With only two conditions, each profile contains a single transition and therefore provides little more information than the direction of the corresponding fold change.

Running Pattern Profiler

The function first selects proteins using the differential-expression table. For each selected protein, it then aggregates replicates within conditions, standardises the resulting profile, selects or accepts a number of clusters, and performs fuzzy c-means clustering. The example below evaluates two to five clusters and uses the Xie–Beni index to choose among them.

pp <- pattern_profiler_analysis(
  se_proc          = res$se_proc,
  DEPs_results     = res$DEPs_results,
  assay_name       = "Impseqrob_min",
  filter_mode      = "any",
  alpha            = 0.05,
  condition_order  = c("A", "B", "D"),
  aggregate        = "median",
  c_range          = 2:5,
  auto_select_c    = TRUE,
  selection_method = "xb",
  min_membership   = 0.25,
  seed             = 42,
  seeds            = c(42, 123, 456),
  verbose          = FALSE
)

The returned object contains the chosen cluster number, the estimated fuzzifier (m), selection diagnostics, the fitted Mfuzz object, and a long-format table for inspection and visualisation. The overview below confirms that all selected proteins passed the preprocessing checks. The output contains more rows than proteins because a protein can meet the membership threshold in more than one cluster.

run_overview <- data.frame(
  Measure = c(
    "Proteins selected",
    "Proteins clustered",
    "Rows in long_output",
    "Selected clusters",
    "Fuzzifier (m)"
  ),
  Value = c(
    format(pp$n_features_input, scientific = FALSE),
    format(pp$n_features_final, scientific = FALSE),
    format(pp$n_rows_output, scientific = FALSE),
    format(pp$optimal_c, scientific = FALSE),
    format(round(pp$m, 3), nsmall = 3)
  )
)

knitr::kable(
  run_overview,
  caption = "Overview of the Pattern Profiler run."
)

Selecting proteins for clustering

Clustering every quantified protein can obscure biologically responsive patterns with a large number of stable profiles. filter_mode therefore lets the user define the protein set before clustering.

For this dataset, the three modes produce substantially different input sizes. The counts below are obtained before missing-value and variance checks are applied by Pattern Profiler.

dep_assay <- as.data.frame(res$DEPs_results)
dep_assay <- dep_assay[dep_assay$Assay == "Impseqrob_min", ]

filter_counts <- data.frame(
  Setting = c(
    'filter_mode = "any"',
    'filter_mode = "specific", comparison = "B-A"',
    'filter_mode = "all"'
  ),
  Proteins = c(
    length(unique(dep_assay$Protein.IDs[dep_assay$adj.P.Val <= 0.05])),
    length(unique(dep_assay$Protein.IDs[
      dep_assay$Comparison == "B-A" & dep_assay$adj.P.Val <= 0.05
    ])),
    nrow(res$se_proc)
  )
)

knitr::kable(
  filter_counts,
  caption = "Number of proteins selected by three filtering strategies."
)

The "any" mode retains 794 proteins that respond in at least one comparison, whereas a "specific" analysis of B-A would retain 497. The "all" mode would include all 1,997 quantified proteins and is useful when coordinated variation among non-significant proteins is also of interest, but it may make the dominant clusters less specific to the biological response.

Choosing the number of clusters

The number of clusters determines the resolution of the analysis. Too few clusters can merge distinct profiles, whereas too many can divide one pattern into small, weakly supported groups. When auto_select_c = TRUE, NADIA fits each candidate value in c_range with multiple seeds and reports four complementary diagnostics.

The default selection_method = "xb" minimises the Xie–Beni (XB) index. "consensus" combines the ranks of all four diagnostics and can be useful when they disagree. "elbow" selects the largest change in centroid separation and should be treated as an exploratory alternative rather than as a universal optimum.

selection_table <- pp$selection_metrics
selection_table[c("XB", "XB_sd", "FPC", "AMM", "Dmin")] <- lapply(
  selection_table[c("XB", "XB_sd", "FPC", "AMM", "Dmin")],
  round,
  digits = 4
)

knitr::kable(
  selection_table,
  row.names = FALSE,
  caption = "Cluster-selection diagnostics for c = 2 to 5."
)

All four diagnostics favour two clusters in this example: c = 2 has the lowest XB value and the highest FPC, AMM, and Dmin values. The selected solution therefore provides two well-separated expression patterns without adding poorly supported subdivisions. These metrics are guides rather than biological proof; candidate solutions should still be checked visually and interpreted in the context of the experiment.

Before clustering, NADIA removes profiles that cannot be standardised reliably, including constant profiles and features with excessive missingness. Remaining isolated missing values are filled by k-nearest-neighbour imputation. Failed candidate fits are stored as missing diagnostic values rather than as zeros, so they cannot be mistaken for exceptionally good solutions.

Understanding the soft-clustering output

The main result is long_output. It contains the protein identifier, cluster, membership, and one standardised value for each condition. Because expression is converted to a row-wise z-score, these values describe the relative profile of each protein across the ordered conditions; they must not be interpreted as absolute protein abundance.

knitr::kable(
  head(pp$long_output, 6),
  digits = 3,
  caption = "First rows of the long-format Pattern Profiler output."
)

Each row represents one protein–cluster association that satisfies min_membership. summarize_pattern_profiler() provides an overview of these associations and reports how many proteins occur in more than one cluster.

pp_summary <- summarize_pattern_profiler(pp$long_output)

membership_overview <- data.frame(
  Measure = c(
    "Unique proteins",
    "Protein--cluster associations",
    "Proteins associated with multiple clusters"
  ),
  Value = c(
    pp_summary$n_unique_features,
    pp_summary$n_total_entries,
    pp_summary$n_multi_cluster_features
  )
)

knitr::kable(
  membership_overview,
  caption = "Summary of the soft-clustering assignments."
)

At the analysis threshold of 0.25, 73 proteins are associated with both clusters. These overlapping assignments are not duplicates or errors: they identify profiles that share characteristics with both centroids. The cluster summary shows the size and strength of each set of assignments.

cluster_table <- as.data.frame(pp_summary$cluster_summary)
cluster_table[c("mean_membership", "min_membership", "max_membership")] <-
  lapply(
    cluster_table[c("mean_membership", "min_membership", "max_membership")],
    round,
    digits = 3
  )

knitr::kable(
  cluster_table,
  caption = "Membership summary for each cluster."
)

Both clusters have high average memberships, indicating that the two-pattern solution is well defined overall. A stricter display threshold can be used when only the clearest representatives are needed.

thresholds <- c(0.25, 0.50, 0.70, 0.90)
threshold_table <- data.frame(
  Minimum_membership = thresholds,
  Associations_retained = vapply(
    thresholds,
    function(x) sum(pp$long_output$Membership >= x),
    numeric(1)
  )
)

knitr::kable(
  threshold_table,
  caption = "Effect of applying stricter membership thresholds."
)

Raising the threshold from 0.25 to 0.50 removes low-confidence secondary associations while retaining one best-supported assignment for every protein in this two-cluster solution. At 0.90, only 554 highly characteristic associations remain. The appropriate threshold depends on whether the aim is broad discovery or a conservative list for downstream interpretation.

The threshold supplied to pattern_profiler_analysis() determines which rows are retained in long_output. Plotting functions can apply an additional, stricter threshold, but they cannot recover associations that were removed during the analysis.

Visualising the expression patterns

Visualisation connects the numerical memberships to their biological meaning. NADIA provides interactive Highcharts plots for inspecting all protein profiles within individual clusters and for comparing cluster centroids.

profile_plots <- cluster_profile_highchart_list(
  pp$long_output,
  conditions = pp$conditions,
  min_membership = 0.70,
  centroid_summary = "median"
)

profile_plots[[1]]

centroid_plot <- cluster_centroids_highchart(
  pp$long_output,
  conditions = pp$conditions,
  min_membership = 0.70,
  centroid_summary = "median",
  title = "Pattern Profiler cluster centroids"
)

centroid_plot

Saving and reusing the results

Pattern Profiler results can be saved either as a standalone Parquet table or inside a NADIA project. Both approaches avoid repeating the clustering when the profiles need to be inspected or plotted again.

parquet_file <- file.path(tempdir(), "pattern_profiler.parquet")

invisible(capture.output(pattern_profiler_analysis(
  se_proc          = res$se_proc,
  DEPs_results     = res$DEPs_results,
  assay_name       = "Impseqrob_min",
  filter_mode      = "any",
  condition_order  = c("A", "B", "D"),
  auto_select_c    = FALSE,
  c                = pp$optimal_c,
  min_membership   = 0.25,
  seed             = 42,
  output_file      = parquet_file,
  verbose          = FALSE
)))

reloaded <- read_pattern_profiler_data(
  parquet_file,
  min_membership = 0.70
)

data.frame(
  Rows_saved = nrow(pp$long_output),
  Rows_reloaded_at_0.70 = nrow(reloaded)
)
#>   Rows_saved Rows_reloaded_at_0.70
#> 1        867                   748

unlink(parquet_file)

project_file <- file.path(tempdir(), "pattern_profiler_example.nadia")

write_nadia(
  project_file,
  preprocessing = nadia_dia,
  result = res,
  verbose = FALSE
)

nadia_add_pattern_profiler(
  project_file,
  pattern_profiler = pp,
  verbose = FALSE
)

stored_project <- read_nadia(project_file)
stored_profiles <- nadia_pattern_profiler(stored_project)

data.frame(
  Rows_original = nrow(pp$long_output),
  Rows_recovered = nrow(stored_profiles)
)
#>   Rows_original Rows_recovered
#> 1           867            867

unlink(c(project_file, paste0(project_file, ".wal")))

Practical recommendations

Pattern Profiler is most useful as an exploratory layer after a well-controlled differential-expression analysis. The following practices make the results easier to reproduce and interpret:

• provide an explicit condition_order that reflects the experimental design;
• begin with filter_mode = "any", then broaden or restrict the protein set to answer a specific biological question;
• inspect all cluster-selection diagnostics rather than treating one index as definitive;
• keep random seeds fixed and check that the main profiles remain stable across plausible cluster numbers;
• use membership to distinguish representative proteins from ambiguous ones;
• interpret standardised trajectories as relative shapes, not abundance differences; and
• perform pathway or functional enrichment only after verifying that the corresponding cluster is coherent and biologically interpretable.

With three or more ordered conditions, this workflow complements pairwise differential expression by revealing groups of proteins that share a response across the experiment. It does not establish regulation or causality by itself, but it provides focused protein sets for subsequent biological validation.

References

Kumar L, Futschik ME (2007). “Mfuzz: a software package for soft clustering of microarray data.” Bioinformation, 2(1), 5–7.

Session information

The package versions used to build this vignette are recorded below to support reproducibility.

sessionInfo()
#> R version 4.6.1 (2026-06-24)
#> Platform: x86_64-pc-linux-gnu
#> Running under: Ubuntu 26.04.1 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-r0.3.32.so;  LAPACK version 3.12.0
#> 
#> locale:
#>  [1] LC_CTYPE=en_US.UTF-8       LC_NUMERIC=C               LC_TIME=en_US.UTF-8       
#>  [4] LC_COLLATE=en_US.UTF-8     LC_MONETARY=en_US.UTF-8    LC_MESSAGES=en_US.UTF-8   
#>  [7] LC_PAPER=en_US.UTF-8       LC_NAME=C                  LC_ADDRESS=C              
#> [10] LC_TELEPHONE=C             LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C       
#> 
#> time zone: Etc/UTC
#> tzcode source: system (glibc)
#> 
#> attached base packages:
#> [1] tcltk     stats4    stats     graphics  grDevices utils     datasets  methods   base     
#> 
#> other attached packages:
#>  [1] DynDoc_1.91.0               widgetTools_1.91.0          SummarizedExperiment_1.43.0
#>  [4] Biobase_2.73.2              GenomicRanges_1.65.4        Seqinfo_1.3.2              
#>  [7] IRanges_2.47.5              S4Vectors_0.51.10           BiocGenerics_0.59.12       
#> [10] generics_0.1.4              MatrixGenerics_1.25.0       matrixStats_1.5.0          
#> [13] NADIA_0.99.1                BiocStyle_2.41.0           
#> 
#> loaded via a namespace (and not attached):
#>   [1] splines_4.6.1         norm_1.0-11.1         tibble_3.3.1          janitor_2.2.1        
#>   [5] pROC_1.19.1           xts_0.14.3            XML_3.99-0.25         tidyHeatmap_1.13.1   
#>   [9] lifecycle_1.0.5       Rdpack_2.6.6          edgeR_4.99.6          doParallel_1.0.17    
#>  [13] lattice_0.23-1        MASS_7.3-66           dendextend_1.19.1     backports_1.5.1      
#>  [17] magrittr_2.0.5        limma_3.99.0          sass_0.4.10           rmarkdown_2.32       
#>  [21] jquerylib_0.1.4       yaml_2.3.12           rlist_0.4.6.2         otel_0.2.0           
#>  [25] DBI_1.3.0             buildtools_1.0.0      minqa_1.2.8           RColorBrewer_1.1-3   
#>  [29] lubridate_1.9.5       abind_1.4-8           rrcovNA_0.5-3         purrr_1.2.2          
#>  [33] sandwich_3.1-3        sva_3.61.0            circlize_0.4.18       reactable_0.4.5      
#>  [37] Mfuzz_2.73.0          maketools_1.3.2       genefilter_1.95.0     vegan_2.7-6          
#>  [41] annotate_1.91.0       permute_0.9-10        highcharter_0.9.5     codetools_0.2-20     
#>  [45] DelayedArray_0.39.8   tidyselect_1.2.1      gmm_1.9-1             shape_1.4.6.1        
#>  [49] farver_2.1.2          lme4_2.0-6            viridis_0.6.5         duckdb_1.5.6         
#>  [53] jsonlite_2.0.0        GetoptLong_1.1.1      e1071_1.7-17          survival_3.8-12      
#>  [57] iterators_1.0.14      foreach_1.5.2         tools_4.6.1           limpa_1.5.2          
#>  [61] Rcpp_1.1.2            glue_1.8.1            gridExtra_2.3.1       SparseArray_1.13.4   
#>  [65] BiocBaseUtils_1.15.1  xfun_0.61             mgcv_1.9-4            TTR_0.24.4           
#>  [69] dplyr_1.2.1           withr_3.0.3           BiocManager_1.30.27   fastmap_1.2.0        
#>  [73] boot_1.3-32           digest_0.6.39         timechange_0.4.0      R6_2.6.1             
#>  [77] imputeLCMD_2.1        BERT_1.9.0            colorspace_2.1-3      RSQLite_3.53.3       
#>  [81] tidyr_1.3.2           data.table_1.18.6.1   class_7.3-24          robustbase_0.99-7    
#>  [85] httr_1.4.9            htmlwidgets_1.6.4     S4Arrays_1.13.2       pkgconfig_2.0.3      
#>  [89] gtable_0.3.6          blob_1.3.0            ComplexHeatmap_2.29.0 S7_0.2.2             
#>  [93] impute_1.87.0         XVector_0.53.0        sys_3.4.3             pcaPP_2.0-5          
#>  [97] htmltools_0.5.9       clue_0.3-68           scales_1.4.0          logging_0.10-111     
#> [101] tmvtnorm_1.7          png_0.1-9             tkWidgets_1.91.1      reformulas_0.4.4     
#> [105] snakecase_0.11.1      knitr_1.52            rjson_0.2.23          nlme_3.1-171         
#> [109] curl_8.0.0            nloptr_2.2.1          proxy_0.4-29          cachem_1.1.0         
#> [113] zoo_1.9-1             GlobalOptions_0.1.4   stringr_1.6.0         parallel_4.6.1       
#> [117] arrow_25.0.1          AnnotationDbi_1.75.2  pillar_1.11.1         grid_4.6.1           
#> [121] vctrs_0.7.3           pcaMethods_2.5.0      xtable_1.8-8          cluster_2.1.8.3      
#> [125] evaluate_1.0.5        mvtnorm_1.4-2         cli_3.6.6             locfit_1.5-9.12      
#> [129] compiler_4.6.1        rlang_1.3.0           crayon_1.5.3          rrcov_1.7-7          
#> [133] labeling_0.4.3        stringi_1.8.9         viridisLite_0.4.3     BiocParallel_1.47.0  
#> [137] assertthat_0.2.1      Biostrings_2.81.9     Matrix_1.7-6          patchwork_1.3.2      
#> [141] bit64_4.8.6           ggplot2_4.0.3         KEGGREST_1.53.6       statmod_1.5.2        
#> [145] rbibutils_2.4.1       broom_1.0.13          memoise_2.0.1         bslib_0.12.0         
#> [149] quantmod_0.4.29       DEoptimR_1.2-2        bit_4.6.0