To integrate multi-omics datasets and prioritize biologically relevant gene-level alterations, we applied a modified version of a previously established framework37 in R. Using this framework, we derived a unified abundance metric- termed the 'S score'- which consolidates differential features across transcriptomic, proteomic, and phosphoproteomic datasets.
Data Normalization and Feature Weighting: For each feature (e.g., gene, protein, or phosphosite) within a given dataset, log₂ fold-change values were first standardized to z-scores (zi) by subtracting the dataset-specific mean and dividing by the standard deviation. This normalization allows cross-comparison between datasets with differing dynamic ranges and distributions. z_i=(logFC_ij-μ_j)/σ_j where: μj is the mean logFC value in dataset j σj is the standard deviation of logFC values in dataset j
To account for differences in dataset size, each z-score was scaled by a dataset-specific weight (wi), calculated as the inverse square root of the number of observations (Nj) (e.g., quantified genes or proteins). The resulting weighted z-scores (wzi) balance the influence of each dataset when integrating signals across omics layers. w_i=1/√(N_j ) wz_i = z_i * w_i
S score Derivation: Following normalization, features were merged across datasets by gene identifier. For each gene, the weighted z-scores were summed across all data types to generate a combined z-score (comb_wzi). comb_wz_i =∑_(j_1)^(j_n) wz_i
A composite weight (comb_wk) was then derived by taking the square root of the sum of squared individual weights. comb_w_k = √(∑_(j_1)^(j_n)) w_i^2
The final S score was calculated by dividing the combined z-score by this composite weight, producing a standardized metric that is independent of the number of contributing datasets. S–score =(comb_wz_i )/(comb_w_k )
p-values associated with S scores were computed assuming a standard normal distribution and adjusted for multiple hypothesis testing using the Benjamini-Hochberg procedure to control the false discovery rate (S score; adjusted p-value).
Network Construction Using PCSF: To identify functionally enriched subnetworks within the protein-protein interaction landscape, we applied the Prize-Collecting Steiner Forest (PCSF) algorithm as described by Akhmedov et al. 63, integrating S score-derived features with mIP-MS-derived high-confidence PRKD2 interactors to construct PRKD2-centered functional subnetworks. PCSF is well-suited for reconstructing biologically meaningful modules by balancing the inclusion of informative nodes (terminals) with the cost of connecting them through intermediate (Steiner) nodes.
In our implementation, genes corresponding to S score-integrated features with B-H adjusted p-values < 0.05 were represented as nodes, and their S scores were used as node-specific weights (prizes), denoted as p(v). For high-confidence PRKD2 interactors identified by mIP-MS, fold-change values (Bait IP vs. control) were also incorporated as node-specific weights to enhance prioritization of experimentally supported interaction partners within the network framework. The network was modeled as a graph G = (V, E), where V represents the set of nodes (genes) and E denotes the set of edges, incorporating comprehensive connectivity information from multiple curated databases including CORUM, Reactome, IntAct, DIP, HPRD, BioGRID and STRING. Each edge e ∈ E was assigned a cost c(e), derived from interaction confidence scores in the STRING database, restricted to high-confidence interactions (combined score ≥ 0.7). For databases that do not provide explicit interaction scores, only high-confidence or experimentally validated connections were retained, and a default cost equivalent to a STRING confidence score of 0.7 was arbitrarily assigned to these edges. The goal of the algorithm is to identify a subnetwork G′ = (V′, E′) that maximizes the cumulative prize of included nodes while minimizing the total cost of edges, weighted by a penalty parameter λ. This is expressed by the objective function: maximize ∑(v∈V') p(v) - λ ∑(e∈E') c(e)
Here, λ governs the balance between including high scoring nodes and limiting the number of low-confidence or costly edges. The output subnetwork represents a parsimonious yet functionally coherent module, connecting S score-enriched nodes through biologically supported interactions. The resultant PCSF network was further clustered using the Louvain community detection 64 algorithm implemented in igraph package (R) to identify modular structures within the network. Functional enrichment analysis was then performed on each cluster using Reactome pathway annotations, and the results were mapped back onto the network to enable enrichment-driven visualization of functional modules. This approach facilitates the discovery of critical pathways and gene clusters associated with PRKD2-linked molecular alterations.