Gene set enrichment analysis (GSEA) is one of the most widely used approaches for identifying predefined gene sets enriched for differential expression between two experimental conditions. However, standard GSEA often fails to account for correlations among genes, as gene-level statistics are typically computed independently. In contrast, regularization methods such as the lasso and elastic-net jointly estimate regression coefficients in high-dimensional settings and have therefore been widely used to identify outcome-associated genes in correlated gene expression data. More recently, mirror statistics based on lasso estimates have been proposed for variable selection with false discovery rate control in high-dimensional models. In this study, we extend the mirror statistics framework to GSEA by incorporating various shrinkage estimators, including the lasso, elastic-net, debiased lasso, and ridge regression. Through extensive benchmark analyses, we demonstrate that mirror statistics based on ridge regression coefficients outperform competing approaches in terms of error control and detection power, particularly when gene expression data exhibit strong correlations. We further apply the proposed method to gene expression data from The Cancer Genome Atlas Breast Invasive Carcinoma cohort and identify biologically relevant cancer pathways that are not detected by conventional GSEA.
In bacterial and archaeal genomes, functionally linked genes often cluster in operons that enable coregulation of expression of these genes and production of their protein products in stoichiometric amounts. Many operons are shared by genomes of distantly related bacteria and archaea due in part to evolutionary conservation and in part to horizontal gene transfer (HGT). In contrast, similarity between species in their gene order along the chromosome can be merely a result of evolutionary closeness such that synteny has not yet been disrupted by genome dynamic events occurring during evolution. In general, however, accurate differentiation of operons from spurious gene clusters is a non-trivial task that depends on an underlying model of neutral genome evolution. Here, we employ a recently developed stochastic model of genome rearrangement (“jump model”) that accounts for HGT across prokaryote species evolving along a phylogenetic tree to infer the size distribution of shared gene strings (synteny blocks) under neutral evolution. Analytic expressions are derived for the expected number of synteny blocks of a given size (or of maximal size) depending on the evolutionary distance between the genomes and the rates of different types of evolutionary events. This analysis is related to the well-studied family of stick-breaking problems, but the discrete structure and stochastic nature of the evolutionary process provide for the development of a simple, independent model. We demonstrate the predictive power of this model by computer simulations of synthetic data as well as by simulating genomes on real trees obtained from the Alignable Tight Genome Clusters database.
Novel technologies for the acquisition of protein expression data at the single cell level are emerging rapidly. Although there exists a substantial body of computational algorithms and tools for the analysis of single cell gene expression (scRNAseq) data, tools for even basic tasks such as clustering or cell type identification for single cell proteomic (scProteomics) data are relatively scarce. Adoption of algorithms that have been developed for scRNAseq into scProteomics is challenged by the larger number of drop-outs, missing data, and noise in single cell proteomic data. Graph contrastive learning (GCL) on cell-to-cell similarity graphs derived from single cell protein expression profiles show promise in cell type identification. However, missing edges and noise in the cell-to-cell similarity graph requires careful design of convolution matrices to overcome the imperfections in these graphs. Here, we introduce sc P rofiterole (Single Cell Proteomics Clustering via Spectral Filters), a computational framework to facilitate effective use of spectral graph filters in GCL-based clustering of single cell proteomic data. Since clustering assumes a homophilic network topology, we consider three types of homophilic filters: (i) random walks, (ii) heat kernels (HK), (iii) beta kernels (BK). Direct implementation of these filters is computationally prohibitive, thus, the filters are either truncated or approximated in practice. To overcome this limitation, sc P rofiterole uses Arnoldi orthonormalization to implement polynomial interpolations of any given spectral graph filter. Our results on comprehensive single cell proteomic data show that (i) GCL with learnable polynomial coefficients that are carefully initialized improves the effectiveness and robustness of cell type identification, (ii) HK and BK improve clustering performance over adjacency matrices or random walks, and (iii) polynomial interpolation of spectral filters outperforms approximation or truncation. The source code for sc P rofiterole and Supplementary Data are available at https://github.com/mustafaCoskunAgu/scProfiterole .
Accurately identifying topologically associated domains (TADs) from high-throughput chromosome conformation capture (Hi-C) contact maps is fundamental to decoding chromatin architecture and its regulatory functions. Despite numerous existing tools, achieving a balance between computational time and the mathematical optimality of TAD partitions remains a significant challenge. In this study, we formulate TAD identification as a graph partitioning problem guided by the principle of Infomap entropy minimization. We introduce InfoTAD, a novel algorithm that models the hierarchical organization of chromatin interactions through an Infomap entropy encoding tree. A primary theoretical contribution of this work is the rigorous proof that finding an optimal encoding tree with minimal Infomap entropy is Nondeterministic Polynomial-time hard (NP-hard). To circumvent this complexity, we propose an efficient approximation algorithm that integrates a discretization strategy with dynamic programming, specifically tailored to the linear constraints of Hi-C contact maps. Comparative benchmarks on simulated datasets show that InfoTAD consistently achieves higher accuracy and lower Infomap entropy than other methods. Furthermore, application to real Hi-C contact matrices from human cell lines (GM12878 and IMR90) reveals that the boundaries identified by InfoTAD are significantly enriched with structural proteins, underscoring its biological precision and potential for advancing genomic research.
