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.
Efficient synthesis of large protein libraries is key to making high-throughput biochemistry scalable. Advances in DNA microarray technology now allow more than 170,000 designed oligonucleotides to be synthesized in a single array, dramatically reducing cost and enabling pooled amplification for downstream mutagenesis reactions. Effective amplification of short oligonucleotides into long coding sequences requires efficient primer design (PD) without cross-hybridization. However, no PD method currently guarantees complete coverage of the protein-coding sequences with maximum efficiency and no cross-hybridization over multiple proteins or multiple variants of the same protein. Here, we present PrimerDesigner, a suite of methods to design the most efficient primers for synthesizing large protein libraries with complete protein-coding sequence coverage and without cross-hybridization. We first prove that PD with complete coverage and without cross-hybridization is NP-hard, even for a single protein. As a solution, we formulate the PD problem using integer linear programming (ILP). When no cross-hybridization is possible, we solve the PD problem for a single protein in linear time. Moreover, we extend our ILP formulation to handle multiple variants of the same protein. We demonstrate that PrimerDesigner produces optimal solutions in only a few minutes for a single protein and within a couple of hours for multiple proteins while achieving higher efficiency than a greedy baseline approach. We expect PrimerDesigner to enable the synthesis of large protein libraries at an unprecedented scale and efficiency.
Approximate membership query structures are used throughout sequence bioinformatics, from read screening and metagenomic classification to assembly, indexing, and error correction. Among them, Bloom filters remain the default choice. They are not the most efficient structures in either time or memory, but they provide an effective compromise between compactness, speed, simplicity, and dynamic insertions, which explains their widespread adoption in practice. Their main drawback is poor cache locality, since each query typically requires several random memory accesses. Blocked Bloom filters alleviate this issue by restricting accesses for any given element to a single memory block, but this usually comes with a loss in accuracy at fixed memory. In this work, we introduce the Super Bloom Filter, a Bloom filter variant designed for streaming k -mer queries on biological sequences. Super Bloom uses minimizers to group adjacent k -mers into super- k -mers and assigns all k -mers of a group to the same memory block, thereby amortizing random accesses over consecutive k -mer queries and improving cache efficiency. We further combine this layout with the findere scheme, which reduces false positives by requiring consistent evidence across overlapping subwords. We provide a theoretical analysis of the construction of Super Bloom filters, showing how minimizer density controls the expected reduction in memory transfers, and derive a practical parameterization strategy linking memory budget, block size, collision overhead, and the number of hash functions to robust false-positive control. Across a broad range of memory budgets and numbers of hash functions, Super Bloom consistently outperforms existing Bloom filter implementations, with several-fold time improvements. As a practical validation, we integrated it into a Rust reimplementation of BioBloom Tools, a sequence screening tool that builds filters from reference genomes and classifies reads through k -mer membership queries for applications such as host removal and contamination filtering. This replacement yields substantially faster indexing and querying than both the original C++ implementation and Rust variants based on Bloom filters and blocked Bloom filters. The findere scheme also reduces false positives by several orders of magnitude, with some configurations yielding no observed false positives among 10 9 randomly queried k -mers. Code is available at https://github.com/EtienneC-K/SuperBloom and https://github.com/Malfoy/SBB .
Single-cell RNA-seq provides detailed molecular snapshots of individual cells but is notoriously noisy. Variability stems from biological differences and technical factors, such as amplification bias and limited RNA capture efficiency, making it challenging to adapt computational pipelines to heterogeneous datasets or evolving technologies. As a result, most studies still rely on principal component analysis (PCA) for dimensionality reduction, valued for its interpretability and robustness, in spite of its known bias in high dimensions. Here, we improve upon PCA with a random matrix theory (RMT)-based approach that guides the inference of sparse principal components using existing sparse PCA algorithms. We first introduce a novel biwhitening algorithm that self-consistently estimates the magnitude of transcriptomic noise affecting each gene in individual cells, without assuming a specific noise distribution. This enables the use of an RMT-based criterion to automatically select the sparsity level, rendering sparse PCA nearly parameter-free. Our mathematically grounded approach retains the interpretability of PCA while enabling robust, hands-off inference of sparse principal components. Across seven single-cell RNA-seq technologies and four sparse PCA algorithms, we show that this method systematically improves the reconstruction of the principal subspace and consistently outperforms PCA-, autoencoder-, and diffusion-based methods in cell type classification tasks.
