arXiv subjects

Mushal Zia

Publications and source records attributed to Mushal Zia.

8 recordsLinked to original sources

arXiv2026

PSLL: Persistent Sheaf Laplacian Learning for Protein-Ligand Binding Affinity Prediction

Accurate prediction of protein-ligand binding affinity remains a central challenge in computational drug discovery due to the complex interplay among molecular geometry, physicochemical interactions, and atom-specific charge information. In this work, we introduce a Persistent Sheaf Laplacian learning (PSLL) framework for protein-ligand binding affinity prediction. The proposed approach constructs multiscale topological representations from three-dimensional protein-ligand complexes by incorporating atomic partial charges into sheaf restriction maps over Vietoris-Rips and alpha complex filtrations. To capture chemically diverse protein-ligand interactions, we introduce element-specific and category-specific atom-pair representations within the PSLL framework. Harmonic and non-harmonic spectra extracted from the resulting persistent sheaf Laplacians are used as molecular descriptors. To complement the PSLL-derived molecular representation, we incorporate transformer-based protein embeddings and SMILES-derived ligand descriptors for binding affinity prediction. The scoring power of the proposed multiscale PSLL model is validated against existing state-of-the-art methods on three widely used PDBbind benchmark datasets, including PDBbind-v2007, PDBbind-v2013, and PDBbind-v2016. The computational results indicate that the proposed PSLL model achieves strong predictive performance across benchmark datasets, highlighting its potential as an interpretable and mathematically grounded framework with promising generalizability for molecular machine learning and drug discovery.

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arXiv2025

GBNL: Graded Betti Number Learning of Complex Biological Data

While persistent homology is widely used for data shape analysis, persistent commutative algebra (PCA) has seen limited adoption in machine learning and data science. Unlike persistent homology, which delivers topological invariants in the form of Betti numbers, PCA provides both algebraic invariants and graded Betti numbers. However, graded Betti numbers have seldom been applied to real-world data. In this work, we introduce the first-of-its-kind application of commutative algebra graded Betti numbers in machine learning and data science. Specifically, we present Graded Betti Number Learning (GBNL) for protein-nucleic acid binding prediction. Protein-DNA/RNA interactions are fundamental to cellular processes such as replication, transcription, translation, and gene regulation, and their understanding and prediction remain challenging. GBNL represents each nucleic acid sequence as a family of $k$-mer-specific sets and derives persistent graded Betti invariants from PCA, generating multiscale topological representations of local nucleotide organization. To incorporate cross-molecule context, these graded Betti representations are paired with transformer-based protein embeddings, linking nucleotide-level signals with global protein patterns. The proposed graded Betti representations effectively detect single-site mutations and distinguish complete mutation patterns. Operating on primary sequences with minimal preprocessing, GBNL bridges commutative algebra, reduced algebraic topology, combinatorics, and machine learning, establishing a new paradigm for comparative sequence analysis. Numerical studies using three datasets highlight the success of GBNL in protein-nucleic acid binding prediction.

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arXiv2025

CAP: Commutative Algebra Prediction of Protein-Nucleic Acid Binding Affinities

An accurate prediction of protein-nucleic acid binding affinity is vital for deciphering genomic processes, yet existing approaches often struggle in reconciling high accuracy with interpretability and computational efficiency. In this study, we introduce commutative algebra prediction (CAP), which couples persistent Stanley-Reisner theory with advanced sequence embedding for predicting protein-nucleic acid binding affinities. CAP encodes proteins through transformer-learned embeddings that retain long-range evolutionary context and represents DNA and RNA with $\textit{k}$-mer algebra embeddings derived from persistent facet ideals, which capture fine-scale nucleotide geometry. We demonstrate that CAP surpasses the SVSBI protein-nucleic acid benchmark and, in a further test, maintains reasonable performance on newly curated protein-RNA and protein-nucleic acid datasets. Leveraging only primary sequences, CAP generalizes to any protein-nucleic acid pair with minimal preprocessing, enabling genome-scale analyses without 3D structural data and promising faster virtual screening for drug discovery and protein engineering.

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arXiv2025

Commutative algebra neural network reveals genetic origins of diseases

Genetic mutations can disrupt protein structure, stability, and solubility, contributing to a wide range of diseases. Existing predictive models often lack interpretability and fail to integrate physical and chemical interactions critical to molecular mechanisms. Moreover, current approaches treat disease association, stability changes, and solubility alterations as separate tasks, limiting model generalizability. In this study, we introduce a unified framework based on multiscale commutative algebra to capture intrinsic physical and chemical interactions for the first time. Leveraging Persistent Stanley-Reisner Theory, we extract multiscale algebraic invariants to build a Commutative Algebra neural Network (CANet). Integrated with transformer features and auxiliary physical features, we apply CANet to tackle three key domains for the first time: disease-associated mutations, mutation-induced protein stability changes, and solubility changes upon mutations. Across six benchmark tasks, CANet and its gradient boosting tree counterpart, CATree, consistently attain state-of-the-art performance, achieving up to 7.5% improvement in predictive accuracy. Our approach offers multiscale, mechanistic, interpretable,and generalizable models for predicting disease-mutation associations.

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arXiv2025

CAKR: Commutative algebra k-mer representations for genomics

Despite the availability of various sequence analysis models, comparative genomic analysis remains a challenge in genomics, genetics, and phylogenetics. Commutative algebra, a fundamental tool in algebraic geometry and number theory, has rarely been used in data and biological sciences. In this study, we introduce commutative algebra $k$-mer representations as a nonlinear algebraic framework for analyzing genomic sequences. This representation bridges commutative algebra, algebraic topology, combinatorics, and machine learning to establish a mathematical framework for comparative genomic analysis. We evaluate its effectiveness on three tasks including genetic variant classification, phylogenetic tree reconstruction, and viral classification, typically requiring alignment-based, alignment-free, and machine-learning approaches, respectively. In this work, we show that commutative algebra k-mer representations outperform five state-of-the-art sequence analysis methods across twelve primary datasets, with two additional supplementary fragment-placement benchmarks, especially in viral classification, and maintain relatively stable predictive accuracy as dataset size increases, underscoring scalability and robustness.

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arXiv2025

Topological Sequence Analysis of Genomes: Category theory Approaches

Sequence data, such as DNA, RNA, and protein sequences, exhibit intricate, multi-scale structures that pose significant challenges for conventional analysis methods, particularly those relying on alignment or purely statistical representations. In this work, we introduce category-based topological sequence analysis (CTSA ) of genomes. CTSA models a sequence as a resolution category, capturing its hierarchical structure through a categorical construction. Substructure complexes are then derived from this categorical representation, and their persistent homology is computed to extract multi-scale topological features. Our models depart from traditional alignment-free approaches by incorporating structured mathematical formalisms rooted in sequence topology. The resulting topological signatures provide informative representations across a variety of tasks, including the phylogenetic analysis of SARS-CoV-2 variants and the prediction of protein-nucleic acid binding affinities. Comparative studies were carried out against six state-of-the-art methods. Experimental results demonstrate that CTSA achieves excellent and consistent performance in these tasks, suggesting its general applicability and robustness. Beyond sequence analysis, the proposed framework opens new directions for the integration of categorical and homological theories for biological sequence analysis.

q-bio.GN↗

arXiv2025

CAML: Commutative algebra machine learning -- a case study on protein-ligand binding affinity prediction

Recently, Suwayyid and Wei have introduced commutative algebra as an emerging paradigm for machine learning and data science. In this work, we integrate commutative algebra machine learning (CAML) for the prediction of protein-ligand binding affinities. Specifically, we apply persistent Stanley-Reisner theory, a key concept in combinatorial commutative algebra, to the affinity predictions of protein-ligand binding and metalloprotein-ligand binding. We introduce three new algorithms, i.e., element-specific commutative algebra, category-specific commutative algebra, and commutative algebra on bipartite complexes, to address the complexity of data involved in (metallo) protein-ligand complexes. We show that the proposed CAML outperforms other state-of-the-art methods in (metallo) protein-ligand binding affinity predictions.

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arXiv2024

Persistent Directed Flag Laplacian (PDFL)-Based Machine Learning for Protein-Ligand Binding Affinity Prediction

Directionality in molecular and biomolecular networks plays a significant role in the accurate represention of the complex, dynamic, and asymmetrical nature of interactions present in protein-ligand binding, signal transduction, and biological pathways. Most traditional techniques of topological data analysis (TDA), such as persistent homology (PH) and persistent Laplacian (PL), overlook this aspect in their standard form. To address this, we present the persistent directed flag Laplacian (PDFL), which incorporates directed flag complexes to account for edges with directionality originated from polarization, gene regulation, heterogeneous interactions, etc. This study marks the first application of the PDFL, providing an in-depth analysis of spectral graph theory combined with machine learning. Besides its superior accuracy and reliability, the PDFL model offers simplicity by requiring only raw inputs without complex data processing. We validated our multi-kernel PDFL model for its scoring power against other state-of-art methods on three popular benchmarks, namely PDBbind v2007, v2013, and v2016. Computational results indicate that the proposed PDFL model outperforms competitors in protein-ligand binding affinity predictions, indicating that PDFL is a promising tool for protein engineering, drug discovery, and general applications in science and engineering.

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