Efficient inference of dynamic gene regulatory networks using discrete penalty

2025-07-30

AI Summary

Inferring gene regulatory networks (GRNs) from high-dimensional transcriptomic data is hindered by sparsity bias and hypersensitivity to hyperparameters. To address these challenges, we propose a joint dynamic GRN inference framework based on discrete ℓ₀ regularization—replacing conventional ℓ₁ penalties—to enable unbiased, direct control over network sparsity. We design a scalable mixed-integer optimization algorithm capable of modeling population-level heterogeneity via arbitrary tree-structured hypergraphs, thereby enhancing interpretability and robustness. The method jointly integrates single-cell and spatial transcriptomic data. Applied to a glioblastoma cohort, it successfully reconstructs dynamic GRNs across tumor subclusters, revealing hypoxia-gradient-driven network rewiring and systematically characterizing regulatory differences between primary and recurrent tumor microenvironments.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Social Networks and Social Media: Computational social science
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Gene regulatory networks (GRNs) orchestrate cellular decision making and survival strategies. Inferring the structure of these networks from high-dimensional transcriptomics data is a central challenge in systems biology. Traditional approaches to GRN inference, such as the graphical lasso and its joint extensions, rely on $ell_1$ penalty to induce sparsity but can bias network recovery and require extensive hyperparameter tuning. Here, we present a scalable framework for the joint inference of dynamic GRNs using a discrete $ell_0$ penalty, enabling direct and unbiased control over network sparsity. Leveraging recent algorithmic advances, we efficiently solve the resulting mixed-integer optimization problem for populations structured as arbitrary tree hypergraphs, accommodating both continuous and categorical distinctions among biological samples. After validating our method on synthetic benchmarks, we apply it to single-cell and spatial transcriptomics data from glioblastoma (GBM) patient tumors. Our approach reconstructs gene networks across tumor clusters, maps network rewiring along hypoxia gradients, and reveals niche-specific differences between primary and recurrent tumors. By providing a robust and interpretable tool for GRN inference in complex tissues, our work facilitates high-resolution dissection of tumor heterogeneity and adaptation, with broad applicability to emerging large-scale transcriptomic datasets.

Problem

• Infer dynamic gene regulatory networks from transcriptomics data
• Overcome bias and tuning issues in traditional sparse network methods
• Analyze tumor heterogeneity using scalable discrete penalty framework

Innovation

• Uses discrete $ell_0$ penalty for unbiased sparsity control
• Solves mixed-integer optimization for tree-structured populations
• Applies to single-cell and spatial transcriptomics data