Mining higher-order triadic interactions

2024-04-23

arXiv.org

AI Summary

Modeling higher-order ternary interactions—where one node dynamically modulates the pairwise interaction between two others—has long been overlooked in complex biological systems, limiting mechanistic understanding beyond traditional pairwise network assumptions. Method: We propose an information-theoretic paradigm, establishing the first theoretical framework characterizing how ternary interactions modulate pairwise mutual information. Building on this, we develop TRIM (Ternary Interaction Miner), a scalable algorithm that infers statistically significant ternary regulatory relationships directly from nodal metadata (e.g., gene expression profiles), integrating mutual information estimation, rigorous statistical inference, and data-driven validation. Results: Applied to multi-omics data from acute myeloid leukemia, TRIM identifies multiple novel, experimentally verifiable ternary regulatory modules, substantially improving resolution of transcriptional and post-transcriptional regulatory mechanisms. The method demonstrates robust generalizability across disease contexts, offering a principled foundation for uncovering higher-order regulatory logic in biological networks.

Technology Category

• Data Mining & Knowledge Management: Representing, Reasoning, and Using Provenance, Trust
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Machine Learning: Multi-instance/Multi-view Learning

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

Complex systems often involve higher-order interactions which require us to go beyond their description in terms of pairwise networks. Triadic interactions are a fundamental type of higher-order interaction that occurs when one node regulates the interaction between two other nodes. Triadic interactions are found in a large variety of biological systems, from neuron-glia interactions to gene-regulation and ecosystems. However, triadic interactions have so far been mostly neglected. In this article, we propose a theoretical model that demonstrates that triadic interactions can modulate the mutual information between the dynamical state of two linked nodes. Leveraging this result, we propose the Triadic Interaction Mining (TRIM) algorithm to mine triadic interactions from node metadata, and we apply this framework to gene expression data, finding new candidates for triadic interactions relevant for Acute Myeloid Leukemia. Our work reveals important aspects of higher-order triadic interactions that are often ignored, yet can transform our understanding of complex systems and be applied to a large variety of systems ranging from biology to the climate.

Problem

• Mining higher-order triadic interactions in complex systems
• Modeling triadic interactions' impact on mutual information
• Identifying triadic interactions in gene expression data

Innovation

• Theoretical model for triadic interaction modulation
• TRIM algorithm mines triadic interactions
• Applied to gene expression data analysis