Entropy-weighted fuzzy integration of sparse gaussian graphical models in multiple organ metabolomics

Inferring conditional dependency structures from high-dimensional data with small sample sizes remains a fundamental challenge in systems biology, particularly when dependencies span multiple biological compartments. We present QFL, a multilayer network framework that integrates multiple sparse Gaussian graphical models (GGMs) via information-theoretic fusion, and apply it to a controlled multi-organ untargeted metabolomics PM_2.5 dataset, a representative benchmark for cross-organ high-dimensional small-sample network inference under systemic toxicological perturbation. Tissue-specific sparse GGMs are estimated using a sequential inference strategy that couples a q-order partial correlation screening procedure with ψ-learning for strict false discovery rate (FDR) control. This approach yields networks that statistically outperform degree-preserving random graph ensembles in topology-based consistency tests. Sparse graphs are then integrated by an entropy-weighted fuzzy weighted information (FWI) model that assigns each variable a multilayer information score. To characterize the latent multilayer structure, the resulting node-level information scores are decomposed into within-layer and cross-layer contributions. Cross-layer contributions are further resolved into structural-bridge and path-dependence components, which map variables onto a two-dimensional landscape of topological participation. Application to the empirical dataset demonstrated the framework's capacity to quantify systematic patterns of cross-layer statistical dependency propagation, revealing distinct structural phenotypes and identifying dose-dependent topological rerouting. QFL provides a robust computational framework that reconstructs sparse GGMs and characterizes complex cross-layer dependencies in high-dimensional biological systems.