Quantifying Pathway Identifiability under Partial Metabolomics for Measurement Prioritization

Motivation: Incomplete metabolite coverage is a persistent limitation in pathway-level analysis. Under partial metabolomics, multiple pathway configurations may be consistent with the same observed measurements, leading to structural ambiguity in biological interpretation. Existing approaches typically rely on imputation or enrichment scoring but do not explicitly quantify pathway identifiability or guide measurement prioritization. Results: We introduce a unified operator-based framework for pathway identifiability under partial metabolomics. Condition-specific pathway graphs are aligned using a Johnson-Lindenstrauss stabilized fused Gromov-Wasserstein (JL-FGW) operator, integrating topology and metabolite features under het- erogeneous coverage. Pathway ambiguity is quantified through a composite underdetermination functional combining transport entropy, alignment instability, and structural risk. Measurement prioritization is formulated as an optimization problem over the sensitivity of this functional, yielding a computable estimator for next-best metabolite selection without enumerating latent pathway completions. Rather than proposing another generic pathway scoring method, we address a different decision problem: under incomplete metabolite observation, which additional measurements are expected to maximally reduce pathway-level uncertainty? Under synthetic masking, the framework achieves low regret relative to mechanistic and heuristic measurement-selection baselines. In real metabolomics cohorts, pathway coverage is highly dataset-dependent, and the framework identifies a compact set of pathways for which recommendation-based identifiability benchmarking is feasible. Sensitivity analysis indicates stable ranking under moderate perturbations of composite weights, and runtime analysis confirms tractability for curated pathways and moderate genome-scale models. Availability: Code and synthetic evaluation scripts are available for peer review and will be publicly released upon publication.