A Proteomics-Informed Geometric Framework for Identifiability and Panel Design in Genome-Scale Metabolic Networks

Genome-scale metabolic models provide a stoichiometric description of biochemical networks, yet most analytical frameworks remain data- or flux-centric, implicitly assuming full observability or well-defined flux states. Under realistic experimental conditions, metabolomics measurements capture only a sparse and condition-dependent subset of metabolites, raising a more fundamental question: which aspects of metabolic mechanism remain identifiable under partial observation, and how should measurements be designed to preserve them? Here, we introduce an operator-centric, metabolite-focused geometric framework for metabolism that treats each biological condition as a mechanistic operator rather than a collection of measured variables or inferred fluxes. Starting from stoichiometry, we construct a Dirac-operator–based formulation whose induced metabolite Laplacian encodes reaction-mediated coupling. Condition-specific gene-level proteomics enter exclusively as modulators of reaction coupling through gene–protein–reaction rules, yielding a family of condition-dependent mechanistic operators that define a spectral geometry on the space of metabolites. Within this framework, partial metabolomic observability is formalized as an operator restriction problem, and identifiability is defined as the stability of low-frequency operator geometry under metabolite masking. This definition is agnostic to steady-state assumptions and avoids imputing unobserved quantities. Building on this criterion, we derive a geometry-aware active measurement strategy that selects metabolite panels which optimally preserve mechanistic structure across conditions. Applying the framework to the human genome-scale metabolic model Human1, we show that proteomics- informed operator geometry is substantially more stable under partial observation than topology-based or unweighted baselines, and that compact, condition-aware metabolite panels can be identified without relying on flux optimization or heuristic centrality measures. Together, this work reframes metabolic analysis around mechanistic operator geometry, providing a principled approach to identifiability and experimental design under sparse, noisy, and condition-specific molecular measurements.