Admissibility and Persistence in Metabolic Systems: A Tier‑7 Instantiation within the Paton System

Biological metabolism consists of interconnected biochemical reactions that transform energy and matter within living systems. Traditional metabolic analysis focuses on reaction kinetics, thermodynamic feasibility, and biochemical regulation. This paper introduces a structural interpretation based on the Paton System. Within this framework, metabolic persistence depends on the admissibility of biochemical states and the reachability of reaction pathways under thermodynamic and enzymatic constraints. A metabolic system continues to function only while at least one admissible continuation path remains available through the reaction network. When admissible coordination collapses, metabolic systems transition toward failure states such as substrate depletion, pathway interruption, or systemic metabolic breakdown. This interpretation reframes metabolic stability as a structural admissibility problem rather than solely a biochemical optimisation problem. The result provides a domain-neutral structural account of metabolic persistence consistent with previously established Paton System principles and extends the framework’s Tier-7 domain instantiations into biological metabolism.