A Spin-Glass Metabolic Hamiltonian optimized by Quantum Annealing Reveals Thermodynamic Phases of Cancer Metabolism
Understanding why specific metabolic states become stable in cancer has remained a fundamental challenge, as current pathway-centric frameworks lack a unifying physical principle governing global metabolic organization. We introduce the Metabolic Spin-Glass (MSG) model, which represents cellular metabolism using a thermodynamically informed effective Hamiltonian that integrates reference reaction free energies, cofactor-mediated network couplings, and patient-specific transcriptomic fields within a frustrated many-body optimization framework. The Hamiltonian is formulated as a binary optimization problem and solved using hybrid quantum annealing. Embedding gastric cancer transcriptomes (n = 497) reveals that malignant phenotypes occupy distinct low-energy configurations within the effective metabolic landscape rather than representing isolated pathway perturbations. A thermodynamic order parameter stratifies patients into prognostically distinct subtypes independently of transcriptomic classification, suggesting clinically applicable non-redundant biomarkers. This work establishes a thermodynamically informed spin-glass energy-landscape framework for patient-specific characterization and stratification of cancer metabolic organization.