The Bioenergetic Stability Index (ISB): A Deterministic Multi-Scale Thermodynamic Framework of Focal Saddle-Node Bifurcation in Major Depressive Phenotypes

Background: Contemporary models of major depressive phenotypes frequently emphasize monoaminergic stochasticity, thereby limiting the integration of rigorous thermodynamic constraints and cumulative allostatic load. This study introduces a deterministically grounded paradigm, mathematically defining depression as a macroscopic manifestation of focal bioenergetic depletion driven by the spatiotemporal failure of astrocytic glutamate clearance. Methods: A deterministic, multi-scale Ordinary and Partial Differential Equation (ODE-PDE) architecture was constructed utilizing empirical multi-modal matrices: spatial connectomics mapped via Euclidean 3D topological constraints (Destrieux Atlas), continuous transcriptomic arrays (AHBA), receptor kinetics (Neuromaps PET), and pan-ancestry mtDNA-CN baseline synthesis (gnomAD). Adhering to strict thermodynamic parsimony, the network was rigidly calibrated at steady-state (d[ATP]/dt = 0) prior to systemic stress simulation. A deterministic Monte Carlo cohort (N=40,000) was evaluated over 1,000 biological days, strictly constrained by absolute in vivo cerebral metabolic limits. Results: Cumulative allostatic load induced focal, dose-dependent down-regulation of astrocytic Excitatory Amino Acid Transporters (EAAT) via RNA velocity decay kinetics. Under extreme environmental stress (Ωext > 3.0), the Euclidean spatial constraints isolated the toxicity, driving the epicenter network toward a critical topological phase transition (Saddle-Node Bifurcation at [ATP] < 0.5 mM). Pan-ancestry simulation revealed pronounced gene-environment (GxE) synchronization; cohorts with lower baseline mtDNA-CN buffering capacities (e.g., African ancestry) exhibited absolute deterministic focal collapse rates of 19.29%, compared to 15.34% in highly buffered cohorts (e.g., European ancestry). Conclusions: Systemic neuro-degradation is deterministic and strictly preceded by localized thermodynamic collapse. This computational framework provides a quantifiable, biophysically grounded paradigm that isolates focal bioenergetic depletion as the primary substrate for depressive phenotypes, underscoring the necessity of targeted neuro-energetic stabilization.