Emergent Threshold Dynamics in Unified Metabolic-Regulatory Models: Achieving Spontaneous Homeostasis Through Bidirectional ATP-Pathway Coupling

Abstract

BackgroundFor decades, computational biology has failed to create unified models where metabolic state and regulatory control are bidirectionally coupled: metabolic models optimize flux but cannot represent dynamic regulation, while regulatory models treat ATP as a fixed parameter rather than a dynamic variable affected by pathway activity. This fundamental limitation prevents computational recapitulation of emergent threshold behaviors--spontaneous homeostasis, adaptive reorganization, pathway switching--observed in living organisms. The challenge requires formalisms where (1) metabolic state governs regulatory decisions AND (2) regulatory choices consume metabolic resources, producing emergent dynamics from feedback rather than programming. MethodsWe introduce Signal Hierarchical Petri Nets, extending Hybrid Petri Nets with bidirectional metabolic-regulatory coupling through energy-dependent layer organization. Unlike classical approaches, ATP is simultaneously a regulatory signal (governing pathway availability through quantitative thresholds) and a material substrate (consumed by pathway activity). When ATP depletes below 1000 {micro}M, high-cost pathways automatically become unavailable; pathway activity consuming ATP creates feedback affecting subsequent pathway accessibility. This bidirectional coupling enables emergent threshold behaviors impossible in classical formalisms. We demonstrate the paradigm through macrocyclic peptide transport across 53 metabolic conditions, where drug accumulation depends on ATP-governed pathway reorganization. ResultsThe formalism produces three emergent behaviors never achieved in unified metabolic-regulatory models. (1) Spontaneous homeostasis without programming: Despite 113-fold permeability variation from N-methylation, ATP-replete cells maintain constant drug accumulation (CV=0.066%)--homeostatic compensation emerges from ATP-consumption feedback, not explicit control logic. (2) Threshold-triggered reorganization: ATP depletion to 300 {micro}M triggers 8533-fold active-to-passive transport shifts with paradoxical 141% accumulation increase from efflux collapse. (3) Tissue-specific dynamics from identical parameters: Tumor hypoxia (ATP=1200 {micro}M) versus normal tissue (ATP=5000 {micro}M) produces 6.62-fold selectivity differences from differential pathway accessibility--same model, different emergent outcomes. Computational predictions achieve r=0.911 correlation with experimental cyclosporin permeability (n=32). ConclusionsSignal Hierarchical Petri Nets represent the first computational formalism achieving emergent threshold dynamics through bidirectional metabolic-regulatory coupling. The paradigm enables in silico recapitulation of adaptive cellular behaviors previously impossible to model, with applications extending beyond drug transport to any biological system where metabolic state governs regulatory reorganization: cancer metabolism, ischemia, synthetic biology, and aging research. Author SummaryLiving cells exhibit remarkable adaptive behaviors: they maintain stable internal conditions despite environmental changes (homeostasis), reorganize their biochemical machinery when energy runs low, and switch between operating modes at precise threshold values. For decades, computational biologists have struggled to build models that recapitulate these emergent behaviors--our computer simulations could only exhibit the dynamics we explicitly programmed into them. We solved this fundamental challenge by creating a new computational formalism where metabolic state and regulatory control form a bidirectional feedback loop: energy availability governs which biochemical pathways can operate, while pathway activity consumes energy. This simple coupling produces complex emergent behaviors never seen in previous computational models. Our simulations spontaneously exhibit homeostasis--maintaining constant drug levels despite 113-fold variation in membrane permeability--without any programmed control logic. The same model produces different emergent behaviors in different tissue contexts: tumor cells versus normal cells show 6-fold differences in drug accumulation from identical parameters, purely from different starting energy levels. We demonstrate this paradigm using drug transport as a case study, but the implications extend far beyond: cancer metabolism, brain injury during stroke, synthetic biology circuit design, and aging research all involve systems where metabolic-regulatory feedback governs cellular adaptation. This formalism provides computational biology with a long-missing capability--the ability to model emergent threshold behaviors computationally.