Mathematical coupling model for dependency-gated longevity interventions
Most longevity interventions fail not because the compounds are ineffective, but because they're applied in the wrong cellular state. Our framework mathematically models the dependencies between interventions, ensuring each phase establishes the necessary conditions for the next.
Cellular state gates intervention efficacy. Energy depletion blocks autophagy. Absent autophagy, senolysis creates debris crisis. Damaged environments prevent stem cell activation. Epigenetic reset requires structural stability.
The framework isn't just a protocol—it's a mathematical model of coupled biological systems with explicit transition criteria.
Each phase influences every other phase. Strong coupling (dark orange) indicates critical dependencies. Weak coupling (light teal) represents secondary effects.
| From / To | Energy (E) | Clearance (C) | Senolysis (S) | Regeneration (R) | Programmatic (P) |
|---|---|---|---|---|---|
| Energy (E) | — | Strong | Moderate | Strong | Moderate |
| Clearance (C) | Moderate | — | Strong | Strong | Moderate |
| Senolysis (S) | Weak | Strong | — | Strong | Moderate |
| Regeneration (R) | Moderate | Moderate | Strong | — | Strong |
| Programmatic (P) | Weak | Weak | Moderate | Strong | — |
Each phase requires measurable biomarker thresholds before progressing to the next. These aren't arbitrary—they represent cellular readiness for downstream interventions.
| Phase | Activation Criteria | Biomarkers | Typical Duration |
|---|---|---|---|
| Phase 1: Energy | NAD+/NADH ratio > 2.5, ATP production stable | NAD+ levels, VO₂max, lactate threshold | 4-8 weeks |
| Phase 2: Clearance | LC3-II/LC3-I > 1.2, p62 clearance observed | Autophagy markers, protein aggregates | 6-12 weeks |
| Phase 3: Senolysis | p16 expression < threshold, SASP reduction | p16, IL-6, MMP-3, senescence markers | 3-6 months (pulsed) |
| Phase 4: Regeneration | Stem cell markers elevated, niche cleared | CD34+, Oct4, tissue-specific markers | 6-12 months |
| Phase 5: Programmatic | Epigenetic age < chronological, DNAm shift | Horvath clock, GrimAge, PhenoAge | 12-24 months |
Complete mathematical and biological foundation published at American Longevity Science.
Formal treatment of intervention dependencies using graph theory and differential equations. Defines coupling strength metrics.
Read paper →Biomarker thresholds for phase progression. Clinical validation of transition gates.
Read paper →Why senolysis fails without prior autophagy activation. Mathematical proof and clinical evidence.
Read paper →Graph-based representation of biological dependencies. Pathway analysis and network effects.
Read paper →From theory to practice. Protocol design, monitoring systems, and safety frameworks.
Read paper →Risk mitigation through proper sequencing. Adverse event prevention and monitoring protocols.
Read paper →Traditional supplement stacks ignore cellular state. Example failure modes:
This isn't about "optimizing" a supplement stack. The order creates the biological possibility:
The framework has been validated through:
Individual variation in transition timing based on:
Platform development focuses on AI-driven state monitoring and personalized transition criteria.
Explore our pipeline, investment opportunity, or dive deeper into the research.