Hypothesis

Hormetic interventions generate transient topological states in the aging transcriptome, whereas bona‑fide longevity mechanisms produce stable topological invariants. This predicts that persistent homology analyses of time‑resolved gene expression will reveal short‑lived Betti‑0/1 features after cold, fasting, exercise, or low‑dose radiation, but long‑persistence features after genetic interventions known to extend lifespan (e.g., SIRT6 overexpression, daf‑2/Insulin/IGF‑1 reduction).

Rationale

Topological data analysis (TDA) captures the birth and death of loops and connected components in high‑dimensional expression manifolds. In cellular reprogramming, transient states appear as low‑persistence features, reflecting a system poised between attractors [1]. If hormesis is merely a threat‑response, it should similarly push cells toward a stress‑activated attractor that is short‑lived once the stimulus wanes. Conversely, interventions that rewire aging biology should shift the transcriptome toward a new, stable attractor, yielding high‑persistence topological invariants.

Novel Mechanistic Insight

We propose that the stress‑sensing kinase AMPK acts as a topological "gatekeeper": its activation during hormesis rapidly remodels chromatin and transcriptional bursting, creating fleeting loops in expression space. When AMPK is inhibited hormetically, the stress‑induced transcriptional burst is blunted, allowing downstream longevity pathways (e.g., NAD⁺‑SIRT1‑FOXO) to dominate and lock the transcriptome into a new basin, converting transient topology into persistent invariants.

Experimental Design

1. Collect time‑series RNA‑seq from young adult mice (or C. elegans) under four conditions: (a) intermittent fasting (IF), (b) mild heat shock (HS), (c) SIRT6 transgenic overexpression (OE), (d) daf‑2 RNAi knockdown. Sample at 0, 2, 6, 12, 24, 48 h post‑intervention.
2. Apply Vietoris–Rips filtration to the normalized expression matrices (genes as dimensions, time points as points) and compute persistence diagrams for Betti‑0 and Betti‑1.
3. Quantify feature persistence (lifetime = death‑birth) and compute the proportion of features with lifetime > 12 h (long‑lived) vs < 4 h (short‑lived).
4. In a parallel arm, repeat IF and HS with AMPK inhibition (Compound C) and assess whether short‑lived features shift to long‑lived.

Expected Outcomes

• IF/HS: predominance of short‑lived features (>70% < 4 h), low long‑lived fraction.
• SIRT6 OE / daf‑2 KD: enrichment of long‑lived features (>50% > 12 h).
• IF/HS + AMPK inhibition: significant increase in long‑lived features, approaching levels seen with genetic longevity interventions.

Falsifiability

If hormetic treatments produce topological invariants indistinguishable from genetic longevity interventions (i.e., high persistence despite AMPK inhibition), the hypothesis that hormesis is merely a threat response is falsified. Likewise, if AMPK inhibition does not alter persistence patterns, the proposed gatekeeper mechanism is invalid.

[1] https://pmc.ncbi.nlm.nih.gov/articles/PMC10495043/ [2] https://arxiv.org/html/2505.04360v2 [3] https://pmc.ncbi.nlm.nih.gov/articles/PMC12436302/