Hypothesis

Rapamycin and caloric restriction (CR) generate nearly identical topological shapes in the manifold of age‑associated gene expression, indicating they activate a shared stress‑response program rather than repairing underlying molecular damage.

Mechanistic Basis

mTOR inhibition triggers AMPK activation and HIF‑1α stabilization, reproducing the low‑energy signaling cascade that occurs during nutrient scarcity. This cascade drives a cyclic transcriptional program where stress‑responsive genes oscillate in coordinated waves, creating persistent loops (1‑dimensional holes) and higher‑order voids (2‑dimensional holes) in the expression space. True damage‑reversal interventions—such as senolytic clearance or NAD⁺ boosting—should collapse these loops by resolving DNA‑damage signalling and reducing transcriptional noise, thereby simplifying the manifold’s topology.

Testable Predictions

1. Persistence diagrams of rapamycin‑treated and CR‑treated old mice will show overlapping Betti‑0 (connected components), Betti‑1 (loops), and Betti‑2 (voids) distributions when computed from the 576 BiT age genes.
2. Senolytic‑treated or NAD⁺‑boosted animals will exhibit significantly lower Betti‑1 and Betti‑2 values, reflecting a reduction in cyclic and void‑like structures.
3. The Wasserstein distance between rapamycin and CR diagrams will be smaller than the distance between either and a genuine repair intervention.

Experimental Design

• Use aged (24‑month) C57BL/6 mice divided into four groups: control, rapamycin (14 ppm diet), 40 % CR, and senolytic combo (dasatinib + quercetin).
• Harvest liver, hippocampus, and muscle after 8 weeks; perform single‑cell RNA‑seq.
• Extract expression of the 576 BiT age genes per cell, build a Vietoris‑Rips complex, and compute persistent homology and persistent topological Laplacians to obtain Betti‑0,‑1,‑2 and Laplacian spectra.
• Compare diagrams using bottleneck and Wasserstein distances; assess statistical significance with permutation testing.

Potential Outcomes

If rapamycin and CR share topological fingerprints while senolytics diverge, the hypothesis is supported: lifespan extension via mTOR inhibition is a phenocopy of scarcity signalling, not a reversal of damage. Conversely, distinct topological shifts for rapamycin would falsify the stress‑mimicry claim and suggest unique rejuvenating mechanisms.

This approach directly tests whether pharmacological longevity interventions reshape the transcriptome’s shape or merely walk the same stress‑worn path.