Topological Lock: A Persistent Homology Framework Predicts a Dimensional Collapse that Drives Coordinated Hallmark Aging

Hypothesis

Aging reflects a topological constraint: as organisms age, the high‑dimensional space of gene expression loses independent loops and voids, collapsing onto a lower‑dimensional attractor that simultaneously drives the classic hallmarks.

Mechanistic Basis

Recent work shows that aging hallmarks form an interconnected network [1] and that transcriptional shifts resemble those of long‑lived states [2]. Age‑invariant genes, enriched for protein‑stability pathways, are missing from epigenetic alteration, senescence, and extracellular‑matrix modules [3], hinting that these three processes sit at a boundary where adaptive compensation fails. Persistent homology can detect transient cell states during differentiation [4]; we propose that an analogous analysis will reveal a conserved loss of specific Betti numbers (e.g., β1 and β2) as chronological age advances. This loss represents a Topological Lock that reduces the number of viable expression trajectories, forcing cells into a limited set of states that manifest as epigenetic drift, secretory senescence, and matrix remodeling.

Testable Predictions

1. Single‑cell RNA‑seq from multiple tissues across the lifespan will show a stereotyped, species‑specific decline in the persistence of 1‑dimensional loops (β1) and 2‑dimensional voids (β2) at a conserved physiological age, independent of genetic background.
2. Interventions known to extend lifespan (dietary restriction, rapamycin, genetic reduction of IGF‑1 signaling) will preserve higher Betti numbers longer than controls, correlating with delayed onset of the three boundary hallmarks.
3. Artificial reduction of topological complexity—e.g., CRISPRi knock‑down of genes that act as "topological organizers" such as chromatin‑loop regulators (CTCF, cohesin subunits)—will accelerate the decline in β1/β2 and precipitate early emergence of epigenetic drift, SASP, and matrix‑degrading transcripts.
4. Restoring lost topological features, for instance by overexpressing factors that promote enhancer‑promoter looping, will rescue Betti numbers and attenuate hallmark progression without directly altering any single hallmark.

Potential Experiments

• Perform time‑resolved scRNA‑seq on mouse liver, brain, and muscle from 2 mo to 30 mo; compute persistent homology barcodes for each cohort and track β1/β2 trajectories.
• Compare wild‑type mice to those on a 30 % calorie‑restricted diet; test whether the age at which β1 falls below a threshold is shifted.
• Use inducible shRNA against CTCF in adult mice; measure hallmarks (DNA methylation clocks, p16^Ink4a^ SASP, collagen‑crosslinking) and persistent homology at 6 mo and 12 mo.
• In parallel, over‑express the looping factor Mediator subunit MED1 in aged mice and assess whether β1/β2 recover and hallmark scores improve.

Possible Confounds

Technical noise can distort homology estimates; we will mitigate this by using robust dimensionality reduction (e.g., scVI) and bootstrapping barcode stability. Cell‑type composition shifts could masquerade as topological loss; therefore analyses will be restricted to matched cell‑type clusters or performed on integrated multi‑omics data.

If the predicted dimensional collapse fails to appear across species or interventions, the hypothesis of a topological upstream controller will be falsified, steering research back toward molecular‑centric models.