Hypothesis

Persistent homology applied to high‑dimensional gene co‑expression networks will reveal a progressive loss of topological invariants—specifically β₁ (loops) and β₂ (voids)—that precedes and causally contributes to functional decline across multiple tissues. Restoring these lost topological features by targeting hub genes that sustain feedback circuits and higher‑order chromatin interactions will delay age‑related phenotypes.

Rationale

Recent work shows that persistent homology quantifies structural brain aging from MRI, capturing loops (β₁) and voids (β₂) that correlate with cognitive decline better than chronological age【1](https://arxiv.org/html/2511.05520v1)​. However, transcriptome analyses remain confined to manifold approximations (UMAP, Monocle3) and lack true topological invariants【2](https://pmc.ncbi.nlm.nih.gov/articles/PMC10277839/)​,【3](https://pmc.ncbi.nlm.nih.gov/articles/PMC12157388/)​,【4](https://pmc.ncbi.nlm.nih.gov/articles/PMC12481971/)​. This gap overlooks the fact that gene regulatory systems are intrinsically topological: feedback loops generate stable expression states (β₁), while higher‑order chromatin arrangements create voids (β₂) that buffer noise. Aging‑associated transcriptional drift likely erodes these invariants, leading to loss of coordination and increased stochasticity.

Mechanistic Insight

We propose that β₁ reflects the integrity of cyclic feedback circuits—such as the core clock, NF‑κB, and p53‑MDM2 loops—whose persistence ensures timely gene bursts and repression. β₂ captures higher‑order organizational voids formed by enhancer‑promoter chromatin hubs; their disappearance signifies regulatory disintegration and ectopic contacts. As cells age, cumulative DNA damage and epigenetic noise degrade these structures, reducing β₁ and β₂ counts in persistence diagrams of co‑expression networks. This topological collapse precedes measurable functional decline because it reduces the network’s capacity to buffer perturbations and maintain attractor states.

Testable Predictions

1. Cross‑tissue topological decay – In young (3 mo) versus aged (24 mo) mice, single‑cell RNA‑seq from blood, liver, and muscle will show a statistically significant reduction in β₁ and β₂ (p < 0.01, effect size >0.5) computed from k‑nearest‑neighbor co‑expression graphs, while β₀ (connected components) remains unchanged.
2. Causal link – CRISPR‑activation of hub genes predicted to sustain loops (e.g., Bmal1 for circadian feedback, Nrf2 for oxidative stress response) in aged mice will increase β₁ and β₂ levels toward youthful values, concomitant with improved tissue‑specific functional assays (e.g., grip strength, glucose tolerance).
3. Rescue specificity – Perturbing non‑hub genes that do not affect network topology will not alter β₁/β₂, confirming that the observed functional improvements are topology‑dependent.
4. Predictive power – Baseline β₁/β₂ values from peripheral blood transcriptomes will predict frailty index and mortality risk better than chronological age or traditional epigenetic clocks (AUC improvement >0.07).

Experimental Approach

• Generate single‑cell transcriptomes (10x Genomics) from multiple tissues of young and aged mice (n = 5 per group).
• Construct k‑NN co‑expression graphs (k = 10) per tissue, compute persistence diagrams using Ripser, and extract β₁, β₂ landscapes.
• Validate topological changes with bulk RNA‑seq time series to ensure robustness across scales.
• Perform in vivo AAV‑CRISPRa targeting selected hub genes in aged mice; reassess topology and phenotype after 4 weeks.
• Apply survival analysis and frailty scoring to correlate topological metrics with outcomes.

Falsifiability

If aged tissues show no significant decrease in β₁/β₂ compared to young, or if modulating hub genes fails to rescue topological invariants and functional readouts, the hypothesis would be refuted. Conversely, confirmation would establish topological invariants as causal biomarkers and therapeutic targets in aging research.