Hypothesis

Aging is accompanied by a progressive loss of topological complexity in the transcriptome manifold, measurable as a decline in higher-order Betti numbers (β₁, β₂) derived from persistent homology of gene expression coordinates.

Mechanistic Basis

Single‑cell RNA‑seq captures cell‑specific expression vectors that, when aggregated, form a high‑dimensional point cloud. Chromatin accessibility changes and transcriptional noise with age are predicted to smooth this cloud, filling in loops and voids that correspond to persistent homology classes. Consequently:

• β₀ (connected components) remains stable or increases slightly due to clonal expansion.
• β₁ (loops) and β₂ (voids) decrease monotonically with chronological age.

It's increasingly clear that this view extends recent applications of TDA to cancer transcriptomics arXiv preprint on TDA in cancer and integrates hallmarks of aging such as altered intercellular communication PMC10277839 and mitochondrial dysfunction PMC12157388 by treating them as drivers of topological simplification.

Testable Predictions

1. In murine tissues (e.g., liver, brain) sampled across the lifespan, persistent homology of normalized expression profiles will show a statistically significant negative correlation between age and β₁/β₂ (p < 0.01, Spearman).
2. Interventions known to extend lifespan—rapamycin, dietary restriction, or senolytic treatment—will attenuate the age‑related decline in β₁ and β₂ compared with controls.
3. Artificially increasing transcriptional noise (e.g., via heterozygous knockout of RNA polymerase II fidelity factors) will accelerate the loss of β₁/β₂, whereas enhancing chromatin barrier integrity (e.g., over‑expressing histone H1) will preserve topological features.

Experimental Approach

• Generate single‑cell RNA‑seq atlases from young (3 mo), middle (12 mo), and old (24 mo) mice for at least two tissues.
• Preprocess data (log‑normalize, batch‑correct) and construct a Vietoris–Rips complex on the first 30 PCs.
• Compute persistence diagrams and extract Betti numbers β₀, β₁, β₂ across filtration scales.
• Use mixed‑effects models to test age and treatment effects on Betti numbers, controlling for animal ID.
• Validate findings in human peripheral blood mononuclear cells from publicly available age‑stratified datasets (e.g., GTEx).

Potential Implications

If confirmed, topological metrics could serve as integrative, theory‑driven biomarkers of biological age that capture multi‑gene interactions missed by single‑gene clocks. Moreover, linking topological decay to specific molecular mechanisms would provide a unifying framework for evaluating geroprotective strategies.

Keywords: topological data analysis, persistent homology, Betti numbers, aging transcriptome, single‑cell RNA‑seq