Hypothesis

Aging drives a measurable loss of topological complexity in the high‑dimensional gene expression manifold, detectable as a rise in persistence entropy and a decline in higher‑order Betti numbers before conventional differential expression signatures reach significance.

Mechanistic basis

Gene expression states occupy a shape whose loops and voids reflect coordinated regulatory programs across cells. Persistent homology quantifies these features: Betti‑0 counts connected components, Betti‑1 counts loops, Betti‑2 counts voids, and persistence entropy summarizes the distribution of feature lifetimes. With age, cumulative stochastic damage and drift in transcription factor networks reduce the stability of multi‑gene co‑activation patterns, causing short‑lived loops to disappear and long‑lived features to become noisy. This topological simplification lowers the richness of the expression space, which we hypothesize manifests as increasing persistence entropy and decreasing Betti‑1/Betti‑2 persistence.

Testable predictions

1. In mouse liver, kidney, brain and heart single‑cell RNA‑seq datasets collected from young (2 mo), middle (12 mo) and old (24 mo) animals, persistence entropy will show a monotonic increase with age, while Betti‑1 and Betti‑2 persistence will decrease significantly (p<0.01, ANOVA).
2. The age‑related change in persistence entropy will precede, by at least 4 months, the detection of organ‑specific differential expression thresholds used in standard aging clocks (e.g., BiT age) and will correlate stronger with functional readouts such as serum ALT/AST (liver) or creatinine clearance (kidney).
3. Persistence entropy calculated from peripheral blood mononuclear cells of humans will stratify individuals with same chronological age into high‑ and low‑risk groups for age‑related morbidity, independent of transcriptomic age predictors.

Falsifiability

If longitudinal analysis reveals no significant trend in persistence entropy or Betti‑number persistence across aging, or if these topological metrics fail to outperform DEG‑based clocks in predicting physiological decline, the hypothesis is refuted.

References (inline)

• Multi‑organ mouse transcriptomics show organ‑specific aging patterns 1
• Established TDA pipelines for single‑cell biology 2
• Binarized BiT age clock performance 3
• Transcriptomic signatures predict mortality across species 4
• Distinction between topological overlap networks and true TDA 5