Hypothesis

Temporal persistence diagrams constructed from aging transcriptomes will exhibit a predictable increase in Betti‑1 (loops) and a decrease in Betti‑0 (connected components) that mirrors the erosion of gene‑regulatory circuitry across tissues, and these topological trajectories will correlate with biological age and mortality risk.

Mechanistic reasoning

1. Lost feedback loops generate persistent holes – In youthful transcriptomes, co‑expressed genes form tightly coupled modules that appear as dense clusters in expression space, yielding low‑dimensional simplicial complexes with few 1‑dimensional holes. Age‑associated epigenetic drift (e.g., loss of enhancer‑promoter contacts) weakens specific pairwise correlations, causing the birth of loops that persist over filtration scales because the remaining correlations cannot fill the gap. These loops represent topological signatures of decoupled regulatory programs.

2. Component fragmentation reflects module dissolution – As aging proceeds, whole transcriptional programs split into semi‑independent sub‑modules, increasing the number of connected components in the Vietoris–Rips complex at low filtration values. Persistent homology therefore records a decline in Betti‑0 that tracks the progressive loss of global coordination.

3. Tissue‑specific rates encode functional decline – Tissues with high regenerative demand (e.g., intestine, skin) are expected to show faster Betti‑1 accrual, whereas post‑mitotic tissues (brain, heart) may display slower loop formation but earlier Betti‑0 loss, mirroring their distinct aging phenotypes.

Testable predictions

• Prediction 1: In cross‑sectional human RNA‑Seq datasets (GTEx, SRA) stratified by age, the average persistence entropy of Betti‑1 features will rise monotonically with donor age in each tissue (Spearman ρ > 0.4, p < 0.001).
• Prediction 2: Individuals whose transcriptomic Betti‑1 trajectory exceeds the tissue‑specific median by >1 SD will have a hazard ratio for all‑cause mortality ≥1.3 after adjusting for chronological age and sex (Cox model).
• Prediction 3: Interventions known to preserve chromatin topology (e.g., NAD⁺ supplementation, rapamycin) will attenuate the age‑related increase in Betti‑1 in murine tissues by ≥20 % compared with controls (two‑way ANOVA, interaction p < 0.01).

Falsifiability

If longitudinal sampling of the same individuals shows no systematic change in Betti‑1 or Betti‑0 entropy with age, or if the topological metrics fail to predict mortality beyond standard covariates, the hypothesis is refuted. Likewise, a lack of differential response to topological‑preserving interventions would falsify the mechanistic link between chromatin loop integrity and transcriptional topology.

Implementation sketch

• Process raw FASTQ → TPM matrices per sample.
• Build a Vietoris–Rips filtration on the top 5000 most variable genes using Pearson distance.
• Compute persistence diagrams with Ripser or GUDHI; extract Betti‑0 and Betti‑1 persistence landscapes.
• Summarize each diagram by persistence entropy and average lifespan of homological features.
• Model associations with age, mortality, and treatment status using mixed‑effects models.

This framework directly addresses the gap highlighted by —temporal persistence analysis of multi‑tissue transcriptomic manifolds—and offers a concrete, falsifiable route to uncover the topological invariants of biological decay.