Topological Entropy of Aging Transcriptomes Predicts Tissue-Specific Functional Decline via Persistent Homology of Gene Expression Manifolds

Hypothesis Aged transcriptomes exhibit increased topological entropy, reflected by higher Betti numbers and longer-lived homology classes in persistence diagrams, which directly correlates with loss of tissue‑specific function and predicts physiological decline across organisms.

Background Aging drives a DiCo pattern where developmental divergence gives way to convergent expression, accompanied by upregulated inflammation, oxidative stress, and downregulated mitochondrial/ribosomal programs (DiCo pattern; inflammatory/mitochondrial signatures; Aging Fly Cell Atlas). Concurrently, cell‑to‑cell transcriptional variance rises, suggesting a remodelling of the underlying expression manifold (transcriptional variance). Meta‑analysis of multi‑species cohorts confirms these patterns are robust (multi‑species meta‑analysis). Parallel changes in 3D genome architecture, such as increased TAD boundary strength in aged brain, hint that large‑scale structural reorganization accompanies transcriptional shifts (TAD boundary strength). Persistent homology quantifies shape features such as loops (β₁) and voids (β₂) that survive across filtration scales, providing a scalar topological entropy metric.

Mechanistic Rationale This hypothesis proposes that convergent aging expression reduces the dimensionality of gene‑regulatory networks, collapsing distinct developmental trajectories into a lower‑dimensional attractor. This collapse creates redundant regulatory cycles that manifest as persistent 1‑dimensional homology (loops) in the expression point cloud. Simultaneously, stochastic stress‑induced bursts generate transient higher‑dimensional features (voids) that appear as short‑lived β₂ classes. The net increase in β₁ persistence and β₂ birth‑death entropy captures both deterministic convergence and stochastic noise, together constituting topological entropy. This entropy reflects a loss of information‑rich, high‑dimensional states required for specialized tissue functions, thereby linking topology to functional decline.

Testable Predictions

1. Persistence diagrams constructed from single‑cell RNA‑seq of young versus aged tissues will show a statistically significant increase in the total persistence (sum of lifetimes) of H₁ classes and a rise in the Shannon entropy of H₂ birth‑death pairs, using pipelines that leverage recent quantum‑algorithm advances (quantum algorithms for persistence).
2. The magnitude of this topological entropy will correlate negatively with tissue‑specific functional readouts (e.g., contractile force in muscle, electrophysiological firing rate in neurons, filtration rate in kidney) across individuals.
3. Perturbations that suppress convergent aging signatures—such as chronic NAD⁺ boosting or inhibition of NF‑κB—will reduce the observed increase in H₁ persistence and H₂ entropy, rescuing functional metrics.
4. Machine‑learning models using topological entropy as a feature will outperform differential‑expression‑only predictors of age‑related mortality in cross‑validation cohorts.

Methods Outline

• Obtain publicly available single‑cell atlases (Aging Fly Cell Atlas, Tabula Muris Senescence, human GTEx aging subsets) (Aging Fly Cell Atlas; Tabula Muris Senescence; GTEx aging subsets).
• Construct gene‑expression point clouds per tissue, age bin, and individual; apply Vietoris–Rips filtration; compute persistence diagrams for H₀, H₁, H₂ using existing pipelines (e.g., GUDHI, Ripser) that leverage recent quantum‑algorithm advances for efficiency (quantum algorithms for persistence).
• Summarize diagrams via persistence landscapes or persistence entropy; calculate Betti number curves and entropy measures.
• Fit linear mixed‑effects models relating topological entropy to functional phenotypes, controlling for batch and species.
• Validate predictions in intervention cohorts (e.g., NAD⁺ booster mouse study) and in independent human aging datasets.

Potential Outcomes and Falsifiability If aged tissues show no increase in H₁ persistence or H₂ entropy compared to young controls, or if these topological metrics fail to predict functional decline, the hypothesis is falsified. Conversely, a consistent rise in topological entropy that predicts loss of function and is reversible by pathway‑specific interventions would support the mechanistic link between manifold topology and aging‑associated functional decay.