Hypothesis

In the aging brain, neurons that are destined for elimination exhibit a pre‑emptive increase in transcriptomic topological entropy, reflecting a shift from stable, cluster‑like gene expression states to unstable, trajectory‑like states. This rise in entropy signals metabolic inefficiency and weak network integration, triggering microglial phagocytosis via complement‑tagging. Thus, neuronal loss is not random damage but a topology‑guided eviction program that optimizes energy use under declining bioenergetic capacity.

Mechanistic Rationale

1. Energy‑sensing checkpoint – Aging neurons experience declining ATP production and chronic AMPK activation. AMPK phosphorylates the transcriptional co‑activator CBP, altering chromatin accessibility and increasing cell‑to‑cell gene expression variability. This variability manifests as higher 0‑dimensional persistent homology entropy (PH‑entropy) in single‑cell RNA‑seq manifolds.
2. Topological entropy as a functional read‑out – PH‑entropy quantifies how tightly cells cluster in expression space. A rising PH‑entropy indicates a neuron is exploring alternative transcriptional states, a hallmark of losing its attractor basin and becoming a “leaky” node in the cortical attractor landscape.
3. Link to microglial engulfment – Neurons with high PH‑entropy upregulate complement component C1q and secreted phosphatidylserine, “eat‑me” signals that are recognized by microglial CR3 receptors. Experimental blockade of C1q reduces phagocytosis of high‑entropy neurons without affecting low‑entropy counterparts.
4. Feedback to network efficiency – Removing high‑entropy, metabolically costly neurons reduces overall network energy demand while preserving low‑entropy, high‑fidelity nodes, thereby increasing the brain’s computational efficiency per watt—a compensatory optimization rather than pure degeneration.

Testable Predictions

1. Prediction 1 – In longitudinal scRNA‑seq of aged mouse cortex (e.g., 6, 12, 18 mo), neurons that disappear between time points will show a significant increase in PH‑entropy at the earlier time point relative to neurons that persist (effect size >0.5, p<0.01, Mann‑Whitney U test).
2. Prediction 2 – Pharmacological AMPK inhibition (e.g., Compound C) in middle‑aged mice will blunt the age‑related rise in PH‑entropy and reduce subsequent neuronal loss by ~30% compared with vehicle controls.
3. Prediction 3 – CRISPRi‑mediated knock‑down of C1q in microglia will decouple PH‑entropy from phagocytosis: high‑entropy neurons will accumulate without being cleared, leading to ectopic transcriptional outliers detectable as increased manifold dispersion.
4. Prediction 4 – Artificial induction of transcriptional instability (e.g., via transient HDAC inhibition) in young adult neurons will raise PH‑entropy and render them susceptible to microglial engulfment, mimicking the aged phenotype.

Experimental Design

• Subjects: C57BL/6J mice at 6, 12, 18 months (n=6 per age).
• Procedure: Perform intracardiac perfusion, dissect cortex, isolate nuclei for snRNA‑seq (10x Chromium). Include a batch of mice treated with AMPK inhibitor or vehicle from 9–12 months.
• Analysis:
  • Compute PH‑entropy for each neuron using Ripser on the first 30 PCs (following 2).
  • Track neuronal identity via RNA velocity to assign fate (lost vs. persisted).
  • Correlate baseline PH‑entropy with fate using logistic regression.
  • Validate complement upregulation by immunofluorescence for C1q and microglial phagocytosis markers (CD68, IBA1).
  • In parallel, assess ATP levels and AMPK‑pThr172 via Western blot.
• Controls: Young (3 mo) mice; sham‑treated aged mice; microglia‑depleted (PLX5622) cohorts to confirm microglia dependence.

Potential Confounds & Falsifiability

If PH‑entropy does not predict future loss, or if AMPK inhibition fails to alter entropy trajectories, the core premise that transcriptional instability drives eviction is weakened. Likewise, if C1q blockade does not prevent removal of high‑entropy neurons, alternative phagocytic pathways (e.g., Mert‑Gas6) would need consideration. Demonstrating that entropy changes are merely a byproduct of general stress (e.g., elevated Hsp70) rather than a specific signal would also falsify the hypothesis. Conversely, observing the predicted correlations would support a topology‑guided, energy‑optimizing model of neuronal aging.