t01 — Essential proteins are hubs; the redundancy ratio does not help
Supplied working report; original verdicts not validated.
Review status: Needs review. This is an archival source note, not a passed proof.
notes.md
# t01 — Essential proteins are hubs; the redundancy ratio does not help ## Design Essentiality is a null-mutant viability label from the SGD phenotype file: a protein-coding gene whose null mutant is annotated `inviable` is essential; one annotated `viable` is non-essential. Interaction degree and the mean degree of a protein's partners come from the STRING v12 yeast network, keeping edges at combined score ≥ 700 (high confidence). Two predictions were pre-registered: essential proteins have higher degree (P1), and a degree-to-partner-redundancy ratio predicts better than degree alone (P2). ## What the data show 1,237 essential and 4,936 non-essential genes are present in the network. Essential proteins average 64 partners versus 30 for non-essential ones (median 36 vs 14). Degree alone separates the two with AUC 0.743 (bootstrap 95% CI 0.728–0.757); the medium-confidence threshold (≥400) gives 0.702. The ratio degree/(1 + mean partner degree) reaches AUC 0.657, which is 0.086 lower than degree alone (bootstrap CI −0.099 to −0.073). Given degree, partner redundancy carries a partial rank correlation of +0.04 with essentiality — no independent signal, and in the opposite direction to the posted mechanism. ## Meaning The hub part of the claim is strongly supported, and it is the whole story: degree alone is the best predictor here. Dividing degree by partner redundancy only re-weights the degree signal (hubs attach to many low-degree partners), and it degrades prediction. The "ratio, not degree alone" refinement is not supported in this operationalisation. ## Caveats Mean partner degree is one reading of "redundancy of partners"; it does not capture paralogy or pathway buffering. Essentiality is laboratory-conditional.