Topology, Autocatalysis, and Epigenetic Control: How Network Architecture Shapes Biological State Transitions Across Scales

Abstract

Version 3 (2026-09-26) corrects errors found by an independent audit of version 2 and by re-checking every cited arXiv abstract. It removes two overstatements from the abstract (that autocatalytic completeness defines a lower bound on network complexity, and that topological data analysis and GNN attribution independently recover a hub-centric signature), stops presenting the cited authors' findings as "we show", corrects the false statement that the abstract of arXiv:2606.05196 does not report its re-analysis of 122 Boolean network models (it does), attributes the phrase "exponential suppression" to that paper's version 1 abstract, ties the genes TP53, BRCA1, ESR1 and MYC to the consensus ranking they belong to and expands SA correctly as Saliency Attribution, corrects the corpus count from 13 considered and 6 filtered to 12 and 5, and updates the revision status of arXiv:2605.16781. The thesis is unchanged. The full list of corrections is at the top of the PDF, and the version 2 change log remains as an appendix. A follow-up review on the same day led to three further wording fixes: the third primitive no longer merges two papers ("topological and hub structure of interaction networks"), the Limitations section no longer links the Betti-3 structures to the confirmed driver genes, and an internal reference was removed from the change log. A candidate structural pattern emerges across several recent preprints in molecular networks, population biology, genomics, and biomolecular systems: the architecture of a network, meaning its topology, stoichiometric constraints, and feedback geometry, does not merely describe a biological state but may actively govern which states are reachable, how transitions between them occur, and at what cost. This synthesis draws on seven papers spanning q-bio.MN, q-bio.PE, q-bio.GN, and q-bio.BM to argue, explicitly as a heuristic reading rather than a formal derivation, that three structural primitives, (1) autocatalytic closure, (2) epigenetic feedback geometry, and (3) topological and hub structure of interaction networks, may jointly constrain the landscape of accessible biological states at molecular, cellular, and ecological scales. The cited sources report that, under mild and general conditions, any RAF set is stoichiometrically autocatalytic, so that one autocatalytic completeness condition implies the other; that DNA methylation feedback separates timescales and may reshape expression landscapes without requiring external switching signals; and, in two separate studies of cancer networks, that persistent homology recovers structurally relevant driver genes and that graph neural network attribution peaks around disease-associated hubs. Whether these two cancer-network results pick out related genes has not been tested; we propose it as a hypothesis. The control-theoretic framing of aging as progressive loss of safe controllability provides a unifying vocabulary: each primitive can be read as a constraint on the reachable set of biological states. The central falsification path is that intervention order in epigenetic reprogramming should predict outcome in a manner calculable from Lie brackets of the relevant vector fields, a prediction of this synthesis that is experimentally testable in organoid or in vitro cell-fate switching assays. One weakly connected source is segregated to an explicit addendum, the selection process is detailed in a dedicated subsection, and abstract-only reading limitations are flagged throughout. Authorship: Saluca Agentic AI Research Team (Saluca LLC). AI-drafted synthesis from an arXiv preprint corpus; version 1 drafted 2026-06-07, version 3 revised 2026-09-26. Cited arXiv preprints: 2605.07433, 2605.11450, 2605.14562, 2605.16781, 2605.17220, 2605.19071, 2605.19252, 2605.21502, 2605.21945, 2605.25523, 2605.29958, 2606.05196 AI disclosure. This work was produced with an agentic AI research apparatus operated by Saluca Labs. The apparatus drafted, searched and analysed under direction. Cristian Ruvalcaba is the human author and is accountable for the content. No AI system is listed as an author or contributor, because authorship entails accountability that a model cannot hold; this disclosure is the credit, and it is deliberately the whole of it.