Yi Zhao, Thomas P. Wytock, Kimberly A. Reynolds and Adilson E. Motter (2024), Science Advances 10(35):eado3232 — DOI-10.1126/sciadv.ado3232, ARXIV-2409.04513
Key takeaways
- What “irreversible” means here. A transient perturbation is irreversible when switching one gene off (knockout) or on (overexpression) until the network settles, then releasing it, leaves the network in a different attractor from the one it started in. In a deterministic model this is permanent by construction; the authors say noise and the cell cycle would make it long-lived rather than permanent.
- The model. RegulonDB’s network (1859 genes, 5119 signed edges, 148 dual or unknown edges dropped) is cut to its largest origon, rooted at phoB (1406 genes), and trimmed to a core of 87 genes and 290 edges. No gene outside the core can cause irreversibility. The rules are not known, so the paper samples sign-consistent, nested canalizing Boolean rules (about 10^61 are possible), with two parameters, nestedness r and bias s, and two input orderings (“concentrated” and “diffuse” control). Updates are synchronous.
- The structural result. 51 of the 87 core genes admit an irreversible perturbation for some rules. The other 36 cannot: 32 are leaves and 4 feed only autorepressive leaves. Every gene that can influence a positive circuit (a cycle with an even number of repressions) is irreversible for some rules. A path-weight count K_u of routes to strongly connected components containing positive circuits accounts for 55–62% of the variance in irreversibility probability (p̂_u = aK_u^b, b = 0.68 ± 0.09 diffuse, 0.93 ± 0.14 concentrated).
- Which way the transitions go. Weighted by basin size, the rate of irreversibility roughly halves, and the initial attractors’ basins average about one-eighth of the final ones’: transient perturbations tend to move the network from small basins to large ones.
- crp knockout is the most irreversible perturbation, with 68 irreversible response genes. Against RNA-seq of strains evolved for 10 days after a permanent crp knockout, the sign predicted by the shortest signed path from crp matches the observed change for 10 of 11 strongly changed genes in batch and 33 of 42 in chemostat (average precision 0.99 and 0.85, P < 0.01). Among strongly changed genes, the irreversible responders matched the predicted sign 8 of 9 times and the reversible ones 2 of 2 in batch, 28 of 34 against 5 of 8 in chemostat; P = 0.03 for the two conditions together.
- A testable prediction. Transient crp knockdown by inducible CRISPR interference should leave self-activating, crp-activated genes (zraR, melR, rhaRS) switched on, in growth conditions chosen to put them in a bistable range. A Hill-function model says stronger self-activation and steeper responses favour it.
Standing in the record
Filed on 2026-10-09 at the owner’s request, with no stated context, and read on its own merits the same day (NOTE-655).
The record’s standard for evidence of alternative stable states is THEORY-136: only hysteresis, dependence on the initial state, or a lasting shift after a temporary disturbance, with slow return excluded, comes close. This paper defines irreversibility as the third of these and predicts it across a whole regulatory network, but shows it only in models. The finding is filed as THEORY-178, Proposed until an experiment of that kind is read.