Topology of the simplest gene switch
arXiv:2503.01717 · doi:10.1103/rr6n-fn82
Abstract
Complex gene regulatory networks often display emergent simple behavior. Sometimes this simplicity can be traced to a nearly equivalent energy landscape, but not always. Here, we show how a topological theory for stochastic and biochemical networks can predict phase transitions between dynamical regimes, where the simplest landscape paradigm would fail. We demonstrate the utility of this topological approach for a simple gene network, revealing a new oscillatory regime in addition to previously recognized multimodal stationary phases. We show how local winding numbers predict the steady-state locations in the single-mode and bimodal phases, and a flux analysis predicts the respective strengths of the steady-state peaks.
5 pages, 4 figures, Supplementary material. In v2: streamlined explanations in the main text and added appendices about global spectrum and counting statistics; In v3: added DOI
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