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  • Open Access

Topology of the simplest gene switch

Aleksandra Nelson1, Peter Wolynes1,2,3,4, and Evelyn Tang1,3,*

  • 1Center for Theoretical Biological Physics, Rice University, Houston, Texas 77005, USA
  • 2Department of Chemistry, Rice University, Houston, Texas 77005, USA
  • 3Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA
  • 4Department of Biosciences, Rice University, Houston, Texas 77005, USA

  • *Contact author: e.tang@rice.edu
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Phys. Rev. Research 7, 043115 – Published 29 October, 2025

DOI: https://doi.org/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.

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Phys. Rev. Research 7, 043115– Published 29 October, 2025
  • Received 24 February 2025
  • Revised 10 July 2025
  • Accepted 7 October 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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