Operon dynamics with state dependent transcription and/or translation delays

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Springer Science and Business Media LLC


Transcription and translation retrieve and operationalize gene encoded information in cells. These processes are not instantaneous and incur significant delays. In this paper we study Goodwin models of both inducible and repressible operons with state-dependent delays. The paper provides justification and derivation of the model, detailed analysis of the appropriate setting of the corresponding dynamical system, and extensive numerical analysis of its dynamics. Comparison with constant delay models shows significant differences in dynamics that include existence of stable periodic orbits in inducible systems and multistability in repressible systems. A combination of parameter space exploration, numerics, analysis of steady state linearization and bifurcation theory indicates the likely presence of Shilnikov-type homoclinic bifurcations in the repressible operon model.


This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: http://dx.doi.org/10.1007/s00285-021-01693-0


operon dynamics state dependent transcription translation delays


Gedeon, T., Humphries, A. R., Mackey, M. C., Walther, H. O., & Wang, Z. (2022). Operon dynamics with state dependent transcription and/or translation delays. Journal of Mathematical Biology, 84(1), 1-74.
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