Control design for sustained oscillation in a two-gene regulatory network

Roderick Edwards, Sehjeong Kim, P. van den Driessche

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)


Control strategies for gene regulatory networks have begun to be explored, both experimentally and theoretically, with implications for control of disease as well as for synthetic biology. Recent work has focussed on controls designed to achieve desired stationary states. Another useful objective, however, is the initiation of sustained oscillations in systems where oscillations are normally damped, or even not present. Alternatively, it may be desired to suppress (by damping) oscillations that naturally occur in an uncontrolled network. Here we address these questions in the context of piecewise-affine models of gene regulatory networks with affine controls that match the qualitative nature of the model. In the case of two genes with a single relevant protein concentration threshold per gene, we find that control of production terms (constant control) is effective in generating or suppressing sustained oscillations, while control of decay terms (linear control) is not effective. We derive an easily calculated condition to determine an effective constant control. As an example, we apply our analysis to a model of the carbon response network in Escherichia coli, reduced to the two genes that are essential in understanding its behavior.

Original languageEnglish
Pages (from-to)453-478
Number of pages26
JournalJournal of Mathematical Biology
Issue number4
Publication statusPublished - Apr 2011
Externally publishedYes


  • Feedback control
  • Gene regulatory networks
  • Oscillations
  • Piecewise-affine systems

ASJC Scopus subject areas

  • Modelling and Simulation
  • Agricultural and Biological Sciences (miscellaneous)
  • Applied Mathematics


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