Robust tunable transcriptional oscillators using dynamic inversion

Vishwesh V. Kulkarni, Aditya A. Paranjape, Soon-Jo Chung

Research output: Chapter in Book/Report/Conference proceedingChapter


We present a theory and associated algorithms to synthesize controllers that may be used to build robust tunable oscillations in biological networks. As an illustration, we build robust tunable oscillations in the celebrated repressilator synthesized by Elowitz and Leibler. The desired oscillations in a set of mRNA's and proteins are obtained by injecting an oscillatory input as a reference and by synthesizing a dynamic inversion based tracking controller. This approach ensures that the repressilator can exhibit oscillations irrespective of (1) the maximum number of proteins per cell and (2) the ratio of the protein lifetimes to the mRNA lifetimes. The frequency and the amplitude of at least one output (either mRNA or protein) can now be controlled arbitrarily. In addition, we characterize the gain stability of this 3-node network and generalize it to the case of -node networks.

Original languageEnglish (US)
Title of host publicationA Systems Theoretic Approach to Systems and Synthetic Biology I
Subtitle of host publicationModels and System Characterizations
PublisherSpringer Netherlands
Number of pages17
ISBN (Electronic)9789401790413
ISBN (Print)940179040X, 9789401790406
StatePublished - Mar 1 2014


  • Adaptive control
  • Dynamic inversion
  • Elowitz-Leibler
  • Protein
  • Stability
  • Tracking controller
  • Transcriptional network
  • Zames-Falb multiplier
  • adaptive control
  • mRNA

ASJC Scopus subject areas

  • Medicine(all)

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