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Robust Tunable Transcriptional Oscillators Using Dynamic Inversion

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A Systems Theoretic Approach to Systems and Synthetic Biology I: Models and System Characterizations

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Abstract

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 \({\fancyscript{L}}_2\) gain stability of this 3-node network and generalize it to the case of \(N\)-node networks.

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Acknowledgments

We thank Prof. Michael Elowitz (California Institute of Technology) for clarifying our doubts on the ODE model of the EL repressilator. This research is supported, in part, by the NSF CAREER Award 0845650, NSF BIO Computing, NSF Computing and Communications Foundationsx, and the U.S. Army Research Office Award W911NF-10-1-0296. Competing Interests: There are none. Author’s Contributions: VVK derived Lemmae 1 and 2, and Theorems 3 and 4. VVK, AAP, and SJC synthesized the dynamic inversion control. AAP simulated the closed loop system using MATLAB.

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Authors and Affiliations

  1. University of Minnesota, Minneapolis, MN, USA

    Vishwesh V. Kulkarni

  2. University of Illinois at Urbana Champaign, Urbana, IL, USA

    Aditya A. Paranjape & Soon-Jo Chung

Authors
  1. Vishwesh V. Kulkarni
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  2. Aditya A. Paranjape
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  3. Soon-Jo Chung
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Corresponding author

Correspondence to Vishwesh V. Kulkarni .

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Editors and Affiliations

  1. Electrical and Computer Engineering, University of Minnesota, Minneapolis, Minnesota, USA

    Vishwesh V. Kulkarni

  2. Bioengineering, Imperial College, London, United Kingdom

    Guy-Bart Stan

  3. Biotechnology, Indian Institute of Technology Madras, Chennai, India

    Karthik Raman

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Kulkarni, V.V., Paranjape, A.A., Chung, SJ. (2014). Robust Tunable Transcriptional Oscillators Using Dynamic Inversion. In: Kulkarni, V., Stan, GB., Raman, K. (eds) A Systems Theoretic Approach to Systems and Synthetic Biology I: Models and System Characterizations. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-9041-3_4

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