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Robust Tunable Transcriptional Oscillators Using Dynamic Inversion

Kulkarni, Vishwesh V. and Paranjape, Aditya A. and Chung, Soon-Jo (2014) Robust Tunable Transcriptional Oscillators Using Dynamic Inversion. In: A Systems Theoretic Approach to Systems and Synthetic Biology I: Models and System Characterizations. Springer Netherlands , Berlin, pp. 103-119. ISBN 978-94-017-9040-6. http://resolver.caltech.edu/CaltechAUTHORS:20161201-103533605

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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 L_2 gain stability of this 3-node network and generalize it to the case of N-node networks.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1007/978-94-017-9041-3_4DOIArticle
http://link.springer.com/chapter/10.1007%2F978-94-017-9041-3_4PublisherArticle
ORCID:
AuthorORCID
Chung, Soon-Jo0000-0002-6657-3907
Additional Information:© 2014 Springer Science+Business Media Dordrecht. 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.
Group:GALCIT
Funders:
Funding AgencyGrant Number
NSFCCF-0845650
Army Research Office (ARO)W911NF-10-1-0296
Subject Keywords:Transcriptional network; Elowitz-Leibler; Dynamic inversion; Adaptive control; ℒ1 adaptive control; mRNA; Protein; Tracking controller; Stability; Zames-Falb multiplier
Record Number:CaltechAUTHORS:20161201-103533605
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20161201-103533605
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:72491
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:01 Dec 2016 19:30
Last Modified:04 Jan 2017 19:30

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