Robustness analysis of a nucleic acid controller for a dynamic biomolecular process using the structured singular value

Nuno Paulino, Mathias Foo, Jongmin Kim, Declan Bates

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)
9 Downloads (Pure)


In the field of synthetic biology, theoretical frameworks and software tools are now available that allow control systems represented as chemical reaction networks to be translated directly into nucleic acid-based chemistry, and hence implement embedded control circuitry for biomolecular processes. However, the development of tools for analysing the robustness of such controllers is still in its infancy. An interesting feature of such control circuits is that, although the transfer function of a linear system can be easily implemented via a chemical network of catalysis, degradation and annihilation reactions, this introduces additional nonlinear dynamics, due to the annihilation kinetics. We exemplify this problem for a dynamical biomolecular feedback system, and demonstrate how the structured singular value (μ) analysis framework can be extended to rigorously analyse the robustness of this class of system. We show that parametric uncertainty in the system affects the location of its equilibrium, and that this must be taken into account in the analysis. We also show that the parameterisation of the system can be scaled for experimental feasibility without affecting its robustness properties, and that a statistical analysis via Monte Carlo simulation fails to uncover the worst-case uncertainty combination found by μ-analysis.

Original languageEnglish
Pages (from-to)34-44
Number of pages11
JournalJournal of Process Control
Early online date15 May 2019
Publication statusPublished - Jun 2019

Bibliographical note

NOTICE: this is the author’s version of a work that was accepted for publication in Journal of Process Control. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Process Control [78], (2019) DOI: 10.1016/j.jprocont.2019.02.009

© 2019, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International


  • Chemical reaction networks
  • Nonlinear systems
  • Robustness
  • Synthetic biology
  • Systems and control theory

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modelling and Simulation
  • Computer Science Applications
  • Industrial and Manufacturing Engineering


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