On the stability of nucleic acid feedback control systems

Nuno Paulino, Mathias Foo, Jongmin Kim, Declan G. Bates

Research output: Contribution to journalArticle

Abstract

Recent work has shown how chemical reaction network theory may be used to design dynamical systems that can be implemented biologically in nucleic acid-based chemistry. While this has allowed the construction of advanced open-loop circuitry based on cascaded DNA strand displacement (DSD) reactions, little progress has so far been made in developing the requisite theoretical machinery to inform the systematic design of feedback controllers in this context. Here, we develop a number of foundational theoretical results on the equilibria, stability, and dynamics of nucleic acid controllers. In particular, we show that the implementation of feedback controllers using DSD reactions introduces additional nonlinear dynamics, even in the case of purely linear designs, e.g. PI controllers. By decomposing the effects of these non-observable nonlinear dynamics, we show that, in general, the stability of the linear system design does not necessarily imply the stability of the underlying chemical reaction network, which can be lost under experimental variability when feedback interconnections are introduced. We provide an in-depth theoretical analysis, and present an example to illustrate when the linear design does not capture the instability of the full nonlinear system implemented as a DSD reaction network, and we further confirm these results using Visual DSD, a bespoke software tool for simulating nucleic acid-based circuits. Our analysis highlights the many interesting and unique characteristics of this important new class of feedback control systems.
Original languageEnglish
Article number 109103
Pages (from-to)(In-Press)
JournalAutomatica
Volume119
Early online date29 Jun 2020
DOIs
Publication statusPublished - Sep 2020

Keywords

  • Synthetic biology
  • Chemical reaction networks
  • Nucleic acids
  • trand displacement circuits
  • Feedback control
  • Nonlinear systems

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