On the stability of nucleic acid feedback controllers
For researchers designing nucleic acid-based feedback control systems, this work reveals a critical gap between linear design and nonlinear implementation, providing necessary theoretical insights for stability analysis.
The paper develops foundational theory for nucleic acid feedback controllers, showing that DNA strand displacement implementations introduce nonlinear dynamics that can cause instability even when the linear design is stable. This is demonstrated through analysis and simulation of a PI controller example.
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 network, which can be lost under experimental variability when feedback interconnections are introduced. We provide an in-depth theoretical analysis of an example illustrating this phenomenon, whereby 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 VisualDSD, a bespoke software tool for simulating nucleic acid-based circuits. Our analysis highlight the many interesting and unique characteristics of this important new class of feedback control systems.