关于核酸反馈控制器稳定性的研究
On the stability of nucleic acid feedback controllers
AI总结：
本文研究了在核酸基化学中使用反馈控制器的设计稳定性问题，通过分析DSD反应引入的非线性动态，揭示了线性设计与实际化学网络稳定性之间的差异，并通过实例和软件工具验证了这一现象。
摘要：
近期的研究展示了如何利用化学反应网络理论来设计可以生物实现的动态系统，基于级联DNA链置换（DSD）反应构建了先进的开环电路。然而，迄今为止，在开发用于此背景下反馈控制器系统设计的理论工具方面进展有限。本文开发了关于核酸控制器平衡、稳定性和动态的基础理论结果。特别地，我们证明了使用DSD反应实现反馈控制器会引入额外的非线性动态，即使在纯线性设计（如PI控制器）的情况下也是如此。通过分解这些不可观测非线性动态的影响，我们表明，一般情况下线性系统设计的稳定性并不必然意味着底层化学网络的稳定性，当引入反馈互连时，这种稳定性可能在实验变异下丧失。我们深入分析了一个示例，展示了线性设计无法捕捉作为DSD反应网络实现的完整非线性系统的不稳定性，并进一步通过定制的VisualDSD软件工具验证了这些结果。我们的分析突显了这一重要新类反馈控制系统许多有趣且独特的特性。
英文摘要：
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.
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