带输出抑制的对偶积分（Rein）控制的结构稳定性特性
Structural Stability Properties of Antithetic Integral (Rein) Control with Output Inhibition
AI总结：
本研究针对带输出抑制的对偶积分Rein控制器（AIRC）结构，证明其在温和假设下可确保受控网络的结构稳定性和结构完美适应特性，结果适用于多类生化网络，并提供了验证结构特性条件的计算方法。
摘要：
完美适应是一种已被充分研究的生化稳态行为，是生化调控的核心。尽管稳态和完美适应的概念并不新颖，但其潜在机制及相关的生化调控基元尚未被完全阐明。控制理论的研究揭示了完美适应与积分控制（一种常用的工程控制策略）之间的关联。特别是，近期提出的Antithetic Integral Controller（AIC，对偶积分控制器）已被证明能够成功为其所连接的网络提供完美适应特性。AIC所依赖的两种分子的互补结构为生化网络调控提供了一种灵活的方式，这一特性催生了大量相关研究，包括从数学上阐明其特性、推广其结构以及开发其实现的实验方法。Antithetic Integral Rein Controller（AIRC，对偶积分Rein控制器）是AIC的扩展，其中两种控制器分子均用于调控，由于它有望克服AIC的某些局限性，因而颇具应用前景。本文聚焦于一种带输出抑制的AIRC结构，该结构将两个AIC整合在单一结构中。我们证明，在温和假设下，该控制器能够确保受控网络的结构稳定性和结构完美适应特性，这意味着该特性与网络和控制器的参数无关。该研究结果具有很强的普适性，适用于单分子质量作用网络以及更广泛的网络类别，包括协同网络和Michaelis-Menten网络。我们还提供了一种系统且易用的计算方法，用于验证给定网络是否满足结构特性成立的条件。
英文摘要：
Perfect adaptation is a well-studied biochemical homeostatic behavior lying at the core of biochemical regulation. While the concepts of homeostasis and perfect adaptation are not new, their underlying mechanisms and associated biochemical regulation motifs are not yet fully understood. Insights from control theory unraveled the connections between perfect adaptation and integral control, a prevalent engineering control strategy. In particular, the recently introduced Antithetic Integral Controller (AIC) has been shown to successfully ensure perfect adaptation properties to the network it is connected to. The complementary structure of the two molecules the AIC relies upon allows for a versatile way to control biochemical networks, a property which gave rise to an important body of literature pertaining to mathematically elucidating its properties, generalizing its structure, and developing experimental methods for its implementation. The Antithetic Integral Rein Controller (AIRC), an extension of the AIC in which both controller molecules are used for control, holds many promises as it supposedly overcomes certain limitations of the AIC. We focus here on an AIRC structure with output inhibition that combines two AICs in a single structure. We demonstrate that rhis controller ensure structural stability and structural perfect adaptation properties for the controlled network under mild assumptions, meaning that this property is independent of the parameters of the network and the controller. The results are very general and valid for the class of unimolecular mass-action networks as well as more general networks, including cooperative and Michaelis-Menten networks. We also provide a systematic and accessible computational way for verifying whether a given network satisfies the conditions under which the structural property would hold.
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