Integral feedback control is commonly used in mechanical and electrical systems to achieve zero steady-state error following an external disturbance. Equivalently, in biological systems, a property known as robust perfect adaptation guarantees robustness to environmental perturbations and return to the pre-disturbance state. Previously, Briat et al proposed a biomolecular design for integral feedback control (robust perfect adaptation) called the antithetic feedback motif. The antithetic feedback controller uses the sequestration binding reaction of two biochemical species to record the integral of the error between the current and the desired output of the network it controls. The antithetic feedback motif has been successfully built using synthetic components in vivo in Escherichia coli and Saccharomyces cerevisiae cells. However, these previous synthetic implementations of antithetic feedback have not produced perfect integral feedback control due to the degradation and dilution of the two controller species. Furthermore, previous theoretical results have cautioned that integral control can only be achieved under stability conditions that not all antithetic feedback motifs necessarily fulfill. In this paper, we study how to design antithetic feedback motifs that simultaneously achieve good stability and small steady-state error properties, even as the controller species are degraded and diluted. We provide simple tuning guidelines to achieve flexible and practical synthetic biological implementations of antithetic feedback control. We use several tools and metrics from control theory to design antithetic feedback networks, paving the path for the systematic design of synthetic biological controllers.

积分反馈控制通常用于机械和电气系统，以在外部干扰后实现零稳态误差。等效地，在生物系统中，被称为稳健完美适应的特性保证了对环境扰动的稳健性并返回到扰动前的状态。此前，Briat等人提出了一种用于积分反馈控制（稳健完美适应）的生物分子设计，称为对立反馈基序。对立反馈控制器使用两种生化物质的螯合结合反应来记录电流与其控制的网络的期望输出之间的误差积分。对偶反馈主题已经使用合成部件已成功建立在体内的大肠杆菌和酿酒酵母细胞。然而，由于两种控制器种类的退化和稀释，这些以前的对立反馈的综合实现并没有产生完美的积分反馈控制。此外，先前的理论结果警告说，积分控制只能在并非所有对立反馈基序都必须满足的稳定性条件下实现。在本文中，我们研究了如何设计同时实现良好稳定性和小稳态误差特性的对立反馈基序，即使控制器种类被降解和稀释。我们提供了简单的调整指南，以实现对反反馈控制的灵活实用的合成生物学实现。我们使用控制理论中的几种工具和度量来设计对立的反馈网络，