关于生物化学中输入信号导数的估计
On Estimating Derivatives of Input Signals in Biochemistry
AI总结：
本文对用于生化过程PID控制的导数模块CRN进行了严格数学分析，量化了误差，并展示了其在合成生物学误差校正设计及BioModels中振荡器与控制系统模型识别中的应用。
摘要：
输入信号导数的在线估计在控制理论与工程中广泛应用。然而，在化学反应网络（CRN）领域，实现这一目标会引发若干特定问题。此前已提出一种用于生化过程PID控制的导数模块CRN模式，并利用Tikhonov极限定理证明了其正确性。本文对该CRN进行了详细的数学分析，从而阐明了所计算的量，并量化了作为反应动力学参数函数的误差。从合成生物学的角度，我们展示了如何利用这一分析设计误差校正项，以借助CRN在线计算涉及导数的函数。从系统生物学的角度，我们给出了BioModels中包含（在子图满射的意义下）核心导数CRN的模型列表，其中大多数是细胞中的振荡器和控制系统模型，并详细讨论了其中两个例子：一个昼夜节律钟模型和一个双稳态开关模型。
英文摘要：
The online estimation of the derivative of an input signal is widespread in control theory and engineering. In the realm of chemical reaction networks (CRN), this raises however a number of specific issues on the different ways to achieve it. A CRN pattern for implementing a derivative block has already been proposed for the PID control of biochemical processes, and proved correct using Tikhonov's limit theorem. In this paper, we give a detailed mathematical analysis of that CRN, thus clarifying the computed quantity and quantifying the error done as a function of the reaction kinetic parameters. In a synthetic biology perspective, we show how this can be used to design error correcting terms to compute online functions involving derivatives with CRNs. In the systems biology perspective, we give the list of models in BioModels containing (in the sense of subgraph epimorphisms) the core derivative CRN, most of which being models of oscillators and control systems in the cell, and discuss in detail two such examples: one model of the circadian clock and one model of a bistable switch.
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