确定性反应网络中消除中间物种的解的一致逼近
Uniform Approximation of Solutions by Elimination of Intermediate Species in Deterministic Reaction Networks
摘要：
化学反应通常通过中间物质的形成和消耗来进行。一个例子是在酶促反应中底物-酶复合物的产生和随后的降解。在本文中，我们提供了一个设置，常微分方程的基础上，在其中的中间物种的存在对生物系统的整体动力学的影响很小。该结果提供了一种通过消除中间组分来进行模型降阶的方法。我们在多尺度环境中研究这个问题，其中物种丰度以及反应速率尺度到不同的数量级。不同的时间和浓度标度由单个参数$N$参数化。我们发现，原来的反应系统的解决方案是一致的紧凑的时间间隔近似的一个减少的反应系统的解决方案，没有中间体和解决方案的某些限制反应系统，这并不依赖于$N$。已知的近似技术，如吉洪诺夫和Fenichel的定理不能很容易地在这个框架中使用。
英文摘要：
Chemical reactions often proceed through the formation and the consumption of intermediate species. An example is the creation and subsequent degradation of the substrate-enzyme complexes in an enzymatic reaction. In this paper we provide a setting, based on ordinary differential equations, in which the presence of intermediate species has little effect on the overall dynamics of a biological system. The result provides a method to perform model reduction by elimination of intermediate species. We study the problem in a multiscale setting, where the species abundances as well a the reaction rates scale to different orders of magnitudes. The different time and concentration scales are parameterised by a single parameter $N$. We show that a solution to the original reaction system is uniformly approximated on compact time intervals to a solution of a reduced reaction system without intermediates and to a solution of a certain limiting reaction systems, which does not depend on $N$. Known approximation techniques such as the theorems by Tikhonov and Fenichel cannot readily be used in this framework.
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