Dynamic and Static Limitation in Multiscale Reaction Networks, Revisited
Dynamic and Static Limitation in Multiscale Reaction Networks, Revisited
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DOI：
10.1016/s0065-2377(08)00003-3
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发表时间：
2008-01-01
期刊：
影响因子：
--
通讯作者：
Radulescu, O.
中科院分区：
文献类型：
--
作者：
Gorban, A. N.;Radulescu, O.
极限步的概念给出了极限简化：整个网络表现为单个步。这是化学动力学中最常用的模型简化方法。然而，在其基本形式，这个想法是只适用于最简单的线性循环的稳定状态。对于简单循环，非平稳行为也受到单个步骤的限制，但不是限制平稳速率的同一步骤。在这一章中，我们将为所有线性多尺度网络发展一个静态和动态极限的一般理论。我们的主要数学工具是有限集上的辅助离散动力系统和专门开发的反应图的“循环手术”算法。利用对角占优矩阵特征向量的新估计，引入了具有良好分离常数的反应网络的多尺度系综，并研究了这类系统的典型性质。对于任何给定的反应速率常数的顺序的显式近似的稳态，弛豫谱和相关的特征向量（“模式”）。特别是，我们证明了系统的分离常数的特征值是真实的（阻尼振荡是不可能的）。对于具有模块化结构的系统，我们建议选择这样的模块，它是可能的，以明确的形式解决每个模块的动力学方程。所有这样的“可解”网络的描述。得到的多尺度近似，我们称之为“主导系统”是计算成本低，鲁棒性。这些占主导地位的系统可用于直接计算的稳态和松弛动力学，特别是当动力学信息是不完整的，设计的实验和挖掘的实验数据，并可以作为一个强大的第一近似微扰理论或预处理。
The concept of the limiting step gives the limit simplification: the whole network behaves as a single step. This is the most popular approach for model simplification in chemical kinetics. However, in its elementary form this idea is applicable only to the simplest linear cycles in steady states. For simple cycles the nonstationary behavior is also limited by a single step, but not the same step that limits the stationary rate. In this chapter, we develop a general theory of static and dynamic limitation for all linear multiscale networks. Our main mathematical tools are auxiliary discrete dynamical systems on finite sets and specially developed algorithms of "cycles surgery" for reaction graphs. New estimates of eigenvectors for diagonally dominant matrices are used.Multiscale ensembles of reaction networks with well-separated constants are introduced and typical properties of such systems are studied. For any given ordering of reaction rate constants the explicit approximation of steady state, relaxation spectrum and related eigenvectors ("modes") is presented. In particular, we prove that for systems with well-separated constants eigenvalues are real (damped oscillations are improbable). For systems with modular structure, we propose the selection of such modules that it is possible to solve the kinetic equation for every module in the explicit form. All such "solvable" networks are described. The obtained multiscale approximations, that we call "dominant systems" are computationally cheap and robust. These dominant systems can be used for direct computation of steady states and relaxation dynamics, especially when kinetic information is incomplete, for design of experiments and mining of experimental data, and could serve as a robust first approximation in perturbation theory or for preconditioning.