多尺度反应网络的动态和静态限制
Dynamic and static limitation in multiscale reaction networks, revisited
摘要：
极限步的概念给出了极限简化：整个网络表现为一个单一的步骤。然而，在其最简单的形式，这个想法是只适用于最简单的线性循环的稳定状态。对于这种最简单的循环，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。我们发展了一个一般的理论，静态和动态限制的所有线性多尺度网络。对角占优矩阵的特征向量的新的估计。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，稳态，弛豫谱和相关的本征向量（“模式”）的显式近似。所得到的多尺度近似，我们称之为“占主导地位的系统”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。
英文摘要：
The concept of limiting step gives the limit simplification: the whole network behaves as a single step. However, in its simplest form this idea is applicable only to the simplest linear cycles in steady states. For such the simplest cycles the nonstationary behaviour is also limited by a single step, but not the same step that limits the stationary rate. We develop a general theory of static and dynamic limitation for all linear multiscale networks. 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. 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.
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