反应网络的多尺度分析
Multiscale Analysis of Reaction Networks
摘要：
在大多数自然科学中，目前有一种见解，即有必要弥合可以在不同尺度上观察到的不同过程之间的差距。在化学反应领域尤其如此，在化学反应领域，不同类型的原子和分子之间形成键的能力创造了我们在日常生活中体验到的大部分特性，尤其是在所有生物活动中。基本上有两种类型的过程与生化反应网络有关，分子之间的相互作用和涉及其构象变化的相互作用，因此在某种意义上，它们的内部状态。第一种过程可以用所谓的质量作用动力学来近似，但对于第二种过程则不一定如此，在第二种过程中，分子状态并不定义任何种类的密度或浓度。在本文中，我们证明了研究反应网络的随机制定，我们可以构建一个相干近似在特定的时空尺度和粒子数的必要性。连续极限程序自然地产生Fokker-Planck类型的方程，其中浓度的演变与构象变化的演变相比发生在较慢的时间尺度上，例如由与其他（通常较小）分子的结合或解结合事件触发。我们应用渐近理论推导出生化反应系统的有效动力学，即宏观动力学。该理论也可以应用于其他过程，其中实体可以由许多内部状态描述，状态的变化发生在由生灭过程描述的其他实体的到来。
英文摘要：
In most natural sciences there is currently the insight that it is necessary to bridge gaps between different processes which can be observed on different scales. This is especially true in the field of chemical reactions where the abilities to form bonds between different types of atoms and molecules create much of the properties we experience in our everyday life, especially in all biological activity. There are essentially two types of processes related to biochemical reaction networks, the interactions among molecules and interactions involving their conformational changes, so in a sense, their internal state. The first type of processes can be conveniently approximated by the so-called mass-action kinetics, but this is not necessarily so for the second kind where molecular states do not define any kind of density or concentration. In this paper we demonstrate the necessity to study reaction networks in a stochastic formulation for which we can construct a coherent approximation in terms of specific space-time scales and the number of particles. The continuum limit procedure naturally creates equations of Fokker-Planck type where the evolution of the concentration occurs on a slower time scale when compared to the evolution of the conformational changes, for example triggered by binding or unbinding events with other (typically smaller) molecules. We apply the asymptotic theory to derive the effective, i.e. macroscopic dynamics of the biochemical reaction system. The theory can also be applied to other processes where entities can be described by finitely many internal states, with changes of states occuring by arrival of other entities described by a birth-death process.
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