Institut Mittag-Leffler.
Uppsala University, Department of Mathematics.
Artif Life. 2020 Summer;26(3):327-337. doi: 10.1162/artl_a_00327. Epub 2020 Jul 22.
A crucial question within the fields of origins of life and metabolic networks is whether or not a self-replicating chemical reaction system is able to persist in the presence of side reactions. Due to the strong nonlinear effects involved in such systems, they are often difficult to study analytically. There are however certain conditions that allow for a wide range of these reaction systems to be well described by a set of linear ordinary differential equations. In this article, we elucidate these conditions and present a method to construct and solve such equations. For those linear self-replicating systems, we quantitatively find that the growth rate of the system is simply proportional to the sum of all the rate constants of the reactions that constitute the system (but is nontrivially determined by the relative values). We also give quantitative descriptions of how strongly side reactions need to be coupled with the system in order to completely disrupt the system.
生命起源和代谢网络领域的一个关键问题是，自我复制的化学反应系统是否能够在存在副反应的情况下持续存在。由于这些系统中涉及到强烈的非线性效应，因此它们通常很难进行分析研究。然而，存在某些条件可以使这些反应系统中的很大一部分能够很好地用一组线性常微分方程来描述。在本文中，我们阐明了这些条件，并提出了一种构建和求解这些方程的方法。对于那些线性自我复制系统，我们定量地发现系统的增长率与构成系统的所有反应的速率常数的总和成正比（但由相对值非平凡地确定）。我们还定量地描述了副反应需要与系统耦合到何种程度才能完全破坏系统。
