Skorb Ekaterina V, Semenov Sergey N
ChemBio Cluster, ITMO University, Lomonosova St. 9, Saint Petersburg 191002, Russia.
Department of Organic Chemistry, Weizmann Institute of Science, Rehovot 76100, Israel.
Life (Basel). 2019 May 20;9(2):42. doi: 10.3390/life9020042.
Network autocatalysis, which is autocatalysis whereby a catalyst is not directly produced in a catalytic cycle, is likely to be more common in chemistry than direct autocatalysis is. Nevertheless, the kinetics of autocatalytic networks often does not exactly follow simple quadratic or cubic rate laws and largely depends on the structure of the network. In this article, we analyzed one of the simplest and most chemically plausible autocatalytic networks where a catalytic cycle is coupled to an ancillary reaction that produces the catalyst. We analytically analyzed deviations in the kinetics of this network from its exponential growth and numerically studied the competition between two networks for common substrates. Our results showed that when quasi-steady-state approximation is applicable for at least one of the components, the deviation from the exponential growth is small. Numerical simulations showed that competition between networks results in the mutual exclusion of autocatalysts; however, the presence of a substantial noncatalytic conversion of substrates will create broad regions where autocatalysts can coexist. Thus, we should avoid the accumulation of intermediates and the noncatalytic conversion of the substrate when designing experimental systems that need autocatalysis as a source of positive feedback or as a source of evolutionary pressure.
网络自催化是一种自催化过程，其中催化剂并非在催化循环中直接产生，在化学领域可能比直接自催化更为常见。然而，自催化网络的动力学通常并不完全遵循简单的二次或三次速率定律，并且在很大程度上取决于网络的结构。在本文中，我们分析了最简单且在化学上最合理的自催化网络之一，其中一个催化循环与一个产生催化剂的辅助反应相耦合。我们分析了该网络动力学与指数增长的偏差，并通过数值方法研究了两个网络对共同底物的竞争。我们的结果表明，当准稳态近似适用于至少一个组分时，与指数增长的偏差较小。数值模拟表明，网络之间的竞争导致自催化剂相互排斥；然而，底物大量的非催化转化会产生自催化剂可以共存的广阔区域。因此，在设计需要自催化作为正反馈源或进化压力源的实验系统时，我们应避免中间体的积累和底物的非催化转化。
