Autocatalysis is a deceptively simple concept, referring to the situation that a chemical species $X$ catalyzes its own formation. From the perspective of chemical kinetics, autocatalysts show a regime of super-linear growth. Given a chemical reaction network, however, it is not at all straightforward to identify species that are autocatalytic in the sense that there is a sub-network that takes $X$ as input and produces more than one copy of $X$ as output. The difficulty arises from the need to distinguish autocatalysis e.g. from the superposition of a cycle that consumes and produces equal amounts of $X$ and a pathway that produces $X$. To deal with this issue, a number of competing notions, such as exclusive autocatalysis and autocatalytic cycles, have been introduced. A closer inspection of concepts and their usage by different authors shows, however, that subtle differences in the definitions often makes conceptually matching ideas difficult to bring together formally. In this contribution we make some of the available approaches comparable by translating them into a common formal framework that uses integer hyperflows as a basis to study autocatalysis in large chemical reaction networks. As an application we investigate the prevalence of autocatalysis in metabolic networks.

翻译：从化学动能学的角度来看,自动催化器显示一种超线性增长的系统。然而,鉴于化学反应网络,要确定自动催化的物种并非简单易行,因为有一个子网络需要用X美元作为投入,并产生超过1美元作为产出,因此,自动催化器是一个简单的概念。从化学动能学的角度看,自动催化器显示的是化学动能的周期的叠加情况。从化学动能学的角度来看,自动催化器显示的是,从化学反应网络来看,有一些相互竞争的概念,如独家催化和自动催化循环,但从不同作者对概念及其使用的仔细检查表明,定义的微妙差异往往使得难以在概念上正式地将想法相匹配。在这种贡献中,我们通过将其转化成一个共同的正式框架来比较一些现有方法,在进行大规模化分析时,我们利用整流的超导性超能力网络来研究。