Biomathematics Research Centre, University of Canterbury, Christchurch, New Zealand.
Acta Biotheor. 2023 Oct 27;71(4):21. doi: 10.1007/s10441-023-09472-8.
The emergence of an autocatalytic network from an available set of elements is a fundamental step in early evolutionary processes, such as the origin of metabolism. Given the set of elements, the reactions between them (chemical or otherwise), and with various elements catalysing certain reactions, a Reflexively Autocatalytic F-generated (RAF) set is a subset R[Formula: see text] of reactions that is self-generating from a given food set, and with each reaction in R[Formula: see text] being catalysed from within R[Formula: see text]. RAF theory has been applied to various phenomena in theoretical biology, and a key feature of the approach is that it is possible to efficiently identify and classify RAFs within large systems. This is possible because RAFs can be described as the (nonempty) subsets of the reactions that are the fixed points of an (efficiently computable) interior map that operates on subsets of reactions. Although the main generic results concerning RAFs can be derived using just this property, we show that for systems with at least 12 reactions there are generic results concerning RAFs that cannot be proven using the interior operator property alone.Kindly check and confirm the edit made in the title.I confirm that the edit is fine.
从可用元素集中出现自动催化网络是早期进化过程（如新陈代谢的起源）的基本步骤。给定一组元素、它们之间的反应（化学的或其他的），以及各种元素催化某些反应，那么一个自催化生成的反射集（RAF）是一个子集 R[公式：见正文]，它是从给定的食物集中自我生成的，并且 R[公式：见正文]中的每个反应都在 R[公式：见正文]内被催化。RAF 理论已被应用于理论生物学中的各种现象，该方法的一个关键特征是，可以在大型系统中有效地识别和分类 RAF。这是可能的，因为 RAF 可以被描述为反应的非空子集，这些子集是一个（高效可计算）内部映射的不动点，该映射作用于反应子集上。尽管关于 RAF 的主要通用结果可以仅使用此属性推导出来，但我们表明，对于至少具有 12 个反应的系统，存在关于 RAF 的通用结果，这些结果不能仅使用内部运算符属性来证明。
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