发表机构
Leipzig University; Max Planck Institute for Mathematics in the Sciences; University of Vienna; Universidad Nacional de Colombia; University of Copenhagen（莱比锡大学; 马克斯·普朗克科学数学研究所; 维也纳大学; 哥伦比亚国立大学; 哥本哈根大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究探讨反射性自催化（RAFs）与化学计量自催化中极小性概念的关系，证明单催化不可约RAFs的Kőnig图结构，并揭示其可含指数多个自催化核。
AI 中文摘要
自催化，即化学子系统在供应充足食物分子时维持自身组分的能力，与地球上生命的起源密切相关。自威廉·奥斯特瓦尔德（Wilhelm Ostwald）关于显式自催化反应的思考以来，多年来发展出了不同的自催化概念。其中最突出的两种是反射性自催化F-生成集（RAFs）和化学计量自催化。在证明了每个RAFs在合理条件下通常具有化学计量自催化性之后，我们在此考察这两种极小性概念之间的关系：不可约RAFs和自催化核。为此，我们克服了RAFs和化学计量自催化分别在催化反应系统（CRS）和化学反应网络（CRNs）这两种不同的化学反应系统中形式化的障碍。我们证明了CRS中的反应构成相应CRNs中反应关于其特定催化作用的等价类。利用当每个CRS反应与单一催化作用关联时CRN和CRS可典范等同的事实，我们证明了单催化的不可约RAFs的Kőnig图由不含食物和废物物种的强连通块组成，这些块被反应顶点分隔，每个反应顶点包含一个自催化核。实际上，单个不可约RAFs通常可包含指数多个自催化核。
英文摘要
Autocatalysis, the ability of a chemical subsystem to sustain its own constituents when supplied with sufficient food molecules, has been closely related to the origin of life on Earth. Emerging from Wilhelm Ostwald's considerations about an explicit autocatalytic reaction, different notions of autocatalysis have been developed over the years. The two most prominent are reflexively autocatalytic F-generated sets (RAFs) and stoichiometric autocatalysis. After having shown that each RAFs is, under reasonable conditions, in general stoichiometrically autocatalytic, we examine here the relationship between the two notions of minimality: irreducible RAFs and autocatalytic cores. To this end, we overcome the obstacle that RAFs and stoichiometric autocatalysis have been formalized in distinct systems of chemical reactions, i.e., catalytic reaction systems (CRS) and chemical reaction networks (CRNs), respectively. We show that reactions in a CRS constitute equivalence classes of reactions of the corresponding CRNs w.r.t. their specific catalyzations. Using the fact that CRN and CRS can be canonically identified whenever each CRS reaction is associated with a single catalyzation, we demonstrate that the Kőnig graph of a monocatalyzed, irreducible RAF is composed of strong blocks devoid of food and waste species that are separated by reaction vertices, each of which contains an autocatalytic core. In fact, a single irreducible RAF can, in general, contain exponentially many autocatalytic cores.
Comments37 Pages: 31 main text and 6 SI. 10 Figures: 4 in main text and 6 in SI
