Autocatalytic sets and chemical organizations: modeling self-sustaining reaction networks at the origin of life

Two related but somewhat different approaches have been proposed to formalize the notion of a self-sustaining chemical reaction network. One is the notion of collectively autocatalytic sets, formalized as RAF theory, and the other is chemical organization theory. Both formalisms have been argued to be relevant to the origin of life. RAF sets and chemical organizations are defined differently, but previously some relationships between the two have been shown. Here, we refine and explore these connections in more detail. In particular, we show that so-called closed RAFs are chemical organizations, but that the converse is not necessarily true. We then introduce and apply a procedure to show how chemical organizations can be used to find all closed RAFs within any chemical reaction system. We end with a discussion of why and how closed RAFs could be important in the context of the origin and early evolution of life.