Bridging two theoretical frameworks of autocatalysis: RAF sets and stoichiometric autocatalysis

Autocatalysis lies at the heart of many (bio)chemical processes and is key to processes leading up to the origin of life. Two seemingly very different formalisms have emerged that define autocatalysis. Kauffman introduced collective autocatalysis to describe systems of molecules that mutually catalyze each other's formation, emphasizing the self-sustaining character of autocatalytic systems. This view is mathematically formalized in the theory of Reflexively Autocatalytic and Food-generated sets (RAF). In parallel, stoichiometric autocatalysis emerged from the theory of Chemical Reaction Networks (CRN), focusing on the net-productive, self-amplifying character of autocatalytic subnetworks. These two frameworks have coexisted independently in the literature, since RAF theory considers each reaction as explicitly catalyzed, while the CRN approach often excludes explicitly catalyzed reactions altogether. Nevertheless, both frameworks describe reaction networks and thus admit a common mathematical representation in terms of stoichiometric matrices. We highlight this connection and show that the two formalisms are less disparate than they might appear. To illustrate this point we prove that, under mild and general conditions, any RAF is stoichiometrically autocatalytic.