A loop conjecture for metabolic closure

Although in the last few decades a variety of theoretical tools have been developed to better understand living organisms, their impact on experimental research has been rather limited. A common element between these theories is the idea of metabolic closure, i.e., the systems that produce all their metabolites and catalysts. In spite of an increasing consensus on the relevance of closure, a formal and operative definition has remained elusive. In this paper we revisit RAF sets and chemical organization theory and show how these two theories overlap and could help bring forth real world results. We also state a theorem ensuring the presence of a cycle of interdependent catalysts for RAF sets and conjecture that these cycles give stability to the network. This conjecture is illustrated and supported by computer simulations. Unavoidably, our viewpoint introduces the notion of fluxes and thus a temporal dimension to the purely algebraic model of RAF sets. The results of this work show that the incorporation of closure, topological and dynamical tools altogether is a promising path for a deeper understanding of living systems.