Autopoietic and (M,R) systems

From the many attempts to produce a conceptual framework for the organization of living systems, the notions of (M,R) systems and Autopoiesis stand out for their rigor, their presupposition of the circularity of metabolism, and the new epistemologies that they imply. From their inceptions, these two notions have been essentially disconnected because each has defined its own language and tools. Here we demonstrate the existence of a deep conceptual link between (M,R) systems and Autopoietic systems. This relationship permits us to posit that Autopoietic systems, which have been advanced as capturing the central aspects of living systems, are a subset of (M,R) systems. This result, in conjunction with previous theorems proved by Rosen, can be used to outline a demonstration that the operation of Autopoietic systems cannot be simulated by Turing machines. This powerful result shows the potential of linking these two models. Finally, we suggest that the formalism of (M,R) systems could be used to model the circularity of metabolism.