A decomposition theorem in chemical organizations

The Chemical Organization Theory (COT) is an abstract reaction network model that has a deep connection to autopoiesis as they share the same central topic: Organization. The main characteristic of autopoietic systems is that they preserve their own organization; this constitutes their identity. In terms of COT, organizations are special reaction networks which are closed and self-maintaining. Organizations compose the majority of stable behaviours of a reaction network (Peter and Dittrich, 2011), in particular every fixed point can be mapped to an organization (Dittrich and Di Fenizio, 2007). Obtaining the set of organizations of a network is a central objective in COT, but it is usually a complex computational task. This work intends to reveal the underlying mathematical structure of organizations. We state a theorem of decomposition for organizations to understand the difficulties of verifying if a set of molecular species is an organization. This suggests a step towards the development of more efficient algorithms and the classification of reaction networks in terms of how complex it is to obtain its set of organizations. We also discuss the consequences of this theorem in relation to autopoietic systems.