Layering in networks: The case of biochemical systems

Networked systems are characterised by their scale and structure. In particular, biochemical reaction networks involve complicated interconnections of chemical reaction pathways and cycles, occurring on a number of different time and space scales even within a cell. This paper seeks to formalise a method of layering the dynamics of a biochemical network by decomposing its stoichiometric matrix into a sum of stoichiometric matrices, each of which we identify with a layer. We derive a condition to test when a given layer directly communicates with another. We also examine singular perturbation by considering decomposition into fast and slow layers, characterising the approximate dynamics through the quasi-steady state approximation in terms of a perturbation of the dynamics of the slow layer.