Deduction of intracellular sub-systems from a topological description of the network

Non-linear behaviour of biochemical networks, such as intracellular gene, protein or metabolic networks, is commonly represented using graphs of the underlying topology. Nodes represent abundance of molecules and edges interactions between pairs of molecules. These graphs are linear and thus based on an implicit linearization of the kinetic reactions in one or several dynamic modes of the total system. It is common to use data from different sources -- experiments conducted under different conditions or even on different species -- meaning that the graph will be a superposition of linearizations made in many different modes. The mixing of different modes makes it hard to identify functional modules, that is sub-systems that carry out a specific biological function, since the graph will contain many interactions that do not naturally occur at the same time. The ability to establish a boundary between the sub-system and its environment is critical in the definition of a module, contrary to a motif in which only internal interactions count. Identification of functional modules should therefore be done on graphs depicting the mode in which their function is carried out, i.e. graphs that only contain edges representing interactions active in the specific mode. In general, when an interaction between two molecules is established, one should always state the mode of the system in which it is active.