Figure 3

Novel aspects in the Co-dependence Notation. The diagram shows a simple model involving three biochemical species A, B and C rendered as a directed hypergraph, a bipartite graph and rendered in the Co-dependence Notation. Further the mapping of the Co-dependence Notation into the ordinary differential equation (ODE) formalism is depicted. Similar to bipartite graphs, the Co-dependence Notation comprises two different kinds of node, called species and process. Rectangles (Co-dependence Notation part at the bottom of the diagram, c and d) represent molecular species, clouds denote transformation processes, thick arrows represent material flow and thin dashed lines represent informational flow. One novel aspect in the Co-dependence Notation is the use of small, unfilled circles to label information sources i.e. to label entities that play a functional role in their associated process. Consequently a thick arc in conjunction with a small circle represents a co-dependency between the species and process nodes associated by the link. In this co-dependent relationship, the species influences as information source the process that is transforming the species. As indicated in the diagram sections c and d, the visual emphasis of information sources enables the mapping of the Co-dependence Notation into ODEs. A further novel aspect in the Co-dependence Notation is the optional use of information processing nodes to represent constants or computed logical entities such as rate constants, external stimuli or genetic switches. Information processing nodes also belong to the class of process nodes yet are rendered as large circles. Thus, links in Co-dependence models cannot only connect species nodes with process nodes but can also directly relate two or more process nodes with each other. This facilitates the representation of both species transformation and information processing within a single conceptual framework. The diagram section E shows how Co-dependence models decompose complex systems into simpler elements called compartments.