Figure 1

Petri net elements and the representation of a chemical reaction in the form of a Petri net. a) Petri nets are weighted, directed, bipartite graphs consisting of nodes and arcs. The nodes of a Petri net, places and transitions, are interconnected by arcs. An arc always connects a place with a transition or vice versa, but never two places or two transitions with each other. Places may contain (be marked with) tokens, while transitions move tokens rather than containing them. Petri nets provide a useful, mechanism-oriented framework to represent chemical or biochemical reactions. Panel (a) shows a Petri net model of the synthesis of water from its elements, hydrogen and oxygen. Individual molecules are represented by tokens in the respective places. In the example shown, two out of three molecules of hydrogen react with one molecule of oxygen to give two molecules of water. The chemical reaction is modeled by firing of the transition T. Numbers adjacent to arcs are called arc weights. When no number is given, the arc weight by definition is one. The arc weight indicates how many tokens are removed from a place (outgoing arc) or moved into a place (ingoing arc) when a transition fires. Arc weights can be used to represent the stoichiometry of a chemical reaction, accordingly. After two molecules of water have been formed (b), the transition cannot fire a second time because one molecule of hydrogen is missing so that the stoichiometry of the reaction is not fulfilled. c) Standard Petri nets, so-called place/transition nets are composed of places, transitions, tokens and (standard) arcs. Extended Petri nets in addition have read arcs and/or inhibitory arcs that put an additional constraint on the firing licence of a transition, depending on the marking of its pre-places (for details see Figure 5).