Petri Nets in the Biosciences

“You still have to do the experiment, but the predictions that theory make are becoming so much powerful these days that we can perhaps save 90 percent of the experimenting and concentrate on the 10 percent where we know that the most important results will lie.” This amazing statement concerning the importance of modeling and simulation in the life sciences was made recently by Dr. Lidin, the chairman of the Nobel committee when announcing the winner of the Nobel Prize for Chemistry 2013. He also emphasized that we have reached a point where computer simulation results are as informative as real experiments [1]. Although the Nobel Prize for Chemistry last year has been awarded for achievements based on numerical simulation, results of other modeling and simulation methods in the biosciences are of similar importance. One approach often used nowadays in biology, medicine, biochemistry, and related disciplines to quantitativelymodel, analyze, and simulate biological systems are Petri nets. This powerful modeling mechanism has several advantages, such as: Petri nets can be used without the need for detailed and difficult to obtainmeasurement data (such as enzyme activities or metabolite levels), can model many different processes in the life sciences (such as gene regulatory processes, metabolism, developmental processes), provide a graphical and easy to understand representation which simplifies dealing with models for non-modelers, and comewith a richmathematical framework supporting their qualitative and quantitative analysis. In its simplest form as developed by Carl Adam Petri in the 1960s, a Petri net is a graphical and mathematical representation for discrete and parallel systems. The basic elements are places, transitions, and arcs that connect places and transitions. The consumption and producFigure 1: A simple biochemical process which could be modeled as a Petri net. Fumarate (a biochemical substance) is transformed into succinate (another substance). This reaction is catalyzed (i. e., positively stimulated) by an enzyme, succinate dehydrogenase. In a representation as classical Petri net the specific activity of the enzyme (i. e., the kinetic parameters/time) is not considered. Malonate inhibits (i. e., negatively influences) the reaction, which could be modeled by including inhibitory arcs into Petri nets. This diagram does not use the typical graphical elements of a Petri net, instead the domain-specific graphical representation is used: circles represent metabolites, rounded-corner rectangles represent proteins such as enzymes, arcs can be consumption (without arrow), production (with arrow), catalysis (with circle at the end of the line), or inhibition (with bar at the end of the line); the used standard is called Systems Biology Graphical Notation (see the article by Le Novère et al. [5] for more details). Note that in classical Petri nets (with inhibitory arcs) the inhibition (the transition may only fire whenmalonate does not contain any token) can be modeled and simulated, but has restrictions in the analysis.