How to model and simulate biological pathways with Petri Nets - a new challenge for system biology

1.1 Petri nets – suitable than other mathematical descriptions In 1999, we surveyed which architecture is suitable when modeling and simulating biopathway for biological and medical scientists. At that time, there were ODE-based attempts for modeling and simulating chemical reactions- e.g. Gepasi [19], E-Cell[29]- and others- e.g. the Lisp based architecture QSIM [13] and our other work, the pi-Calculus based architecture, Bio-Calculus [21]. Unfortunately, applications based on these architectures are not acceptable in their fields. This is due to poor GUI interfaces, e.g. lacking biopathway editors, or their architectures themselves. To overcome this situation, we came to the conclusion that an architecture based on Petri nets should be suitable because of their intuitive graphical representation and their capabilities for mathematical analyses. 1.2 Various types of Petri nets have been used for describing biological pathways Researches on Petri nets have a long history of nearly 40 years from the paper by Dr. Petri [25]. The first attempt to use Petri nets for modeling biological pathways was made by [26], giving a method to represent metabolic pathways. Hofestädt [9] expanded this method to model metabolic networks. Subsequently, several enhanced Petri nets have been used to model biological phenomena. Genrich et al. [5] modeled metabolic pathways with a colored Petri net by assigning enzymatic reaction speeds to the transitions, and simulated a chain of these reactions quantitatively. Voss et al. [30] used the colored Petri net in a different way, accomplishing