Simulation and analysis of metabolic networks by time-dependent Petri nets.
Ina Koch, Stefan Schuster, Monika Heiner · German Conference on Bioinformatics · 1999
Traditional mathematical models are focussed on the construction of kinetic models by solving algebraic equations for steady states and systems of differential equations for time-dependent states (for a review see Heinrich & Schuster [4]). Petri net theory exhibits a mathematical formalism to model, analyze, and simulate discrete event systems with inherent concurrency (Peterson [7], Starke [9]). There are many applications in the field of modeling and control of discrete systems and in the field of concurrent software development (Heiner [3]). The first application of Petri nets to modeling of metabolic pathways was published by Reddy et al. [8]. In recent years Petri net theory was applied to model metabolic pathways in relation to genetic and cell communication (Hofestadt & Thelen[6]), to investigate quantitative properties of biochemical networks (Hofestadt [5]), and to model stochastic systems using stochastic Petri nets (Goss & Peccoud [1]), which succeeded in analyzing the stabilizing effect of the protein Rom on the genetic network controlling ColE1 plasmid replication (Goss & Peccoud [2]).