title: Modelling and simulating reaction-diffusion systems using coloured Petri nets.
abstract: Reaction-diffusion systems often play an important role in systems biology when developmental processes are involved. Traditional methods of modelling and simulating such systems require substantial prior knowledge of mathematics and/or simulation algorithms. Such skills may impose a challenge for biologists, when they are not equally well-trained in mathematics and computer science. Coloured Petri nets as a high-level and graphical language offer an attractive alternative, which is easily approachable. In this paper, we investigate a coloured Petri net framework integrating deterministic, stochastic and hybrid modelling formalisms and corresponding simulation algorithms for the modelling and simulation of reaction-diffusion processes that may be closely coupled with signalling pathways, metabolic reactions and/or gene expression. Such systems often manifest multiscaleness in time, space and/or concentration. We introduce our approach by means of some basic diffusion scenarios, and test it against an established case study, the Brusselator model.
authors.affiliation: Control and Simulation Center, Harbin Institute of Technology, Postbox 3006, 150080 Harbin, China. Electronic address: liufei@hit.edu.cn.
authors.forename: Fei
authors.initials: F
authors.lastname: Liu
authors.affiliation: Magdeburg Centre for Systems Biology and Lehrstuhl für Regulationsbiologie, Otto von Guericke Universität Magdeburg, Germany. Electronic address: mary-ann.blaetke@ovgu.de.
authors.forename: Mary-Ann
authors.initials: MA
authors.lastname: Blätke
authors.affiliation: Department of Computer Science, Brandenburg University of Technology, Postbox 10 13 44, 03013 Cottbus, Germany. Electronic address: monika.heiner@b-tu.de.
authors.forename: Monika
authors.initials: M
authors.lastname: Heiner
authors.affiliation: Control and Simulation Center, Harbin Institute of Technology, Postbox 3006, 150080 Harbin, China. Electronic address: myang@hit.edu.cn.
authors.forename: Ming
authors.initials: M
authors.lastname: Yang
mesh_terms: D003198:Computer Simulation; D004058:Diffusion; D008954:Models, Biological; D015203:Reproducibility of Results; D013269:Stochastic Processes; D049490:Systems Biology / Q000379:methods*
keywords: Brusselator; Coloured stochastic/continous/hybrid Petri nets; Multiscaleness; Petri net framework; Reaction–diffusion systems