title: Modeling biological gradient formation: combining partial differential equations and Petri nets.
abstract: Both Petri nets and differential equations are important modeling tools for biological processes. In this paper we demonstrate how these two modeling techniques can be combined to describe biological gradient formation. Parameters derived from partial differential equation describing the process of gradient formation are incorporated in an abstract Petri net model. The quantitative aspects of the resulting model are validated through a case study of gradient formation in the fruit fly.
authors.affiliation: LIACS, Leiden University, Leiden, The Netherlands.
authors.forename: Laura M F
authors.initials: LM
authors.lastname: Bertens
authors.affiliation: LIACS, Leiden University, Leiden, The Netherlands.
authors.forename: Jetty
authors.initials: J
authors.lastname: Kleijn
authors.affiliation: Mathematical Institute, Leiden University, Leiden, The Netherlands.
authors.forename: Sander C
authors.initials: SC
authors.lastname: Hille
authors.affiliation: Department of Computer Science, Brandenburg Technical University Cottbus-Senftenberg, Cottbus, Germany.
authors.forename: Monika
authors.initials: M
authors.lastname: Heiner
authors.affiliation: School of Computing Science, Newcastle University, Newcastle Upon Tyne, UK.
authors.forename: Maciej
authors.initials: M
authors.lastname: Koutny
authors.affiliation: LIACS, Leiden University, Leiden, The Netherlands.
authors.forename: Fons J
authors.initials: FJ
authors.lastname: Verbeek
keywords: Gradient formation; Partial differential equation; Petri net; Process validation ; Quantitative modeling