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Modeling biological gradient formation: combining partial differential equations and Petri nets |
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| Authors: | Laura M F Bertens Jetty Kleijn Sander C Hille Monika Heiner Maciej Koutny Fons J Verbeek |
| Affiliation: | 1.LIACS,Leiden University,Leiden,The Netherlands;2.Mathematical Institute,Leiden University,Leiden,The Netherlands;3.Department of Computer Science,Brandenburg Technical University Cottbus-Senftenberg,Cottbus,Germany;4.School of Computing Science,Newcastle University,Newcastle Upon Tyne,UK |
| 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. |
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