Affiliations: [a] Department of Mathematics and Computer Science, Faculty of Science, Port Said University, 42521 - Port Said, Egypt. mherajy@sci.psu.edu.eg | [b] Computer Science Institute, Brandenburg University of Technology, Postbox 10 13 44, 03013 Cottbus, Germany. monika.heiner@b-tu.de
Correspondence:
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Address for correspondence: Department of Mathematics and Computer Science, Faculty of Science, Port Said University, 42521 - Port Said, Egypt
Abstract: Continuous Petri nets (CPN) provide a graphical tool to model and analyse the deterministic dynamic behaviour of biological reaction networks. They can be considered as an alternative to the traditional ODE representation of biological models, enjoying a visual depiction of reaction networks. A model constructed as CPN can take advantages of quantitative (e.g., transient and steady state analysis) as well as qualitative (e.g., structural analysis) techniques. However, there are different semantics of CPN due to varying interpretations of transition rates. Choosing an appropriate semantics and corresponding simulator is not a straightforward procedure for the modelling of certain biological systems. In this paper, we compare two widely used semantics of CPN: adaptive semantics and bio-semantics. In the adaptive case, the enabling of continuous transitions may vary and the ODEs are correspondingly adjusted during model execution in order to avoid negative markings, while continuous transitions are always enabled in the bio-semantics and ODEs are never altered during the whole simulation period. We discuss the implementation complexity of both approaches in the context of systems biology and present two case studies to illustrate the best utilisation and individual strength of the two interpretations.
Keywords: Continuous Petri Nets, Adaptive semantics, Bio-semantics, Modelling Biological Networks, Deterministic Simulation, Liver Iron Metabolism
