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Adaptive and Bio-semantics of Continuous Petri Nets : Choosing the Appropriate Interpretation

Herajy M., Heiner M.

Fundamenta Informaticae

2018

Vol. 160, nr 1/2

53--80

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.

Petri Net-Based Collaborative Simulation and Steering of Biochemical Reaction Networks

Herajy M., Heiner M.

Fundamenta Informaticae

2014

Vol. 129, nr 1/2

49--67

Computational steering is an interactive remote control of a long running application. The user can adopt it, e.g., to adjust simulation parameters on the fly. Simulation of large-scale biochemical networks is often computationally expensive, particularly stochastic and hybrid simulation. Such extremely time-consuming computations necessitate an interactive mechanism to permit users to try different paths and ask 'what-if-questions' while the simulation is in progress. Furthermore, with the progress of computational modelling and the simulation of biochemical networks, there is a need to manage multi-scale models, which may contain species or reactions at different scales. In this context, Petri nets are of special importance, since they provide an intuitive visual representation of reaction networks. In this paper, we introduce a framework and its implementation for combining Petri nets and computational steering for the representation and interactive simulation of biochemical networks. The main merits of the developed framework are: intuitive representation of biochemical networks by means of Petri nets, distributed collaborative and interactive simulation, and tight coupling of simulation and visualisation.