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Petri Nets for Modelling and Analysing Trophic Networks

Baldan P., Bocci M., Brigolin D., Cocco N., Heiner M., Simeoni M.

Fundamenta Informaticae

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2018

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Vol. 160, nr 1/2

27--52

EN

We consider trophic networks, a kind of networks used in ecology to represent feeding interactions (what-eats-what) in an ecosystem. Starting from the observation that trophic networks can be naturally modelled as Petri nets, we explore the possibility of using Petri nets for the analysis and simulation of trophic networks. We define and discuss different continuous Petri net models, whose level of accuracy depends on the information available for the modelled trophic network. The simplest Petri net model we construct just relies on the topology of the network. We also propose a technique for deriving a more refined model that embeds into the Petri net the known constraints on the transition rates that represent the knowledge on metabolism and diet of the species in the network. Finally, if the information of the biomass amounts for each species at steady state is available, we discuss a way of further refining the Petri net model in order to represent dynamic behaviour. We apply our Petri net technology to a case study of the Venice lagoon and analyse the results.

2

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

Herajy M., Heiner M.

Fundamenta Informaticae

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2018

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Vol. 160, nr 1/2

53--80

EN

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.

3

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

Herajy M., Heiner M.

Fundamenta Informaticae

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2014

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Vol. 129, nr 1/2

49--67

EN

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.

4

Time Petri Nets for Modelling and Analysis of Biochemical Networks

Popova-Zeugmann L., Heiner M., Koch I.

Fundamenta Informaticae

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2005

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Vol. 67, nr 1-3

149--162

EN

Biochemical networks are modelled at different abstraction levels. Basically, qualitative and quantitative models can be distinguished, which are typically treated as separate ones. In this paper, we bridge the gap between qualitative and quantitative models and apply time Petri nets for modelling and analysis of molecular biological systems. We demonstrate how to develop quantitative models of biochemical networks in a systematic manner, starting from the underlying qualitative ones. For this purpose we exploit the well-established structural Petri net analysis technique of transition invariants, which may be interpreted as a characterisation of the system's steady state behaviour. For the analysis of the derived quantitative model, given as time Petri net, we present structural techniques to decide the time-dependent realisability of a transition sequence and to calculate its shortest and longest time length. All steps of the demonstrated approach consider systems of integer linear inequalities. The crucial point is the total avoidance of any state space construction. Therefore, the presented technology may be applied also to infinite systems, i.e. unbounded Petri nets.