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

Herajy, Mostafa; Heiner, Monika

doi:10.3233/fi-2018-1674

Cited by 12 publications

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“…Firing rates are often state-dependent and follow specific kinetic laws. In the case study considered in this paper, all firing rates follow mass-action kinetics [41].…”

Section: Methodsmentioning

confidence: 99%

Spatial quorum sensing modelling using coloured hybrid Petri nets and simulative model checking

et al. 2019

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Background Quorum sensing drives biofilm formation in bacteria in order to ensure that biofilm formation only occurs when colonies are of a sufficient size and density. This spatial behaviour is achieved by the broadcast communication of an autoinducer in a diffusion scenario. This is of interest, for example, when considering the role of gut microbiota in gut health. This behaviour occurs within the context of the four phases of bacterial growth, specifically in the exponential stage (phase 2) for autoinducer production and the stationary stage (phase 3) for biofilm formation. Results We have used coloured hybrid Petri nets to step-wise develop a flexible computational model for E.coli biofilm formation driven by Autoinducer 2 (AI-2) which is easy to configure for different notions of space. The model describes the essential components of gene transcription, signal transduction, extra and intra cellular transport, as well as the two-phase nature of the system. We build on a previously published non-spatial stochastic Petri net model of AI-2 production, keeping the assumptions of a limited nutritional environment, and our spatial hybrid Petri net model of biofilm formation, first presented at the NETTAB 2017 workshop. First we consider the two models separately without space, and then combined, and finally we add space. We describe in detail our step-wise model development and validation. Our simulation results support the expected behaviour that biofilm formation is increased in areas of higher bacterial colony size and density. Our analysis techniques include behaviour checking based on linear time temporal logic. Conclusions The advantages of our modelling and analysis approach are the description of quorum sensing and associated biofilm formation over two phases of bacterial growth, taking into account bacterial spatial distribution using a flexible and easy to maintain computational model. All computational results are reproducible. Electronic supplementary material The online version of this article (10.1186/s12859-019-2690-z) contains supplementary material, which is available to authorized users.

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“…Firing rates are often state-dependent and follow specific kinetic laws. In the case study considered in this paper, all firing rates follow mass-action kinetics [41].…”

Section: Methodsmentioning

confidence: 99%

Spatial quorum sensing modelling using coloured hybrid Petri nets and simulative model checking

et al. 2019

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“…They are of paramount importance when simulating models with abundance number of molecules where stochastic simulation is not of a big help because of the long simulation time. Please note that there are different interpretations of the underlying semantics of CPN (Herajy and Heiner 2018a , b ). In this paper, we are more interested in the bio-semantics of CPN where the execution of transitions is closely related to the deterministic simulation and the undelaying semantics of a system of ODEs.…”

Section: Modeling and Verification Tools: Petri Nets And Model Checkingmentioning

confidence: 99%

“…When a CPN is simulated, each place will have an ordinary differential equation (ODE) that represents its dynamics. The corresponding ODEs are generated by the help of known kinetic laws (e.g., Mass action or Michaelis–Menten kinetics), see (Herajy and Heiner 2018a , b ) for more details.…”

Section: Modeling and Verification Tools: Petri Nets And Model Checkingmentioning

confidence: 99%

Formal verification confirms the role of p53 protein in cell fate decision mechanism

et al. 2022

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The bio-cell cycle is controlled by a complex biochemical network of signaling pathways. Modeling such challenging networks accurately is imperative for the understanding of their detailed dynamical behavior. In this paper, we construct, analyze, and verify a hybrid Petri net (HPN) model of a complex biochemical network that captures the role of an important protein (namely p53) in deciding the fate of the cell. We model the behavior of the cell nucleus and cytoplasm as two stochastic and continuous Petri nets, respectively, combined together into a single HPN. We use simulative model checking to verify three different properties that capture the dynamical behavior of p53 protein with respect to the intensity of the ionizing radiation (IR) to which the cell is exposed. For each IR dose, 1000 simulation runs are carried out to verify each property. Our verification results showed that the fluctuations in p53, which relies on IR intensity, are compatible with the findings of the preceding simulation studies that have previously examined the role of p53 in cell fate decision.

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“…Moreover, in order to model continuous concentration changes of biological processes, CPN were proposed in [1]. e semantics of a CPN model corresponds to a system of Ordinary Differential Equations (ODEs) [29]. Furthermore, in order to incorporate both discrete and continuous modelling capabilities in one model, HPN were proposed in [1] and further augmented to Generalised HPN (GHPN ) in [25].…”

Section: Petri Netsmentioning

confidence: 99%

A Graphical Approach for Hybrid Simulation of 3D Diffusion Bio-Models via Coloured Hybrid Petri Nets

Ismail

Herajy

Atlam

et al. 2020

Modelling and Simulation in Engineering

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Three-dimensional modelling of biological systems is imperative to study the behaviour of dynamic systems that require the analysis of how their components interact in space. However, there are only a few formal tools that offer a convenient modelling of such systems. The traditional approach to construct and simulate 3D models is to build a system of partial differential equations (PDEs). Although this approach may be computationally efficient and has been employed by many researchers over the years, it is not always intuitive since it does not provide a visual depiction of the modelled systems. Indeed, a visual modelling can help to conceive a mental image which eventually contributes to the understanding of the problem under study. Coloured Hybrid Petri Nets (HPNC) are a high-level representation of classical Petri nets that offer hybrid as well as spatial modelling of biological systems. In addition to their graphical representations, HPNC models are also scalable. This paper shows how HPNC can be used to construct and simulate systems that require three-dimensional as well as hybrid (stochastic/continuous) modelling. We use calcium diffusion in three dimensions to illustrate our main ideas. More specifically, we show that creating 3D models using HPNC can yield more flexible models as the structure can be easily scaled up and down by just modifying a few parameters. This advantage of convenient model configuration facilitates the design of different experiments without the need to alter the model structure.

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

Cited by 12 publications

References 0 publications

Spatial quorum sensing modelling using coloured hybrid Petri nets and simulative model checking

Spatial quorum sensing modelling using coloured hybrid Petri nets and simulative model checking

Formal verification confirms the role of p53 protein in cell fate decision mechanism

A Graphical Approach for Hybrid Simulation of 3D Diffusion Bio-Models via Coloured Hybrid Petri Nets

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