Coloured Petri nets for multilevel, multiscale and multidimensional modelling of biological systems

Liu, Fei; Heiner, Monika; Gilbert, David

doi:10.1093/bib/bbx150

Cited by 28 publications

(19 citation statements)

References 69 publications

(98 reference statements)

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“…Thus, the basic modelling strategy can be applied to a large variety of problems evolving in time and space. See [48] for a recent review paper illustrating the wide use of coloured Petri nets for multi-level, multiscale, and multi-dimensional modelling of biological systems.…”

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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Section: Methodsmentioning

confidence: 99%

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

et al. 2019

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“…extend low-level PN with a set of finite colour sets [6,7]. PN C offer a parameterised approach to construct large biological systems; there are many coloured net classes, among them coloured continuous Petri nets (CPN C ) [7] and coloured stochastic Petri nets (SPN C ) [31].…”

Section: Coloured Hybrid Petri Nets Coloured Petri Nets (Pn C )mentioning

confidence: 99%

“…HPN provide a flexible tool to integrate smoothly continuous and discrete states. Furthermore, coloured Petri nets (PN C ) [6,7] have been introduced to provide a high-level representation of standard and quantitative Petri nets by associating colours with places and transitions.…”

Section: Introductionmentioning

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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“…The combination of PNs with a programming language provides the primitives for encoding data manipulation and creating compact and parameterizable models [14]. Therefore, coloured PNs offer a convenient framework to model complex multi-scale [15], multi-level and multi-dimensional aspects of a biomolecular system, see also [16] for a recent review.…”

Section: Introductionmentioning

confidence: 99%

BioModelKit – An Integrative Framework for Multi-Scale Biomodel-Engineering

Blätke

2018

Journal of Integrative Bioinformatics

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While high-throughput technology, advanced techniques in biochemistry and molecular biology have become increasingly powerful, the coherent interpretation of experimental results in an integrative context is still a challenge. BioModelKit (BMK) approaches this challenge by offering an integrative and versatile framework for biomodel-engineering based on a modular modelling concept with the purpose: (i) to represent knowledge about molecular mechanisms by consistent executable sub-models (modules) given as Petri nets equipped with defined interfaces facilitating their reuse and recombination; (ii) to compose complex and integrative models from an ad hoc chosen set of modules including different omic and abstraction levels with the option to integrate spatial aspects; (iii) to promote the construction of alternative models by either the exchange of competing module versions or the algorithmic mutation of the composed model; and (iv) to offer concepts for (omic) data integration and integration of existing resources, and thus facilitate their reuse. BMK is accessible through a public web interface (www.biomodelkit.org), where users can interact with the modules stored in a database, and make use of the model composition features. BMK facilitates and encourages multi-scale model-driven predictions and hypotheses supporting experimental research in a multilateral exchange.

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Coloured Petri nets for multilevel, multiscale and multidimensional modelling of biological systems

Cited by 28 publications

References 69 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

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

BioModelKit – An Integrative Framework for Multi-Scale Biomodel-Engineering

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