A Graphical Approach for Hybrid Modelling of Intracellular Calcium Dynamics Based on Coloured Hybrid Petri Nets

Ismail, Amr; Herajy, Mostafa; Heiner, Monika

doi:10.1007/978-3-030-17297-8_13

Cited by 4 publications

(5 citation statements)

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“…In both cases, the diffusion pattern used here is 1D diffusion. Other examples that utilize calcium diffusion in 2D grid can be found in [ 34 ] and for 3D grids in [ 49 ]. Moreover, calcium binding and unbinding with the buffer is modelled as a reversible reaction (green colour), calcium input is modelled via a synthesis reaction (blue colour), and calcium pumps are modelled by degradation reactions (purple colour).…”

Section: Resultsmentioning

confidence: 99%

“…However, we also discuss how a quantitative model can be derived from this structure. Interested readers may wish to consult the many publications that discuss the use of Petri nets to model biological reaction networks, for example: modelling break-repair systems, circadian oscillation and T7 phage model in [ 26 ], modelling Eukaryotic cell cycle in [ 10 ], modelling yeast cell cycles in [ 27 ], modelling the cyanobacterial circadian gene clock system in [ 20 ], modelling the Brusselator in [ 23 ], modelling bacterial colonies with phase variable genes in [ 29 ], modelling the cell fate decision mechanism in [ 33 ] or modelling intracellular calcium dynamics in [ 34 ].…”

Section: Methodsmentioning

confidence: 99%

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Design patterns for the construction of computational biological models

Herajy,

Liu,

Heiner

2024

Briefings in Bioinformatics

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Computational biological models have proven to be an invaluable tool for understanding and predicting the behaviour of many biological systems. While it may not be too challenging for experienced researchers to construct such models from scratch, it is not a straightforward task for early stage researchers. Design patterns are well-known techniques widely applied in software engineering as they provide a set of typical solutions to common problems in software design. In this paper, we collect and discuss common patterns that are usually used during the construction and execution of computational biological models. We adopt Petri nets as a modelling language to provide a visual illustration of each pattern; however, the ideas presented in this paper can also be implemented using other modelling formalisms. We provide two case studies for illustration purposes and show how these models can be built up from the presented smaller modules. We hope that the ideas discussed in this paper will help many researchers in building their own future models.

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Section: Resultsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Design patterns for the construction of computational biological models

Herajy,

Liu,

Heiner

2024

Briefings in Bioinformatics

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“…x-dimension, y-dimension, and z-dimension are defined by the colour sets xdim, ydim, and zdim, respectively. Based on the previously defined colour sets to encode twodimensional space [33], we define, in this paper, a threedimensional compound colour set, Grid 3D, representing a cube form. Moreover, we define six variables, a, x of type xdim, b, y of type ydim, and c, z of type zdim, as well as three-dimensional coordinates, (x, y, z) to address every component in space.…”

Section: Colour Representation Of 3dmentioning

confidence: 99%

“…In [33], we have adopted a model for the stochastic part that accounts for the eight states of each subunit. However, for the purpose of constructing a 3D model, we employ the reduced system for the interactions of the calcium subunits from [37], which exhibits less subunit states.…”

Section: Calcium Release Intracellular Calcium Is Organised By the Rmentioning

confidence: 99%

“…Modifier arc Table 1 for all colourrelated definitions. It is an extension of our model published in [33]. e meaning of arcs and nodes is illustrated in the legend and briefly described in Section 2. e colour code is as follows: dark red: colour set names, red: marking, blue: arc expressions, violet: guards, and black: node names.…”

Section: Modelling and Simulation In Engineeringmentioning

confidence: 99%

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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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