Accelerated Simulation of Hybrid Biological Models with Quasi-Disjoint Deterministic and Stochastic Subnets

Herajy, Mostafa; Heiner, Monika

doi:10.1007/978-3-319-47151-8_2

Cited by 6 publications

(6 citation statements)

References 29 publications

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“…Each condition was simulated in the stochastic setting using the Gillespie [31] algorithm. The simulation was also performed in the hybrid setting using a simulator comprising three components: (1) an ODE solver, we specifically use the CVODE library [59], for the continuous part, (2) Gillespie simulation for the stochastic part, and (3) the synchronisation between the continuous and stochastic net components is done via the improved Hybrid Rejection-based Stochastic Simulation Algorithm (HRSSA) [60], which combines the accelerated method introduced in [60] with the hybrid rejection-based stochastic algorithm from [61].…”

Section: Discussion - Model Validationmentioning

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: Discussion - Model Validationmentioning

confidence: 99%

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

et al. 2019

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“…e motivation of GHPN , compared to HPN , is to support more timing features, including stochastic, discrete deterministic, and continuous deterministic firing of transitions [25]. GHPN simulation approaches combine stochastic simulation algorithms with ODE numerical integrators, employing appropriate mechanisms to synchronise the stochastic and deterministic firings of biological events [25,30]. More specifically, in GHPN , places are further classified into two categories: discrete and continuous.…”

Section: Petri Netsmentioning

confidence: 99%

“…Unfortunately, the basic idea presented in [43] cannot simulate our HPN C model in reasonable time. erefore, we have added recently more efficient simulation techniques to Snoopy (c.f., [10,30]) which permit to execute larger models in a more efficient way.…”

Section: Simulation Procedurementioning

confidence: 99%

“…Our optimised hybrid algorithms developed in [30,44] can be viewed as a generalisation of the simulation idea of the Ca 2+ model in [16], though they have been independently developed. In other words, we have developed in [30] a general approach to group all reactions of the stochastic regime into independent/dependent reactions based on their connection with the continuous regime. We call the dependent reactions interface reactions.…”

Section: Simulation Procedurementioning

confidence: 99%

“…In summary, the simulation results presented in this paper are based on the hybrid simulation algorithms introduced in [30,44,46]. e integration time step adaptivity for the underlying ODEs system is achieved by an efficient ODE solver from [47].…”

Section: Simulation Procedurementioning

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

Ismail

Herajy

Heiner

2019

Computational Biology

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Accelerated Simulation of Hybrid Biological Models with Quasi-Disjoint Deterministic and Stochastic Subnets

Cited by 6 publications

References 29 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

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

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