FG Datenstrukturen und Softwarezuverlässigkeit
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Institute
BTU
A Case Study in Design and Verification of Manufacturing Systems with Hierarchical Petri Nets
(1999)
A Graphical Approach for Hybrid Simulation of 3D Diffusion Bio-Models via Coloured Hybrid Petri Nets
(2020)
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 () 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, models are also scalable. This paper shows how 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 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.
Whole-cell modeling aims to incorporate all main genes and processes, and their interactions of a cell in one model. Whole-cell modeling has been regarded as the central aim of systems biology but also as a grand challenge, which plays essential roles in current and future systems biology. In this paper, we analyze whole-cell modeling challenges and requirements and classify them into three aspects (or dimensions): heterogeneous biochemical networks, uncertainties in components, and representation of cell structure. We then explore how to use different Petri net classes to address different aspects of whole-cell modeling requirements. Based on these analyses, we present a Petri nets-based framework for whole-cell modeling, which not only addresses many whole-cell modeling requirements, but also offers a graphical, modular, and hierarchical modeling tool. We think this framework can offer a feasible modeling approach for whole-cell model construction.
BioModelKit: Spatial Modelling of Complex Multiscale Molecular Biosystems based on Modular Models
(2018)
Membrane systems are a very powerful computational modelling formalism inspired by the internal organisation of living cells. Modelling of membrane systems is challenged by composing many structurally similar components, which may result in very large models. Furthermore, some components may suffer from a lack of precise kinetic parameters. Coloured fuzzy Petri nets combine coloured Petri nets with fuzzy kinetic parameters, and thus offer an approach to address these challenges. In this paper, we use coloured fuzzy Petri nets to model and simulate membrane systems which are enriched by fuzzy kinetic parameters. We also introduce a methodology and workflow utilising coloured fuzzy Petri nets for modelling and simulating general biological systems which have to cope with incomplete knowledge of their kinetic data.
Coloured Hybrid Petri Nets: an Adaptable Modelling Approach for Multi-scale Biological Networks
(2018)
Coloured Petri nets for multilevel, multiscale and multidimensional modelling of biological systems
(2019)
Snoopy is a powerful modelling and simulation tool for various types of Petri nets, which have been applied to a wide range of biochemical reaction networks. We present an enhanced version of Snoopy, now supporting coloured and uncoloured stochastic, continuous and hybrid Petri Nets with fuzzy kinetic parameters. Colour helps to cope with modelling challenges imposed by larger and more complex networks. Fuzzy parameters are specifically useful when kinetic parameter values can not be precisely measured or estimated. By running fuzzy simulation we obtain output bands of the variables of interest induced by the effect of the fuzzy kinetic parameters. Simulation is always done on the uncoloured level. For this purpose, coloured fuzzy Petri nets are automatically unfolded to their corresponding uncoloured counterparts. Combining the power of fuzzy kinetic parameters with the modelling convenience of coloured Petri nets provides a new quality in user support with sophisticated modelling and analysis features.
We present a methodology for systematically extending epidemic models to multilevel and multiscale spatio-temporal pandemic ones. Our approach builds on the use of coloured stochastic and continuous Petri nets facilitating the sound component-based extension of basic SIR models to include population stratification and also spatio-geographic information and travel connections, represented as graphs, resulting in robust stratified pandemic metapopulation models. The epidemic components and the spatial and stratification data are combined together in these coloured models and built in to the underlying expanded models. As a consequence this method is inherently easy to use, producing scalable and reusable models with a high degree of clarity and accessibility which can be read either in a deterministic or stochastic paradigm. Our method is supported by a publicly available platform PetriNuts; it enables the visual construction and editing of models; deterministic, stochastic and hybrid simulation as well as structural and behavioural analysis. All models are available as Supplementary Material, ensuring reproducibility. All uncoloured Petri nets can be animated within a web browser at https://www-dssz.informatik.tu-cottbus.de/DSSZ/Research/ModellingEpidemics, assisting the comprehension of those models. We aim to enable modellers and planners to construct clear and robust models by themselves.
Fuzzy stochastic Petri nets for modeling biological systems with uncertain kinetic parameters
(2016)
Integrated modelling of biological systems is challenged by composing components with sufficient kinetic data and components with insufficient kinetic data or components built only using experts’ experience and knowledge. Fuzzy continuous Petri nets (FCPNs) combine continuous Petri nets with fuzzy inference systems, and thus offer an hybrid uncertain/certain approach to integrated modelling of such biological systems with uncertainties. In this paper, we give a formal definition and a corresponding simulation algorithm of FCPNs, and briefly introduce the FCPN tool that we have developed for implementing FCPNs. We then present a methodology and workflow utilizing FCPNs to achieve hybrid (uncertain/certain) modelling of biological systems illustrated with a case study of the Mercaptopurine metabolic pathway. We hope this research will promote the wider application of FCPNs and address the uncertain/certain integrated modelling challenge in the systems biology area.
Integrated modelling of biological systems is becoming a necessity for constructing models containing the major biochemical processes of such systems in order to obtain a holistic understanding of their dynamics and to elucidate emergent behaviours. Hybrid modelling methods are crucial to achieve integrated modelling of biological systems. This paper reviews currently popular hybrid modelling methods, developed for systems biology, mainly revealing why they are proposed, how they are formed from single modelling formalisms and how to simulate them. By doing this, we identify future research requirements regarding hybrid approaches for further promoting integrated modelling of biological systems.
Modeling and Simulation of Multi-scale Environmental Systems with Generalized Hybrid Petri Nets
(2015)
Modeling biological gradient formation: combining partial differential equations and Petri nets
(2016)
Dynamics of cell fate decisions are commonly investigated by inferring temporal sequences of gene expression states by assembling snapshots of individual cells where each cell is measured once. Ordering cells according to minimal differences in expression patterns and assuming that differentiation occurs by a sequence of irreversible steps, yields unidirectional, eventually branching Markov chains with a single source node. In an alternative approach, we used multi-nucleate cells to follow gene expression taking true time series. Assembling state machines, each made from single-cell trajectories, gives a network of highly structured Markov chains of states with different source and sink nodes including cycles, revealing essential information on the dynamics of regulatory events. We argue that the obtained networks depict aspects of the Waddington landscape of cell differentiation and characterize them as reachability graphs that provide the basis for the reconstruction of the underlying gene regulatory network.