We present a methodology for systematically extending epidemic models to multilevel and multiscal... more 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. 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 the models are available as supplementary material, ensuring reproducibility.
This report documents the program and the outcomes of Dagstuhl Seminar 14481 "Multiscale Spa... more This report documents the program and the outcomes of Dagstuhl Seminar 14481 "Multiscale Spatial Computational Systems Biology". This seminar explored challenges arising from the need to model and analyse complex biological systems at multiple scales (spatial and temporal), which falls within the general remit of Computational Systems Biology. A distinguishing factor of the seminar was the modelling exercise-where teams explored different modelling paradigms, in order to better understand the details of the approaches, their challenges, potential applications, and their pros and cons. This activity was carried out in a collaborative and self-directed manner using the Open Space Technology approach as evidenced by a high degree of communication both within and between the teams. Eight teams were formed, and reports from five of them are included in this document.
Formal models have been shown useful for analysis of regulatory systems. Here we focus on signall... more Formal models have been shown useful for analysis of regulatory systems. Here we focus on signalling cascades, a recurrent pattern of biological regulatory systems. We choose the formalism of stochastic Petri nets for this modelling and we express the properties of interest by formulas of a temporal logic. Such properties can be evaluated with either numeric or simulation based methods. The former one suffers from the combinatorial state space explosion problem, while the latter suffers from time explosion due to rare event phenomena. In this paper, we demonstrate the use of rare event techniques to tackle the analysis of signalling cascades. We compare the effectiveness of the COSMOS statistical model checker, which implements importance sampling methods to speed up rare event simulations, with the numerical model checker MARCIE on several properties. More precisely, we study three properties that characterise the ordering of events in the signalling cascade. We establish an intere...
In this chapter we introduce qualitative, stochastic as well as continuous Petri nets and related... more In this chapter we introduce qualitative, stochastic as well as continuous Petri nets and related analysis techniques in a rather informal way, and use as run-ning example a model of the influence of the Raf Kinase Inhibitor Protein (RKIP) on the Extracellular signal Regulated Kinase (ERK) signalling pathway. We show how the qualitative and quantitative analyses complement each other, and how Petri nets can be used for step-wise modelling and analysis of biochemical networks as well as for structured design of systems of ordinary differential equations. 1
Abstract—Signalling cascades are a recurrent pattern of biological regulatory systems whose analy... more Abstract—Signalling cascades are a recurrent pattern of biological regulatory systems whose analysis has deserved a lot of attention. It has been shown that Stochastic Petri Nets (SPN) are appro-priate to model such systems and evaluate the probabilities of specific properties. Such an evaluation can be done numerically when the combinatorial state space explosion is manageable or statistically otherwise. However, when the probabilities to be evaluated are too small, random simulation requires more sophisticated techniques for the handling of rare events. In this paper, we show how such involved methods can be successfully applied for signalling cascades. More precisely, we study three relevant properties of a signalling cascade with the help of the COSMOS tool. Our experiments point out interesting dependencies between quantitative parameters of the regulatory system and its transient behaviour. In addition, they demonstrate that we can go beyond the capabilities of MARCIE, which p...
Abstract. In Petri net systems, liveness is an important property cap-turing the idea of no trans... more Abstract. In Petri net systems, liveness is an important property cap-turing the idea of no transition (action) becoming non-fireable (unattain-able). Additionally, in some situations it is particularly interesting to check if the net system is (marking) monotonically live, i.e., it remains live for any marking greater than the initial one. In this paper, we dis-cuss structural conditions preserving liveness under arbitrary marking increase. It is proved that the deadlock trap property (DTP) is a neces-sary condition for liveness monotonicity of ordinary nets, and necessary and sufficient for some subclasses. We illustrate also how the result can be used to study liveness monotonicity for non-ordinary nets using a sim-ulation preserving the firing language. Finally, we apply these conditions to several case studies of biomolecular networks. 1
This tutorial would not have been possible unless the support of Monika Heiner and my supervisor ... more This tutorial would not have been possible unless the support of Monika Heiner and my supervisor Wolfgang Marwan. I am very grateful for their encouragement, guidance and support that enabled me to develop my understanding of Petri nets and skills. Further I like to thank Christian Rohr and Martin Schwarick as representatives of Monika Heiners team, who develop the three fabulous Petri net tools; Snoopy, Charlie and Marcie. I also thank my colleague Jan-Thierry Wegener, who provided a first documentation of Charlie. I like to give credit to Qian Gao and Esther Bamigboye for revising an improving the text, which was very helpful and educational for me.
Recently hybrid modelling and simulation of biochemical systems have attracted increasing interes... more Recently hybrid modelling and simulation of biochemical systems have attracted increasing interest. This is motivated by the need of simulating systems which integrate different sub-cellular models, and the fact that bio networks themselves are inherently stochastic, however stochastic simulation is time expensive. Compared to other methods of biological modelling, Petri nets are characterized by their intuitive visual representation and executability of biological models. In this paper, we present a hybrid Petri net class that incorporates both continuous and stochastic capabilities. The presented class is intended to model and simulate hybrid biological systems such that they contain some parts which are simulated deterministically while other parts are simulated stochastically.
ACM Transactions on Modeling and Computer Simulation, 2015
This article defines a novel spatial-temporal modelling and analysis methodology applied to a sys... more This article defines a novel spatial-temporal modelling and analysis methodology applied to a systems biology case study, namely phase variation patterning in bacterial colony growth. We employ coloured stochastic Petri nets to construct the model and run stochastic simulations to record the development of the circular colonies over time and space. The simulation output is visualised in 2D, and sector-like patterns are automatically detected and analysed. Space is modelled using 2.5 dimensions considering both a rectangular and circular geometry, and the effects of imposing different geometries on space are measured. We close by outlining an interpretation of the Petri net model in terms of finite difference approximations of partial differential equations (PDEs). One result is the derivation of the “best” nine-point diffusion model. Our multidimensional modelling and analysis approach is a precursor to potential future work on more complex multiscale modelling.
Algebraic and Discrete Mathematical Methods for Modern Biology, 2015
ABSTRACT We present a unifying Petri net framework comprising the qualitative, stochastic, con- t... more ABSTRACT We present a unifying Petri net framework comprising the qualitative, stochastic, con- tinuous and hybrid paradigm for modelling and analysing biological reaction networks. By means of a running case study we demonstrate how the different paradigms contribute in complementary ways to the overall understanding of emergent network properties. The framework is supported by four tools, Snoopy, Charlie, Marcie, and MC2, which will also be of use in the suggested exercises.
The tool Snoopy provides a unifying Petri net framework which has particularly many application s... more The tool Snoopy provides a unifying Petri net framework which has particularly many application scenarios in systems and synthetic biology. The framework consists of two levels: uncoloured and coloured. Each level comprises a family of related Petri net classes, sharing structure, but being specialized by their kinetic information. Petri nets of all net classes within one level can be converted into each other, while changing the level involves user-guided folding or automatic unfolding. Models can be hierarchically structured, allowing for the mastering of larger networks. Snoopy supports the simultaneous use of several Petri net classes; the graphical user interface adapts dynamically to the active one. Built-in animation and simulation (depending on the net class) are complemented by export to various analysis tools. Snoopy facilitates the extension by new Petri net classes thanks to its generic design.
Petri nets offer a graphical & intuitive notation for biochemical reaction networks, such as gene... more Petri nets offer a graphical & intuitive notation for biochemical reaction networks, such as gene regulatory, signal transduction or metabolic networks. Moreover, they may serve as an umbrella formalism combining different modelling paradigms, where each perspective contributes to a better understanding of the biochemical system under study. In this spirit of BioModel Engineering, we developed over the last two decades our unifying Petri net framework comprising the traditional time-free Petri nets (PN) as well as quantitative, i.e. time-dependent Petri nets such as stochastic Petri nets (SPN), continuous Petri nets (CPN), and hybrid Petri nets (HPN), as well as their coloured counterparts [1]. Coloured Petri nets permit, among others, the convenient and flexible encoding of spatial attributes, and thus the modelling of processes evolving in time and space, which are usually treated as stochastic or deterministic partial differential equations (PDE). In our approach, the discretisat...
We present a methodology for systematically extending epidemic models to multilevel and multiscal... more 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. 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 the models are available as supplementary material, ensuring reproducibility. ar X iv :2 10 7. 00 83 5v 1 [ qbi ...
The Cancer Stem Cell (CSC) involvement into tumor progression, tumor recurrence, and therapy resi... more The Cancer Stem Cell (CSC) involvement into tumor progression, tumor recurrence, and therapy resistance is one of the most studied subject of current cancer research [10,4,8,6]. Nevertheless, due to the complex dynamics characterizing the CSC tumor, a comprehensive theory has not been established yet. To this end, some advises can be obtained combining mathematical modeling and experimental data [5,9,2,7]. Indeed, mathematical modeling is a powerful instrument which may drive the comprehension of a biological system, providing a clear description of its essential dynamics. The aim of this talk is hence to show how the CSC tumor growth could be described/studied through the application of mathematical models. In details two different modeling approaches are presented: the former one consists in a multilevel/multiscale model [1], which details both molecular and cellular aspects. By means of this framework we were able to reproduce the tumor growth trend observed in mice, highlighting...
This report documents the program and the outcomes of Dagstuhl Seminar 14481 “Multiscale Spatial ... more This report documents the program and the outcomes of Dagstuhl Seminar 14481 “Multiscale Spatial Computational Systems Biology”. This seminar explored challenges arising from the need to model and analyse complex biological systems at multiple scales (spatial and temporal), which falls within the general remit of Computational Systems Biology. A distinguishing factor of the seminar was the modelling exercise – where teams explored different modelling paradigms, in order to better understand the details of the approaches, their challenges, potential applications, and their pros and cons. This activity was carried out in a collaborative and self-directed manner using the Open Space Technology approach as evidenced by a high degree of communication both within and between the teams. Eight teams were formed, and reports from five of them are included in this document. Seminar November 24–28, 2014 – http://www.dagstuhl.de/14481 1998 ACM Subject Classification D.2.1 Requirements/Specifica...
Signalling cascades are a recurrent pattern of biological regulatory systems whose analysis has d... more Signalling cascades are a recurrent pattern of biological regulatory systems whose analysis has deserved a lot of attention. It has been shown that stochastic Petri nets are appropriate to model such systems and evaluate the probabilities of specific properties. Such an evaluation can be done numerically when the combinatorial state space explosion is manageable or statistically otherwise. However, when the probabilities to be evaluated are too small, random simulation requires more sophisticated techniques for the handling of rare events. In this paper, we show how such involved methods can be successfully applied for signalling cascades. More precisely, we study three relevant properties of a signalling cascade with the help of the COSMOS tool. Our experiments point out interesting dependencies between quantitative parameters of the regulatory system and its transient behaviour. In addition, they demonstrate that we can go beyond the capabilities of MARCIE, which provides one of t...
In this chapter we introduce qualitative, stochastic as wel l as continuous Petri nets and relate... more In this chapter we introduce qualitative, stochastic as wel l as continuous Petri nets and related analysis techniques in a rather infor mal way, and use as running example a model of the influence of the Raf Kinase Inhibit or Protein (RKIP) on the Extracellular signal Regulated Kinase (ERK) signall i g pathway. We show how the qualitative and quantitative analyses complement e ach other, and how Petri nets can be used for step-wise modelling and analysis of bioc hemical networks as well as for structured design of systems of ordinary differe ntial equations.
This chapter gives the author’s personal reflections on an exciting field of research that will h... more This chapter gives the author’s personal reflections on an exciting field of research that will help in our quest to gain deep understanding of living organisms by elucidating the components and their interactions that govern their behaviour.
Spike is a command line tool for continuous, stochastic & hybrid simulation of (coloured) Petri n... more Spike is a command line tool for continuous, stochastic & hybrid simulation of (coloured) Petri nets (PN). It allows import from and export to various PN data formats. Its abilities comprise the manipulation of PN models by changing arc weights, markings or functions. It also unfolds coloured PN. To comply with the demand for reproducible simulation experiments, Spike is supported by a script language which allows for model and simulation configuration.
In Petri net systems, liveness is an important property cap- turing the idea of no transition (ac... more In Petri net systems, liveness is an important property cap- turing the idea of no transition (action) becoming non-fireable (unattain- able). Additionally, in some situations it is particularly interesting to check if the net system is (marking) monotonically live, i.e., it remains live for any marking greater than the initial one. In this paper, we dis- cuss structural conditions preserving liveness under arbitrary marking increase. It is proved that the deadlock trap property (DTP) is a neces- sary condition for liveness monotonicity of ordinary nets, and necessary and sucient for some subclasses. We illustrate also how the result can be used to study liveness monotonicity for non-ordinary nets using a sim- ulation preserving the firing language. Finally, we apply these conditions to several case studies of biomolecular networks.
We present a methodology for systematically extending epidemic models to multilevel and multiscal... more 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. 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 the models are available as supplementary material, ensuring reproducibility.
This report documents the program and the outcomes of Dagstuhl Seminar 14481 "Multiscale Spa... more This report documents the program and the outcomes of Dagstuhl Seminar 14481 "Multiscale Spatial Computational Systems Biology". This seminar explored challenges arising from the need to model and analyse complex biological systems at multiple scales (spatial and temporal), which falls within the general remit of Computational Systems Biology. A distinguishing factor of the seminar was the modelling exercise-where teams explored different modelling paradigms, in order to better understand the details of the approaches, their challenges, potential applications, and their pros and cons. This activity was carried out in a collaborative and self-directed manner using the Open Space Technology approach as evidenced by a high degree of communication both within and between the teams. Eight teams were formed, and reports from five of them are included in this document.
Formal models have been shown useful for analysis of regulatory systems. Here we focus on signall... more Formal models have been shown useful for analysis of regulatory systems. Here we focus on signalling cascades, a recurrent pattern of biological regulatory systems. We choose the formalism of stochastic Petri nets for this modelling and we express the properties of interest by formulas of a temporal logic. Such properties can be evaluated with either numeric or simulation based methods. The former one suffers from the combinatorial state space explosion problem, while the latter suffers from time explosion due to rare event phenomena. In this paper, we demonstrate the use of rare event techniques to tackle the analysis of signalling cascades. We compare the effectiveness of the COSMOS statistical model checker, which implements importance sampling methods to speed up rare event simulations, with the numerical model checker MARCIE on several properties. More precisely, we study three properties that characterise the ordering of events in the signalling cascade. We establish an intere...
In this chapter we introduce qualitative, stochastic as well as continuous Petri nets and related... more In this chapter we introduce qualitative, stochastic as well as continuous Petri nets and related analysis techniques in a rather informal way, and use as run-ning example a model of the influence of the Raf Kinase Inhibitor Protein (RKIP) on the Extracellular signal Regulated Kinase (ERK) signalling pathway. We show how the qualitative and quantitative analyses complement each other, and how Petri nets can be used for step-wise modelling and analysis of biochemical networks as well as for structured design of systems of ordinary differential equations. 1
Abstract—Signalling cascades are a recurrent pattern of biological regulatory systems whose analy... more Abstract—Signalling cascades are a recurrent pattern of biological regulatory systems whose analysis has deserved a lot of attention. It has been shown that Stochastic Petri Nets (SPN) are appro-priate to model such systems and evaluate the probabilities of specific properties. Such an evaluation can be done numerically when the combinatorial state space explosion is manageable or statistically otherwise. However, when the probabilities to be evaluated are too small, random simulation requires more sophisticated techniques for the handling of rare events. In this paper, we show how such involved methods can be successfully applied for signalling cascades. More precisely, we study three relevant properties of a signalling cascade with the help of the COSMOS tool. Our experiments point out interesting dependencies between quantitative parameters of the regulatory system and its transient behaviour. In addition, they demonstrate that we can go beyond the capabilities of MARCIE, which p...
Abstract. In Petri net systems, liveness is an important property cap-turing the idea of no trans... more Abstract. In Petri net systems, liveness is an important property cap-turing the idea of no transition (action) becoming non-fireable (unattain-able). Additionally, in some situations it is particularly interesting to check if the net system is (marking) monotonically live, i.e., it remains live for any marking greater than the initial one. In this paper, we dis-cuss structural conditions preserving liveness under arbitrary marking increase. It is proved that the deadlock trap property (DTP) is a neces-sary condition for liveness monotonicity of ordinary nets, and necessary and sufficient for some subclasses. We illustrate also how the result can be used to study liveness monotonicity for non-ordinary nets using a sim-ulation preserving the firing language. Finally, we apply these conditions to several case studies of biomolecular networks. 1
This tutorial would not have been possible unless the support of Monika Heiner and my supervisor ... more This tutorial would not have been possible unless the support of Monika Heiner and my supervisor Wolfgang Marwan. I am very grateful for their encouragement, guidance and support that enabled me to develop my understanding of Petri nets and skills. Further I like to thank Christian Rohr and Martin Schwarick as representatives of Monika Heiners team, who develop the three fabulous Petri net tools; Snoopy, Charlie and Marcie. I also thank my colleague Jan-Thierry Wegener, who provided a first documentation of Charlie. I like to give credit to Qian Gao and Esther Bamigboye for revising an improving the text, which was very helpful and educational for me.
Recently hybrid modelling and simulation of biochemical systems have attracted increasing interes... more Recently hybrid modelling and simulation of biochemical systems have attracted increasing interest. This is motivated by the need of simulating systems which integrate different sub-cellular models, and the fact that bio networks themselves are inherently stochastic, however stochastic simulation is time expensive. Compared to other methods of biological modelling, Petri nets are characterized by their intuitive visual representation and executability of biological models. In this paper, we present a hybrid Petri net class that incorporates both continuous and stochastic capabilities. The presented class is intended to model and simulate hybrid biological systems such that they contain some parts which are simulated deterministically while other parts are simulated stochastically.
ACM Transactions on Modeling and Computer Simulation, 2015
This article defines a novel spatial-temporal modelling and analysis methodology applied to a sys... more This article defines a novel spatial-temporal modelling and analysis methodology applied to a systems biology case study, namely phase variation patterning in bacterial colony growth. We employ coloured stochastic Petri nets to construct the model and run stochastic simulations to record the development of the circular colonies over time and space. The simulation output is visualised in 2D, and sector-like patterns are automatically detected and analysed. Space is modelled using 2.5 dimensions considering both a rectangular and circular geometry, and the effects of imposing different geometries on space are measured. We close by outlining an interpretation of the Petri net model in terms of finite difference approximations of partial differential equations (PDEs). One result is the derivation of the “best” nine-point diffusion model. Our multidimensional modelling and analysis approach is a precursor to potential future work on more complex multiscale modelling.
Algebraic and Discrete Mathematical Methods for Modern Biology, 2015
ABSTRACT We present a unifying Petri net framework comprising the qualitative, stochastic, con- t... more ABSTRACT We present a unifying Petri net framework comprising the qualitative, stochastic, con- tinuous and hybrid paradigm for modelling and analysing biological reaction networks. By means of a running case study we demonstrate how the different paradigms contribute in complementary ways to the overall understanding of emergent network properties. The framework is supported by four tools, Snoopy, Charlie, Marcie, and MC2, which will also be of use in the suggested exercises.
The tool Snoopy provides a unifying Petri net framework which has particularly many application s... more The tool Snoopy provides a unifying Petri net framework which has particularly many application scenarios in systems and synthetic biology. The framework consists of two levels: uncoloured and coloured. Each level comprises a family of related Petri net classes, sharing structure, but being specialized by their kinetic information. Petri nets of all net classes within one level can be converted into each other, while changing the level involves user-guided folding or automatic unfolding. Models can be hierarchically structured, allowing for the mastering of larger networks. Snoopy supports the simultaneous use of several Petri net classes; the graphical user interface adapts dynamically to the active one. Built-in animation and simulation (depending on the net class) are complemented by export to various analysis tools. Snoopy facilitates the extension by new Petri net classes thanks to its generic design.
Petri nets offer a graphical & intuitive notation for biochemical reaction networks, such as gene... more Petri nets offer a graphical & intuitive notation for biochemical reaction networks, such as gene regulatory, signal transduction or metabolic networks. Moreover, they may serve as an umbrella formalism combining different modelling paradigms, where each perspective contributes to a better understanding of the biochemical system under study. In this spirit of BioModel Engineering, we developed over the last two decades our unifying Petri net framework comprising the traditional time-free Petri nets (PN) as well as quantitative, i.e. time-dependent Petri nets such as stochastic Petri nets (SPN), continuous Petri nets (CPN), and hybrid Petri nets (HPN), as well as their coloured counterparts [1]. Coloured Petri nets permit, among others, the convenient and flexible encoding of spatial attributes, and thus the modelling of processes evolving in time and space, which are usually treated as stochastic or deterministic partial differential equations (PDE). In our approach, the discretisat...
We present a methodology for systematically extending epidemic models to multilevel and multiscal... more 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. 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 the models are available as supplementary material, ensuring reproducibility. ar X iv :2 10 7. 00 83 5v 1 [ qbi ...
The Cancer Stem Cell (CSC) involvement into tumor progression, tumor recurrence, and therapy resi... more The Cancer Stem Cell (CSC) involvement into tumor progression, tumor recurrence, and therapy resistance is one of the most studied subject of current cancer research [10,4,8,6]. Nevertheless, due to the complex dynamics characterizing the CSC tumor, a comprehensive theory has not been established yet. To this end, some advises can be obtained combining mathematical modeling and experimental data [5,9,2,7]. Indeed, mathematical modeling is a powerful instrument which may drive the comprehension of a biological system, providing a clear description of its essential dynamics. The aim of this talk is hence to show how the CSC tumor growth could be described/studied through the application of mathematical models. In details two different modeling approaches are presented: the former one consists in a multilevel/multiscale model [1], which details both molecular and cellular aspects. By means of this framework we were able to reproduce the tumor growth trend observed in mice, highlighting...
This report documents the program and the outcomes of Dagstuhl Seminar 14481 “Multiscale Spatial ... more This report documents the program and the outcomes of Dagstuhl Seminar 14481 “Multiscale Spatial Computational Systems Biology”. This seminar explored challenges arising from the need to model and analyse complex biological systems at multiple scales (spatial and temporal), which falls within the general remit of Computational Systems Biology. A distinguishing factor of the seminar was the modelling exercise – where teams explored different modelling paradigms, in order to better understand the details of the approaches, their challenges, potential applications, and their pros and cons. This activity was carried out in a collaborative and self-directed manner using the Open Space Technology approach as evidenced by a high degree of communication both within and between the teams. Eight teams were formed, and reports from five of them are included in this document. Seminar November 24–28, 2014 – http://www.dagstuhl.de/14481 1998 ACM Subject Classification D.2.1 Requirements/Specifica...
Signalling cascades are a recurrent pattern of biological regulatory systems whose analysis has d... more Signalling cascades are a recurrent pattern of biological regulatory systems whose analysis has deserved a lot of attention. It has been shown that stochastic Petri nets are appropriate to model such systems and evaluate the probabilities of specific properties. Such an evaluation can be done numerically when the combinatorial state space explosion is manageable or statistically otherwise. However, when the probabilities to be evaluated are too small, random simulation requires more sophisticated techniques for the handling of rare events. In this paper, we show how such involved methods can be successfully applied for signalling cascades. More precisely, we study three relevant properties of a signalling cascade with the help of the COSMOS tool. Our experiments point out interesting dependencies between quantitative parameters of the regulatory system and its transient behaviour. In addition, they demonstrate that we can go beyond the capabilities of MARCIE, which provides one of t...
In this chapter we introduce qualitative, stochastic as wel l as continuous Petri nets and relate... more In this chapter we introduce qualitative, stochastic as wel l as continuous Petri nets and related analysis techniques in a rather infor mal way, and use as running example a model of the influence of the Raf Kinase Inhibit or Protein (RKIP) on the Extracellular signal Regulated Kinase (ERK) signall i g pathway. We show how the qualitative and quantitative analyses complement e ach other, and how Petri nets can be used for step-wise modelling and analysis of bioc hemical networks as well as for structured design of systems of ordinary differe ntial equations.
This chapter gives the author’s personal reflections on an exciting field of research that will h... more This chapter gives the author’s personal reflections on an exciting field of research that will help in our quest to gain deep understanding of living organisms by elucidating the components and their interactions that govern their behaviour.
Spike is a command line tool for continuous, stochastic & hybrid simulation of (coloured) Petri n... more Spike is a command line tool for continuous, stochastic & hybrid simulation of (coloured) Petri nets (PN). It allows import from and export to various PN data formats. Its abilities comprise the manipulation of PN models by changing arc weights, markings or functions. It also unfolds coloured PN. To comply with the demand for reproducible simulation experiments, Spike is supported by a script language which allows for model and simulation configuration.
In Petri net systems, liveness is an important property cap- turing the idea of no transition (ac... more In Petri net systems, liveness is an important property cap- turing the idea of no transition (action) becoming non-fireable (unattain- able). Additionally, in some situations it is particularly interesting to check if the net system is (marking) monotonically live, i.e., it remains live for any marking greater than the initial one. In this paper, we dis- cuss structural conditions preserving liveness under arbitrary marking increase. It is proved that the deadlock trap property (DTP) is a neces- sary condition for liveness monotonicity of ordinary nets, and necessary and sucient for some subclasses. We illustrate also how the result can be used to study liveness monotonicity for non-ordinary nets using a sim- ulation preserving the firing language. Finally, we apply these conditions to several case studies of biomolecular networks.
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