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### Citations

181 |
Boolean formalization of genetic control circuits
- Thomas
- 1973
(Show Context)
Citation Context ...networks of interactions that cannot be easily understood without resorting to formal modelling and automated analysis. The generalized logical formalism initially proposed by René Thomas in the 70s =-=[25, 26, 27]-=-, is a discrete modelling formalism that has proved to be an effective way to capture regulation processes and analyze them. It has been successfully applied to the study of a variety of regulatory ne... |

178 |
Dynamical behaviour of biological regulatory networks– I: biological role of feedback loops and practical use of the concept of the loop-characteristic state
- Thomas, Kaufman
- 1995
(Show Context)
Citation Context ...networks of interactions that cannot be easily understood without resorting to formal modelling and automated analysis. The generalized logical formalism initially proposed by René Thomas in the 70s =-=[25, 26, 27]-=-, is a discrete modelling formalism that has proved to be an effective way to capture regulation processes and analyze them. It has been successfully applied to the study of a variety of regulatory ne... |

126 |
Regulatory networks seen as asynchronous automata: A logical description
- Thomas
- 1991
(Show Context)
Citation Context ...networks of interactions that cannot be easily understood without resorting to formal modelling and automated analysis. The generalized logical formalism initially proposed by René Thomas in the 70s =-=[25, 26, 27]-=-, is a discrete modelling formalism that has proved to be an effective way to capture regulation processes and analyze them. It has been successfully applied to the study of a variety of regulatory ne... |

123 |
Coloured Petri Nets Modelling and Validation of Concurrent Systems.
- Jensen, Kristensen
- 2009
(Show Context)
Citation Context ...into account the neighboring relation δ . 2.3 Petri net semantics In order to analyze regulatory bundles, a Petri net semantics has been defined [5]. For this purpose, a colored variant of Petri nets =-=[13]-=- has been used in which: • places model containers of tokens, the latter being arbitrary values, e.g., pairs of integers as in the following; • transitions model activities that consume and produce to... |

49 |
Stochastic simulation of coupled reaction-diffusion processes
- Stundzia, Lumsden
- 1996
(Show Context)
Citation Context ...tic regulation on a complex dynamic geometry. Various formalism have been proposed to face these needs relying on various explicit representations of space [24]: molecular dynamics, spatial Gillespie =-=[23]-=-, partial differential equations (PDE), lattice based methods (e.g., cellular automata), etc. See Fig 13 for a brief taxonomy of space representation in biological modelling. In this context, we want ... |

30 | 2002c), ‘The topological structures of membrane computing
- Giavitto, Michel
(Show Context)
Citation Context ...patial evolutions, enumerations of the possible evolutions, graphical rendering of spatial information. To do so, we resort to topological collections. Topological collections have been introduced in =-=[9]-=- to describe arbitrary complex spatial structures that appear in biological systems [10]. They have been used to represents states of dynamical systems with a time varying structure [7, 12]. We will u... |

24 |
Declarative definition of group indexed data structures and approximation of their domains
- Giavitto, Michel
- 2001
(Show Context)
Citation Context ...ted degrees. 3.1 Placing modules on grids Simple topological collections can be defined as group based fields (GBF), that can be considered as associative arrays whose indexes are elements in a group =-=[8]-=-. The latter is defined by a finite presentation: a set of generators together with some constraints on their combinations. Thus a GBF can be pictured as a labelled graph where the underlying graph is... |

23 |
Modeling the topological organization of cellular processes
- Giavitto, Michel
- 2003
(Show Context)
Citation Context ...ial information. To do so, we resort to topological collections. Topological collections have been introduced in [9] to describe arbitrary complex spatial structures that appear in biological systems =-=[10]-=-. They have been used to represents states of dynamical systems with a time varying structure [7, 12]. We will use them in this paper as a unifying framework to represent arbitrary neighborhood relati... |

17 | Topological collections, transformations and their application to the modeling and the simulation of dynamical systems
- Giavitto
- 2003
(Show Context)
Citation Context ... introduced in [9] to describe arbitrary complex spatial structures that appear in biological systems [10]. They have been used to represents states of dynamical systems with a time varying structure =-=[7, 12]-=-. We will use them in this paper as a unifying framework to represent arbitrary neighborhood relationships. In this context, a neighborhood relationship between modules is represented by a labelled gr... |

16 |
Topological rewriting and the geometrization of programming
- Giavitto, Spicher
(Show Context)
Citation Context ... introduced in [9] to describe arbitrary complex spatial structures that appear in biological systems [10]. They have been used to represents states of dynamical systems with a time varying structure =-=[7, 12]-=-. We will use them in this paper as a unifying framework to represent arbitrary neighborhood relationships. In this context, a neighborhood relationship between modules is represented by a labelled gr... |

11 | 2008): Quickly prototyping Petri nets tools with SNAKES. Petri net newsletter October
- Pommereau
(Show Context)
Citation Context ...ay, which allows to explore all the possible evolutions of the spatial structure. 4.4 Implementation and applications Spatialized regulatory bundles have been implemented as a prototype, using SNAKES =-=[18, 17]-=- for the Petri net part, and MGS [16] for the topological collections part. SNAKES is a general purpose Petri net library implemented in Python, that is particularly suitable for the quick development... |

8 |
Chaouiya C, Thieffry D (2008) Segmenting the fly embryo: logical analysis of the role of the Segment Polarity cross-regulatory module
- Sánchez
(Show Context)
Citation Context ... an effective way to capture regulation processes and analyze them. It has been successfully applied to the study of a variety of regulatory networks comprising relatively large numbers of components =-=[20, 21]-=-. This formalism however does not provide any modelling device to specifically address the question of multi-cellular systems, where the regulatory networks of cells can influence each other in a way ... |

7 |
Using rewriting techniques in the simulation of dynamical systems: Application to the modeling of sperm crawling
- Spicher, Michel
- 2005
(Show Context)
Citation Context ...o produce a graphical rendering of an n-BDG. Here also, MGS simplifies the problem by proposing graph layout algorithms that have been already proved relevant to represent graphically cells positions =-=[19, 22]-=-. In an n-BDG, a notion of distance can be defined as the length of the shortest path between two nodes. If such a path does not exist, i.e., if the graph is not connected, the distance can be assumed... |

5 | 2002): Accretive Rules in Cayley P Systems
- Giavitto, Michel, et al.
(Show Context)
Citation Context ... in a disconnected tissue, which may be undesirable too. However, the simplicity of grids is well adapted to model, e.g., accretive growth that occurs at the borders of a tissue like leaves in plants =-=[11]-=-. Notice also that the graphical rendering of GBF is trivial to obtain because the grids are predefined. 3.2 A generalization of grids In order to overcome the limitations of grids in the presence of ... |

5 |
2006.Computer simulations reveal properties of the cell–cell signaling network at the shoot apex in Arabidopsis
- Reuille, Bohn-Courseau, et al.
(Show Context)
Citation Context ...o produce a graphical rendering of an n-BDG. Here also, MGS simplifies the problem by proposing graph layout algorithms that have been already proved relevant to represent graphically cells positions =-=[19, 22]-=-. In an n-BDG, a notion of distance can be defined as the length of the shortest path between two nodes. If such a path does not exist, i.e., if the graph is not connected, the distance can be assumed... |

5 |
Arjunan S, Tomita M (2005) Space in systems biology of signaling pathways-towards intracellular molecular crowding in silico
- Takahashi
(Show Context)
Citation Context ...cell signaling, mechanical stresses and genetic regulation on a complex dynamic geometry. Various formalism have been proposed to face these needs relying on various explicit representations of space =-=[24]-=-: molecular dynamics, spatial Gillespie [23], partial differential equations (PDE), lattice based methods (e.g., cellular automata), etc. See Fig 13 for a brief taxonomy of space representation in bio... |

4 |
Gheorghe (2004): Population P systems
- Bernardini, Marian
(Show Context)
Citation Context ... is an arc from s toward s′. Such a graph defines a transition system that is suitable to perform model-checking of various reachability- or causality-related properties. For instance, consider state =-=[1,0,0]-=- of the previous network (indexed as [xA,xB,xC]). Only component B may evolve, because KB(xA) 7→ 1, KA(xC) 7→ 1 and KC(xB) 7→ 0 in state [1,0,0]; this yields a new state [1,1,0]. The state space reach... |

4 | Thieffry (2006): Qualitative Petri Net Modelling of Genetic Networks - Chaouiya, Remy, et al. |

4 |
Pommereau (2009): An Approach to State Space Reduction for Systems with Dynamic Process Creation
- Klaudel, Koutny, et al.
(Show Context)
Citation Context ...fiers); another possibility is to resort to abstraction, for instance by applying to module identifiers a state space reduction technique originally designed for systems with dynamic process creation =-=[14, 15]-=-. Finally, we intend to study an alternative approach for spatial information in order to address systems such as blood-cells populations. The idea is to implement the spatial relation as a purely sto... |

3 |
2009): Modélisation de tissus biologiques : localisation et abstraction
- Castagnet
(Show Context)
Citation Context ...igration, division or apoptosis has been added. This prototype implementation has been applied to the study of two simple biology-inspired examples, allowing to test various features of our framework =-=[3]-=-: 1. A system with transcription signal cascading resulting in a cell division allowed to observe the alternation of growth phases and divisions, which can be interpreted as a mutual influence between... |

3 |
Pommereau (2009): A Petri net based framework for a qualitative modelling of regulatory networks encompassing inter-cellular signalling
- Chaouiya, Klaudel, et al.
(Show Context)
Citation Context ...information should be compatible with existing graphical rendering techniques. Contributions. Our starting point is a modelling approach developed in [2, 6] and extended later to introduce modularity =-=[5, 4]-=-. This approach itself is based on logical regulatory networks [25, 26, 27] that allow for modelling regulation within a biological system. A Petri net semantics is provided in order to analyze the va... |

3 |
Pommereau (to appear): A modular, qualitative modelling of regulatory networks using Petri nets, chapter 12 of Modeling in Systems Biology – the Petri Net Approach
- Chaouiya, Klaudel, et al.
(Show Context)
Citation Context ...information should be compatible with existing graphical rendering techniques. Contributions. Our starting point is a modelling approach developed in [2, 6] and extended later to introduce modularity =-=[5, 4]-=-. This approach itself is based on logical regulatory networks [25, 26, 27] that allow for modelling regulation within a biological system. A Petri net semantics is provided in order to analyze the va... |

3 | Thieffry (to appear): Petri net representation of multi-valued logical regulatory networks. Natural Computing - Chaouiya, Naldi, et al. |

3 |
Pommereau (to appear): State Space Reduction for Dynamic Process Creation
- Klaudel, Koutny, et al.
(Show Context)
Citation Context ...fiers); another possibility is to resort to abstraction, for instance by applying to module identifiers a state space reduction technique originally designed for systems with dynamic process creation =-=[14, 15]-=-. Finally, we intend to study an alternative approach for spatial information in order to address systems such as blood-cells populations. The idea is to implement the spatial relation as a purely sto... |

3 |
The MGS homepage. Available at http://mgs. spatial-computing.org
- Michel, Giavitto, et al.
(Show Context)
Citation Context ...ll be computed dynamically with respect to some lower-level neighboring information. Topological collections of various kinds have been implemented in an experimental programming languages called MGS =-=[16]-=-. This language is used here to implement a database that records the neighborhood relationships and that can be queried and updated efficiently. 3 Representing spatial information In this section, we... |

3 |
SNAKES is the net algebra kit for editors and simulators. Available at http: //pommereau.blogspot.com/2010/01/snakes.html
- Pommereau
(Show Context)
Citation Context ...ay, which allows to explore all the possible evolutions of the spatial structure. 4.4 Implementation and applications Spatialized regulatory bundles have been implemented as a prototype, using SNAKES =-=[18, 17]-=- for the Petri net part, and MGS [16] for the topological collections part. SNAKES is a general purpose Petri net library implemented in Python, that is particularly suitable for the quick development... |

3 |
Schraven (2007): A logical model provides insights into T cell receptor signaling
- Saez-Rodriguez, Simeoni, et al.
(Show Context)
Citation Context ... an effective way to capture regulation processes and analyze them. It has been successfully applied to the study of a variety of regulatory networks comprising relatively large numbers of components =-=[20, 21]-=-. This formalism however does not provide any modelling device to specifically address the question of multi-cellular systems, where the regulatory networks of cells can influence each other in a way ... |