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## Compositional modelling and Analysis of LArge MoleculAr Regulatory networks (2010)

### Citations

3239 | D.: Model checking
- Clarke, Grumberg, et al.
- 1999
(Show Context)
Citation Context ...sm chosen to model the system, and thus provides yet another link between the different formalisms. The main formalism used in this domain is that of Temporal Logics. The Computation Tree Logic CTL ∗ =-=[12]-=- is an extension of classical logic that allows reasoning about an infinite tree of state transitions. It uses operators about branches (non-deterministic choices) and time (state transitions). Two pa... |

2314 |
Abstract interpretation: a unified lattice model for static analysis of programs by construction or approximation of fixpoints
- Cousot, Cousot
- 1977
(Show Context)
Citation Context ...l-checking, within a single formalism (see for instance [30]). 3.2 Hierarchy of abstractions In [20] we exhibited a formal hierarchy of abstractions, based on the framework of Abstract Interpretation =-=[13]-=-, that relates Boolean, stochastic, discrete and continuous semantics. We first show how these different semantics can be formally related by simple Galois connections, as required in the theory of ab... |

777 |
A General Method for Numerically Simulating the Stochastic Time Evolution of Coupled Chemical Reactions
- Gillespie
(Show Context)
Citation Context ...ote that a discrete semantics for compounds does not necessarily imply a logical time: Continuous Time Markov Chains (CTMCs) are a well known, and correct with respect to the Chemical Master Equation =-=[24]-=-, way to model the evolution of finite number of molecules involved in biochemical reactions. Discrete semantics provide qualitative information when quantitative experimental data is missing, whereas... |

653 | Metabolic stability and epigenesis in randomly constructed genetic nets
- Kauffman
- 1969
(Show Context)
Citation Context ...orks The logical formalism applies to Gene Regulatory Networks, in that it describes influences between regulatory products in an abstract, discrete way. Already in the sixties, Sugita [52], Kauffman =-=[33]-=- and others proposed a qualitative representation of regulatory networks. Here, we rely on the asynchronous, generalized logical formalization introduced by R. Thomas and colleagues [55, 57, 54]. In t... |

289 |
The logical analysis of continuous, nonlinear biochemical control circuits, Theor Biol 39:103–129
- Glass, SA
- 1973
(Show Context)
Citation Context ...DEs to structured models - as shown in section 3.3. Piecewise Affine Differential Equation (PADE) models have been proposed by Glass and Kauffman in the seventies to model genetic regulatory networks =-=[25]-=-. They are specific types of ODE models in which step functions are used to describe the influence of transcription factors on gene expression. Step functions are introduced as a simplification of the... |

241 |
Representation and simulation of biochemical processes using the pi-calculus process algebra.
- Regev, Silverman, et al.
- 2001
(Show Context)
Citation Context ...en models centered around the notion of reactions and those focused on regulations (or influences). In the first category are all process calculi that emerged from the pioneering use of π-calculus in =-=[41]-=-. They focus on (possible) interaction and are compoundcentered. None of the partners in CALAMAR uses such formalisms. They currently only provide very few specific analysis tools (mostly stochastic s... |

190 | Qualitative simulation of genetic regulatory networks using piecewise-linear models
- Jong, Gouzé, et al.
(Show Context)
Citation Context ...f this formalism is that it is possible to obtain a description of the dynamics of gene networks in the form of a state transition graph, simply using qualitative information on biological parameters =-=[15]-=-. In this respect, this formalism is closely related to the (generalized) logical formalism of Section 2.2. A significant difference however is that the dynamics of the generalized logical models is d... |

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 ...52], Kauffman [33] and others proposed a qualitative representation of regulatory networks. Here, we rely on the asynchronous, generalized logical formalization introduced by R. Thomas and colleagues =-=[55, 57, 54]-=-. In this framework, regulatory networks are represented by Logical Regulatory Graphs (LRG) which include: • nodes that represent regulatory components (be it genes, proteins or even phenomenological ... |

155 |
Biological Feedback
- Thomas, d’Ari
- 1990
(Show Context)
Citation Context ...52], Kauffman [33] and others proposed a qualitative representation of regulatory networks. Here, we rely on the asynchronous, generalized logical formalization introduced by R. Thomas and colleagues =-=[55, 57, 54]-=-. In this framework, regulatory networks are represented by Logical Regulatory Graphs (LRG) which include: • nodes that represent regulatory components (be it genes, proteins or even phenomenological ... |

127 |
et al.: The systems biology markup language (SBML): A medium for representation and exchange of biochemical network models.
- Hucka, Finney, et al.
- 2003
(Show Context)
Citation Context ...ms. We will not present them in any more details, but see [27] for a review. The second group of formalisms of the first category (reaction-centered) is that of rule-based languages. It includes SBML =-=[32]-=- and BIOCHAM [5]. We will show in section 2.4.1 that these formalisms relate to a bipartite multigraph, i.e., a Petri Net (PN), with compounds and reactions, the latter corresponding to consumption an... |

127 |
Regulatory networks seen as asynchronous automata: A logical description
- Thomas
- 1991
(Show Context)
Citation Context ...tate. In contrast, in the asynchronous updating, a unique change is performed at each step, hence each state has as many potentially subsequent states as the number of nodes that are called to change =-=[56]-=-. These discrete dynamics are generally represented by a State Transition Graph (STG). Since STG sizes exponentially increase with the number of regulatory components, methods relating structural prop... |

100 | Application of formal methods to biological regulatory networks: extending Thomas’ asynchronous logical approach with temporal logic.
- Bernot, Comet, et al.
- 2004
(Show Context)
Citation Context ...his logic, Fφ is equivalent to trueUφ, φWψ to (φUψ)∨Gφ, and the following duality properties hold: ¬(EF(φ)) = AG(¬φ), ¬(E φUψ) = A(¬ψW¬φ) and ¬(EφWψ) = A(¬ψU¬φ), where ¬ denotes negation. We refer to =-=[7, 22, 1, 2, 3, 5]-=- for examples of biological properties of a system expressed by Temporal Logic formulae. In BIOCHAM, the CTL fragment of CTL ∗ is used for the (non-deterministic) Boolean semantics: each temporal oper... |

95 | M.L.: Petri Net Representations in Metabolic Pathways. In:
- Reddy, Mavrovouniotis, et al.
- 1993
(Show Context)
Citation Context ...DE models is defined at the continuous level. INRIARelationships between different formalisms and levels of details 11 2.4 Petri Nets The use of Petri nets to model biochemical networks is quite old =-=[40]-=- but was mostly limited to metabolic pathway representation and analysis. In recent years however, they have become a more and more widely used formalism in the Systems Biology community and for a var... |

91 | Positive and negative circuits in dynamical systems
- Gouze
- 1998
(Show Context)
Citation Context ...s instead of simple algebraic operators. We also describe a type system allowing the automatic derivation of a regulation network corresponding to that of the Jacobian matrix (as used for instance in =-=[26, 48, 50]-=-) even when precise quantitative information is lacking, provided that the kinetic laws satisfy some general properties satisfied by the usual kinetics (Mass Action, Michaelis Menten, Hill, etc.). As ... |

85 | Validation of qualitative models of genetic regulatory networks by model checking: analysis of the nutritional stress response in E.Coli.
- Batt, Ropers, et al.
- 2005
(Show Context)
Citation Context ...his logic, Fφ is equivalent to trueUφ, φWψ to (φUψ)∨Gφ, and the following duality properties hold: ¬(EF(φ)) = AG(¬φ), ¬(E φUψ) = A(¬ψW¬φ) and ¬(EφWψ) = A(¬ψU¬φ), where ¬ denotes negation. We refer to =-=[7, 22, 1, 2, 3, 5]-=- for examples of biological properties of a system expressed by Temporal Logic formulae. In BIOCHAM, the CTL fragment of CTL ∗ is used for the (non-deterministic) Boolean semantics: each temporal oper... |

79 | Petri nets for systems and synthetic biology
- Heiner, Gilbert, et al.
- 2008
(Show Context)
Citation Context ...eaction models and logical regulatory graphs, which allows their use as a common language that can gather different kinds of analyses, like model-checking, within a single formalism (see for instance =-=[30]-=-). 3.2 Hierarchy of abstractions In [20] we exhibited a formal hierarchy of abstractions, based on the framework of Abstract Interpretation [13], that relates Boolean, stochastic, discrete and continu... |

78 |
Necessary conditions for multistationarity and stable periodicity
- Snoussi
- 1998
(Show Context)
Citation Context ...s instead of simple algebraic operators. We also describe a type system allowing the automatic derivation of a regulation network corresponding to that of the Jacobian matrix (as used for instance in =-=[26, 48, 50]-=-) even when precise quantitative information is lacking, provided that the kinetic laws satisfy some general properties satisfied by the usual kinetics (Mass Action, Michaelis Menten, Hill, etc.). As ... |

78 |
Graphical requirements for multistationarity.
- Soule
- 2003
(Show Context)
Citation Context ...s instead of simple algebraic operators. We also describe a type system allowing the automatic derivation of a regulation network corresponding to that of the Jacobian matrix (as used for instance in =-=[26, 48, 50]-=-) even when precise quantitative information is lacking, provided that the kinetic laws satisfy some general properties satisfied by the usual kinetics (Mass Action, Michaelis Menten, Hill, etc.). As ... |

77 | N.: Modelling and querying interaction networks in the biochemical abstract machine biocham
- Fages, Soliman, et al.
- 2004
(Show Context)
Citation Context ...his logic, Fφ is equivalent to trueUφ, φWψ to (φUψ)∨Gφ, and the following duality properties hold: ¬(EF(φ)) = AG(¬φ), ¬(E φUψ) = A(¬ψW¬φ) and ¬(EφWψ) = A(¬ψU¬φ), where ¬ denotes negation. We refer to =-=[7, 22, 1, 2, 3, 5]-=- for examples of biological properties of a system expressed by Temporal Logic formulae. In BIOCHAM, the CTL fragment of CTL ∗ is used for the (non-deterministic) Boolean semantics: each temporal oper... |

77 | Rules for modeling signal-transduction systems.
- Hlavacek, Faeder, et al.
- 2006
(Show Context)
Citation Context ...tion 2.4.1 that these formalisms relate to a bipartite multigraph, i.e., a Petri Net (PN), with compounds and reactions, the latter corresponding to consumption and production of the former. See also =-=[31]-=- for a review of rule-based modelling frameworks for Systems Biology. The other category of formalisms is the one focusing on Gene Regulation Networks (GRNs). We will detail later the differences betw... |

74 |
BIOCHAM: An environment for modeling biological systems and formalizing experimental knowledge
- Calzone, Fages, et al.
(Show Context)
Citation Context ...resent them in any more details, but see [27] for a review. The second group of formalisms of the first category (reaction-centered) is that of rule-based languages. It includes SBML [32] and BIOCHAM =-=[5]-=-. We will show in section 2.4.1 that these formalisms relate to a bipartite multigraph, i.e., a Petri Net (PN), with compounds and reactions, the latter corresponding to consumption and production of ... |

66 | Symbolic Model Checking of Biochemical Networks. In:
- Chabrier, Fages
- 2003
(Show Context)
Citation Context |

65 | Petri net modelling of biological networks
- Chaouiya
- 2007
(Show Context)
Citation Context ... (see e.g. [18]). This high level of expressiveness comes at the cost of few analytical means. For an overview of the various classes of PN employed in the field of biochemical network modelling, see =-=[29, 8]-=-. 2.5 Others Between purely qualitative and highly non-linear ODE systems lie many different formalisms. We refer to [39] for a comparison of such formalisms, from Hill-based equations, to piecewise-a... |

59 | Model building and model checking for biochemical processes.
- Antoniotti, Policriti, et al.
- 2003
(Show Context)
Citation Context |

49 |
A method for the generation of standardized qualitative dynamical systems of regulatory networks,” Theoretial biology and medical modeling,
- Mendoza, Xenarios
- 2005
(Show Context)
Citation Context ...y use a structured model. Once again, we have already given some pointers to precise articles since an exhaustive RR n° 722118 Soliman et al. [39, 44] ODE PADE inria-00461084, version 1 - 3 Mar 2010 =-=[36, 58]-=- [28, 46, 17] Boolean Multi-valued Logical [14, 39] [14] [39] [25, 45, 15, 11] Discrete-time Figure 9: A tentative scheme illustrating existing links between the different formalisms employed for the ... |

45 |
Logical identification of all steady states: the concept of feedback loop characteristic states.
- Snoussi, Thomas
- 1993
(Show Context)
Citation Context ...tructured model. Once again, we have already given some pointers to precise articles since an exhaustive RR n° 722118 Soliman et al. [39, 44] ODE PADE inria-00461084, version 1 - 3 Mar 2010 [36, 58] =-=[28, 46, 17]-=- Boolean Multi-valued Logical [14, 39] [14] [39] [25, 45, 15, 11] Discrete-time Figure 9: A tentative scheme illustrating existing links between the different formalisms employed for the modelling of ... |

40 |
W.E.: Stochastic kinetic analysis of the escherichia coli stress circuit using σ32-targeted antisense.
- Srivastava, Peterson, et al.
- 2001
(Show Context)
Citation Context ...epending on the type of the involved distributions. Most models of biochemical networks are equivalent to Continuous Time Markov Chains and thus can be simulated using Gillespie’s algorithm (see e.g. =-=[51]-=-). In hybrid functional Petri nets, there are both discrete and continuous places and transitions. Moreover, the arc weights might vary with the marking of the places. This most extended version of PN... |

26 |
Constructing biological pathway models with hybrid functional petri nets
- Doi, Fujita, et al.
(Show Context)
Citation Context ...us places and transitions. Moreover, the arc weights might vary with the marking of the places. This most extended version of PN can be very convenient to represent some biological features (see e.g. =-=[18]-=-). This high level of expressiveness comes at the cost of few analytical means. For an overview of the various classes of PN employed in the field of biochemical network modelling, see [29, 8]. 2.5 Ot... |

26 | Abstract interpretation and types for systems biology. Theor Comput Sci
- Fages, Soliman
- 2008
(Show Context)
Citation Context ...aphs, which allows their use as a common language that can gather different kinds of analyses, like model-checking, within a single formalism (see for instance [30]). 3.2 Hierarchy of abstractions In =-=[20]-=- we exhibited a formal hierarchy of abstractions, based on the framework of Abstract Interpretation [13], that relates Boolean, stochastic, discrete and continuous semantics. We first show how these d... |

25 | Qualitative analysis of regulatory graphs: A computational tool based on a discrete formal framework, in:
- Chaouiya
- 2003
(Show Context)
Citation Context ...y parameters as the number of possible interaction combinations). These sets of logical parameters can equivalently be defined by truth tables, logical or evolution functions, decision diagrams (e.g. =-=[10, 38]-=-). inria-00461084, version 1 - 3 Mar 2010 This qualitative level of description is very well adapted to regulatory networks for which precise, quantitative data is scarcely available. Given a state of... |

25 |
Comparing different ODE modelling approaches for gene regulatory networks,
- Polynikis, Hogan, et al.
- 2009
(Show Context)
Citation Context ...s classes of PN employed in the field of biochemical network modelling, see [29, 8]. 2.5 Others Between purely qualitative and highly non-linear ODE systems lie many different formalisms. We refer to =-=[39]-=- for a comparison of such formalisms, from Hill-based equations, to piecewise-affine with or without quasi-steady-state assumptions. On the other side, models taking into account the stochasticity imp... |

22 | A general computational method for robustness analysis with applications to synthetic gene networks,
- Rizk, Batt, et al.
- 2009
(Show Context)
Citation Context ...y been developed as an SBML model, using the CellDesigner tool. It represents a comprehensive map of the RB/E2F pathway [6] shown in Figure 1. 2.1.2 BIOCHAM BIOCHAM (the BIOCHemical Abstract Machine) =-=[21, 5, 43]-=- is a software environment for modelling biochemical systems. It is based on two aspects: 1. the formalization of biological properties in temporal logic. 2. the analysis and simulation of rule-based ... |

22 |
Boolean formalisation of genetic control circuits
- Thomas
- 1973
(Show Context)
Citation Context ...52], Kauffman [33] and others proposed a qualitative representation of regulatory networks. Here, we rely on the asynchronous, generalized logical formalization introduced by R. Thomas and colleagues =-=[55, 57, 54]-=-. In this framework, regulatory networks are represented by Logical Regulatory Graphs (LRG) which include: • nodes that represent regulatory components (be it genes, proteins or even phenomenological ... |

20 |
Noise in random boolean networks
- Peixoto, Drossel
(Show Context)
Citation Context ...se models, the wiring is random (though fixing the number of incoming interactions for all nodes), the logical functions are also randomly chosen and the updating is performed synchronously (see e.g. =-=[19]-=- for a review). Studies of these models mainly relate to the number and lengths of the attractors. In the context of Boolean Regulatory Graph as defined by R. Thomas, a number of formal results concer... |

17 |
Mathematical aspects of mass action kinetics
- Feinberg
- 1977
(Show Context)
Citation Context ... component levels increases the complexity of the model and hence its analysis. 2.3 Ordinary Differential Equations (ODEs) ODEs are a fundamental modelling tool for mathematical biology and chemistry =-=[23]-=-. When precise kinetic data is available, it allows simulation via numerical integration, and bifurcation analysis in low-dimensional models when one or two parameters are unknown. In the context of C... |

17 |
Transforming boolean models to continuous models: methodology and application to t-cell receptor signaling.
- Wittmann, Krumsiek, et al.
- 2009
(Show Context)
Citation Context ...y use a structured model. Once again, we have already given some pointers to precise articles since an exhaustive RR n° 722118 Soliman et al. [39, 44] ODE PADE inria-00461084, version 1 - 3 Mar 2010 =-=[36, 58]-=- [28, 46, 17] Boolean Multi-valued Logical [14, 39] [14] [39] [25, 45, 15, 11] Discrete-time Figure 9: A tentative scheme illustrating existing links between the different formalisms employed for the ... |

16 | Discrete time piecewise affine models of genetic regulatory networks
- Coutinho, Fernandez, et al.
- 2006
(Show Context)
Citation Context ...dy given some pointers to precise articles since an exhaustive RR n° 722118 Soliman et al. [39, 44] ODE PADE inria-00461084, version 1 - 3 Mar 2010 [36, 58] [28, 46, 17] Boolean Multi-valued Logical =-=[14, 39]-=- [14] [39] [25, 45, 15, 11] Discrete-time Figure 9: A tentative scheme illustrating existing links between the different formalisms employed for the modelling of regulatory networks. The arrows indica... |

16 | Formal cell biology in Biocham
- Fages, Soliman
- 2008
(Show Context)
Citation Context ...y been developed as an SBML model, using the CellDesigner tool. It represents a comprehensive map of the RB/E2F pathway [6] shown in Figure 1. 2.1.2 BIOCHAM BIOCHAM (the BIOCHemical Abstract Machine) =-=[21, 5, 43]-=- is a software environment for modelling biochemical systems. It is based on two aspects: 1. the formalization of biological properties in temporal logic. 2. the analysis and simulation of rule-based ... |

16 | A unique transformation from ordinary differential equations to reaction networks
- Soliman, Heiner
(Show Context)
Citation Context ...s, in general the reverse mapping is not unique. Conditions and algorithms have been proposed about how to map back an ODE system to a CPN, so that the mapping is unique and biologically relevant. In =-=[49]-=- we provide sufficient conditions to recover in a unique way a structured model, like a continuous PN, from a given system of ODEs. These conditions mostly restrict the type of kinetics allowed for ea... |

16 |
Functional analysis of chemical systems in vivo using a logical circuit equivalent, II. The idea of a molecular automaton.
- Sugita
- 1963
(Show Context)
Citation Context ...regulatory networks The logical formalism applies to Gene Regulatory Networks, in that it describes influences between regulatory products in an abstract, discrete way. Already in the sixties, Sugita =-=[52]-=-, Kauffman [33] and others proposed a qualitative representation of regulatory networks. Here, we rely on the asynchronous, generalized logical formalization introduced by R. Thomas and colleagues [55... |

14 |
Dynamical roles of biological regulatory circuits
- Thieffry
- 2007
(Show Context)
Citation Context ...ircuits (encompassing an even number of inhibitions) are necessary for multistationarity, whereas negative circuits (encompassing an odd number of inhibitions) are required for oscillatory behaviours =-=[53, 57]-=-. Moreover, circuit analysis provides a valuable tool for conducting model reductions [37] and could be useful as well for identifying functional modules in regulatory networks. 2.2.1 Boolean framewor... |

10 | P.: From minimal signed circuits to the dynamics of Boolean regulatory networks
- Remy, Ruet
(Show Context)
Citation Context ...can provide sufficient conditions for multistationarity or sustained oscillations in some specific cases, typically when we enforce the system to remain in the context of functionality of the circuit =-=[42]-=-. 2.2.2 Multi-level logical framework In many cases, Boolean variables are sufficient to convey the role of regulatory components, but this all-or-none description must be extended when, for example, ... |

9 |
Model reduction using piecewise-linear approximations preserves dynamic properties of the carbon starvation response
- Ropers, Baldazzi, et al.
- 2009
(Show Context)
Citation Context ...quite often what the modellers have in mind even when they use a structured model. Once again, we have already given some pointers to precise articles since an exhaustive RR n° 722118 Soliman et al. =-=[39, 44]-=- ODE PADE inria-00461084, version 1 - 3 Mar 2010 [36, 58] [28, 46, 17] Boolean Multi-valued Logical [14, 39] [14] [39] [25, 45, 15, 11] Discrete-time Figure 9: A tentative scheme illustrating existing... |

8 |
A modular, qualitative modelling of regulatory networks using petri nets
- Chaouiya, Klaudel, et al.
(Show Context)
Citation Context ...ace names and an associated composition operation. This last feature is of a particular interest in the context of the CALAMAR project to handle the compositional building of large biochemical models =-=[4]-=-. 2.4.3 Further Petri Nets extensions A number of extensions have been designed to increase the expressive power of Petri nets. It is not our purpose here to review all these extensions but rather to ... |

7 |
Modeling and simulation of molecular biology using petri nets: modeling goals of various approaches
- Hardy, Robillard
(Show Context)
Citation Context ... (see e.g. [18]). This high level of expressiveness comes at the cost of few analytical means. For an overview of the various classes of PN employed in the field of biochemical network modelling, see =-=[29, 8]-=-. 2.5 Others Between purely qualitative and highly non-linear ODE systems lie many different formalisms. We refer to [39] for a comparison of such formalisms, from Hill-based equations, to piecewise-a... |

7 | On coupling models using modelchecking: Effects of irinotecan injections on the mammalian cell cycle
- Maria, Fages, et al.
- 2009
(Show Context)
Citation Context ...pecific behavior observed in experiments and formalized in temporal logic. Coupled with other methods such as bifurcation diagrams, this search assists the modeller/biologist in the modelling process =-=[35]-=-. A model is defined by a set of reaction rules, possibly equipped with kinetic expressions, a list of parameter values and initial conditions. A specification that accounts for the relevant biologica... |

7 |
A reduction method for logical regulatory graphs preserving essential dynamical properties
- Naldi, Remy, et al.
- 2009
(Show Context)
Citation Context ...eas negative circuits (encompassing an odd number of inhibitions) are required for oscillatory behaviours [53, 57]. Moreover, circuit analysis provides a valuable tool for conducting model reductions =-=[37]-=- and could be useful as well for identifying functional modules in regulatory networks. 2.2.1 Boolean framework The approximation of genetic regulation by such discrete modelling was justified by the ... |

6 |
A comprehensive imodular map of molecular interactions in RB/E2F pathway
- Calzone, Gelay, et al.
(Show Context)
Citation Context ...c or continuous simulations). One of the starting models for CALAMAR has actually been developed as an SBML model, using the CellDesigner tool. It represents a comprehensive map of the RB/E2F pathway =-=[6]-=- shown in Figure 1. 2.1.2 BIOCHAM BIOCHAM (the BIOCHemical Abstract Machine) [21, 5, 43] is a software environment for modelling biochemical systems. It is based on two aspects: 1. the formalization o... |

6 |
Petri net representation of multi-valued logical regulatory graphs
- Chaouiya, Naldi, et al.
(Show Context)
Citation Context ...phs and Petri nets Logical Regulatory Graphs can also be represented by means of Petri nets, although the translation is rather tricky compared to the intuitive PN representation of reaction networks =-=[9]-=-. Briefly, in this PN representation, pairs of complementary places account for regulatory nodes and transitions account for regulatory effects by specific interaction combinations. Figure 6: Standard... |

5 |
Relations between gene regulatory networks and cell dynamics in boolean models
- Didier, Remy
(Show Context)
Citation Context ...attached to the node P1, in different equivalent forms. The current level of P2 is denoted xP 2. proving the necessary conditions evoked above. The converse of these rules is not true in general (see =-=[16]-=-). Anyway, we can provide sufficient conditions for multistationarity or sustained oscillations in some specific cases, typically when we enforce the system to remain in the context of functionality o... |

5 |
Mapping multivalued onto Boolean dynamics
- Didier, Remy, et al.
(Show Context)
Citation Context ...ed that the multivalued to Boolean mapping proposed years ago by Van Ham, Snoussi and Thomas is indeed the sole mapping that could preserve both the regulatory structures and the dynamical behaviours =-=[28, 47, 17]-=-. With this preliminary work, existing methods that apply so far on Boolean models will be extended to the multi-level case. The picture is both simpler if one considers simple reaction models and mor... |

4 | Comparison between boolean and piecewise affine differential models for genetic networks
- Chaves, Tournier, et al.
- 2009
(Show Context)
Citation Context ...ers to precise articles since an exhaustive RR n° 722118 Soliman et al. [39, 44] ODE PADE inria-00461084, version 1 - 3 Mar 2010 [36, 58] [28, 46, 17] Boolean Multi-valued Logical [14, 39] [14] [39] =-=[25, 45, 15, 11]-=- Discrete-time Figure 9: A tentative scheme illustrating existing links between the different formalisms employed for the modelling of regulatory networks. The arrows indicate studies, which compare d... |

4 |
Biological Network Analysis, chapter Petri nets
- Koch, Heiner
- 2008
(Show Context)
Citation Context ...he expressive power of Petri nets. It is not our purpose here to review all these extensions but rather to mention those that are actually used to model biochemical networks. In continuous Petri Nets =-=[34]-=-, places are assigned a continuous marking (real positive number). Such a marking typically carries the concentrations of the compounds (denoted by the places). Each transition is associated with a fi... |

4 |
Decision diagrams for the representation of logical models of regulatory networks.
- Naldi, Thieffry, et al.
- 2007
(Show Context)
Citation Context ...y parameters as the number of possible interaction combinations). These sets of logical parameters can equivalently be defined by truth tables, logical or evolution functions, decision diagrams (e.g. =-=[10, 38]-=-). inria-00461084, version 1 - 3 Mar 2010 This qualitative level of description is very well adapted to regulatory networks for which precise, quantitative data is scarcely available. Given a state of... |

3 |
Process calculi abstractions for biology. Algorithmic Bioprocesses
- Guerriero, Prandi, et al.
- 2009
(Show Context)
Citation Context ...r which they are quite efficient, and stochastic model-checking, which remains computationally very expensive), but can be mapped to ODE systems. We will not present them in any more details, but see =-=[27]-=- for a review. The second group of formalisms of the first category (reaction-centered) is that of rule-based languages. It includes SBML [32] and BIOCHAM [5]. We will show in section 2.4.1 that these... |

3 |
How to deal with variables with more than two levels
- Ham
- 1979
(Show Context)
Citation Context ...ed that the multivalued to Boolean mapping proposed years ago by Van Ham, Snoussi and Thomas is indeed the sole mapping that could preserve both the regulatory structures and the dynamical behaviours =-=[28, 47, 17]-=-. With this preliminary work, existing methods that apply so far on Boolean models will be extended to the multi-level case. The picture is both simpler if one considers simple reaction models and mor... |

3 |
Qualitative dynamis of piecewise-linear differential equations: a discrete mapping approach. Dyn Stab Syst
- Snoussi
- 1989
(Show Context)
Citation Context ...ers to precise articles since an exhaustive RR n° 722118 Soliman et al. [39, 44] ODE PADE inria-00461084, version 1 - 3 Mar 2010 [36, 58] [28, 46, 17] Boolean Multi-valued Logical [14, 39] [14] [39] =-=[25, 45, 15, 11]-=- Discrete-time Figure 9: A tentative scheme illustrating existing links between the different formalisms employed for the modelling of regulatory networks. The arrows indicate studies, which compare d... |

3 |
Generalized kinetic logics, chapter 7
- Snoussi, Thomas, et al.
- 1990
(Show Context)
Citation Context ...ed that the multivalued to Boolean mapping proposed years ago by Van Ham, Snoussi and Thomas is indeed the sole mapping that could preserve both the regulatory structures and the dynamical behaviours =-=[28, 47, 17]-=-. With this preliminary work, existing methods that apply so far on Boolean models will be extended to the multi-level case. The picture is both simpler if one considers simple reaction models and mor... |