On the Relation Between the Logical Structure of Systems and Their Ability to Generate Multiple Steady States or Sustained Oscillations

Thomas, René

doi:10.1007/978-3-642-81703-8_24

Cited by 320 publications

(300 citation statements)

References 29 publications

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“…Now, underlying circuits in networks are known since the 1980's to be responsible for the diversity in their dynamical behaviours. Indeed, in [4], Thomas formulated two conjectures concerning the importance of circuits and their relation to the dynamics of networks:…”

Section: Circuits and Intersecting Circuitsmentioning

confidence: 99%

“…The theory of biological regulatory networks [1,3,4,65] was born in parallel to the theory of neural networks [66,67]. It is now an extensive research topic which aims at interpreting the "omic" data from bio-array devices.…”

Section: Appendix B Biological Regulation Network Modelingmentioning

confidence: 99%

“…A huge mathematical effort has been done to identify the sources of the attractor multiplicity, known to be closely related to the number of positive circuits underlying regulatory networks [4,15,22,23,57,75,76,77,78] as well as to understand the causes of attractor uniqueness. Both these problems are of high interest if we want to explain the number of differentiated functions (around 300 for the human being [57]) as well as the presence of some unique functions that are devoted to one tissue.…”

Section: Appendix F Biological Importance Of Attractorsmentioning

confidence: 99%

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“Immunetworks”, intersecting circuits and dynamics

Demongeot

Elena

Noual

et al. 2011

Journal of Theoretical Biology

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This paper proposes a study of biological regulatory networks based on a multi-level strategy. Given a network, the first structural level of this strategy consists in analysing the architecture of the network interactions in order to describe it. The second dynamical level consists in relating the patterns found in the architecture to the possible dynamical behaviours of the network. It is known that circuits are the patterns that play the most important part in the dynamics of a network in the sense that they are responsible for the diversity of its asymptotic behaviours. Here, we pursue further this idea and argue that beyond the influence of underlying circuits, intersections of circuits also impact significantly on the dynamics of a network and thus need to be payed special attention to. For some genetic regulation networks involved in the control of the immune system ("immunetworks"), we show that the small number of attractors can be explained by the presence, in the underlying structures of these networks, of intersecting circuits that "inter-lock".

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Section: Circuits and Intersecting Circuitsmentioning

confidence: 99%

Section: Appendix B Biological Regulation Network Modelingmentioning

confidence: 99%

Section: Appendix F Biological Importance Of Attractorsmentioning

confidence: 99%

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“Immunetworks”, intersecting circuits and dynamics

Demongeot

Elena

Noual

et al. 2011

Journal of Theoretical Biology

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“…This approach has rapidly developed in Systems Biology for reasoning on large interaction networks, with for instance, the analysis of qualitative attractors in a logical dynamics of gene networks à la Thomas [3,4,5], reachability and temporal logic properties in reaction networks [6,7,8,9,10], structural invariants in the Petri net representation of the reactions [11,12,13,14,15,16], or model reductions using graph theory concepts [17,18]. These qualitative analysis tools do not rely on kinetic information, but on the structure of the reaction network which has thus to be correctly written as a set of formal reactions, with well-identified reactants, products and modifiers (and in certain cases their stoichiometry) for each reaction.…”

Section: Introductionmentioning

confidence: 99%

Inferring reaction systems from ordinary differential equations

Fages

Gay

Soliman

2015

Theoretical Computer Science

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In Mathematical Biology, many dynamical models of biochemical reaction systems are presented with Ordinary Differential Equations (ODE). Once kinetic parameter values are fixed, this simple mathematical formalism completely defines the dynamical behavior of a system of biochemical reactions and provides powerful tools for deterministic simulations, parameter sensitivity analysis, bifurcation analysis, etc. However, without requiring any information on the reaction kinetics and parameter values, various qualitative analyses can be performed using the structure of the reactions, provided the reactants, products and modifiers of each reaction are precisely defined. In order to apply these structural methods to parametric ODE models, we study a mathematical condition for expressing the consistency between the structure and the kinetics of a reaction, without restricting to Mass Action law kinetics. This condition, satisfied in particular by standard kinetic laws, entails a remarkable property of independence of the influence graph from the kinetics of the reactions. We derive from this study a heuristic algorithm which, given a system of ODEs as input, computes a system of reactions with the same ODE semantics, by inferring well-formed reactions whenever possible. We show how this strategy is capable of automatically curating the writing of ODE models in SBML, and present some statistics obtained on the model repository biomodels.net. 1 .

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“…It has been shown in several instances that multistationarity is a good description of biological processes such as epigenesis (Guespin-Michel et al, 2003), differentiation and memory (Delbrück, 1949;Demongeot, 1998;Casadesus and D'Ari, 2002). Thomas (1981) conjectured that a…”

Section: Introductionmentioning

confidence: 99%

Epigenesis and Dynamic Similarity in Two Regulatory Networks in Pseudomonas Aeruginosa

et al. 2004

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Mucoidy and cytotoxicity arise from two independent modifications of the phenotype of the bacterium Pseudomonas aeruginosa that contribute to the mortality and morbidity of cystic fibrosis. We show that, even though the transcriptional regulatory networks controlling both processes are quite different from a molecular or mechanistic point of view, they may be identical from a dynamic point of view: epigenesis may in both cases be the cause of the acquisition of these new phenotypes. This was highlighted by the identity of formal graphs modelling these networks. A mathematical framework based on formal methods from computer science was defined and implemented with a software environment. It allows an easy and rigorous validation and certification of these models and of the experimental methods that can be proposed to falsify or validate the underlying hypothesis.

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On the Relation Between the Logical Structure of Systems and Their Ability to Generate Multiple Steady States or Sustained Oscillations

Cited by 320 publications

References 29 publications

“Immunetworks”, intersecting circuits and dynamics

“Immunetworks”, intersecting circuits and dynamics

Inferring reaction systems from ordinary differential equations

Epigenesis and Dynamic Similarity in Two Regulatory Networks in Pseudomonas Aeruginosa

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