Robustness and fragility of Boolean models for genetic regulatory networks

Chaves, Madalena; Albert, Réka; Sontag, Eduardo D.

doi:10.1016/j.jtbi.2005.01.023

Cited by 297 publications

(277 citation statements)

References 44 publications

(104 reference statements)

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“…Since Kauffman introduced this eponymous model at the end of the 1960's, numerous studies (see [68,69,70] for instance) have worked on generalisations of it. Random Boolean networks constitute one of these generalisations.…”

Section: Appendix C Kauffman Boolean Network and Random Boolean Netmentioning

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: Appendix C Kauffman Boolean Network and Random Boolean Netmentioning

confidence: 99%

“…When 1 ≤ c ≤ 2, the number of possible limit cycles has recently been proven to be in general super-polynomial with respect to n [68,69,70,71,72].…”

Section: Appendix C Kauffman Boolean Network and Random Boolean Netmentioning

confidence: 99%

“Immunetworks”, intersecting circuits and dynamics

Demongeot

Elena

Noual

et al. 2011

Journal of Theoretical Biology

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“…the links among the system's nodes) and very intuitive qualitative representation of the system and its behaviour. In addition, various analytical methods can be used to study Boolean models (Glass & Kauffman 1973;Thomas 1973;Edwards & Glass 2000;Chaves et al 2005). …”

Section: Introductionmentioning

confidence: 99%

Studying the effect of cell division on expression patterns of the segment polarity genes

Chaves

Albert

2008

J. R. Soc. Interface.

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The segment polarity gene family, and its gene regulatory network, is at the basis of Drosophila embryonic development. The network's capacity for generating and robustly maintaining a specific gene expression pattern has been investigated through mathematical modelling. The models have provided several useful insights by suggesting essential network links, or uncovering the importance of the relative time scales of different biological processes in the formation of the segment polarity genes' expression patterns. But the developmental pattern formation process raises many other questions. Two of these questions are analysed here: the dependence of the signalling protein sloppy paired on the segment polarity genes and the effect of cell division on the segment polarity genes' expression patterns. This study suggests that cell division increases the robustness of the segment polarity network with respect to perturbations in biological processes.

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“…This turns the system non-deterministic: states may have several potential successors and the structure of the state transition graph may be highly complex. Alternatively, one can consider, for example, random asynchronous schemes (Chaves et al 2005;Stoll et al 2012), time delays (Siebert and Bockmayr 2006) or priority classes (Fauré et al 2006).…”

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confidence: 99%

“…Albert and Othmer 2003;Chaves et al 2005;González et al 2006;Sánchez et al 2008), to eukaryotic cell cycle (see Fauré and Thieffry 2009 for a survey). Immune response has also been tackled with logical modelling, from the early work of Kaufman et al (1999), to more recent modelling efforts to account for T cell activation, differentiation and survival (e.g.…”

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confidence: 99%

Logical Modelling of Regulatory Networks, Methods and Applications

Chaouiya

Rémy

2013

Bull Math Biol

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About 40 years ago, seminal work by S. Kauffman (1969) and R. Thomas (1973) paved the way to the establishment of a coarse-grained, "logical" modelling of gene regulatory networks. This gave rise to an increasingly active field of research, which ranges from theoretical studies to models of networks controlling a variety of cellular processes (Bornholdt 2008;Glass and Siegelmann 2010). Briefly, in these models, genes (or regulatory components) are assigned discrete values that account for their functional levels of expression (or activity). A regulatory function defines the evolution of the gene level, depending on the levels of its regulators. This abstracted representation of molecular mechanisms is very convenient for handling large networks for which precise kinetic data are lacking.Within the logical framework, one can distinguish several approaches that differ in the way of defining a model and its behaviour. In random Boolean networks, first introduced by S. Kauffman, the components are randomly assigned a set of regulators and a regulatory function that drives their evolution, depending on these regulators (Kauffman 1969). In threshold Boolean networks, the function is derived from a given regulatory structure as a sum of the input signals, possibly considering a threshold (Bornholdt 2008;Li et al. 2004). In the generalised logical approach introduced by R. Thomas, the logical functions are general, but are constrained by the regulatory graph. Whenever necessary or useful, the formalism supports multi-valued variables C. Chaouiya ( )

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Robustness and fragility of Boolean models for genetic regulatory networks

Cited by 297 publications

References 44 publications

“Immunetworks”, intersecting circuits and dynamics

“Immunetworks”, intersecting circuits and dynamics

Studying the effect of cell division on expression patterns of the segment polarity genes

Logical Modelling of Regulatory Networks, Methods and Applications

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