Graphic requirements for multistability and attractive cycles in a Boolean dynamical framework

Rémy, Élisabeth; Ruet, Paul; Thieffry, Denis

doi:10.1016/j.aam.2007.11.003

Cited by 156 publications

(149 citation statements)

References 29 publications

(40 reference statements)

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“…In the field of genetic networks, they have been investigated for various classes of systems, ranging from ordinary differential equations (Soulé 2006) to synchronous (Remy et al 2008) and asynchronous (Richard et al 2004 The vertices represent either genes, metabolites, or proteins, while the edges indicate the regulations among them. Edges with an arrow stand for positive regulations (activations), while edges with a tee head stand for negative regulations (inhibitions).…”

Section: Influence Graphs and Sign Consistency Constraintsmentioning

confidence: 99%

Detecting Inconsistencies in Large Biological Networks with Answer Set Programming

et al. 2008

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We introduce an approach to detecting inconsistencies in large biological networks by using Answer Set Programming (ASP). To this end, we build upon a recently proposed notion of consistency between biochemical/genetic reactions and high-throughput profiles of cell activity. We then present an approach based on ASP to check the consistency of large-scale data sets. Moreover, we extend this methodology to provide explanations for inconsistencies by determining minimal representations of conflicts. In practice, this can be used to identify unreliable data or to indicate missing reactions.

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Section: Influence Graphs and Sign Consistency Constraintsmentioning

confidence: 99%

Detecting Inconsistencies in Large Biological Networks with Answer Set Programming

et al. 2008

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“…Since then, these conjectures have been proven in different frameworks [20,21,22,23,24,25,26,27,28,29]. As for intersecting circuits, we will argue here that beyond the impact that circuits have on the dynamical behaviour of a network, the interactions of circuits via their intersections also account significantly for certain dynamical properties of networks.…”

Section: Circuits and Intersecting Circuitsmentioning

confidence: 90%

“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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“…To capture local structural aspects we introduce the concept of local interaction graphs. It has already been used in [5] and [4] (see also references therein). In the following, we denote with s i the state that coincides with s in all components j = i and takes the value 1 − s i in the i-th component.…”

Section: Functionality and Local Interaction Graphsmentioning

confidence: 99%

“…To obtain a refined representation of the structure of the system with respect to its dynamics, we exploit the concept of local interactions graphs. It was already successfully used in [5] and [4], and allows for a better understanding of what structures in the interaction graph influence the system's behavior in a given state. Combining these ideas, we introduce local interaction graphs of singular steady states which allow us to identify subnetworks that govern the behavior of the whole system.…”

Section: Introductionmentioning

confidence: 99%

Deriving Behavior of Boolean Bioregulatory Networks from Subnetwork Dynamics

Siebert

2009

Math.Comput.Sci.

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Abstract. In the well-known discrete modeling framework developed by R. Thomas, the structure of a biological regulatory network is captured in an interaction graph, which, together with a set of Boolean parameters, gives rise to a state transition graph describing all possible dynamical behaviors. For complex networks the analysis of the dynamics becomes more and more difficult, and efficient methods to carry out the analysis are needed. In this paper, we focus on identifying subnetworks of the system that govern the behavior of the system as a whole. We present methods to derive trajectories and attractors of the network from the dynamics suitable subnetworks display in isolation. In addition, we use these ideas to link the existence of certain structural motifs, namely circuits, in the interaction graph to the character and number of attractors in the state transition graph, generalizing and refining results presented in [10]. Lastly, we show for a specific class of networks that all possible asymptotic behaviors of networks in that class can be derived from the dynamics of easily identifiable subnetworks.

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Graphic requirements for multistability and attractive cycles in a Boolean dynamical framework

Cited by 156 publications

References 29 publications

Detecting Inconsistencies in Large Biological Networks with Answer Set Programming

Detecting Inconsistencies in Large Biological Networks with Answer Set Programming

“Immunetworks”, intersecting circuits and dynamics

Deriving Behavior of Boolean Bioregulatory Networks from Subnetwork Dynamics

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