From minimal signed circuits to the dynamics of Boolean regulatory networks

Rémy, Élisabeth; Ruet, Paul

doi:10.1093/bioinformatics/btn287

Cited by 55 publications

(41 citation statements)

References 41 publications

(56 reference statements)

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“…While the necessary association of negative and positive feedback loops with periodicity and multistability, respectively, is at this point well-documented in both the continuous and discrete case, Boolean modeling has recently been used to show that the nontrivial converse of these associations is also true--i.e., that negative and positive feedback loops are sufficient for these dynamics [47]. This is an intriguing result since it implies that the existence of feedback loops in the graph structure of a network can provide information on the existence of periodic cycles and fixed points.…”

Section: Mechanisms Of Dynamics; Boolean Studies Of the Feedback Loopmentioning

confidence: 92%

“…This function is a crucial property of memory, hence it can be argued that one of the main functions of positive feedback is to form the basis for cellular "memory modules" [32,45,46]. The dependence of multistability on positive feedback loops has also been demonstrated in Boolean models [38][39][40][41]47].…”

Section: Mechanisms Of Dynamics; Boolean Studies Of the Feedback Loopmentioning

confidence: 99%

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Boolean Modeling of Biochemical Networks

Helikar¹,

Kochi

Konvalina

et al. 2011

TOBIOIJ

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Abstract:The use of modeling to observe and analyze the mechanisms of complex biochemical network function is becoming an important methodological tool in the systems biology era. Number of different approaches to model these networks have been utilized--they range from analysis of static connection graphs to dynamical models based on kinetic interaction data. Dynamical models have a distinct appeal in that they make it possible to observe these networks in action, but they also pose a distinct challenge in that they require detailed information describing how the individual components of these networks interact in living cells. Because this level of detail is generally not known, dynamic modeling requires simplifying assumptions in order to make it practical. In this review Boolean modeling will be discussed, a modeling method that depends on the simplifying assumption that all elements of a network exist only in one of two states.Keywords: Systems biology, dynamical modeling, signal transduction, boolean networks.The modern era of cellular biochemistry has been characterized by the discovery of large interaction networks that are notable for their highly nonlinear connection structures. Such structures complicate study since they are often quite difficult to reduce into linear subsets that function in isolation from the embedding network [1,2]. It is for this reason that the concept of "systems biology" has been developed and is now being applied to these complicated biochemical networks [1,3,4].One of the first steps taken toward applying a systems approach to understanding biochemical networks was to begin organizing the connection information determined in the laboratory by creating connection maps (wiring diagrams) that could then be analyzed using graph theory concepts. While these studies have been highly successful [5], the fact that cells are dynamical systems means the next major step in the study of these systems involves the creation of models that take into account how they move and function in time. Thus we are now in a new era of creating large-scale dynamical models of biochemical systems.An obvious choice for the modeling of dynamical systems is to describe the system with a system of differential equations, and this approach has been used extensively to study protein and/or gene interactions in a variety of relatively small models (for examples, see [6][7][8][9]). One of the advantages of continuous modeling via differential equations is that one can potentially describe molecular interactions with high precision and in quantitative terms that correspond to realistic laboratory measurements. However, that precision tends to make them computationally unwieldy for the large scale models necessary for the systems approach. There *Address correspondence to this author at the Department of Mathematics, University of Nebraska at Omaha, 6001 Dodge Street, Omaha, NE 68182, USA; Tel: 402 554-3110: Fax: 402 554-2975; E-mail: jrogers@unmc.edu is currently a great deal of work being done in order to simpl...

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Section: Mechanisms Of Dynamics; Boolean Studies Of the Feedback Loopmentioning

confidence: 92%

Section: Mechanisms Of Dynamics; Boolean Studies Of the Feedback Loopmentioning

confidence: 99%

Boolean Modeling of Biochemical Networks

Helikar¹,

Kochi

Konvalina

et al. 2011

TOBIOIJ

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“…In particular, the additional complexity brought by the different possible ways of updating automata states has been dealt with in the past by imposing restrictions on the updating mode (e.g. restrictions to the nondeterministic asynchronous one [22,23,27,29], the parallel one, or some deterministic [1,2,8,14] or probabilistic ones [9,15,25]). …”

Section: The Modelling Of Interaction Systems Standpointmentioning

confidence: 99%

Synchronism versus asynchronism in monotonic Boolean automata networks

Noual

Sené

2017

Nat Comput

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This paper focuses on Boolean automata networks and the updatings of automata states in these networks. More specifically, we study how synchronous updates impact on the global behaviour of a network. On this basis, we define different types of network sensitivity to synchronism, which are effectively satisfied by some networks. We also relate this synchronism-sensitivity to some properties of the structure of networks and to their underlying mechanisms.

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“…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%

“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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From minimal signed circuits to the dynamics of Boolean regulatory networks

Abstract: Supplementary data are available at Bioinformatics online.

Cited by 55 publications

References 41 publications

Boolean Modeling of Biochemical Networks

Boolean Modeling of Biochemical Networks

Synchronism versus asynchronism in monotonic Boolean automata networks

“Immunetworks”, intersecting circuits and dynamics

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