Boolean Dynamics of Biological Networks with Multiple Coupled Feedback Loops

Kwon, Yung-Keun; Cho, Kwang-Hyun

doi:10.1529/biophysj.106.097097

Cited by 54 publications

(41 citation statements)

References 33 publications

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“…In particular, the corollary corresponds to a previous result having stated that the Boolean dynamics converges to a unique fixed point in an acyclic Boolean network [31]. It is also relevant to the previous results showed that limit-cycle attractors can be induced by negative feedback loops [32, 33]. In addition, Theorem 1 can reduce the computation of attractors in a large scale network by easily obtaining the converging values of the NFU nodes.…”

Section: Resultssupporting

confidence: 72%

Properties of Boolean dynamics by node classification using feedback loops in a network

Kwon

2016

BMC Syst Biol

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BackgroundBiological networks keep their functions robust against perturbations. Many previous studies through simulations or experiments have shown that feedback loop (FBL) structures play an important role in controlling the network robustness without fully explaining how they do it. Hence, there is a pressing need to more rigorously analyze the influence of FBL structures on network robustness.ResultsIn this paper, I propose a novel node classification notion based on the FBL structures involved. More specifically, I classify a node as a no-FBL-in-upstream (NFU) or no-FBL-in-downstream (NFD) node if no feedback loop is involved with any upstream or downstream path of the node, respectively. Based on those definitions, I first prove that every NFU node is eventually frozen in Boolean dynamics. Thus, NFU nodes converge to a fixed value determined by the upstream source nodes. Second, I prove that a network is robust against an arbitrary state perturbation subject to a non-source NFD node. This implies that a network state eventually sustains the attractor despite a perturbation subject to a non-source NFD node. Inspired by this result, I further propose a perturbation-sustainable probability that indicates how likely a perturbation effect is to be sustained through propagations. I show that genes with a high perturbation-sustainable probability are likely to be essential, disease, and drug-target genes in large human signaling networks.ConclusionTaken together, these results will promote understanding of the effects of FBL on network robustness in a more rigorous manner.Electronic supplementary materialThe online version of this article (doi:10.1186/s12918-016-0322-z) contains supplementary material, which is available to authorized users.

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Section: Resultssupporting

confidence: 72%

Properties of Boolean dynamics by node classification using feedback loops in a network

Kwon

2016

BMC Syst Biol

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“…For these and other reasons, Boolean networks and more general multistate discrete models, such as logical models (Thomas and D'Ari, 1990), have been used quite extensively to model a variety of biochemical networks; see, e.g., Kauffman, (1969aKauffman, ( , 1969b, Kwon and Cho (2007), Davidich andBornholdt, Elspas (2008, 1959). They are intuitive and are amenable to extensive computational analysis.…”

Section: Introductionmentioning

confidence: 99%

The Dynamics of Conjunctive and Disjunctive Boolean Network Models

2010

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For many biological networks, the topology of the network constrains its dynamics. In particular, feedback loops play a crucial role. The results in this paper quantify the constraints that (unsigned) feedback loops exert on the dynamics of a class of discrete models for gene regulatory networks. Conjunctive (resp. disjunctive) Boolean networks, obtained by using only the AND (resp. OR) operator, comprise a subclass of networks that consist of canalyzing functions, used to describe many published gene regulation mechanisms. For the study of feedback loops, it is common to decompose the wiring diagram into linked components each of which is strongly connected. It is shown that for conjunctive Boolean networks with strongly connected wiring diagram, the feedback loop structure completely determines the long-term dynamics of the network. A formula is established for the precise number of limit cycles of a given length, and it is determined which limit cycle lengths can appear. For general wiring diagrams, the situation is much more complicated, as feedback loops in one strongly connected component can influence the feedback loops in other components. This paper provides a sharp lower bound and an upper bound on the number of limit cycles of a given length, in terms of properties of the partially ordered set of strongly connected components.

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“…The mechanistic basis for this likely lies in the fact that negative feedback loops have been conjectured (and subsequently shown) to be essential for periodic behavior--that is, they tend to keep a system on periodic attractors [32,34,38]. While this result has been confirmed in Boolean networks [39][40][41][42], Boolean modeling has also been used recently to show that as the number of feedback loops (particularly independent negative ones) increases in a network, the cyclic attractors of a network tend to become longer and the dynamics are much closer to chaotic [43]. Using a novel measure of independent negative feedback loops called "distanceto-positive-feedback," it was shown that, as the number of independent negative feedback loops increases, there tends to be a smaller number of larger cycles; a cycle structure associated with chaotic dynamics.…”

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

confidence: 97%

“…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%

“…Again, Boolean models have been used to great effect in studies of coupled feedback loops. Using random Boolean networks, a series of papers by Kwon et al has shown that networks with more coupled positive feedback loops are associated with multistability (i.e., fixed point dynamics), while those with more coupled negative feedback loops are associated with cyclical behavior [39,[51][52][53]. Moreover, the existence of coupled feedback loops is associated with increased robustness of the network (i.e., more resistant to perturbation); a finding that would explain why coupled feedback loops are so common in biological networks.…”

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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Boolean Dynamics of Biological Networks with Multiple Coupled Feedback Loops

Cited by 54 publications

References 33 publications

Properties of Boolean dynamics by node classification using feedback loops in a network

Properties of Boolean dynamics by node classification using feedback loops in a network

The Dynamics of Conjunctive and Disjunctive Boolean Network Models

Boolean Modeling of Biochemical Networks

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