Aggregation of topological motifs in the Escherichia coli transcriptional regulatory network

Dobrin, Radu; Beg, Qasim Khalil; Barabási, Albert László; Oltvai, Zoltán N.

doi:10.1186/1471-2105-5-10

Cited by 199 publications

(99 citation statements)

References 26 publications

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“…(ii) Can topological differences between in-and out-degree distributions (Dobrin et al 2004;Balázi et al 2005) be explained by MNL dynamics? MNL dynamics can downregulate the concentration x i of a fraction of nodes i to zero.…”

Section: Introductionmentioning

confidence: 99%

Living on the edge of chaos: minimally nonlinear models of genetic regulatory dynamics

Hanel

Pöchacker

Thurner

2010

Phil. Trans. R. Soc. A.

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Linearized catalytic reaction equations (modelling, for example, the dynamics of genetic regulatory networks), under the constraint that expression levels, i.e. molecular concentrations of nucleic material, are positive, exhibit non-trivial dynamical properties, which depend on the average connectivity of the reaction network. In these systems, an inflation of the edge of chaos and multi-stability have been demonstrated to exist. The positivity constraint introduces a nonlinearity, which makes chaotic dynamics possible. Despite the simplicity of such minimally nonlinear systems, their basic properties allow us to understand the fundamental dynamical properties of complex biological reaction networks. We analyse the Lyapunov spectrum, determine the probability of finding stationary oscillating solutions, demonstrate the effect of the nonlinearity on the effective in-and out-degree of the active interaction network, and study how the frequency distributions of oscillatory modes of such a system depend on the average connectivity.

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Section: Introductionmentioning

confidence: 99%

Living on the edge of chaos: minimally nonlinear models of genetic regulatory dynamics

Hanel

Pöchacker

Thurner

2010

Phil. Trans. R. Soc. A.

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“…For example, transcriptional regulatory networks of cells (1,2,5,6), neural networks of C. elegans (2), and some electronic circuits (2) are all information processing networks that contain a significant number of feed-forward loop (FFL) motifs. However, in transcriptional regulatory networks these motifs do not exist in isolation but meld into motif clusters (7), while other networks are devoid of FFLs altogether (2).…”

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confidence: 99%

The topological relationship between the large-scale attributes and local interaction patterns of complex networks

Vázquez

Dobrin

Sergi

et al. 2004

Proc. Natl. Acad. Sci. U.S.A.

285

236

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Recent evidence indicates that the abundance of recurring elementary interaction patterns in complex networks, often called subgraphs or motifs, carry significant information about their function and overall organization. Yet, the underlying reasons for the variable quantity of different subgraph types, their propensity to form clusters, and their relationship with the networks' global organization remain poorly understood. Here we show that a network's large-scale topological organization and its local subgraph structure mutually define and predict each other, as confirmed by direct measurements in five well studied cellular networks. We also demonstrate the inherent existence of two distinct classes of subgraphs, and show that, in contrast to the low-density type II subgraphs, the highly abundant type I subgraphs cannot exist in isolation but must naturally aggregate into subgraph clusters. The identified topological framework may have important implications for our understanding of the origin and function of subgraphs in all complex networks.aggregation ͉ subgraphs A number of complex biological and nonbiological networks were recently found to contain network motifs, representing elementary interaction patterns between small groups of nodes (subgraphs) that occur substantially more often than would be expected in a random network of similar size and connectivity (1, 2). Theoretical and experimental evidence indicates that at least some of these recurring elementary interaction patterns carry significant information about the given network's function and overall organization (1-4). For example, transcriptional regulatory networks of cells (1, 2, 5, 6), neural networks of C. elegans (2), and some electronic circuits (2) are all information processing networks that contain a significant number of feed-forward loop (FFL) motifs. However, in transcriptional regulatory networks these motifs do not exist in isolation but meld into motif clusters (7), while other networks are devoid of FFLs altogether (2).In general, all subgraphs have two important properties: their topology and the directionality of their links. In cellular networks, these two properties can be clearly separated from each other. In protein-protein interaction (PPI) networks all links are by definition nondirectional. In contrast, in transcriptional regulatory networks information flow between a transcription factor and the operon (gene) regulated by it is almost always unidirectional (1, 2). Metabolic networks occupy an intermediate position between these two extremes, because most, but not all, metabolic reactions are reversible under various growth conditions. Despite the difference in the relative role of link directionality, the large-scale organization of the three different network types is quite similar, most being characterized by a scale-free connectivity distribution and hierarchical modularity (8-12). The only exception is the incoming degree distribution (i.e., the number of transcription factors regulating a target gene) of regulatory...

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“…Let us now turn to the second order term, W (2) (a, b; x) in Eqs. (18) and (19). Here, we need to distinguish two cases, (i) b − a ≥ l and (ii) b − a < l.…”

Section: Analytical Results For the Matching Probabilitymentioning

confidence: 99%

“…(26), is not correct in general and one expects corrections coming from higher order correlations contained in Eq. (18). These correlations are due to the fact that if a given string x is matched at a position a, this affects the likelihood of matching the same string at any nearby location b with |b − a| < ∼ l. Nevertheless, the approximate result for p(l, k), Eq.…”

Section: Analytical Results For the Matching Probabilitymentioning

confidence: 99%

Analytical solution of a stochastic content-based network model

Mungan

Kabakçinodotoglu

Balcan

et al. 2005

J. Phys. A: Math. Gen.

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We define and completely solve a content-based directed network whose nodes consist of random words and an adjacency rule involving perfect or approximate matches, for an alphabet with an arbitrary number of letters. The analytic expression for the out-degree distribution shows a crossover from a leading power law behavior to a log-periodic regime bounded by a different power law decay. The leading exponents in the two regions have a weak dependence on the mean word length, and an even weaker dependence on the alphabet size. The in-degree distribution, on the other hand, is much narrower and does not show scaling behavior. The results might be of interest for understanding the emergence of genomic interaction networks, which rely, to a large extent, on mechanisms based on sequence matching, and exhibit similar global features to those found here.

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Aggregation of topological motifs in the Escherichia coli transcriptional regulatory network

Cited by 199 publications

References 26 publications

Living on the edge of chaos: minimally nonlinear models of genetic regulatory dynamics

Living on the edge of chaos: minimally nonlinear models of genetic regulatory dynamics

The topological relationship between the large-scale attributes and local interaction patterns of complex networks

Analytical solution of a stochastic content-based network model

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