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Stability depends on positive autoregulation in Boolean gene regulatory networks.

ABSTRACT: Network motifs have been identified as building blocks of regulatory networks, including gene regulatory networks (GRNs). The most basic motif, autoregulation, has been associated with bistability (when positive) and with homeostasis and robustness to noise (when negative), but its general importance in network behavior is poorly understood. Moreover, how specific autoregulatory motifs are selected during evolution and how this relates to robustness is largely unknown. Here, we used a class of GRN models, Boolean networks, to investigate the relationship between autoregulation and network stability and robustness under various conditions. We ran evolutionary simulation experiments for different models of selection, including mutation and recombination. Each generation simulated the development of a population of organisms modeled by GRNs. We found that stability and robustness positively correlate with autoregulation; in all investigated scenarios, stable networks had mostly positive autoregulation. Assuming biological networks correspond to stable networks, these results suggest that biological networks should often be dominated by positive autoregulatory loops. This seems to be the case for most studied eukaryotic transcription factor networks, including those in yeast, flies and mammals.

SUBMITTER: Pinho R

PROVIDER: S-EPMC4222607 | biostudies-literature | 2014 Nov

REPOSITORIES: biostudies-literature

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Stability depends on positive autoregulation in Boolean gene regulatory networks.

Pinho Ricardo R Garcia Victor V Irimia Manuel M Feldman Marcus W MW

PLoS computational biology 20141106 11

Network motifs have been identified as building blocks of regulatory networks, including gene regulatory networks (GRNs). The most basic motif, autoregulation, has been associated with bistability (when positive) and with homeostasis and robustness to noise (when negative), but its general importance in network behavior is poorly understood. Moreover, how specific autoregulatory motifs are selected during evolution and how this relates to robustness is largely unknown. Here, we used a class of G ...[more]

PMID: 25375153

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Project description:BACKGROUND: Various computational models have been of interest due to their use in the modelling of gene regulatory networks (GRNs). As a logical model, probabilistic Boolean networks (PBNs) consider molecular and genetic noise, so the study of PBNs provides significant insights into the understanding of the dynamics of GRNs. This will ultimately lead to advances in developing therapeutic methods that intervene in the process of disease development and progression. The applications of PBNs, however, are hindered by the complexities involved in the computation of the state transition matrix and the steady-state distribution of a PBN. For a PBN with n genes and N Boolean networks, the complexity to compute the state transition matrix is O(nN22n) or O(nN2n) for a sparse matrix. RESULTS: This paper presents a novel implementation of PBNs based on the notions of stochastic logic and stochastic computation. This stochastic implementation of a PBN is referred to as a stochastic Boolean network (SBN). An SBN provides an accurate and efficient simulation of a PBN without and with random gene perturbation. The state transition matrix is computed in an SBN with a complexity of O(nL2n), where L is a factor related to the stochastic sequence length. Since the minimum sequence length required for obtaining an evaluation accuracy approximately increases in a polynomial order with the number of genes, n, and the number of Boolean networks, N, usually increases exponentially with n, L is typically smaller than N, especially in a network with a large number of genes. Hence, the computational efficiency of an SBN is primarily limited by the number of genes, but not directly by the total possible number of Boolean networks. Furthermore, a time-frame expanded SBN enables an efficient analysis of the steady-state distribution of a PBN. These findings are supported by the simulation results of a simplified p53 network, several randomly generated networks and a network inferred from a T cell immune response dataset. An SBN can also implement the function of an asynchronous PBN and is potentially useful in a hybrid approach in combination with a continuous or single-molecule level stochastic model. CONCLUSIONS: Stochastic Boolean networks (SBNs) are proposed as an efficient approach to modelling gene regulatory networks (GRNs). The SBN approach is able to recover biologically-proven regulatory behaviours, such as the oscillatory dynamics of the p53-Mdm2 network and the dynamic attractors in a T cell immune response network. The proposed approach can further predict the network dynamics when the genes are under perturbation, thus providing biologically meaningful insights for a better understanding of the dynamics of GRNs. The algorithms and methods described in this paper have been implemented in Matlab packages, which are attached as Additional files.

Project description:BackgroundQualitative dynamics of small gene regulatory networks have been studied in quite some details both with synchronous and asynchronous analysis. However, both methods have their drawbacks: synchronous analysis leads to spurious attractors and asynchronous analysis lacks computational efficiency, which is a problem to simulate large networks. We addressed this question through the analysis of a major biosynthesis pathway. Indeed the cholesterol synthesis pathway plays a pivotal role in dislypidemia and, ultimately, in cancer through intermediates such as mevalonate, farnesyl pyrophosphate and geranyl geranyl pyrophosphate, but no dynamic model of this pathway has been proposed until now.ResultsWe set up a computational framework to dynamically analyze large biological networks. This framework associates a classical and computationally efficient synchronous Boolean analysis with a newly introduced method based on Markov chains, which identifies spurious cycles among the results of the synchronous simulation. Based on this method, we present here the results of the analysis of the cholesterol biosynthesis pathway and its physiological regulation by the Sterol Response Element Binding Proteins (SREBPs), as well as the modeling of the action of statins, inhibitor drugs, on this pathway. The in silico experiments show the blockade of the cholesterol endogenous synthesis by statins and its regulation by SREPBs, in full agreement with the known biochemical features of the pathway.ConclusionWe believe that the method described here to identify spurious cycles opens new routes to compute large and biologically relevant models, thanks to the computational efficiency of synchronous simulation. Furthermore, to the best of our knowledge, we present here the first dynamic systems biology model of the human cholesterol pathway and several of its key regulatory control elements, hoping it would provide a good basis to perform in silico experiments and confront the resulting properties with published and experimental data. The model of the cholesterol pathway and its regulation, along with Boolean formulae used for simulation are available on our web site http://Bioinformaticsu613.free.fr. Graphical results of the simulation are also shown online. The SBML model is available in the BioModels database http://www.ebi.ac.uk/biomodels/ with submission ID: MODEL0568648427.

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Stability depends on positive autoregulation in Boolean gene regulatory networks.

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Stability depends on positive autoregulation in Boolean gene regulatory networks.

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