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Relative stability of network states in Boolean network models of gene regulation in development.

ABSTRACT: Progress in cell type reprogramming has revived the interest in Waddington's concept of the epigenetic landscape. Recently researchers developed the quasi-potential theory to represent the Waddington's landscape. The Quasi-potential U(x), derived from interactions in the gene regulatory network (GRN) of a cell, quantifies the relative stability of network states, which determine the effort required for state transitions in a multi-stable dynamical system. However, quasi-potential landscapes, originally developed for continuous systems, are not suitable for discrete-valued networks which are important tools to study complex systems. In this paper, we provide a framework to quantify the landscape for discrete Boolean networks (BNs). We apply our framework to study pancreas cell differentiation where an ensemble of BN models is considered based on the structure of a minimal GRN for pancreas development. We impose biologically motivated structural constraints (corresponding to specific type of Boolean functions) and dynamical constraints (corresponding to stable attractor states) to limit the space of BN models for pancreas development. In addition, we enforce a novel functional constraint corresponding to the relative ordering of attractor states in BN models to restrict the space of BN models to the biological relevant class. We find that BNs with canalyzing/sign-compatible Boolean functions best capture the dynamics of pancreas cell differentiation. This framework can also determine the genes' influence on cell state transitions, and thus can facilitate the rational design of cell reprogramming protocols.

SUBMITTER: Zhou JX

PROVIDER: S-EPMC5149109 | biostudies-literature | 2016 Apr-May

REPOSITORIES: biostudies-literature

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Relative stability of network states in Boolean network models of gene regulation in development.

Zhou Joseph Xu JX Samal Areejit A d'Hérouël Aymeric Fouquier AF Price Nathan D ND Huang Sui S

Bio Systems 20160307

Progress in cell type reprogramming has revived the interest in Waddington's concept of the epigenetic landscape. Recently researchers developed the quasi-potential theory to represent the Waddington's landscape. The Quasi-potential U(x), derived from interactions in the gene regulatory network (GRN) of a cell, quantifies the relative stability of network states, which determine the effort required for state transitions in a multi-stable dynamical system. However, quasi-potential landscapes, ori ...[more]

PMID: 26965665

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Project description:Gene-on-gene regulations are key components of every living organism. Dynamical abstract models of genetic regulatory networks help explain the genome's evolvability and robustness. These properties can be attributed to the structural topology of the graph formed by genes, as vertices, and regulatory interactions, as edges. Moreover, the actual gene interaction of each gene is believed to play a key role in the stability of the structure. With advances in biology, some effort was deployed to develop update functions in boolean models that include recent knowledge. We combine real-life gene interaction networks with novel update functions in a boolean model. We use two sub-networks of biological organisms, the yeast cell-cycle and the mouse embryonic stem cell, as topological support for our system. On these structures, we substitute the original random update functions by a novel threshold-based dynamic function in which the promoting and repressing effect of each interaction is considered. We use a third real-life regulatory network, along with its inferred boolean update functions to validate the proposed update function. Results of this validation hint to increased biological plausibility of the threshold-based function. To investigate the dynamical behavior of this new model, we visualized the phase transition between order and chaos into the critical regime using Derrida plots. We complement the qualitative nature of Derrida plots with an alternative measure, the criticality distance, that also allows to discriminate between regimes in a quantitative way. Simulation on both real-life genetic regulatory networks show that there exists a set of parameters that allows the systems to operate in the critical region. This new model includes experimentally derived biological information and recent discoveries, which makes it potentially useful to guide experimental research. The update function confers additional realism to the model, while reducing the complexity and solution space, thus making it easier to investigate.

Project description:BACKGROUND: Due to the rapid data accumulation on pathogenesis and progression of chronic inflammation, there is an increasing demand for approaches to analyse the underlying regulatory networks. For example, rheumatoid arthritis (RA) is a chronic inflammatory disease, characterised by joint destruction and perpetuated by activated synovial fibroblasts (SFB). These abnormally express and/or secrete pro-inflammatory cytokines, collagens causing joint fibrosis, or tissue-degrading enzymes resulting in destruction of the extra-cellular matrix (ECM).We applied three methods to analyse ECM regulation: data discretisation to filter out noise and to reduce complexity, Boolean network construction to implement logic relationships, and formal concept analysis (FCA) for the formation of minimal, but complete rule sets from the data. RESULTS: First, we extracted literature information to develop an interaction network containing 18 genes representing ECM formation and destruction. Subsequently, we constructed an asynchronous Boolean network with biologically plausible time intervals for mRNA and protein production, secretion, and inactivation. Experimental gene expression data was obtained from SFB stimulated by TGFbeta1 or by TNFalpha and discretised thereafter. The Boolean functions of the initial network were improved iteratively by the comparison of the simulation runs to the experimental data and by exploitation of expert knowledge. This resulted in adapted networks for both cytokine stimulation conditions. The simulations were further analysed by the attribute exploration algorithm of FCA, integrating the observed time series in a fine-tuned and automated manner. The resulting temporal rules yielded new contributions to controversially discussed aspects of fibroblast biology (e.g., considerable expression of TNF and MMP9 by fibroblasts stimulation) and corroborated previously known facts (e.g., co-expression of collagens and MMPs after TNFalpha stimulation), but also revealed some discrepancies to literature knowledge (e.g., MMP1 expression in the absence of FOS). CONCLUSION: The newly developed method successfully and iteratively integrated expert knowledge at different steps, resulting in a promising solution for the in-depth understanding of regulatory pathways in disease dynamics. The knowledge base containing all the temporal rules may be queried to predict the functional consequences of observed or hypothetical gene expression disturbances. Furthermore, new hypotheses about gene relations were derived which await further experimental validation.

Project description:Background Rheumatoid arthritis (RA) is a chronic inflammatory disease, characterized by joint destruction and perpetuated by the synovial membrane (SM). In the inflamed SM, activated synovial fibroblasts (SFB) form the major cell type promoting development and progression of the disease by an abnormal expression/secretion of pro-inflammatory cytokines, tissue-degrading enzymes resulting in a predominant degradation of the extra-cellular matrix (ECM), and collagens causing joint fibrosis. We developed a new procedure, based on human knowledge and formal concept analysis (FCA), to simulate and analyze the temporal behaviour of regulatory and signaling networks. It was applied to a regulatory network (containing 18 genes from 5 functional groups) representing ECM formation and destruction in TGFβ - and TNFα -stimulated SFB. Results For the modelling of SFB-controlled ECM turnover in rheumatic diseases, Boolean network architecture was used as well as extensive literature information and revision by experimental gene expression data from stimulated SFB. In course of revision, the additional experimental information resulted in different biologically reasonable changes, yielding two Boolean networks that describe TGFβ and TNFα effects, respectively. The final simulations were further analyzed by the attribute exploration algorithm of FCA, integrating again the observed time series in a more fine-grained and automated manner. The generated temporal rules clearly reveal subtle regulatory relationships between different genes, co-expression patterns and converse gene expression regulation in rheumatic diseases. Conclusion The developed Boolean network based method for the dynamical analysis of regulatory and signaling networks represents a reliable systems biological solution for the improved understanding of complex regulatory pathways and the interactions among different genes in disease. The resulting knowledge base can be used for further analysis of the ECM system in human fibroblasts and may be queried to predict the functional consequences of observed (e.g. in diseases as RA) or hypothetical (e.g. for therapeutic purposes) gene expression disturbances.

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Relative stability of network states in Boolean network models of gene regulation in development.

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Relative stability of network states in Boolean network models of gene regulation in development.

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