Structural Identification of Piecewise-Linear Models of Genetic Regulatory Networks

Porreca, Riccardo; Jong, Hidde de; Ferrari-Trecate, Giancarlo

doi:10.1089/cmb.2008.0109

Cited by 39 publications

(26 citation statements)

References 43 publications

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“…We can also consider a version of Equation (8) in which there exists a hidden node (x h ) affecting (x 1 ) as shown in Figure 1(B), as well as process noise.…”

Section: Formulating a Dynamical System As A Grnmentioning

confidence: 99%

“…In the last years, many data-driven mathematical tools have been developed and applied to reconstruct graph representations of gene regulatory networks (GRNs) from data. These include Bayesian networks, regression, correlation, mutual information and system-based approaches [4][5][6][7][8][9][10]. Also, these approaches either focus on static or on time series data.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Exact Reconstruction of Gene Regulatory Networks using Compressive Sensing

Chang

Gray

Tomlin

2014

Preprint

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Background:We consider the problem of reconstructing a gene regulatory network structure from limited time series gene expression data, without any a priori knowledge of connectivity. We assume that the network is sparse, meaning the connectivity among genes is much less than full connectivity. We develop a method for network reconstruction based on compressive sensing, which takes advantage of the network's sparseness. Results: For the case in which all genes are accessible for measurement, and there is no measurement noise, we show that our method can be used to exactly reconstruct the network. For the more general problem, in which hidden genes exist and all measurements are contaminated by noise, we show that our method leads to reliable reconstruction. In both cases, coherence of the model is used to assess the ability to reconstruct the network and to design new experiments. We demonstrate that it is possible to use the coherence distribution to guide biological experiment design effectively. By collecting a more informative dataset, the proposed method helps reduce the cost of experiments. For each problem, a set of numerical examples is presented. Conclusions:The method provides a guarantee on how well the inferred graph structure represents the underlying system, reveals deficiencies in the data and model, and suggests experimental directions to remedy the deficiencies.

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“…We can also consider a version of Equation (8) in which there exists a hidden node (x h ) affecting (x 1 ) as shown in Figure 1(B), as well as process noise.…”

Section: Formulating a Dynamical System As A Grnmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Exact Reconstruction of Gene Regulatory Networks using Compressive Sensing

Chang

Gray

Tomlin

2014

Preprint

View full text Add to dashboard Cite

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“…But Bayesian networks typically do not accommodate cycles and hence, can not handle feedback motifs that are common in genetic regulatory networks. Both causality and feedback motifs are no longer an issue when the network is modeled as a set of differential equations [8][9][10][11][12][13][14][15][16][17][18]. Identification is then typically optimization based, while approaches depend on whether the data is obtained from steady-state measurements [8][9][10] or dynamic time-series [11][12][13][14][15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%

Inferring stable genetic networks from steady-state data

et al. 2011

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Gene regulatory networks capture the interactions between genes and other cell substances, resulting from the fundamental biological process of transcription and translation. In some applications, the topology of the regulatory network is not known, and has to be inferred from experimental data. The experimental data consist of expression levels of the genes, which are typically measured as mRNA concentrations in micro-array experiments. In a so called genetic perturbation experiment, small perturbations are applied to equilibrium states and the resulting changes in expression activity are measured. This paper develops novel algorithms that identify a sparse and stable genetic network that explains data obtained from noisy genetic perturbation experiments. Our identification algorithm is based on convex relaxations of the sparsity and stability constraints and can also incorporate a variety of prior knowledge of the network structure. Such knowledge can be either qualitative, specifying positive, negative or no interactions between genes, or quantitative, specifying a range of interaction strengths. Our approach is applied to both synthetic and experimental data, obtained for the SOS pathway in Escherichia coli, and the results show that the stability specification not only ensures consistency with the steady-state assumptions, but also significantly increases the identification performance. Since the method is based on convex optimization, it can be efficiently applied to large scale networks.

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“…For example, de Jong et al developed a method for identification of GRNs using the structure of piecewise affine dynamical systems (c.f. [11], [12]). Papachristodoulou et al developed a model for identification of sparse networks using Hill functions to describe the dynamics of gene-gene interaction (c.f.…”

Section: Introductionmentioning

confidence: 99%

Genetic regulatory network identification using multivariate monotone functions

Cooper

Belta

Julius

2011

IEEE Conference on Decision and Control and European Control Conference

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Abstract-We present a method for identification of gene regulatory network topology using a time series of gene expression data. The underlying assumption is that the regulatory effects of a set of regulators to a gene can be described by a multivariate function. The multivariate function is constrained to be continuous, nonnegative and monotonic in each variable. We present necessary and sufficient conditions for the validity of the regulation hypothesis. Checking these conditions can be expressed as a Linear Programming feasibility problem. This paper builds on our previous work, where the regulation is described by a summation of multiple regulator functions, one function for each gene in the regulator set. Our procedure is two phased; the first identifies the correct set of regulators, the second uses the data and the regulator set to generate an appropriate regulator function. This paper focuses on the identification of the correct regulator set. As demonstration, we run our main algorithm on some experimental data from a synthetic gene network in yeast. We are able to show that the correct set of regulators is picked by the algorithm.

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Structural Identification of Piecewise-Linear Models of Genetic Regulatory Networks

Cited by 39 publications

References 43 publications

Exact Reconstruction of Gene Regulatory Networks using Compressive Sensing

Exact Reconstruction of Gene Regulatory Networks using Compressive Sensing

Inferring stable genetic networks from steady-state data

Genetic regulatory network identification using multivariate monotone functions

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