Steady-state probabilities for attractors in probabilistic Boolean networks

Brun, Marcel; Dougherty, Edward R.; Shmulevich, Ilya

doi:10.1016/j.sigpro.2005.02.016

Cited by 104 publications

(60 citation statements)

References 18 publications

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“…In this paper, we advance a probabilistic Boolean network [12,13] on the protein interaction network of yeast cell cycle. We found that both the biological stationary state and the biological pathway are well preserved under a wide range of noise level.…”

Section: Introductionmentioning

confidence: 99%

Stochastic model of yeast cell-cycle network

Zhang

Qian

Ouyang

et al. 2006

Physica D: Nonlinear Phenomena

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Biological functions in living cells are controlled by protein interaction and genetic networks. These molecular networks should be dynamically stable against various fluctuations which are inevitable in the living world. In this paper, we propose and study a stochastic model for the network regulating the cell cycle of the budding yeast. The stochasticity in the model is controlled by a temperature-like parameter β. Our simulation results show that both the biological stationary state and the biological pathway are stable for a wide range of "temperature". There is, however, a sharp transition-like behavior at β c , below which the dynamics is dominated by noise. We also define a pseudo energy landscape for the system in which the biological pathway can be seen as a deep valley.

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Section: Introductionmentioning

confidence: 99%

Stochastic model of yeast cell-cycle network

Zhang

Qian

Ouyang

et al. 2006

Physica D: Nonlinear Phenomena

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“…Though Brun et al have already derived some relations [3], we derive a simpler relation for a special case.…”

Section: Relation Between Steady-state Probabilities and Attractorsmentioning

confidence: 96%

“…The dynamics of a PBN can be studied in the context of a standard Markov chain [10]. Therefore, the theory of Markov chains has been applied to the analysis of PBNs, in particular, the analysis of the steady-state probability distribution [3,4,10,12]. Unfortunately, it takes at least O(2 n ) computational time because the size of a vector representing the probability distribution is 2 n , where n is the number of nodes in a PBN (i.e., the number of genes).…”

Section: Introductionmentioning

confidence: 99%

“…Furthermore, it may be helpful to know attractors in PBNs because singleton or small attractors may correspond to major states in the steady-state probability distribution. Indeed, Brun et al studied relations between attractors and steady-state probability distributions [3]. However, they did not provide efficient algorithms for computing attractors in BNs or PBNs.…”

Section: Introductionmentioning

confidence: 99%

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Distribution and enumeration of attractors in probabilistic Boolean networks

Hayashida

Tamura

Akutsu

et al. 2009

IET Systems Biology

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“…The functions with very small probabilities can simulate perturbations (external stimuli) or changes between biological contexts (Brun et al 2005;Dougherty et al 2007). …”

Section: Probabilistic Boolean Networkmentioning

confidence: 99%

One genetic algorithm per gene to infer gene networks from expression data

Jimenez

Martins-Jr

Santos

2015

Netw Model Anal Health Inform Bioinforma

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Gene regulatory networks inference from gene expression data is an important problem in systems biology field, in which the main goal is to comprehend the global molecular mechanisms underlying diseases for the development of medical treatments and drugs. This problem involves the estimation of the gene dependencies and the regulatory functions governing these interactions to provide a model that explains the dataset (usually obtained from gene expression data) on which the estimation relies. However, such problem is considered an open problem, since it is difficult to obtain a satisfactory estimation of the dependencies given a very limited number of samples subject to experimental noises. Several gene networks inference methods exist in the literature, including those based on genetic algorithms, which codify whole networks as possible solutions (chromosomes). Given the huge search space of possible networks, genetic algorithms are suitable for the task, even though it is still hard to achieve good networks that explain the data by codifying whole networks as solutions. The objective of this work is the proposal of a method based on genetic algorithms to infer gene networks, whose main idea consists in applying one genetic algorithm for each gene independently, instead of applying a unique genetic algorithm to determine the whole network as usually done in the literature. Besides, the method involves the application of a network inference method to generate the initial populations to serve as more promising starting points for the genetic algorithms than random populations. To guide the genetic algorithms, we propose the use of Akaike information criterion (AIC) as fitness function. Results obtained from inference of artificial Boolean networks show that AIC correlates very well with popular topological similarity metrics even in cases with small number of samples. Besides, the benefit of applying one genetic algorithm per gene starting from initial populations defined by a network inference technique is evident according to the results. Comparative analysis involving a recently proposed genetic algorithm method for the same purpose is presented, showing that our method achieves superior performance.

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Steady-state probabilities for attractors in probabilistic Boolean networks

Cited by 104 publications

References 18 publications

Stochastic model of yeast cell-cycle network

Stochastic model of yeast cell-cycle network

Distribution and enumeration of attractors in probabilistic Boolean networks

One genetic algorithm per gene to infer gene networks from expression data

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