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BoolNet–an R package for generation, reconstruction and analysis of Boolean networks. Bioinformatics 2010;26(10):1378–80
"... Motivation: As the study of information processing in living cells moves from individual pathways to complex regulatory networks, mathematical models and simulation become indispensable tools for analyzing the complex behaviour of such networks and can provide deep insights into the functioning of c ..."
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Cited by 30 (2 self)
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Motivation: As the study of information processing in living cells moves from individual pathways to complex regulatory networks, mathematical models and simulation become indispensable tools for analyzing the complex behaviour of such networks and can provide deep insights into the functioning of cells. The dynamics of gene expression, for example, can be modeled with Boolean networks. These are mathematical models of low complexity, but have the advantage of being able to capture essential properties of generegulatory networks. However, current implementations of Boolean networks only focus on different subaspects of this model and do not allow for a seamless integration into existing preprocessing pipelines. Results: BoolNet efficiently integrates methods for synchronous, asynchronous, and probabilistic Boolean networks. This includes reconstructing networks from time series, generating random networks, robustness analysis via perturbation, Markov chain simulations, and identification and visualization of attractors. Availability: The package BoolNet is freely available from the R
Inference of a Probabilistic Boolean Network from a Single Observed Temporal Sequence
, 2007
"... The inference of gene regulatory networks is a key issue for genomic signal processing. This paper addresses the inference of probabilistic Boolean networks (PBNs) from observed temporal sequences of network states. Since a PBN is composed of a finite number of Boolean networks, a basic observation ..."
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Cited by 19 (6 self)
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The inference of gene regulatory networks is a key issue for genomic signal processing. This paper addresses the inference of probabilistic Boolean networks (PBNs) from observed temporal sequences of network states. Since a PBN is composed of a finite number of Boolean networks, a basic observation is that the characteristics of a single Boolean network without perturbation may be determined by its pairwise transitions. Because the network function is fixed and there are no perturbations, a given state will always be followed by a unique state at the succeeding time point. Thus, a transition counting matrix compiled over a data sequence will be sparse and contain only one entry per line. If the network also has perturbations, with small perturbation probability, then the transition counting matrix would have some insignificant nonzero entries replacing some (or all) of the zeros. If a data sequence is sufficiently long to adequately populate the matrix, then determination of the functions and inputs underlying the model is straightforward. The difficulty comes when the transition counting matrix consists of data derived from more than one Boolean network. We address the PBN inference procedure in several steps: (1) separate the data sequence into “pure ” subsequences corresponding to constituent Boolean networks; (2) given a subsequence, infer a Boolean network; and (3) infer the probabilities of perturbation, the probability of there being a switch between constituent Boolean networks, and the selection probabilities governing
Validation of inference procedures for gene regulatory networks
 Curr. Genomics 2007
"... Abstract: The availability of highthroughput genomic data has motivated the development of numerous algorithms to infer gene regulatory networks. The validity of an inference procedure must be evaluated relative to its ability to infer a model network close to the groundtruth network from which th ..."
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Cited by 9 (3 self)
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Abstract: The availability of highthroughput genomic data has motivated the development of numerous algorithms to infer gene regulatory networks. The validity of an inference procedure must be evaluated relative to its ability to infer a model network close to the groundtruth network from which the data have been generated. The input to an inference algorithm is a sample set of data and its output is a network. Since input, output, and algorithm are mathematical structures, the validity of an inference algorithm is a mathematical issue. This paper formulates validation in terms of a semimetric distance between two networks, or the distance between two structures of the same kind deduced from the networks, such as their steadystate distributions or regulatory graphs. The paper sets up the validation framework, provides examples of distance functions, and applies them to some discrete Markov network models. It also considers approximate validation methods based on data for which the generating network is not known, the kind of situation one faces when using real data.
2004, ‘The number and probability of canalizing functions
 Physica D Nonlinear Phenomena
"... Canalizing functions have important applications in physics and biology. For example, they represent a mechanism capable of stabilizing chaotic behavior in Boolean network models of discrete dynamical systems. When comparing the class of canalizing functions to other classes of functions with respec ..."
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Cited by 8 (1 self)
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Canalizing functions have important applications in physics and biology. For example, they represent a mechanism capable of stabilizing chaotic behavior in Boolean network models of discrete dynamical systems. When comparing the class of canalizing functions to other classes of functions with respect to their evolutionary plausibility as emergent control rules in genetic regulatory systems, it is informative to know the number of canalizing functions with a given number of input variables. This is also important in the context of using the class of canalizing functions as a constraint during the inference of genetic networks from gene expression data. To this end, we derive an exact formula for the number of canalizing Boolean functions of n variables. We also derive a formula for the probability that a random Boolean function is canalizing for any given bias p of taking the value 1. In addition, we consider the number and probability of Boolean functions that are canalizing for exactly k variables. Finally, we provide an algorithm for randomly generating canalizing functions with a given bias p and any number of variables, which is needed for Monte Carlo simulations of Boolean networks.
Dynamic Algorithm for Inferring Qualitative Models of Gene Regulatory Networks
 Int. J. Data Min. Bioinf
"... Abstract: We introduce a novel algorithm, DFL (Discrete Function Learning), for reconstructing qualitative models of Gene Regulatory Networks (GRNs) from gene expression data in this paper. We analyse its complexity of O(k ⋅ N ⋅ n2) on the average and its data requirements. The experiments of synthe ..."
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Cited by 8 (4 self)
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Abstract: We introduce a novel algorithm, DFL (Discrete Function Learning), for reconstructing qualitative models of Gene Regulatory Networks (GRNs) from gene expression data in this paper. We analyse its complexity of O(k ⋅ N ⋅ n2) on the average and its data requirements. The experiments of synthetic Boolean networks show that the DFL algorithm is more efficient than current algorithms without loss of prediction performances. The results of yeast cell cycle gene expression data show that the DFL algorithm can identify biologically significant models with reasonable accuracy, sensitivity and high precision with respect to the literature evidences.
Learning genetic regulatory network connectivity from time series data
 Advances in Applied Artificial Intelligence
, 2006
"... Abstract. Recent experimental advances facilitate the collection of time series data that indicate which genes in a cell are expressed. This paper proposes an efficient method to generate the genetic regulatory network inferred from time series data. Our method first encodes the data into levels. Ne ..."
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Cited by 8 (3 self)
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Abstract. Recent experimental advances facilitate the collection of time series data that indicate which genes in a cell are expressed. This paper proposes an efficient method to generate the genetic regulatory network inferred from time series data. Our method first encodes the data into levels. Next, it determines the set of potential parents for each gene based upon the probability of the gene’s expression increasing. After a subset of potential parents are selected, it determines if any genes in this set may have a combined effect. Finally, the potential sets of parents are competed against each other to determine the final set of parents. The result is a directed graph representation of the genetic network’s repression and activation connections. Our results on synthetic data generated from models for several genetic networks with tight feedback are promising. 1
Design of probabilistic Boolean networks under the requirement of contextual data consistency
 IEEE Trans. Signal Process
, 2006
"... Abstract—A key issue of genomic signal processing is the design of gene regulatory networks. A probabilistic Boolean network (PBN) is composed of a family of Boolean networks. It stochastically switches between its constituent networks (contexts). For network design, connectivity and transition rule ..."
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Cited by 6 (5 self)
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Abstract—A key issue of genomic signal processing is the design of gene regulatory networks. A probabilistic Boolean network (PBN) is composed of a family of Boolean networks. It stochastically switches between its constituent networks (contexts). For network design, connectivity and transition rules must be inferred from data via some optimization criterion. Except rarely, the optimal rule for a gene will not be a perfect predictor because there will be inconsistencies in the data. It would be natural to model these inconsistencies to reflect changes in PBN contexts. If we assume inconsistencies result from the data arising from a random function, then design involves finding the realizations of a random function and the probability mass on those realizations so that the resulting random function best fits the data relative to the expectation of its output and does so using a minimal number of realizations. We propose PBN design satisfying the biological assumption that data are consistent within a context, for which the distribution of the network agrees with the empirical distribution of the data, and such that this is accomplished with a minimal number of contexts. The design also satisfies the biological constraint that, because the network spends the great majority of time in its attractors, all data states should be attractor states in the model. Index Terms—Data consistency, gene regulatory network, graphical model, network inference. I.
Multiscale Binarization of Gene Expression Data for Reconstructing Boolean Networks
 IEEE/ACM transactions on computational biology and bioinformatics
, 2011
"... Abstract—Network inference algorithms can assist life scientists in unraveling generegulatory systems on a molecular level. In recent years, great attention has been drawn to the reconstruction of Boolean networks from time series. These need to be binarized, as such networks model genes as binary ..."
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Cited by 4 (1 self)
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Abstract—Network inference algorithms can assist life scientists in unraveling generegulatory systems on a molecular level. In recent years, great attention has been drawn to the reconstruction of Boolean networks from time series. These need to be binarized, as such networks model genes as binary variables (either “expressed ” or “not expressed”). Common binarization methods often cluster measurements or separate them according to statistical or information theoretic characteristics and may require many data points to determine a robust threshold. Yet, time series measurements frequently comprise only a small number of samples. To overcome this limitation, we propose a binarization that incorporates measurements at multiple resolutions. We introduce two such binarization approaches which determine thresholds based on limited numbers of samples and additionally provide a measure of threshold validity. Thus, network reconstruction and further analysis can be restricted to genes with meaningful thresholds. This reduces the complexity of network inference. The performance of our binarization algorithms was evaluated in network reconstruction experiments using artificial data as well as realworld yeast expression time series. The new approaches yield considerably improved correct network identification rates compared to other binarization techniques by effectively reducing the amount of candidate networks. Index Terms—Binarization, generegulatory networks, Boolean networks, reconstruction. Ç
Inferring Boolean network structure via correlation
 Bioinformatics
"... Motivation: Accurate, context specific regulation of gene expression is essential for all organisms. Accordingly, it is very important to understand the complex relations within cellular gene regulatory networks. A tool to describe and analyze the behavior of such networks are Boolean models. The re ..."
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Cited by 3 (0 self)
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Motivation: Accurate, context specific regulation of gene expression is essential for all organisms. Accordingly, it is very important to understand the complex relations within cellular gene regulatory networks. A tool to describe and analyze the behavior of such networks are Boolean models. The reconstruction of a Boolean network from biological data requires identification of dependencies within the network. This task becomes increasingly computationally demanding with large amounts of data created by recent highthroughput technologies. Thus, we developed a method that is especially suited for network structure reconstruction from largescale data. In our approach, we took advantage of the fact that a specific transcription factor often will consistently either activate or inhibit a specific target gene, and this kind of regulatory behavior can be modeled using monotone functions. Results: To detect regulatory dependencies in a network, we examined how the expression of different genes correlates to successive network states. For this purpose we used Pearson correlation as an elementary correlation measure. Given a Boolean network containing only monotone Boolean functions, we prove that the correlation of successive states can identify the dependencies in the network. This method not only finds dependencies in randomly created artificial networks to very high percentage, but also reconstructed large fractions of both a published E. coli regulatory network from simulated data and a yeast cell cycle network from real microarray data. Contact: