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Probabilistic Boolean networks: A rule-based uncertainty model for gene regulatory networks (2002)

by I Shmulevich, E R Dougherty, S Kim, W Zhang
Venue:Bioinform
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From Boolean to Probabilistic Boolean Networks as Models of Genetic Regulatory Networks

by Ilya Shmulevich, Edward R. Dougherty, Wei Zhang - Proc. IEEE , 2002
"... Mathematical and computational modeling of genetic regulatory networks promises to uncover the fundamental principles governing biological systems in an integrarive and holistic manner. It also paves the way toward the development of systematic approaches for effective therapeutic intervention in di ..."
Abstract - Cited by 124 (23 self) - Add to MetaCart
Mathematical and computational modeling of genetic regulatory networks promises to uncover the fundamental principles governing biological systems in an integrarive and holistic manner. It also paves the way toward the development of systematic approaches for effective therapeutic intervention in disease. The central theme in this paper is the Boolean formalism as a building block for modeling complex, large-scale, and dynamical networks of genetic interactions. We discuss the goals of modeling genetic networks as well as the data requirements. The Boolean formalism is justified from several points of view. We then introduce Boolean networks and discuss their relationships to nonlinear digital filters. The role of Boolean networks in understanding cell differentiation and cellular functional states is discussed. The inference of Boolean networks from real gene expression data is considered from the viewpoints of computational learning theory and nonlinear signal processing, touching on computational complexity of learning and robustness. Then, a discussion of the need to handle uncertainty in a probabilistic framework is presented, leading to an introduction of probabilistic Boolean networks and their relationships to Markov chains. Methods for quantifying the influence of genes on other genes are presented. The general question of the potential effect of individual genes on the global dynamical network behavior is considered using stochastic perturbation analysis. This discussion then leads into the problem of target identification for therapeutic intervention via the development of several computational tools based on first-passage times in Markov chains. Examples from biology are presented throughout the paper. 1
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.... Boolean networks are structurally simple yet dynamically complex and have yielded insights into the overall behavior of large genetic networks [22, 31, 32, 33]. Let us give an example borrowed from =-=[34]-=-, showing the logical representation of cell cycle regulation. This process of cellular growth and division is highly regulated. A disbalance in this process results in unregulated cell growth in dise...

Gene Perturbation and Intervention in Probabilistic Boolean Networks

by Ilya Shmulevich, Edward R. Dougherty, Wei Zhang - Bioinformatics
"... Motivation: A major objective of gene regulatory network modeling, in addition to gaining a deeper understanding of genetic regulation and control, is the development of computational tools for the identification and discovery of potential targets for therapeutic intervention in diseases such as can ..."
Abstract - Cited by 88 (27 self) - Add to MetaCart
Motivation: A major objective of gene regulatory network modeling, in addition to gaining a deeper understanding of genetic regulation and control, is the development of computational tools for the identification and discovery of potential targets for therapeutic intervention in diseases such as cancer. We consider the general question of the potential effect of individual genes on the global dynamical network behavior, both from the view of random gene perturbation as well as intervention in order to elicit desired network behavior.
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...t al., 1995) and allow the study of large data sets in a global fashion. Perhaps part of the appeal of Boolean networks lies in the fact that they are structurally simple yet dynamically complex. In (=-=Shmulevich et al., 2002-=-), we introduced a new class of models called Probabilistic Boolean Networks (PBNs), which are probabilistic generalizations of the standard Boolean networks that offer a flexible and powerful modelin...

Combining microarrays and biological knowledge for estimating gene networks via Bayesian networks

by Seiya Imoto, Tomoyuki Higuchi, Takao Goto, Kousuke Tashiro, Satoru Kuhara, Satoru Miyano - In Proceedings of the IEEE Computer Society Bioinformatics Conference (CSB 03 , 2003
"... We propose a statistical method for estimating a gene network based on Bayesian networks from microarray gene expression data together with biological knowledge including protein-protein interactions, protein-DNA interactions, binding site information, existing literature and so on. Unfortunately, m ..."
Abstract - Cited by 80 (6 self) - Add to MetaCart
We propose a statistical method for estimating a gene network based on Bayesian networks from microarray gene expression data together with biological knowledge including protein-protein interactions, protein-DNA interactions, binding site information, existing literature and so on. Unfortunately, microarray data do not contain enough information for constructing gene networks accurately in many cases. Our method adds biological knowledge to the estimation method of gene networks under a Bayesian statistical framework, and also controls the trade-off between microarray information and biological knowledge automatically. We conduct Monte Carlo simulations to show the effectiveness of the proposed method. We analyze Saccharomyces cerevisiae gene expression data as an application. 1.
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...k has become one of the central topics in the field of bioinformatics. Several methodologies have been proposed for constructing a gene network based on gene expression data, such as Boolean networks =-=[1, 2, 32, 42]-=-, differenProceedings of the Computational Systems Bioinformatics (CSB’03) 0-7695-2000-6/03 $17.00 © 2003 IEEE tial equation models [7, 10, 11, 32] and Bayesian networks [13, 14, 17, 18, 20, 22, 23, 3...

External control in Markovian genetic regulatory networks: the imperfect information case

by Aniruddha Datta, Ashish Choudhary, Michael Bittner, Edward Dougherty - Machine Learning , 2004
"... Probabilistic Boolean Networks, which form a subclass of Markovian Genetic Regulatory Networks, have been recently introduced as a rule-based paradigm for modeling gene regulatory networks. In an earlier paper, we introduced external control into Markovian Genetic Regulatory networks. More precisely ..."
Abstract - Cited by 79 (27 self) - Add to MetaCart
Probabilistic Boolean Networks, which form a subclass of Markovian Genetic Regulatory Networks, have been recently introduced as a rule-based paradigm for modeling gene regulatory networks. In an earlier paper, we introduced external control into Markovian Genetic Regulatory networks. More precisely, given a Markovian genetic regulatory network whose state transition probabilities depend on an external (control) variable, a Dynamic Programming-based procedure was developed by which one could choose the sequence of control actions that minimized a given performance index over a finite number of steps. The control algorithm of that paper, however, could be implemented only when one had perfect knowledge of the states of the Markov Chain.This paper presents a control strategy that can be implemented in the imperfect information case, and makes use of the available measurements which are assumed to be probabilistically related to the states of the underlying Markov Chain.
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...2016 http://bioinform atics.oxfordjournals.org/ D ow nloaded from 1 Introduction Probabilistic Boolean Networks (PBN’s) have been recently proposed as a paradigm for studying gene regulatory networks =-=[1]-=-. These networks which allow the incorporation of uncertainty into the inter-gene relationships, are essentially probabilistic generalizations of the standard Boolean networks introduced by Kauffman [...

Binary Analysis and Optimization-Based Normalization of Gene Expression Data

by Ilya Shmulevich, Wei Zhang , 2002
"... Motivation: Most approaches to gene expression analysis use real-valued expression data, produced by highthroughput screening technologies, such as microarrays. Often, some measure of similarity must be computed in order to extract meaningful information from the observed data. The choice of this si ..."
Abstract - Cited by 76 (6 self) - Add to MetaCart
Motivation: Most approaches to gene expression analysis use real-valued expression data, produced by highthroughput screening technologies, such as microarrays. Often, some measure of similarity must be computed in order to extract meaningful information from the observed data. The choice of this similarity measure frequently has a profound effect on the results of the analysis, yet no standards exist to guide the researcher.

Identifying gene regulatory networks from gene expression data

by Vladimir Filkov
"... ..."
Abstract - Cited by 57 (4 self) - Add to MetaCart
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Control of Stationary Behavior in Probabilistic Boolean Networks by Means of Structural Intervention

by Ilya Shmulevich, Edward R. Dougherty, Wei Zhang - Biological Systems , 2002
"... Probabilistic Boolean Networks (PBNs) were recently introduced as mod- els of gene regulatory networks. The dynamical behavior of PBNs, which are probabilistic generalizations of Boolean networks, can be studied using Markov chain theory. In particular, the steady-state or long-run behavior of PBNs ..."
Abstract - Cited by 46 (17 self) - Add to MetaCart
Probabilistic Boolean Networks (PBNs) were recently introduced as mod- els of gene regulatory networks. The dynamical behavior of PBNs, which are probabilistic generalizations of Boolean networks, can be studied using Markov chain theory. In particular, the steady-state or long-run behavior of PBNs may reflect the phenotype or functional state of the cell. Approaches to alter the steady-state behavior in a specific prescribed manner, in cases of aberrant cellular states, such as tumorigenesis, would be highly beneficial. This paper develops a methodology for altering the steady-state probabil- ities of certain states or sets of states with minimal modifications to the underlying rule-based structure. This approach is framed as an optimization problem that we propose to solve using genetic algorithms, which are well suited for capturing the underlying structure of PBNs and are able to locate the optimal solution in a highly efficient manner. Several computer simulation experiments support the proposed methodology.
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...ictions about system behavior in the presence of known conditions. Recently, a new class of models, called Probabilistic Boolean Networks (PBNs), was introduced as a model of gene regulatory networks =-=[12]-=-. This model class incorporates rule-based dependencies between genes, allows the systematic study of global network dynamics, is able to cope with uncertainty, and permits the quantification of the r...

Intervention in context-sensitive probabilistic Boolean networks

by Ranadip Pal, Aniruddha Datta, Michael Bittner, Edward Dougherty , 2005
"... Motivation: Intervention in a gene regulatory network is used to help it avoid undesirable states, such as those associated with a disease. Several types of intervention have been studied in the framework of a probabilistic Boolean network (PBN), which is essentially a finite collection of Boolean n ..."
Abstract - Cited by 45 (15 self) - Add to MetaCart
Motivation: Intervention in a gene regulatory network is used to help it avoid undesirable states, such as those associated with a disease. Several types of intervention have been studied in the framework of a probabilistic Boolean network (PBN), which is essentially a finite collection of Boolean networks in which at any discrete time point the gene state vector transitions according to the rules of one of the constituent networks. For an instantaneously random PBN, the governing Boolean network is randomly chosen at each time point. For a context-sensitive PBN, the governing Boolean network remains fixed for an interval of time until a binary random variable determines a switch. The theory of automatic control has been previously applied to find optimal strategies for manipulating external (control) variables that affect the transition probabilities of an instantaneously random PBN to desirably affect its dynamic evolution over a finite time horizon. This paper extends the methods of external control to context-sensitive PBNs.
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...l to the model network result in the network structure taking on various realizations. Owing to these considerations, a stochastic rule-based regulatory model, the probabilistic Boolean network (PBN) =-=[23]-=-, [24] has been proposed. A PBN is composed of a collection of finite-state-space networks, each called a context and each composed of the same set of genes. At each time point, a random decision is m...

On learning gene regulatory networks under the Boolean network model

by Harri Lähdesmäki, Ilya Shmulevich, Olli Yli-Harja - Machine Learning , 2003
"... Boolean networks are a popular model class for capturing the interactions of genes and global dynamical behavior of genetic regulatory networks. Recently, a significant amount of attention has been focused on the inference or identification of the model structure from gene expression data. We consi ..."
Abstract - Cited by 43 (4 self) - Add to MetaCart
Boolean networks are a popular model class for capturing the interactions of genes and global dynamical behavior of genetic regulatory networks. Recently, a significant amount of attention has been focused on the inference or identification of the model structure from gene expression data. We consider the Consistency as well as Best-Fit Extension problems in the context of inferring the networks from data. The latter approach is especially useful in situations when gene expression measurements are noisy and may lead to inconsistent observations. We propose simple efficient algorithms that can be used to answer the Consistency Problem and find one or all consistent Boolean networks relative to the given examples. The same method is extended to learning gene regulatory networks under the Best-Fit Extension paradigm. We also introduce a simple and fast way of finding all Boolean networks having limited error size in the Best-Fit Extension Problem setting. We apply the inference methods to a real gene expression data set and present the results for a selected set of genes.

Optimal infinitehorizon control for probabilistic Boolean networks

by Ranadip Pal, Student Member, Aniruddha Datta, Senior Member, Edward R. Dougherty - IEEE Transactions on Signal Processing
"... Abstract—External control of a genetic regulatory network is used for the purpose of avoiding undesirable states, such as those associated with disease. Heretofore, intervention has focused on finite-horizon control, i.e., control over a small number of stages. This paper considers the design of opt ..."
Abstract - Cited by 35 (14 self) - Add to MetaCart
Abstract—External control of a genetic regulatory network is used for the purpose of avoiding undesirable states, such as those associated with disease. Heretofore, intervention has focused on finite-horizon control, i.e., control over a small number of stages. This paper considers the design of optimal infinite-horizon control for context-sensitive probabilistic Boolean networks (PBNs). It can also be applied to instantaneously random PBNs. The stationary policy obtained is independent of time and dependent on the current state. This paper concentrates on discounted problems with bounded cost per stage and on average-cost-per-stage problems. These formulations are used to generate stationary policies for a PBN constructed from melanoma gene-expression data. The results show that the stationary policies obtained by the two different formulations are capable of shifting the probability mass of the stationary distribution from undesirable states to desirable ones. Index Terms—Altering steady state, genetic network intervention, infinite-horizon control, optimal control of probabilistic Boolean networks. I.
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