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377
From Boolean to Probabilistic Boolean Networks as Models of Genetic Regulatory Networks
 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 ..."
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Cited by 122 (23 self)
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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, largescale, 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 firstpassage times in Markov chains. Examples from biology are presented throughout the paper. 1
Gene Perturbation and Intervention in Probabilistic Boolean Networks
 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 ..."
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Cited by 85 (26 self)
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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.
Combining microarrays and biological knowledge for estimating gene networks via Bayesian networks
 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 proteinprotein interactions, proteinDNA interactions, binding site information, existing literature and so on. Unfortunately, m ..."
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Cited by 80 (6 self)
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We propose a statistical method for estimating a gene network based on Bayesian networks from microarray gene expression data together with biological knowledge including proteinprotein interactions, proteinDNA 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 tradeoff 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.
External control in Markovian genetic regulatory networks: the imperfect information case
 Machine Learning
, 2004
"... Probabilistic Boolean Networks, which form a subclass of Markovian Genetic Regulatory Networks, have been recently introduced as a rulebased paradigm for modeling gene regulatory networks. In an earlier paper, we introduced external control into Markovian Genetic Regulatory networks. More precisely ..."
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Cited by 76 (27 self)
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Probabilistic Boolean Networks, which form a subclass of Markovian Genetic Regulatory Networks, have been recently introduced as a rulebased 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 Programmingbased 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.
Binary Analysis and OptimizationBased Normalization of Gene Expression Data
, 2002
"... Motivation: Most approaches to gene expression analysis use realvalued 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 ..."
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Cited by 76 (6 self)
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Motivation: Most approaches to gene expression analysis use realvalued 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.
Control of Stationary Behavior in Probabilistic Boolean Networks by Means of Structural Intervention
 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 steadystate or longrun behavior of PBNs ..."
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Cited by 44 (16 self)
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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 steadystate or longrun behavior of PBNs may reflect the phenotype or functional state of the cell. Approaches to alter the steadystate 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 steadystate probabil ities of certain states or sets of states with minimal modifications to the underlying rulebased 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.
Intervention in contextsensitive probabilistic Boolean networks
, 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 ..."
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Cited by 42 (15 self)
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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 contextsensitive 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 contextsensitive PBNs.
On learning gene regulatory networks under the Boolean network model
 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 ..."
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Cited by 41 (3 self)
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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 BestFit 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 BestFit Extension paradigm. We also introduce a simple and fast way of finding all Boolean networks having limited error size in the BestFit 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.
Can Markov Chain Models Mimic Biological Regulation?
, 2002
"... this paper is relatively small, it suggests that models incorporating rulebased transitions among states have a capacity to mimic biology. The ability of such models to enhance our understanding of biological regulation should be further tested by systematically examining the characteristics of the ..."
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Cited by 34 (16 self)
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this paper is relatively small, it suggests that models incorporating rulebased transitions among states have a capacity to mimic biology. The ability of such models to enhance our understanding of biological regulation should be further tested by systematically examining the characteristics of the rules and interconnections that lead to stabilization and switchlike transitions, and by building larger networks that incorporate more extensive prior knowledge of regulatory relationships and more extensive experimental observations of the di#erent stable states the network can occupy. Acknowledgments The authors wish to thank Dr. Shmulevich for his insightful suggestions on the areas of probabilistic Boolean network and Markov chain simulation. Appendix A. Proof Related to Eq. (4) Proof. The following is to prove the sum of Eq. (4) over all possible states, i.e., the sum of transition probability from a state to all possible states, is 1
Optimal infinitehorizon control for probabilistic Boolean networks
 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 finitehorizon control, i.e., control over a small number of stages. This paper considers the design of opt ..."
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Cited by 32 (14 self)
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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 finitehorizon control, i.e., control over a small number of stages. This paper considers the design of optimal infinitehorizon control for contextsensitive 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 averagecostperstage problems. These formulations are used to generate stationary policies for a PBN constructed from melanoma geneexpression 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, infinitehorizon control, optimal control of probabilistic Boolean networks. I.