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Modeling and simulation of genetic regulatory systems: A literature review
 JOURNAL OF COMPUTATIONAL BIOLOGY
, 2002
"... In order to understand the functioning of organisms on the molecular level, we need to know which genes are expressed, when and where in the organism, and to which extent. The regulation of gene expression is achieved through genetic regulatory systems structured by networks of interactions between ..."
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Cited by 729 (15 self)
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In order to understand the functioning of organisms on the molecular level, we need to know which genes are expressed, when and where in the organism, and to which extent. The regulation of gene expression is achieved through genetic regulatory systems structured by networks of interactions between DNA, RNA, proteins, and small molecules. As most genetic regulatory networks of interest involve many components connected through interlocking positive and negative feedback loops, an intuitive understanding of their dynamics is hard to obtain. As a consequence, formal methods and computer tools for the modeling and simulation of genetic regulatory networks will be indispensable. This paper reviews formalisms that have been employed in mathematical biology and bioinformatics to describe genetic regulatory systems, in particular directed graphs, Bayesian networks, Boolean networks and their generalizations, ordinary and partial differential equations, qualitative differential equations, stochastic equations, and rulebased formalisms. In addition, the paper discusses how these formalisms have been used in the simulation of the behavior of actual regulatory systems.
Probabilistic Boolean networks: a rulebased uncertainty model for gene regulatory networks
, 2002
"... Motivation: Our goal is to construct a model for genetic regulatory networks such that the model class: (i ) incorporates rulebased dependencies between genes; (ii ) allows the systematic study of global network dynamics; (iii ) is able to cope with uncertainty, both in the data and the model selec ..."
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Cited by 382 (58 self)
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Motivation: Our goal is to construct a model for genetic regulatory networks such that the model class: (i ) incorporates rulebased dependencies between genes; (ii ) allows the systematic study of global network dynamics; (iii ) is able to cope with uncertainty, both in the data and the model selection; and (iv ) permits the quantification of the relative influence and sensitivity of genes in their interactions with other genes.
Genetic Network Inference: From CoExpression Clustering To Reverse Engineering
, 2000
"... motivation: Advances in molecular biological, analytical and computational technologies are enabling us to systematically investigate the complex molecular processes underlying biological systems. In particular, using highthroughput gene expression assays, we are able to measure the output of the ge ..."
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Cited by 334 (0 self)
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motivation: Advances in molecular biological, analytical and computational technologies are enabling us to systematically investigate the complex molecular processes underlying biological systems. In particular, using highthroughput gene expression assays, we are able to measure the output of the gene regulatory network. We aim here to review datamining and modeling approaches for conceptualizing and unraveling the functional relationships implicit in these datasets. Clustering of coexpression profiles allows us to infer shared regulatory inputs and functional pathways. We discuss various aspects of clustering, ranging from distance measures to clustering algorithms and multiplecluster memberships. More advanced analysis aims to infer causal connections between genes directly, i.e. who is regulating whom and how. We discuss several approaches to the problem of reverse engineering of genetic networks, from discrete Boolean networks, to continuous linear and nonlinear models. We conclude that the combination of predictive modeling with systematic experimental verification will be required to gain a deeper insight into living organisms, therapeutic targeting and bioengineering.
IDENTIFICATION OF GENETIC NETWORKS FROM A SMALL NUMBER OF GENE EXPRESSION PATTERNS UNDER THE BOOLEAN NETWORK MODEL
 PACIFIC SYMPOSIUM ON BIOCOMPUTING 4:1728 (1999)
, 1999
"... ... for inferring genetic network architectures from state transition tables which correspond to time series of gene expression patterns, using the Boolean network model. Their results of computational experiments suggested that a small number of state transition (INPUT/OUTPUT) pairs are sufficient ..."
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Cited by 254 (17 self)
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... for inferring genetic network architectures from state transition tables which correspond to time series of gene expression patterns, using the Boolean network model. Their results of computational experiments suggested that a small number of state transition (INPUT/OUTPUT) pairs are sufficient in order to infer the original Boolean network correctly. This paper gives a mathematical proof for their observation. Precisely, this paper devises a much simpler algorithm for the same problem and proves that, if the indegree of each node (i.e., the number of input nodes to each node) is bounded by a constant, only O(log n) state transition pairs (from 2n pairs) are necessary and sufficient to identify the original Boolean network of n nodes correctly with high probability. We made computational experiments in order to expose the constant factor involved in O(log n) notation. The computational results show that the Boolean network of size 100,000 can be identified by our algorithm from about 100 INPUT/OUTPUT pairs if the maximum indegree is bounded by 2. It is also a merit of our algorithm that the algorithm is conceptually so simple that it is extensible for more realistic network models.
Mutual Information Relevance Networks: Functional Genomic Clustering Using Pairwise Entropy Measurements
 Pacific Symposium on Biocomputing
, 2000
"... Increasing numbers of methodologies are available to find functional genomic clusters in RNA expression data. We describe a technique that computes comprehensive pairwise mutual information for all genes in such a data set. An association with a high mutual information means that one gene is nonra ..."
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Cited by 189 (1 self)
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Increasing numbers of methodologies are available to find functional genomic clusters in RNA expression data. We describe a technique that computes comprehensive pairwise mutual information for all genes in such a data set. An association with a high mutual information means that one gene is nonrandomly associated with another; we hypothesize this means the two are related biologically. By picking a threshold mutual information and using only associations at or above the threshold, we show how this technique was used on a public data set of 79 RNA expression measurements of 2,467 genes to construct 22 clusters, or Relevance Networks. The biological significance of each Relevance Network is explained.
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
Inferring gene regulatory networks from timeordered gene expression data of bacillus subtilis using differential equations
 Pac. Symp. Biocomput
, 2003
"... Abstract. Recently, cDNA microarray experiments have generated large amounts of gene expression data. In timeordered gene expression data, the expression levels are measured at several points in time following some experimental manipulation. A gene regulatory network can be inferred by describing t ..."
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Cited by 76 (17 self)
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Abstract. Recently, cDNA microarray experiments have generated large amounts of gene expression data. In timeordered gene expression data, the expression levels are measured at several points in time following some experimental manipulation. A gene regulatory network can be inferred by describing the gene expression data in terms of a linear system of differential equations. As biologically the gene regulatory network is known to be sparse, we expect most coefficients in such a linear system of differential equations to be zero. In previously proposed methods to infer a linear system of differential equations, some ad hoc assumptions are made to limit the number of nonzero coefficients in the system. Instead, we propose to infer the degree of sparseness of the gene regulatory network from the data, where we determine which coefficients are nonzero by using Akaike’s Information Criterion. 1
Development Of A System For The Inference Of Large Scale Genetic Networks
, 2001
"... Introduction Powerful new technologies, such as DNA microarrays, provide simple and economical ways to explore gene expression patterns on a genomic scale 1,2 . Using observed gene expression data, recent advances of technology in bioinformatics have made gene expression comprehensive and several ..."
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Cited by 74 (3 self)
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Introduction Powerful new technologies, such as DNA microarrays, provide simple and economical ways to explore gene expression patterns on a genomic scale 1,2 . Using observed gene expression data, recent advances of technology in bioinformatics have made gene expression comprehensive and several approaches have been proposed to infer the genetic networks 37 . We previously introduced two topdown approaches for the inference of interrelated mechanism among genes in genetic network that is based on the steady state and temporal analyses of gene expression patterns against some kinds of gene perturbations such as disruption or over expression. The former analysis is performed by a static Boolean network model based on a multilevel digraph approach 8 that can treat a large number of expression data. The latter one is by a dynamic network model such as Ssystem 9 that can infer the interrelated mechanism in genetic netwo
Algorithms for Identifying Boolean Networks and Related Biological Networks Based on Matrix Multiplication and Fingerprint Function
 J. Comp. Biol
"... Due to the recent progress of the DNA microarray technology, a large number of gene expression pro � le data are being produced. How to analyze gene expression data is an important topic in computational molecular biology. Several studies have been done using the Boolean network as a model of a gene ..."
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Cited by 69 (6 self)
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Due to the recent progress of the DNA microarray technology, a large number of gene expression pro � le data are being produced. How to analyze gene expression data is an important topic in computational molecular biology. Several studies have been done using the Boolean network as a model of a genetic network. This paper proposes ef � cient algorithms for identifying Boolean networks of bounded indegree and related biological networks, where identi� cation of a Boolean network can be formalized as a problem of identifying many Boolean functions simultaneously. For the identi � cation of a Boolean network, an 1 time naive algorithm and a simple time algorithm are known, where denotes the number of nodes, denotes the number of examples, and denotes the maximum indegree. This paper presents an improved 2 3 time MonteCarlo type randomized algorithm, where is the exponent of matrix multiplication (currently, 2 376). The algorithm is obtained by combining fast matrix multiplication with the randomized � ngerprint function for string matching. Although the algorithm and its analysis are simple, the result is nontrivial and the technique can be applied to several related problems.