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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 738 (14 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 391 (59 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 336 (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 192 (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 patterns to pathways: gene expression data analysis comes of age.
 Nature Genetics
, 2002
"... ..."
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 124 (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
A comparison of genetic network models
 In Pac. Symp. Biocomputing
, 2001
"... The inference of genetic interactions from measured expression data is one of the most challenging tasks of modern functional genomics. When successful, the learned network of regulatory interactions yields a wealth of useful information. An inferred genetic network contains information about the p ..."
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Cited by 97 (5 self)
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The inference of genetic interactions from measured expression data is one of the most challenging tasks of modern functional genomics. When successful, the learned network of regulatory interactions yields a wealth of useful information. An inferred genetic network contains information about the pathway to which a gene belongs and which genes it interacts with. Furthermore, it explains the gene's function in terms of how it influences other genes and indicates which genes are pathway initiators and therefore potential drug targets. Obviously, such wealth comes at a price and that of genetic network modeling is that it is an extremely complex task. Therefore, it is necessary to develop sophisticated computational tools that are able to extract relevant information from a limited set of microarray measurements and integrate this with different information sources, to come up with reliable hypotheses of a genetic regulatory network. Thus far, a multitude of modeling approaches has been proposed for discovering genetic networks. However, it is unclear what the advantages and disadvantages of each of the different approaches are and how their results can be compared. In this review, genetic network models are put in a historical perspective that explains why certain models were introduced. Various modeling assumptions and their consequences are also highlighted. In addition, an overview of the principal differences and similarities between the approaches is given by considering the qualitative properties of the chosen models and their learning strategies. In pharmacogenomics and related areas, a lot of research is directed towards discovering, understanding and/or controlling the outcome of some particular biological pathway. Numerous examples exist where the manipulation of a key enzyme in such a pathway did not lead to the desired effect We know that the structure of complex genetic and biochemical networks lies hidden in the sequence information of our DNA but it is far from trivial to predict gene expression from the sequence code alone. The current availability of microarray measurements of thousands of gene expression levels during the course of an experiment or after the knockout of a gene provides a wealth of complementary information that may be exploited to unravel the complex interplay between genes. It now becomes possible to start answering some of the truly challenging questions in systems biology. For example, is it possible to model these genetic interactions as a large network of interacting elements and can these interactions be effectively learned from measured expression data? Since Kauffman Although the behavior and properties of artificial networks match the observations made in real biological systems well, the field of genetic network modeling has yet to reach its full maturity. The automatic discovery of genetic networks from expression data alone is far from trivial because of the combinatorial nature of the problem and the poor information content of 1 For reasons of brevity, the authors consistently refer only to the first author of each reference.
Inferring gene regulatory networks from timeordered gene expression data of Bacillus subtilis using differential equations. Pacific
 Symposium on Biocomputing,
, 2003
"... We describe a new method to infer a gene regulatory network, in terms of a linear system of differential equations, from time course gene expression data. As biologically the gene regulatory network is known to be sparse, we expect most coefficients in such a linear system of differential equations ..."
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Cited by 76 (17 self)
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We describe a new method to infer a gene regulatory network, in terms of a linear system of differential equations, from time course gene expression data. 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, the number of nonzero coefficients in the system was limited based on ad hoc assumptions. Instead, we propose to infer the degree of sparseness of the gene regulatory network from the data, where we use Akaike's Information Criterion to determine which coefficients are nonzero. We apply our method to MMGE time course data of Bacillus subtilis.