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719
Using Bayesian networks to analyze expression data
 Journal of Computational Biology
, 2000
"... DNA hybridization arrays simultaneously measure the expression level for thousands of genes. These measurements provide a “snapshot ” of transcription levels within the cell. A major challenge in computational biology is to uncover, from such measurements, gene/protein interactions and key biologica ..."
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Cited by 1076 (18 self)
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DNA hybridization arrays simultaneously measure the expression level for thousands of genes. These measurements provide a “snapshot ” of transcription levels within the cell. A major challenge in computational biology is to uncover, from such measurements, gene/protein interactions and key biological features of cellular systems. In this paper, we propose a new framework for discovering interactions between genes based on multiple expression measurements. This framework builds on the use of Bayesian networks for representing statistical dependencies. A Bayesian network is a graphbased model of joint multivariate probability distributions that captures properties of conditional independence between variables. Such models are attractive for their ability to describe complex stochastic processes and because they provide a clear methodology for learning from (noisy) observations. We start by showing how Bayesian networks can describe interactions between genes. We then describe a method for recovering gene interactions from microarray data using tools for learning Bayesian networks. Finally, we demonstrate this method on the S. cerevisiae cellcycle measurements of Spellman et al. (1998). Key words: gene expression, microarrays, Bayesian methods. 1.
Qualitative Simulation of Genetic Regulatory Networks Using PiecewiseLinear Models
, 2001
"... In order to cope with the large amounts of data that have become available in genomics, mathematical tools for the analysis of networks of interactions between genes, proteins, and other molecules are indispensable. We present a method for the qualitative simulation of genetic regulatory networks ..."
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Cited by 185 (30 self)
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In order to cope with the large amounts of data that have become available in genomics, mathematical tools for the analysis of networks of interactions between genes, proteins, and other molecules are indispensable. We present a method for the qualitative simulation of genetic regulatory networks, based on a class of piecewiselinear (PL) differential equations that has been wellstudied in mathematical biology. The simulation method is welladapted to stateoftheart measurement techniques in genomics, which often provide qualitative and coarsegrained descriptions of genetic regulatory networks. Given a qualitative model of a genetic regulatory network, consisting of a system of PL differential equations and inequality constraints on the parameter values, the method produces a graph of qualitative states and transitions between qualitative states, summarizing the qualitative dynamics of the system. The qualitative simulation method has been implemented in Java in the computer tool Genetic Network Analyzer.
Sensitivity and specificity of inferring genetic regulatory interactions from microarray experiments with dynamic Bayesian networks
 Bioinformatics
, 2003
"... Motivation: Bayesian networks have been applied to infer genetic regulatory interactions from microarray gene expression data. This inference problem is particularly hard in that interactions between hundreds of genes have to be learned from very small data sets, typically containing only a few doze ..."
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Cited by 176 (5 self)
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Motivation: Bayesian networks have been applied to infer genetic regulatory interactions from microarray gene expression data. This inference problem is particularly hard in that interactions between hundreds of genes have to be learned from very small data sets, typically containing only a few dozen time points during a cell cycle. Most previous studies have assessed the inference results on real gene expression data by comparing predicted genetic regulatory interactions with those known from the biological literature. This approach is controversial due to the absence of known gold standards, which renders the estimation of the sensitivity and specificity, that is, the true and (complementary) false detection rate, unreliable and difficult. The objective of the present study is to test the viability of the Bayesian network paradigm in a realistic simulation study. First, gene expression data are simulated from a realistic biological network involving DNAs, mRNAs, inactive protein monomers and active protein dimers. Then, interaction networks are inferred from these data in a reverse engineering approach, using Bayesian networks and Bayesian learning with Markov chain Monte Carlo.
Results: The simulation results are presented as receiver operator characteristics curves. This allows estimating the proportion of spurious gene interactions incurred for a specified target proportion of recovered true interactions. The findings demonstrate how the network inference performance varies with the training set size, the degree of inadequacy of prior assumptions, the experimental sampling strategy and the inclusion of further, sequencebased information.
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
Validation of qualitative models of genetic regulatory networks by model checking: Analysis of the nutritional stress response in Escherichia coli
 Bioinformatics
, 2005
"... The functioning and development of living organisms is controlled by large and complex networks of genes, proteins, small molecules, and their mutual interactions, socalled genetic regulatory networks. In order to gain an understanding of how the behavior of an organism – e.g., the response of a ..."
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Cited by 91 (22 self)
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The functioning and development of living organisms is controlled by large and complex networks of genes, proteins, small molecules, and their mutual interactions, socalled genetic regulatory networks. In order to gain an understanding of how the behavior of an organism – e.g., the response of a
Genetic network analyzer: qualitative simulation of genetic regulatory networks
 Bioinformatics
, 2003
"... Motivation: The study of genetic regulatory networks has received a major impetus from the recent development of experimental techniques allowing the measurement of patterns of gene expression in a massively parallel way. This experimental progress calls for the development of appropriate computer ..."
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Cited by 91 (15 self)
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Motivation: The study of genetic regulatory networks has received a major impetus from the recent development of experimental techniques allowing the measurement of patterns of gene expression in a massively parallel way. This experimental progress calls for the development of appropriate computer tools for the modeling and simulation of gene regulation processes. Results: We present Genetic Network Analyzer (GNA), a computer tool for the modeling and simulation of genetic regulatory networks. The tool is based on a qualitative simulation method that employs coarsegrained models of regulatory networks. The use of GNA is illustrated by a case study of the network of genes and interactions regulating the initiation of sporulation in Bacillus subtilis. Availability: GNA and the model of the sporulation network are available at
Modeling and Querying Biomolecular Interaction Networks
 Theoretical Computer Science
, 2003
"... We introduce a formalism to represent and analyze proteinprotein and proteinDNA interaction networks. We illustrate the expressivity of this language, by proposing a formal counterpart of Kohn's compilation on the mammalian cell cycle control. This e#ectively turns an otherwise static kno ..."
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Cited by 89 (0 self)
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We introduce a formalism to represent and analyze proteinprotein and proteinDNA interaction networks. We illustrate the expressivity of this language, by proposing a formal counterpart of Kohn's compilation on the mammalian cell cycle control. This e#ectively turns an otherwise static knowledge into a discrete transition system incorporating a qualitative description of the dynamics. We then propose to use the Computation Tree Logic CTL as a query language for querying the possible behaviours of the system. We provide examples of biologically relevant queries expressed in CTL about the mammalian cell cycle control and show the e#ectiveness of symbolic model checking tools to evaluate CTL queries in this context.
Petri Net Modelling of Biological Networks
 Briefings in Bioinformatics, 8(4):210 – 219
, 2007
"... Mathematical modelling is increasingly used to get insights into the functioning of complex biological networks. In this context, Petri nets (PNs) have recently emerged as a promising tool among the various methods employed for the modelling and analysis of molecular networks. PNs come with a series ..."
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Cited by 67 (3 self)
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Mathematical modelling is increasingly used to get insights into the functioning of complex biological networks. In this context, Petri nets (PNs) have recently emerged as a promising tool among the various methods employed for the modelling and analysis of molecular networks. PNs come with a series of extensions, which allow different abstraction levels, from purely qualitative to more complex quantitative models.Noteworthily, each of these models preserves the underlying graph, which depicts the interactions between the biological components. This article intends to present the basics of the approach and to foster the potential role PNs could play in the development of the computational systems biology.
Symbolic model checking of biochemical networks
 Computational Methods in Systems Biology (CMSB’03), volume 2602 of LNCS
, 2003
"... Abstract. Model checking is an automatic method for deciding if a circuit or a program, expressed as a concurrent transition system, satisfies a set of properties expressed in a temporal logic such as CTL. In this paper we argue that symbolic model checking is feasible in systems biology and that it ..."
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Cited by 66 (8 self)
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Abstract. Model checking is an automatic method for deciding if a circuit or a program, expressed as a concurrent transition system, satisfies a set of properties expressed in a temporal logic such as CTL. In this paper we argue that symbolic model checking is feasible in systems biology and that it shows some advantages over simulation for querying and validating formal models of biological processes. We report our experiments on using the symbolic model checker NuSMV and the constraintbased model checker DMC, for the modeling and querying of two biological processes: a qualitative model of the mammalian cell cycle control after Kohn's diagrams, and a quantitative model of gene expression regulation. 1 Introduction In recent years, Biology has clearly engaged an elucidation work of highlevel biological processes in terms of their biochemical basis at the molecular level. The mass production of post genomic data, such as ARN expression, protein production and proteinprotein interaction, raises the need of a strong parallel effort on the formal representation of biological processes. Metabolism networks, extracellular and intracellular signaling pathways, and gene expression regulation networks, are very complex dynamical systems. Annotating data bases with qualitative and quantitative information about the dynamics of biological systems, will not be sufficient to integrate and efficiently use the current knowledge about these systems. The design of formal tools for modeling biomolecular processes and for reasoning about their dynamics seems to be a mandatory research path to which the field of formal verification in computer science may contribute a lot.
A computational algebra approach to the reverse engineering of gene regulatory networks
 Journal of Theoretical Biology
, 2004
"... This paper proposes a new method to reverse engineer gene regulatory networks from experimental data. The modeling framework used is timediscrete deterministic dynamical systems, with a finite set of states for each of the variables. The simplest examples of such models are Boolean networks, in whi ..."
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Cited by 65 (9 self)
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This paper proposes a new method to reverse engineer gene regulatory networks from experimental data. The modeling framework used is timediscrete deterministic dynamical systems, with a finite set of states for each of the variables. The simplest examples of such models are Boolean networks, in which variables have only two possible states. The use of a larger number of possible states allows a finer discretization of experimental data and more than one possible mode of action for the variables, depending on threshold values. Furthermore, with a suitable choice of state set, one can employ powerful tools from computational algebra, that underlie the reverseengineering algorithm, avoiding costly enumeration strategies. To perform well, the algorithm requires wildtype together with perturbation time courses. This makes it suitable for small to mesoscale networks rather than networks on a genomewide scale. An analysis of the complexity of the algorithm is performed. The algorithm is validated on a recently published Boolean network model of segment polarity development in Drosophila melanogaster.