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91
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.
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
Model Checking Genetic Regulatory Networks using GNA and CADP
 In: Proceedings of the 11th International SPIN Workshop on Model Checking of Software SPIN’2004
, 2004
"... who are interested in the interdisciplinary methods and applications relevant to the analysis, design and management of complex systems. 15 St. Mary’s St. Brookline MA 02446 l 617.358.1295 l www.bu.edu/systems ..."
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Cited by 47 (7 self)
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who are interested in the interdisciplinary methods and applications relevant to the analysis, design and management of complex systems. 15 St. Mary’s St. Brookline MA 02446 l 617.358.1295 l www.bu.edu/systems
Piecewiselinear models of genetic regulatory networks: equilibria and . . .
 J. MATH. BIOL.
, 2005
"... A formalism based on piecewiselinear (PL) differential equations, originally due to Glass and Kauffman, has been shown to be wellsuited to modelling genetic regulatory networks. However, the discontinuous vector field inherent in the PL models raises some mathematical problems in defining solutio ..."
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Cited by 45 (19 self)
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A formalism based on piecewiselinear (PL) differential equations, originally due to Glass and Kauffman, has been shown to be wellsuited to modelling genetic regulatory networks. However, the discontinuous vector field inherent in the PL models raises some mathematical problems in defining solutions on the surfaces of discontinuity. To overcome these difficulties we use the approach of Filippov, which extends the vector field to a differential inclusion. We study the stability of equilibria (called singular equilibrium sets) that lie on the surfaces of discontinuity. We prove several theorems that characterize the stability of these singular equilibria directly from the state transition graph, which is a qualitative representation of the dynamics of the system. We also formulate a stronger conjecture on the stability of these singular equilibrium sets.
Hybrid modeling and simulation of genetic regulatory networks: a qualitative approach
 ERCIM News
, 2003
"... The functioning and development of living organisms is controlled by large and complex networks of genes, proteins, small molecules, and their interactions, socalled genetic regulatory networks. The concerted efforts of genetics, molecular biology, biochemistry, and physiology have led to the accum ..."
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Cited by 36 (1 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 interactions, socalled genetic regulatory networks. The concerted efforts of genetics, molecular biology, biochemistry, and physiology have led to the accumulation of enormous amounts of data on the molecular components of genetic regulatory networks and their interactions. Notwithstanding the advances in the mapping of the network structure, surprisingly little is understood about how the dynamic behavior of the system emerges from the interactions between the network components. This has incited an increasingly large group of researchers to turn from the structure to the behavior of genetic regulatory networks, against the background of a broader movement nowadays often referred to as systems biology
Qualitative simulation of the initiation of sporulation in Bacillus subtilis
 Bulletin of Mathematical Biology
, 2004
"... Under conditions of nutrient deprivation, the Gram positive soil bacterium Bacillus subtilis can abandon vegetative growth and form a dormant, environmentallyresistant spore instead. The decision to either divide or sporulate is controlled by a ∗Corresponding address: Institut National de Recherche ..."
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Cited by 35 (1 self)
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Under conditions of nutrient deprivation, the Gram positive soil bacterium Bacillus subtilis can abandon vegetative growth and form a dormant, environmentallyresistant spore instead. The decision to either divide or sporulate is controlled by a ∗Corresponding address: Institut National de Recherche en Informatique et en Automatique (INRIA), Unite ́ de recherche RhôneAlpes, 655 avenue de l’Europe, Montbonnot, 38334 Saint Ismier
Qualitatively modelling and analysing genetic regulatory networks: a Petri net approach
 Bioinformatics
, 2007
"... Motivation: New developments in postgenomic technology now provide researchers with the data necessary to study regulatory processes in a holistic fashion at multiple levels of biological organisation. One of the major challenges for the biologist is to integrate and interpret these vast data resou ..."
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Cited by 30 (2 self)
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Motivation: New developments in postgenomic technology now provide researchers with the data necessary to study regulatory processes in a holistic fashion at multiple levels of biological organisation. One of the major challenges for the biologist is to integrate and interpret these vast data resources to gain a greater understanding of the structure and function of the molecular processes that mediate adaptive and cell cycle driven changes in gene expression. In order to achieve this biologists require new tools and techniques to allow pathway related data to be modelled and analysed as network structures, providing valuable insights which can then be validated and investigated in the laboratory. Results: We propose a new technique for constructing and analysing qualitative models of genetic regulatory networks based on the Petri net formalism. We take as our starting point the Boolean network approach of treating genes as binary switches and develop a new Petri net model which uses logic minimization to automate the construction of compact qualitative models. Our approach addresses the shortcomings of Boolean networks by providing access to the wide range of existing Petri net analysis techniques and by using non–determinism to cope with incomplete and inconsistent data. The ideas we present are illustrated by a case study in which the genetic regulatory network controlling sporulation in the bacterium Bacillus subtilis is modelled and analysed. Availability: The Petri net model construction tool and the data files for the B. subtilis sporulation case study are available at
Qualitative analysis and verification of hybrid models of genetic regulatory networks: Nutritional stress response in Escherichia coli
 in Hybrid Systems: Computation and Control
, 2005
"... Abstract. The switchlike character of the dynamics of genetic regulatory networks has attracted much attention from mathematical biologists and researchers on hybrid systems alike. We extend our previous work on a method for the qualitative analysis of hybrid models of genetic regulatory networks, ..."
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Cited by 27 (5 self)
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Abstract. The switchlike character of the dynamics of genetic regulatory networks has attracted much attention from mathematical biologists and researchers on hybrid systems alike. We extend our previous work on a method for the qualitative analysis of hybrid models of genetic regulatory networks, based on a class of piecewiseaffine differential equation (PADE) models, in two directions. First, we present a refinement of the method using a discrete or qualitative abstraction that preserves stronger properties of the dynamics of the PA systems, in particular the sign patterns of the derivatives of the concentration variables. The discrete transition system resulting from the abstraction is a conservative approximation of the dynamics of the PA system and can be computed symbolically. Second, we apply the refined method to a regulatory system whose functioning is not yet wellunderstood by biologists, the nutritional stress response in the bacterium Escherichia coli. 1
Logicbased models for the analysis of cell signaling networks
 Biochemistry
, 2010
"... ABSTRACT: Computational models are increasingly used to analyze the operation of complex biochemical networks, including those involved in cell signaling networks. Here we review recent advances in applying logicbased modeling to mammalian cell biology. Logicbased models represent biomolecular net ..."
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Cited by 23 (1 self)
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ABSTRACT: Computational models are increasingly used to analyze the operation of complex biochemical networks, including those involved in cell signaling networks. Here we review recent advances in applying logicbased modeling to mammalian cell biology. Logicbased models represent biomolecular networks in a simple and intuitive manner without describing the detailed biochemistry of each interaction. A brief description of several logicbased modeling methods is followed by six case studies that demonstrate biological questions recently addressed using logicbased models and point to potential advances in model formalisms and training procedures that promise to enhance the utility of logicbased methods for studying the relationship between environmental inputs and phenotypic or signaling state outputs of complex signaling networks. With accelerating pace, molecular biology and biochemistry are identifying complex patterns of interactions among intracellular and extracellular biomolecules.With respect to cell signaling in eukaryotes, the focus of this review, complex multicomponent networks involving many shared components govern how a cell will respond to diverse environmental cues. Powerful experimen
Piecewiselinear models of genetic regulatory networks: theory and example
 IN BIOLOGY AND CONTROL THEORY: CURRENT CHALLENGES, LECTURE
"... The experimental study of genetic regulatory networks has made tremendous progress in recent years resulting in a huge amount of data on the molecular interactions in model organisms. It is therefore not possible anymore to intuitively understand how the genes and interactions together influence th ..."
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Cited by 14 (4 self)
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The experimental study of genetic regulatory networks has made tremendous progress in recent years resulting in a huge amount of data on the molecular interactions in model organisms. It is therefore not possible anymore to intuitively understand how the genes and interactions together influence the behavior of the system. In order to answer such questions, a rigorous modeling and analysis approach is necessary. In this chapter, we present a family of such models and analysis methods enabling us to better understand the dynamics of genetic regulatory networks. We apply such methods to the network that underlies the nutritional stress response of the bacterium E. coli.