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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 64 (10 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.
A Class of Piecewise Linear Differential Equations Arising In Biological Models
, 2003
"... We investigate the properties of the solutions of a class of piecewiselinear differential equations. The equations are appropriate to model biological systems (e.g., genetic networks) in which there are switchlike interactions between the elements. The analysis uses the concept of Filippov solutio ..."
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Cited by 56 (18 self)
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We investigate the properties of the solutions of a class of piecewiselinear differential equations. The equations are appropriate to model biological systems (e.g., genetic networks) in which there are switchlike interactions between the elements. The analysis uses the concept of Filippov solutions of differential equations with a discontinuous righthand side. It gives an insight into the socalled singular solutions which lie on the surfaces of discontinuity. We show that this notion clarifies the study of several examples studied in the literature.
Graphic Requirements for Multistability and Attractive Cycles in a Boolean Dynamical Framework
, 2008
"... ..."
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 46 (20 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.
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 45 (6 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
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 45 (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.
Dynamic modelling and analysis of biochemical networks: mechanismbased models and modelbased experiments
, 2006
"... Systems biology applies quantitative, mechanistic modelling to study genetic networks, signal transduction pathways and metabolic networks. Mathematical models of biochemical networks can look very different. An important reason is that the purpose and application of a model are essential for the ..."
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Cited by 43 (0 self)
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Systems biology applies quantitative, mechanistic modelling to study genetic networks, signal transduction pathways and metabolic networks. Mathematical models of biochemical networks can look very different. An important reason is that the purpose and application of a model are essential for the selection of the best mathematical framework. Fundamental aspects of selecting an appropriate modelling framework and a strategy for model building are discussed. Concepts and methods from system and control theory provide a sound basis for the further development of improved and dedicated computational tools for systems biology. Identification of the network components and rate constants that are most critical to the output behaviour of the system is one of the major problems raised in systems biology.Current approaches and methods of parameter sensitivity analysis and parameter estimation are reviewed. It is shown how these methods can be applied in the design of modelbased experiments which iteratively yield models that are decreasingly wrong and increasingly gain predictive power.
Automated Symbolic Reachability Analysis; with Application to DeltaNotch Signaling Automata
 Lecture Notes in Computer Science
, 2003
"... This paper describes the implementation of predicate abstraction techniques to automatically compute symbolic backward reachable sets of high dimensional piecewise a#ne hybrid automata, used to model DeltaNotch biological cell signaling networks. These automata are analyzed by creating an abstr ..."
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Cited by 38 (2 self)
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This paper describes the implementation of predicate abstraction techniques to automatically compute symbolic backward reachable sets of high dimensional piecewise a#ne hybrid automata, used to model DeltaNotch biological cell signaling networks. These automata are analyzed by creating an abstraction of the hybrid model, which is a finite state discrete transition system, and then performing the computation on the abstracted system. All the steps, from model generation to the simplification of the reachable set, have been automated using a variety of decision procedure and theoremproving tools. The concluding example computes the reach set for a four cell network with 8 continuous and 256 discrete states. This demonstrates the feasibility of using these tools to compute on high dimensional hybrid automata, to provide deeper insight into realistic biological systems.