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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. Key words: genetic regulatory networks, mathematical modeling, simulation, computational biology.
The LargeScale Organization of Metabolic Networks
, 2000
"... In a cell or microorganism the processes that generate mass, energy, information transfer, and cell fate specification are seamlessly integrated through a complex network of various cellular constituents and reactions. However, despite the key role these networks play in sustaining various cellular ..."
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Cited by 600 (7 self)
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In a cell or microorganism the processes that generate mass, energy, information transfer, and cell fate specification are seamlessly integrated through a complex network of various cellular constituents and reactions. However, despite the key role these networks play in sustaining various cellular functions, their largescale structure is essentially unknown. Here we present the first systematic comparative mathematical analysis of the metabolic networks of 43 organisms representing all three domains of life. We show that, despite significant variances in their individual constituents and pathways, these metabolic networks display the same topologic scaling properties demonstrating striking similarities to the inherent organization of complex nonbiological systems. This suggests that the metabolic organization is not only identical for all living organisms, but complies with the design principles of robust and errortolerant networks, and may represent a common blueprint for the largescale organization of interactions among all cellular constituents.
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.
Stochasticity in transcriptional regulation: origins, consequences, and mathematical representations
 Biophys. J
, 2001
"... ABSTRACT Transcriptional regulation is an inherently noisy process. The origins of this stochastic behavior can be traced to the random transitions among the discrete chemical states of operators that control the transcription rate and to finite number fluctuations in the biochemical reactions for t ..."
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Cited by 129 (3 self)
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ABSTRACT Transcriptional regulation is an inherently noisy process. The origins of this stochastic behavior can be traced to the random transitions among the discrete chemical states of operators that control the transcription rate and to finite number fluctuations in the biochemical reactions for the synthesis and degradation of transcripts. We develop stochastic models to which these random reactions are intrinsic and a series of simpler models derived explicitly from the first as approximations in different parameter regimes. This innate stochasticity can have both a quantitative and qualitative impact on the behavior of generegulatory networks. We introduce a natural generalization of deterministic bifurcations for classification of stochastic systems and show that simple noisy genetic switches have rich bifurcation structures; among them, bifurcations driven solely by changing the rate of operator fluctuations even as the underlying deterministic system remains unchanged. We find stochastic bistability where the deterministic equations predict monostability and viceversa. We derive and solve equations for the mean waiting times for spontaneous transitions between quasistable states in these switches.
BioPEPA: a framework for the modelling and analysis of biological systems
, 2008
"... In this work we present BioPEPA, a process algebra for the modelling and the analysis of biochemical networks. It is a modification of PEPA, originally defined for the performance analysis of computer systems, in order to handle some features of biological models, such as stoichiometry and the use ..."
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Cited by 90 (25 self)
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In this work we present BioPEPA, a process algebra for the modelling and the analysis of biochemical networks. It is a modification of PEPA, originally defined for the performance analysis of computer systems, in order to handle some features of biological models, such as stoichiometry and the use of general kinetic laws. The domain of application is the one of biochemical networks. BioPEPA may be seen as an intermediate, formal, compositional representation of biological systems, on which different kinds of analysis can be carried out. BioPEPA is enriched with some notions of equivalence. Specifically, the isomorphism and strong bisimulation for PEPA have been considered. Finally, we show the translation of three biological models into the new language and we report some analysis results.
Negative autoregulation speeds the response times of transcription networks
 J. Mol. Biol
, 2002
"... A major current challenge is to understand the design principles of gene regulation networks. It is therefore of interest to study the properties of regulatory structures, or “motifs”, that occur frequently ..."
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Cited by 79 (4 self)
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A major current challenge is to understand the design principles of gene regulation networks. It is therefore of interest to study the properties of regulatory structures, or “motifs”, that occur frequently
Model building and model checking for biochemical processes
 Cell Biochemistry and Biophysics
, 2003
"... A central claim of computational systems biology is that, by drawing upon mathematical approaches developed in the context of dynamical systems, kinetic analysis, computational theory and logic, it is possible to create powerful simulation, analysis and reasoning tools for working biologists to be u ..."
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Cited by 65 (4 self)
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A central claim of computational systems biology is that, by drawing upon mathematical approaches developed in the context of dynamical systems, kinetic analysis, computational theory and logic, it is possible to create powerful simulation, analysis and reasoning tools for working biologists to be used in deciphering existing data, devising new experiments and ultimately, understanding functional properties of genomes, proteomes, cells, organs and organisms. In this paper we describe a novel computational tool that achieves many of the goals of this new discipline. The novelty of this system involves an automatonbased semantics of the temporal evolution of complex biochemical reactions starting from the representation given as a set of differential equations. More importantly, the related tools also provide ability to qualitatively reason about the systems using a propositional temporal logic that can express ordered sequence of events succinctly and unambiguously. The implementation of our mathematical and computational models in the Simpathica and XSSYS systems is described briefly. Several example applications of these systems to cellular and biochemical processes are presented: the two most prominent ones are Leibler et al.’s repressilator (an artificial synthesized oscillatory network) and CurtoVoitSorribasCascante’s purine metabolism reaction model.
Environmentally Controlled Invasion of Cancer Cells by Engineered Bacteria
 Journal of Molecular Biology
, 2006
"... Bacteria can sense their environment, distinguish between cell types, and deliver proteins to eukaryotic cells. Here, we engineer the interaction between bacteria and cancer cells to depend on heterologous environmental signals. We have characterized invasin from Yersinia pseudotuburculosis as an ou ..."
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Cited by 58 (0 self)
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Bacteria can sense their environment, distinguish between cell types, and deliver proteins to eukaryotic cells. Here, we engineer the interaction between bacteria and cancer cells to depend on heterologous environmental signals. We have characterized invasin from Yersinia pseudotuburculosis as an output module that enables Escherichia coli to invade cancerderived cells, including HeLa, HepG2, and U2OS lines. To environmentally restrict invasion, we placed this module under the control of heterologous sensors. With the Vibrio fischeri lux quorum sensing circuit, the hypoxiaresponsive fdhF promoter, or the arabinoseinducible araBAD promoter, the bacteria invade cells at densities greater than 10 8 bacteria/ml, after growth in an anaerobic growth chamber or in the presence of 0.02 % arabinose, respectively. In the process, we developed a technique to tune the linkage between a sensor and output gene using ribosome binding site libraries and genetic selection. This approach could be used to engineer bacteria to sense the microenvironment of a tumor and respond by invading cancerous cells and releasing a cytotoxic agent.