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206
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 477 (10 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.
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 143 (23 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.
The topology of the regulatory interactions predicts the expression pattern of the segment polarity genes in Drosophila melanogaster
, 2003
"... Expression of the Drosophila segment polarity genes is initiated by a prepattern of pairrule gene products and maintained by a network of regulatory interactions throughout several stages of embryonic development. Analysis of a model of gene interactions based on differential equations showed tha ..."
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Cited by 118 (11 self)
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Expression of the Drosophila segment polarity genes is initiated by a prepattern of pairrule gene products and maintained by a network of regulatory interactions throughout several stages of embryonic development. Analysis of a model of gene interactions based on differential equations showed that wildtype expression patterns of these genes can be obtained for a wide range of kinetic parameters, which suggests that the steady states are determined by the topology of the network and the type of regulatory interactions between components, not the detailed form of the rate laws. To investigate this, we propose and analyze a Boolean model of this network which is based on a binary ON/OFF representation of transcription and protein levels, and in which the interactions are formulated as logical functions. In this model the spatial and temporal patterns of gene expression are determined by the topology of the network and whether components are present or absent, rather than the absolute levels of the mRNAs and proteins and the functional details of their interactions. The model is able to reproduce the wild type gene expression patterns, as well as the ectopic expression patterns observed in overexpression experiments and various mutants. Furthermore, we compute explicitly all steady states of the network and identify the basin of attraction of each steady state. The model gives important insights into the functioning of the segment polarity gene network, such as the crucial role of the wingless and sloppy paired genes, and the network's ability to correct errors in the prepattern.
Hybrid Modeling and Simulation of Biomolecular Networks
 Hybrid Systems: Computation and Control, LNCS 2034
, 2001
"... In a biological cell, cellular functions and the genetic regulatory apparatus are implemented and controlled by a network of chemical reactions in which regulatory proteins can control genes that produce other regulators, which in turn control other genes. Further, the feedback pathways appear t ..."
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Cited by 83 (7 self)
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In a biological cell, cellular functions and the genetic regulatory apparatus are implemented and controlled by a network of chemical reactions in which regulatory proteins can control genes that produce other regulators, which in turn control other genes. Further, the feedback pathways appear to incorporate switches that result in changes in the dynamic behavior of the cell. This paper describes a hybrid systems approach to modeling the intracellular network using continuous di#erential equations to model the feedback mechanisms and modeswitching to describe the changes in the underlying dynamics. We use two case studies to illustrate a modular approach to modeling such networks and describe the architectural and behavioral hierarchy in the underlying models. We describe these models using Charon [2], a language that allows formal description of hybrid systems. We provide preliminary simulation results that demonstrate how our approach can help biologists in their analysis of noisy genetic circuits. Finally we describe our agenda for future work that includes the development of models and simulation for stochastic hybrid systems.
Duplication models for biological networks
 Journal of Computational Biology
, 2003
"... Are biological networks different from other large complex networks? Both large biological and nonbiological networks exhibit powerlaw graphs (number of nodes with degree k, N.k / � k ¡ ¯), yet the exponents, ¯, fall into different ranges. This may be because duplication of the information in the ..."
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Cited by 68 (4 self)
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Are biological networks different from other large complex networks? Both large biological and nonbiological networks exhibit powerlaw graphs (number of nodes with degree k, N.k / � k ¡ ¯), yet the exponents, ¯, fall into different ranges. This may be because duplication of the information in the genome is a dominant evolutionary force in shaping biological networks (like gene regulatory networks and protein–protein interaction networks) and is fundamentally different from the mechanisms thought to dominate the growth of most nonbiological networks (such as the Internet). The preferential choice models used for nonbiological networks like web graphs can only produce powerlaw graphs with exponents greater than 2. We use combinatorial probabilistic methods to examine the evolution of graphs by node duplication processes and derive exact analytical relationships between the exponent of the power law and the parameters of the model. Both full duplication of nodes (with all their connections) as well as partial duplication (with only some connections) are analyzed. We demonstrate that partial duplication can produce powerlaw graphs with exponents less than 2, consistent with current data on biological networks. The powerlaw exponent for large graphs depends only on the growth process, not on the starting graph.
2004 Integrative analysis of cell cycle control in budding yeast
 Mol. Biol. Cell
, 2007
"... The adaptive responses of a living cell to internal and external signals are controlled by networks of proteins whose interactions are so complex that the functional integration of the network cannot be comprehended by intuitive reasoning alone. Mathematical modeling, based on biochemical rate equat ..."
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Cited by 65 (15 self)
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The adaptive responses of a living cell to internal and external signals are controlled by networks of proteins whose interactions are so complex that the functional integration of the network cannot be comprehended by intuitive reasoning alone. Mathematical modeling, based on biochemical rate equations, provides a rigorous and reliable tool for unraveling the complexities of molecular regulatory networks. The budding yeast cell cycle is a challenging test case for this approach, because the control system is known in exquisite detail and its function is constrained by the phenotypic properties of>100 genetically engineered strains. We show that a mathematical model built on a consensus picture of this control system is largely successful in explaining the phenotypes of mutants described so far. A few inconsistencies between the model and experiments indicate aspects of the mechanism that require revision. In addition, the model allows one to frame and critique hypotheses about how the division cycle is regulated in wildtype and mutant cells, to predict the phenotypes of new mutant combinations, and to estimate the effective values of biochemical rate constants that are difficult to measure directly in vivo.
Perspective: Evolution And Detection Of Genetic Robustness
, 1972
"... Robustness is the invariance of phenotypes in the face of perturbation. The robustness of phenotypes appears at various levels of biological organization, including gene expression, protein folding, metabolic flux, physiological homeostasis, development, and even organismal fitness. The mechanisms u ..."
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Cited by 55 (2 self)
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Robustness is the invariance of phenotypes in the face of perturbation. The robustness of phenotypes appears at various levels of biological organization, including gene expression, protein folding, metabolic flux, physiological homeostasis, development, and even organismal fitness. The mechanisms underlying robustness are diverse, ranging from thermodynamic stability at the RNA and protein level to behavior at the organismal level. Phenotypes can be robust either against heritable perturbations (e.g. mutations) or nonheritable perturbations (e.g. the weather). Here we primarily focus on the first kind of robustness  genetic robustness  and survey three growing avenues of research: (1) measuring genetic robustness in nature and in the laboratory, (2) understanding the evolution of genetic robustness, and (3) exploring the implications of genetic robustness for future evolution.
Robustness and fragility of boolean models for genetic regulatory networks
 J. Theoretical Biology
, 2005
"... Interactions between genes and gene products give rise to complex circuits that enable cells to process information and respond to external signals. Theoretical studies often describe these interactions using continuous, stochastic, or logical approaches. We propose a new modeling framework for gene ..."
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Cited by 53 (10 self)
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Interactions between genes and gene products give rise to complex circuits that enable cells to process information and respond to external signals. Theoretical studies often describe these interactions using continuous, stochastic, or logical approaches. We propose a new modeling framework for gene regulatory networks, that combines the intuitive appeal of a qualitative description of gene states with a high flexibility in incorporating stochasticity in the duration of cellular processes. We apply our methods to the regulatory network of the segment polarity genes, thus gaining novel insights into the development of gene expression patterns. For example, we show that very short synthesis and decay times can perturb the wild type pattern. On the other hand, separation of timescales between pre and posttranslational processes and a minimal prepattern ensure convergence to the wild type expression pattern regardless of fluctuations.
Positive and Negative Feedback: Striking a balance between necessary antagonists
 J. Theor. Biol
, 2002
"... Most biological regulation systems comprise feedback circuits as crucial components. Negative iedback circuits have been well understood for a very long time; indeed, their understanding has been the basis for the engineering of cybernetic machines exhibiting stable behaviour. The importance of posi ..."
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Cited by 41 (6 self)
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Most biological regulation systems comprise feedback circuits as crucial components. Negative iedback circuits have been well understood for a very long time; indeed, their understanding has been the basis for the engineering of cybernetic machines exhibiting stable behaviour. The importance of positive feedback circuits, considered as "vicious circles", has however been underestimated. In this article we give a demonstration based on degree theory for vector fields of the conjecture, made by R.ex Thomas, that the presence of positive feedback circuits is a necessary condition fox' autonomous differential systems, covering a wide class of biologically relevant systems, to possess multiple steady states. We also show ways to derive constraints on the weights of positive and negative feedback circuits. These qualitative and quantitative restilts provide respectively structural constraints (i.e. related to the interaction graph) and numerical constraints (i.e. related to the magnitudes of the interactions) on systems exhibiting complex be haviours, and should make. it easier to reverseengineer the interaction networks animating those systems on the basis of partial, sometimes unreliable, experimental data. X illustrate these concepts on a model multistable switch, in the context of cellular differentiation, showing a requirement ibr sufficient cooperativity. Furtler developments are expected i' tle discovery and modellbg of regulatory networks iu gemral, and in the interpretation of bioarray hybridisation and proteomics experiments in particular.
A gene regulatory network model for cellfate determination during Arabidopsis thaliana flower development that is robust and recovers experimental gene expression profiles
 Plant Cell
, 2004
"... several weeks. ..."