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215
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 415 (9 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.
Probabilistic Boolean networks: a rulebased uncertainty model for gene regulatory networks
, 2002
"... Motivation: Our goal is to construct a model for genetic regulatory networks such that the model class: (i ) incorporates rulebased dependencies between genes; (ii ) allows the systematic study of global network dynamics; (iii ) is able to cope with uncertainty, both in the data and the model selec ..."
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Cited by 233 (44 self)
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Motivation: Our goal is to construct a model for genetic regulatory networks such that the model class: (i ) incorporates rulebased dependencies between genes; (ii ) allows the systematic study of global network dynamics; (iii ) is able to cope with uncertainty, both in the data and the model selection; and (iv ) permits the quantification of the relative influence and sensitivity of genes in their interactions with other genes.
Genetic Network Inference: From CoExpression Clustering To Reverse Engineering
, 2000
"... motivation: Advances in molecular biological, analytical and computational technologies are enabling us to systematically investigate the complex molecular processes underlying biological systems. In particular, using highthroughput gene expression assays, we are able to measure the output of the ge ..."
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Cited by 210 (0 self)
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motivation: Advances in molecular biological, analytical and computational technologies are enabling us to systematically investigate the complex molecular processes underlying biological systems. In particular, using highthroughput gene expression assays, we are able to measure the output of the gene regulatory network. We aim here to review datamining and modeling approaches for conceptualizing and unraveling the functional relationships implicit in these datasets. Clustering of coexpression profiles allows us to infer shared regulatory inputs and functional pathways. We discuss various aspects of clustering, ranging from distance measures to clustering algorithms and multiplecluster memberships. More advanced analysis aims to infer causal connections between genes directly, i.e. who is regulating whom and how. We discuss several approaches to the problem of reverse engineering of genetic networks, from discrete Boolean networks, to continuous linear and nonlinear models. We conclude that the combination of predictive modeling with systematic experimental verification will be required to gain a deeper insight into living organisms, therapeutic targeting and bioengineering.
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 67 (1 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.
Biopathways Representation and Simulation on Hybrid Functional Petri Net
 SOFTWARE TOOLS FOR TECHNOLOGY TRANSFER
"... The following two matters should be resolved for biosimulation tools in order to be accepted by users in biology/medicine; (1) Remove issues which are irrelevant to biological importance, and (2) Allow users to represent biopathways intuitively and understand/manage easily the details of representa ..."
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Cited by 39 (5 self)
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The following two matters should be resolved for biosimulation tools in order to be accepted by users in biology/medicine; (1) Remove issues which are irrelevant to biological importance, and (2) Allow users to represent biopathways intuitively and understand/manage easily the details of representation and simulation mechanism. From these criteria, we firstly define a novel notion of Petri net called hybrid functional Petri net (HFPN). Then, we introduce a software tool, Genomic Object Net, for representing and simulating biopathways, which we have developed by employing the architecture of HFPN. In order to show the effectiveness of Genomic Object Net for representing and simulating biopathways, we show some typical biopathway modelings related to gene regulation (switching mechanism of λ phage, circadian rhythm of Drosophila, lacoperon regulatory mechanism of E. coli), metabolic pathway (glycolitic pathway), and signal transduction (Fas ligand induced apoptosis)), which cover the basic aspects in biopathways. The software is available to academic users from
Feedback Regulation in the Lactose Operon: A Mathematical Modeling Study and Comparison with Experimental Data
 Biophys. J
, 2003
"... ABSTRACT A mathematical model for the regulation of induction in the lac operon in Escherichia coli is presented. This model takes into account the dynamics of the permease facilitating the internalization of external lactose; internal lactose; bgalactosidase, which is involved in the conversion of ..."
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Cited by 34 (0 self)
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ABSTRACT A mathematical model for the regulation of induction in the lac operon in Escherichia coli is presented. This model takes into account the dynamics of the permease facilitating the internalization of external lactose; internal lactose; bgalactosidase, which is involved in the conversion of lactose to allolactose, glucose and galactose; the allolactose interactions with the lac repressor; and mRNA. The final model consists of five nonlinear differential delay equations with delays due to the transcription and translation process. We have paid particular attention to the estimation of the parameters in the model. We have tested our model against two sets of bgalactosidase activity versus time data, as well as a set of data on bgalactosidase activity during periodic phosphate feeding. In all three cases we find excellent agreement between the data and the model predictions. Analytical and numerical studies also indicate that for physiologically realistic values of the external lactose and the bacterial growth rate, a regime exists where there may be bistable steadystate behavior, and that this corresponds to a cusp bifurcation in the model dynamics.
Bayesian inference for nonlinear multivariate diffusion models observed with error
 Computational Statistics and Data Analysis
, 2008
"... Diffusion processes governed by stochastic differential equations (SDEs) are a well established tool for modelling continuous time data from a wide range of areas. Consequently, techniques have been developed to estimate diffusion parameters from partial and discrete observations. Likelihood based i ..."
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Cited by 32 (7 self)
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Diffusion processes governed by stochastic differential equations (SDEs) are a well established tool for modelling continuous time data from a wide range of areas. Consequently, techniques have been developed to estimate diffusion parameters from partial and discrete observations. Likelihood based inference can be problematic as closed form transition densities are rarely available. One widely used solution involves the introduction of latent data points between every pair of observations to allow an EulerMaruyama approximation of the true transition densities to become accurate. In recent literature, Markov chain Monte Carlo (MCMC) methods have been used to sample the posterior distribution of latent data and model parameters; however, naive schemes suffer from a mixing problem that worsens with the degree of augmentation. In this paper, we explore an MCMC scheme whose performance is not adversely affected by the number of latent values. We illustrate the methodology by estimating parameters governing an autoregulatory gene network, using partial and discrete data that is subject to measurement error.
Stochastic models for chemically reacting systems using polynomial stochastic hybrid systems
 Int. J. Robust Nonlinear Control
, 2005
"... Abstract. A stochastic model for chemical reactions is presented, which represents the population of various species involved in a chemical reaction as the continuous state of a polynomial Stochastic Hybrid System (pSHS). pSHSs correspond to stochastic hybrid systems with polynomial continuous vecto ..."
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Cited by 31 (16 self)
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Abstract. A stochastic model for chemical reactions is presented, which represents the population of various species involved in a chemical reaction as the continuous state of a polynomial Stochastic Hybrid System (pSHS). pSHSs correspond to stochastic hybrid systems with polynomial continuous vector fields, reset maps, and transition intensities. We show that for pSHSs, the dynamics of the statistical moments of its continuous states, evolves according to infinitedimensional linear ordinary differential equations (ODEs), which can be approximated by finitedimensional nonlinear ODEs with arbitrary precision. Based on this result, a procedure to build this types of approximation is provided. This procedure is used to construct approximate stochastic models for a variety of chemical reactions that have appeared in literature. These reactions include a simple bimolecular reaction, for which one can solve the master equation; a decayingdimerizing reaction set which exhibits two distinct time scales; a reaction for which the chemical rate equations have a continuum of equilibrium points; and the bistable Schögl reaction. The accuracy of the approximate models is investigated by comparing with Monte Carlo simulations or the solution to the Master equation, when available. 1
F: Designer gene networks: Towards fundamental cellular control. Chaos: An Interdisciplinary
 Journal of Nonlinear Science
"... Submitted to ChaosABSTRACT The engineered control of cellular function through the design of synthetic genetic networks is becoming plausible. Here we show how a naturally occurring network can be used as a parts list for artificial network design, and how model formulation leads to computational an ..."
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Cited by 29 (2 self)
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Submitted to ChaosABSTRACT The engineered control of cellular function through the design of synthetic genetic networks is becoming plausible. Here we show how a naturally occurring network can be used as a parts list for artificial network design, and how model formulation leads to computational and analytical approaches relevant to nonlinear dynamics and statistical physics. We first review the relevant work on synthetic gene networks, highlighting the important experimental findings with regard to genetic switches and oscillators. We then present the derivation of a deterministic model describing the temporal evolution of the concentration of protein in a singlegene network. Bistability in the steadystate protein concentration arises naturally as a consequence of autoregulatory feedback, and we focus on the hysteretic properties of the protein concentration as a function of the degradation rate. We then formulate the effect of an external noise source which interacts with the protein degradation rate. We demonstrate the utility of such a formulation by constructing a protein switch, whereby external noise pulses are used to switch the protein concentration between two values. Following the lead of earlier work, we show how the addition of a second network component can be used to construct a relaxation oscillator, whereby the system is driven
Tyagi S: Stochastic mRNA synthesis in mammalian cells
 PLoS Biol
"... Individual cells in genetically homogeneous populations have been found to express different numbers of molecules of specific proteins. We investigated the origins of these variations in mammalian cells by counting individual molecules of mRNA produced from a reporter gene that was stably integrated ..."
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Cited by 28 (2 self)
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Individual cells in genetically homogeneous populations have been found to express different numbers of molecules of specific proteins. We investigated the origins of these variations in mammalian cells by counting individual molecules of mRNA produced from a reporter gene that was stably integrated into the cell’s genome. We found that there are massive variations in the number of mRNA molecules present in each cell. These variations occur because mRNAs are synthesized in short but intense bursts of transcription beginning when the gene transitions from an inactive to an active state and ending when they transition back to the inactive state. We show that these transitions are intrinsically random and not due to global, extrinsic factors such as the levels of transcriptional activators. Moreover, the gene activation causes burstlike expression of all genes within a wider genomic locus. We further found that bursts are also exhibited in the synthesis of natural genes. The bursts of mRNA expression can be buffered at the protein level by slow protein degradation rates. A stochastic model of gene activation and inactivation was developed to explain the statistical properties of the bursts. The model showed that increasing the level of transcription factors increases the average size of the bursts rather than their frequency. These results demonstrate that gene expression in mammalian cells is subject to large, intrinsically random fluctuations and raise questions about how cells are able to function in the face of such noise.