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125
Real-time kinetics of gene activity in individual bacteria
- Cell
, 2005
"... Protein levels have been shown to vary substantially between individual cells in clonal populations. In prokaryotes, the contribution to such fluctuations from the inherent randomness of gene expression has largely been attributed to having just a few transcriptsofthecorrespondingmRNAs.Bycontrast, e ..."
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Cited by 111 (0 self)
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Protein levels have been shown to vary substantially between individual cells in clonal populations. In prokaryotes, the contribution to such fluctuations from the inherent randomness of gene expression has largely been attributed to having just a few transcriptsofthecorrespondingmRNAs.Bycontrast, eukaryotic studies tend to emphasize chromatin remodeling and burst-like transcription. Here, we study single-cell transcription in Escherichia coli by measuring mRNA levels in individual living cells. The results directly demonstrate transcriptional bursting, similar to that indirectly inferred for eukaryotes.We also measure mRNA partitioning at cell division and correlate mRNA and protein levels in single cells. Partitioning is approximately binomial, and mRNAprotein correlations are weaker earlier in the cell cycle, where cell division has recently randomized the relative concentrations. Our methods further extend protein-based approaches by counting the integer-valued number of transcript with single-molecule resolution. This greatly facilitates kinetic interpretations in terms of the integer-valued random processes that produce the fluctuations.
A Tunable Genetic Switch Based on RNAi and Repressor Proteins for Regulating Gene Expression in Mammalian Cells
, 2007
"... Here, we introduce an engineered, tunable genetic switch that couples repressor proteins and an RNAi target design to effectively turn any gene off. We used the switch to regulate the expression of EGFP in mouse and human cells and found that it offers>99 % repression as well as the ability to tu ..."
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Cited by 35 (1 self)
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Here, we introduce an engineered, tunable genetic switch that couples repressor proteins and an RNAi target design to effectively turn any gene off. We used the switch to regulate the expression of EGFP in mouse and human cells and found that it offers>99 % repression as well as the ability to tune gene expression. To demonstrate the system’s modularity and level of gene silencing, we used the switch to tightly regulate the expression of diphtheria toxin and Cre recombinase, respectively. We also used the switch to tune the expression of a proapoptotic gene and show that a threshold expression level is required to induce apoptosis. This work establishes a system for tight, tunable control of mammalian gene expression that can be used to explore the functional role of various genes as well as to determine whether a phenotype is the result of a threshold response to changes in gene expression.
Incorporating diffusion in complex geometries into stochastic chemical kinetics simulations
- SIAM Journal on Scientific Computing
"... Abstract. A method is developed for incorporating diffusion of chemicals in complex geometries into stochastic chemical kinetics simulations. Systems are modeled using the reaction-diffusion master equation, with jump rates for diffusive motion between mesh cells calculated from the discretization w ..."
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Cited by 30 (3 self)
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Abstract. A method is developed for incorporating diffusion of chemicals in complex geometries into stochastic chemical kinetics simulations. Systems are modeled using the reaction-diffusion master equation, with jump rates for diffusive motion between mesh cells calculated from the discretization weights of an embedded boundary method. Since diffusive jumps between cells are treated as first order reactions, individual realizations of the stochastic process can be created by the Gillespie method. Numerical convergence results for the underlying embedded boundary method, and for the stochastic reaction-diffusion method, are presented in two dimensions. A two-dimensional model of transcription, translation, and nuclear membrane transport in eukaryotic cells is presented to demonstrate the feasibility of the method in studying cell-wide biological processes.
Studying genetic regulatory networks at the molecular level: delayed reaction stochastic models
, 2007
"... Abstract Current advances in molecular biology enable us to access the rapidly increasing body of genetic information. It is still challenging to model gene systems at the molecular level. Here, we propose two types of reaction kinetic models for constructing genetic networks. Time delays involved ..."
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Cited by 26 (5 self)
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Abstract Current advances in molecular biology enable us to access the rapidly increasing body of genetic information. It is still challenging to model gene systems at the molecular level. Here, we propose two types of reaction kinetic models for constructing genetic networks. Time delays involved in transcription and translation are explicitly considered to explore the effects of delays, which may be significant in genetic networks featured with feedback loops. One type of model is based on delayed effective reactions, each reaction modeling a biochemical process like transcription without involving intermediate reactions. The other is based on delayed virtual reactions, each reaction being converted from a mathematical function to model a biochemical function like gene inhibition. The latter stochastic models are derived from the corresponding mean-field models. The former ones are composed of single gene expression modules. We thus design a model of gene expression. This model is verified by our simulations using a delayed stochastic simulation algorithm, which accurately reproduces the stochastic kinetics in a recent experimental study. Various simplified versions of the model are given and evaluated. We then use the two methods to study the genetic toggle switch and the repressilator. We define the ''on'' and ''off'' states of genes and extract a binary code from the stochastic time series. The binary code can be described by the corresponding Boolean network models in certain conditions. We discuss these conditions, suggesting a method to connect Boolean models, mean-field models, and stochastic chemical models. r
The reaction-diffusion master equation as an asymptotic approximation of diffusion to a small target
- SIAM Journal on Applied Mathematics
"... Abstract. The reaction-diffusion master equation (RDME) has recently been used as a model for biological systems in which both noise in the chemical reaction process and diffusion in space of the reacting molecules is important. In the RDME space is partitioned by a mesh into a collection of voxels. ..."
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Cited by 19 (1 self)
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Abstract. The reaction-diffusion master equation (RDME) has recently been used as a model for biological systems in which both noise in the chemical reaction process and diffusion in space of the reacting molecules is important. In the RDME space is partitioned by a mesh into a collection of voxels. There is an unanswered question as to how solutions depend on the mesh spacing. To have confidence in using the RDME to draw conclusions about biological systems, we would like to know that it approximates a reasonable physical model for appropriately chosen mesh spacings. This issue is investigated by studying the dependence on mesh spacing of solutions to the RDME in R3 for the bimolecular reaction A + B → ∅, with one molecule of species A and one molecule of species B present initially. We prove that in the continuum limit the molecules never react and simply diffuse relative to each other. Nevertheless, we show that the RDME with non-zero lattice spacing yields an asymptotic approximation to a specific spatially-continuous diffusion limited reaction (SCDLR) model. We demonstrate that for realistic biological parameters it is possible to find mesh spacings such that the relative error between asymptotic approximations to the solutions of the RDME and the SCDLR models is less than one percent. 1. Introduction. Noise
Cellular growth and division in the gillespie algorithm
- In Systems Biology, IEE Proceedings
, 2004
"... Abstract: Recent experimental studies elucidating the importance of noise in gene regulation have ignited widespread interest in Gillespie's stochastic simulation technique for biochemical networks. We formulate modifications to the Gillespie algorithm which are necessary to correctly simulate ..."
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Cited by 15 (1 self)
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Abstract: Recent experimental studies elucidating the importance of noise in gene regulation have ignited widespread interest in Gillespie's stochastic simulation technique for biochemical networks. We formulate modifications to the Gillespie algorithm which are necessary to correctly simulate chemical reactions with time-dependent reaction rates. We concentrate on time dependence of kinetic rates arising from the periodic process of growth and division of the cellular volume, and demonstrate that a careful re-derivation of the Gillespie algorithm is important when all stochastically simulated reactions have rates slower or comparable to the cellular growth rate. For an unregulated single-gene system, we illustrate our findings using recently proposed hybrid simulation techniques, and systematically compare our algorithm with analytic results obtained from the chemical master equation.
Gene expression profiling of single cells on largescale oligonucleotide arrays
- Nucleic Acids Res
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Crossing the Mesoscale No-Man’s Land via Parallel Kinetic Monte Carlo
, 2009
"... The kinetic Monte Carlo method and its variants are powerful tools for modeling materials at the mesoscale, meaning at length and time scales in between the atomic and continuum. We have completed a 3 year LDRD project with the goal of developing a parallel kinetic Monte Carlo capability and applyin ..."
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Cited by 11 (0 self)
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The kinetic Monte Carlo method and its variants are powerful tools for modeling materials at the mesoscale, meaning at length and time scales in between the atomic and continuum. We have completed a 3 year LDRD project with the goal of developing a parallel kinetic Monte Carlo capability and applying it to materials modeling problems of interest to Sandia. In this report we give an overview of the methods and algorithms developed, and describe our new open-source code called SPPARKS, for Stochastic Parallel PARticle Kinetic Simulator. We also highlight the development of several Monte Carlo models in SPPARKS for specific materials modeling applications, including grain growth, bubble formation, diffusion in nanoporous materials, defect formation in erbium hydrides, and surface growth
Chemical Master Equation and Langevin regimes for a gene transcription model
- in Computational Mathematics and Systems Biology
, 2007
"... Gene transcription models must take account of intrinsic stochasticity. The Chemical Master Equation framework is based on modelling assumptions that are highly appropriate for this context, and the Stochastic Simulation Algorithm (also known as Gillespie’s algorithm) allows for practical simulation ..."
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Cited by 11 (2 self)
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Gene transcription models must take account of intrinsic stochasticity. The Chemical Master Equation framework is based on modelling assumptions that are highly appropriate for this context, and the Stochastic Simulation Algorithm (also known as Gillespie’s algorithm) allows for practical simulations to be performed. However, for large networks and/or fast reactions, such computations can be prohibitatively expensive. The Chemical Langevin regime replaces the massive ordinary differential equation system with a small stochastic differential equation system that is more amenable to computation. Although the transition from Chemical Master Equation to Chemical Langevin Equation can be justified rigorously in the large system size limit, there is very little guidance available about how closely the two models match for a fixed system. Here, we consider a transcription model from the recent literature and show that it is possible to compare first and second moments in the two stochastic settings. To analyse the Chemical Master Equation we use some recent work of Gadgil, Lee and Othmer, and to analyse the Chemical Langevin Equation we use Ito’s Lemma. We find that there is a perfect match—both modelling regimes give the same means, variances and correlations for all components in the system. The model that we analyse involves ‘unimolecular reactions’, and we finish with some numerical simulations involving dimerization to show that the means and variances in the two regimes can also be close when more general ‘bimolecular reactions ’ are involved.