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A fast, robust and tunable synthetic gene oscillator
, 2008
"... One defining goal of synthetic biology is the development of engineeringbased approaches that enable the construction of generegulatory networks according to ‘design specifications’ generated from computational modelling 1–6. This approach provides a systematic framework for exploring how a given ..."
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Cited by 86 (3 self)
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One defining goal of synthetic biology is the development of engineeringbased approaches that enable the construction of generegulatory networks according to ‘design specifications’ generated from computational modelling 1–6. This approach provides a systematic framework for exploring how a given regulatory network generates a particular phenotypic behaviour. Several fundamental gene circuits have been developed using this approach, including toggle switches 7 and oscillators 8–10, and these have been applied in new contexts such as triggered biofilm development 11 and cellular population control 12. Here we describe an engineered genetic oscillator in Escherichia coli that is fast, robust and persistent, with tunable oscillatory periods as fast as 13 min. The oscillator was designed using a previously modelled network architecture comprising linked positive and negative feedback loops 1,13. Using a microfluidic platform tailored for singlecell
CONTINUOUS TIME MARKOV CHAIN MODELS FOR CHEMICAL REACTION NETWORKS
"... A reaction network is a chemical system involving multiple reactions and chemical species. The simplest stochastic models of such networks treat the system as a continuous time Markov chain with the state being the number of molecules of each species and with reactions modeled as possible transition ..."
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Cited by 45 (13 self)
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A reaction network is a chemical system involving multiple reactions and chemical species. The simplest stochastic models of such networks treat the system as a continuous time Markov chain with the state being the number of molecules of each species and with reactions modeled as possible transitions of the chain. This chapter is devoted to the mathematical study of such stochastic models. We begin by developing much of the mathematical machinery we need to describe the stochastic models we are most interested in. We show how one can represent counting processes of the type we need in terms of Poisson processes. This random timechange representation gives a stochastic equation for continuoustime Markov chain models. We include a discussion on the relationship between this stochastic equation and the corresponding martingale problem and Kolmogorov forward (master) equation. Next, we exploit
Modeling and simulating chemical reactions
 SIAM Review
, 2007
"... Many students are familiar with the idea of modeling chemical reactions in terms of ordinary differential equations. However, these deterministic reaction rate equations are really a certain largescale limit of a sequence of finerscale probabilistic models. In studying this hierarchy of models, st ..."
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Cited by 34 (1 self)
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Many students are familiar with the idea of modeling chemical reactions in terms of ordinary differential equations. However, these deterministic reaction rate equations are really a certain largescale limit of a sequence of finerscale probabilistic models. In studying this hierarchy of models, students can be exposed to a range of modern ideas in applied and computational mathematics. This article introduces some of the basic concepts in an accessible manner, and points to some challenges that currently occupy researchers in this area. Short, downloadable MATLAB codes are listed and described. 1
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 meanfield 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, meanfield models, and stochastic chemical models. r
Fluctuating Asymmetry: Methods, Theory, and Applications
 SYMMETRY
, 2010
"... Fluctuating asymmetry consists of random deviations from perfect symmetry in populations of organisms. It is a measure of developmental noise, which reflects a population’s average state of adaptation and coadaptation. Moreover, it increases under both environmental and genetic stress, though resp ..."
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Cited by 11 (1 self)
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Fluctuating asymmetry consists of random deviations from perfect symmetry in populations of organisms. It is a measure of developmental noise, which reflects a population’s average state of adaptation and coadaptation. Moreover, it increases under both environmental and genetic stress, though responses are often inconsistent. Researchers base studies of fluctuating asymmetry upon deviations from bilateral, radial, rotational, dihedral, translational, helical, and fractal symmetries. Here, we review old and new methods of measuring fluctuating asymmetry, including measures of dispersion, landmark methods for shape asymmetry, and continuous symmetry measures. We also review the theory, developmental origins, and applications of fluctuating asymmetry, and attempt to explain conflicting results. In the process, we present examples from the literature, and from our own research at “Evolution Canyon” and elsewhere.
Evolving Noisy Oscillatory Dynamics in Genetic Regulatory Networks
 IN: PROC. 9TH EUROPEAN CONFERENCE ON GENETIC PROGRAMMING. SPRINGER LNCS 3905
, 2006
"... We introduce a genetic programming (GP) approach for evolving genetic networks that demonstrate desired dynamics when simulated as a discrete stochastic process. Our representation of genetic networks is based on a biochemical reaction model including key elements such as transcription, translation ..."
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Cited by 11 (0 self)
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We introduce a genetic programming (GP) approach for evolving genetic networks that demonstrate desired dynamics when simulated as a discrete stochastic process. Our representation of genetic networks is based on a biochemical reaction model including key elements such as transcription, translation and posttranslational modifications. The stochastic, reactionbased GP system is similar but not identical with algorithmic chemistries. We evolved genetic networks with noisy oscillatory dynamics. The results show the practicality of evolving particular dynamics in gene regulatory networks when modelled with intrinsic noise.
Perfect sampling of the master equation for gene regulatory networks
 Biophysical journal
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On Existence and Uniqueness of Stationary Distributions for Stochastic Delay Differential Equations with NonNegativity Constraints
, 2009
"... Deterministic dynamic models with delayed feedback and state constraints arise in a variety of applications in science and engineering. There is interest in understanding what effect noise has on the behavior of such models. Here we consider a multidimensional stochastic delay differential equation ..."
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Cited by 6 (0 self)
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Deterministic dynamic models with delayed feedback and state constraints arise in a variety of applications in science and engineering. There is interest in understanding what effect noise has on the behavior of such models. Here we consider a multidimensional stochastic delay differential equation with normal reflection as a noisy analogue of a deterministic system with delayed feedback and nonnegativity constraints. We obtain sufficient conditions for existence and uniqueness of stationary distributions for such equations. The results are applied to an example from Internet rate control and a simple biochemical reaction system.
A generic abstract machine for stochastic process calculi
, 2010
"... This paper presents a generic abstract machine for simulating a broad range of process calculi with an arbitrary reactionbased simulation algorithm. The abstract machine is instantiated to a particular calculus by defining two functions: one for transforming a process of the calculus to a set of sp ..."
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Cited by 6 (1 self)
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This paper presents a generic abstract machine for simulating a broad range of process calculi with an arbitrary reactionbased simulation algorithm. The abstract machine is instantiated to a particular calculus by defining two functions: one for transforming a process of the calculus to a set of species, and another for computing the set of possible reactions between species. Unlike existing simulation algorithms for chemical reactions, the abstract machine can simulate process calculi that generate potentially unbounded numbers of species and reactions. This is achieved by means of a justintime compiler, which dynamically updates the set of possible reactions and chooses the next reaction machine is instantiated for the stochastic picalculus, and the instantiation is implemented as part of the SPiM stochastic simulator. The structure of the abstract machine facilitates a significant optimisation by allowing channel restrictions to be stored as species complexes. We also present a novel algorithm for simulating chemical reactions with general distributions, based on the Next Reaction Method of Gibson and Bruck. We use our generic framework to simulate a stochastic picalculus model of plasmid cotransfection, where plasmids can form aggregates of arbitrary size and where rates of mRNA degradation are nonexponential. The example illustrates the flexibility of our framework, which allows an appropriate highlevel language to be paired with the required simulation algorithm, based on the biological system under consideration.
Stochastic kinetic modeling of vesicular stomatitis virus intracellular growth
 Electron. J. Probab
, 2009
"... Viruses cause diseases such as influenza, AIDS and SARS, and thereby create a major and ever expanding global threat to human health. A better fundamental understanding of how viruses reproduce may enable the development of more effective antiviral therapies. To reproduce, a virus must infect and u ..."
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Cited by 4 (1 self)
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Viruses cause diseases such as influenza, AIDS and SARS, and thereby create a major and ever expanding global threat to human health. A better fundamental understanding of how viruses reproduce may enable the development of more effective antiviral therapies. To reproduce, a virus must infect and utilize biosynthetic resources from a living host cell. As a model we study vesicular stomatitis virus (VSV), a relatively small virus whose processes of gene expression and genome replication are among the best characterized of all viruses. When cells are infected with a recombinant VSV that expresses green fluorescent protein (GFP), different cells infected by single virus particles produce different levels of GFP and different levels of virus, a finding that cannot be explained by an existing deterministic ODE kinetic model of VSV growth. We hypothesize that such distributions in growth behavior arise in part from fluctuations in the small levels of virus components present when a cell is initially infected. These components are then rapidly amplified by autocatalytic feedbacks in the reaction network that defines virus growth. A modeling approach that accounts for the stochastic firing of each reaction event would be appropriate, but stochastic approaches become computationally intractable as the number of species rapidly grows. We address