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32
Efficient, correct simulation of biological processes in the stochastic picalculus
 Gilmore (Eds.), Proc. Int. Conf. Computational Methods in Systems Biology (CMSB’07
, 2007
"... Abstract. This paper presents a simulation algorithm for the stochastic πcalculus, designed for the efficient simulation of biological systems with large numbers of molecules. The cost of a simulation depends on the number of species, rather than the number of molecules, resulting in a significant ..."
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Cited by 42 (13 self)
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Abstract. This paper presents a simulation algorithm for the stochastic πcalculus, designed for the efficient simulation of biological systems with large numbers of molecules. The cost of a simulation depends on the number of species, rather than the number of molecules, resulting in a significant gain in efficiency. The algorithm is proved correct with respect to the calculus, and then used as a basis for implementing the latest version of the SPiM stochastic simulator. The algorithm is also suitable for generating graphical animations of simulations, in order to visualise system dynamics. 1
Analysis of explicit tauleaping schemes for simulating chemically reacting systems
 Multiscale Model. Simul
"... Abstract. This paper builds a convergence analysis of explicit tauleaping schemes for simulating chemical reactions from the viewpoint of stochastic differential equations. Mathematically, the chemical reaction process is a pure jump process on a lattice with statedependent intensity. The stochast ..."
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Cited by 17 (4 self)
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Abstract. This paper builds a convergence analysis of explicit tauleaping schemes for simulating chemical reactions from the viewpoint of stochastic differential equations. Mathematically, the chemical reaction process is a pure jump process on a lattice with statedependent intensity. The stochastic differential equation form of the chemical master equation can be given via Poisson random measures. Based on this form, different types of tauleaping schemes can be proposed. In order to make the problem wellposed, a modified explicit tauleaping scheme is considered. It is shown that the mean square strong convergence is of order 1/2 and the weak convergence is of order 1 for this modified scheme. The novelty of the analysis is to handle the nonLipschitz property of the coefficients and jumps on the integer lattice.
Time series analysis via mechanistic models. In review; prepublished at arxiv.org/abs/0802.0021
, 2008
"... The purpose of time series analysis via mechanistic models is to reconcile the known or hypothesized structure of a dynamical system with observations collected over time. We develop a framework for constructing nonlinear mechanistic models and carrying out inference. Our framework permits the consi ..."
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Cited by 13 (5 self)
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The purpose of time series analysis via mechanistic models is to reconcile the known or hypothesized structure of a dynamical system with observations collected over time. We develop a framework for constructing nonlinear mechanistic models and carrying out inference. Our framework permits the consideration of implicit dynamic models, meaning statistical models for stochastic dynamical systems which are specified by a simulation algorithm to generate sample paths. Inference procedures that operate on implicit models are said to have the plugandplay property. Our work builds on recently developed plugandplay inference methodology for partially observed Markov models. We introduce a class of implicitly specified Markov chains with stochastic transition rates, and we demonstrate its applicability to open problems in statistical inference for biological systems. As one example, these models are shown to give a fresh perspective on measles transmission dynamics. As a second example, we present a mechanistic analysis of cholera incidence data, involving interaction between two competing strains of the pathogen Vibrio cholerae. 1. Introduction. A
The adaptive explicitimplicit tauleaping method with automatic tau selection
 J. Chem. Phys
, 2007
"... The existing tauselection strategy, which was designed for explicit tauleaping, is here modified to apply to implicit tauleaping, allowing for longer steps when the system is stiff. Further, an adaptive strategy is proposed that identifies stiffness and automatically chooses between the explicit ..."
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Cited by 12 (2 self)
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The existing tauselection strategy, which was designed for explicit tauleaping, is here modified to apply to implicit tauleaping, allowing for longer steps when the system is stiff. Further, an adaptive strategy is proposed that identifies stiffness and automatically chooses between the explicit and the (new) implicit tauselection methods to achieve better efficiency. Numerical testing demonstrates the advantages of the adaptive method for stiff systems. ∗ Author to whom correspondence should be addressed.
MULTILEVEL MONTE CARLO FOR CONTINUOUS TIME MARKOV CHAINS, WITH APPLICATIONS IN BIOCHEMICAL KINETICS
, 2012
"... We show how to extend a recently proposed multilevel Monte Carlo approach to the continuous time Markov chain setting, thereby greatly lowering the computational complexity needed to compute expected values of functions of the state of the system to a specified accuracy. The extension is nontrivia ..."
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Cited by 11 (10 self)
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We show how to extend a recently proposed multilevel Monte Carlo approach to the continuous time Markov chain setting, thereby greatly lowering the computational complexity needed to compute expected values of functions of the state of the system to a specified accuracy. The extension is nontrivial, exploiting a coupling of the requisite processes that is easy to simulate while providing a small variance for the estimator. Further, and in a stark departure from other implementations of multilevel Monte Carlo, we show how to produce an unbiased estimator that is significantly less computationally expensive than the usual unbiased estimator arising from exact algorithms in conjunction with crude Monte Carlo. We thereby dramatically improve, in a quantifiable manner, the basic computational complexity of current approaches that have many names and variants across the scientific literature, including the Bortz–Kalos–Lebowitz algorithm, discrete event simulation, dynamic Monte Carlo, kinetic Monte Carlo, the nfold way, the next reaction method, the residencetime algorithm, the stochastic simulation algorithm, Gillespie’s algorithm, and tauleaping. The new algorithm applies generically, but we also give an example where the coupling idea alone, even without a multilevel discretization, can be used to improve efficiency by exploiting system structure. Stochastically modeled chemical reaction networks provide a very important application for this work. Hence, we use this context for our notation, terminology, natural scalings, and computational examples.
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 6 (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.
Slow scale tauleaping method
"... For chemical systems involving both fast and slow scales, stiffness presents challenges for efficient stochastic simulation. Two different avenues have been explored to solve this problem. One is the slowscale stochastic simulation (ssSSA) based on the stochastic partial equilibrium assumption. The ..."
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Cited by 6 (1 self)
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For chemical systems involving both fast and slow scales, stiffness presents challenges for efficient stochastic simulation. Two different avenues have been explored to solve this problem. One is the slowscale stochastic simulation (ssSSA) based on the stochastic partial equilibrium assumption. The other is the tauleaping method. In this paper we propose a new algorithm, the slowscale tauleaping method, which combines some of the best features of these two methods. Numerical experiments are presented which illustrate the effectiveness of this approach. 1
P.: An adaptive algorithm for simulation of stochastic reactiondiffusion processes
 J. Comput. Phys
, 2010
"... We propose an adaptive hybrid method suitable for stochastic simulation of diffusion dominated reactiondiffusion processes. For such systems, simulation of the diffusion requires the predominant part of the computing time. In order to reduce the computational work, the diffusion in parts of the dom ..."
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Cited by 4 (1 self)
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We propose an adaptive hybrid method suitable for stochastic simulation of diffusion dominated reactiondiffusion processes. For such systems, simulation of the diffusion requires the predominant part of the computing time. In order to reduce the computational work, the diffusion in parts of the domain is treated macroscopically, in other parts with the tauleap method and in the remaining parts with Gillespie’s stochastic simulation algorithm (SSA) as implemented in the next subvolume method (NSM). The chemical reactions are handled by SSA everywhere in the computational domain. A trajectory of the process is advanced in time by an operator splitting technique and the time steps are chosen adaptively. The spatial adaptation is based on estimates of the errors in the tauleap method and the macroscopic diffusion. The accuracy and efficiency of the method are demonstrated in examples from molecular biology where the domain is discretized by unstructured meshes.
Numerical simulation of well stirred biochemical reaction networks governed by the master equation
, 2008
"... ..."
Open Access
"... Refining transcriptional regulatory networks using network evolutionary models and gene histories ..."
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Cited by 2 (0 self)
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Refining transcriptional regulatory networks using network evolutionary models and gene histories