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Hybrid method for the chemical master equation
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis. (ndim)
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis. (ndim)
2007 (English)In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 227, 100-122 p.Article in journal (Refereed) Published
Place, publisher, year, edition, pages
2007. Vol. 227, 100-122 p.
National Category
Computational Mathematics Biochemistry and Molecular Biology
Identifiers
URN: urn:nbn:se:uu:diva-26755DOI: 10.1016/j.jcp.2007.07.020ISI: 000251140100006OAI: oai:DiVA.org:uu-26755DiVA: diva2:54649
Available from: 2007-10-26 Created: 2007-10-26 Last updated: 2017-12-07Bibliographically approved
In thesis
1. Numerical simulation of well stirred biochemical reaction networks governed by the master equation
Open this publication in new window or tab >>Numerical simulation of well stirred biochemical reaction networks governed by the master equation
2008 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

Numerical simulation of stochastic biochemical reaction networks has received much attention in the growing field of computational systems biology. Systems are frequently modeled as a continuous-time discrete space Markov chain, and the governing equation for the probability density of the system is the (chemical) master equation. The direct numerical solution of this equation suffers from an exponential growth in computational time and memory with the number of reacting species in the model. As a consequence, Monte Carlo simulation methods play an important role in the study of stochastic chemical networks. The stochastic simulation algorithm (SSA) due to Gillespie has been available for more than three decades, but due to the multi-scale property of the chemical systems and the slow convergence of Monte Carlo methods, much work is currently being done in order to devise more efficient approximate schemes.

In this thesis we review recent work for the solution of the chemical master equation by direct methods, by exact Monte Carlo methods and by approximate and hybrid methods. We also describe two conceptually different numerical methods to reduce the computational time when studying models using the SSA. A hybrid method is proposed, which is based on the separation of species into two subsets based on the variance of the copy numbers. This method yields a significant speed-up when the system permits such a splitting of the state space. A different approach is taken in an algorithm that makes use of low-discrepancy sequences and the method of uniformization to reduce variance in the computed density function.

Place, publisher, year, edition, pages
Uppsala University, 2008
Series
Information technology licentiate theses: Licentiate theses from the Department of Information Technology, ISSN 1404-5117 ; 2008-003
National Category
Computational Mathematics Biochemistry and Molecular Biology
Research subject
Scientific Computing
Identifiers
urn:nbn:se:uu:diva-85856 (URN)
Supervisors
Available from: 2008-10-15 Created: 2008-09-02 Last updated: 2017-08-31Bibliographically approved
2. Multiscale Stochastic Simulation of Reaction-Transport Processes: Applications in Molecular Systems Biology
Open this publication in new window or tab >>Multiscale Stochastic Simulation of Reaction-Transport Processes: Applications in Molecular Systems Biology
2011 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Quantitative descriptions of reaction kinetics formulated at the stochastic mesoscopic level are frequently used to study various aspects of regulation and control in models of cellular control systems. For this type of systems, numerical simulation offers a variety of challenges caused by the high dimensionality of the problem and the multiscale properties often displayed by the biochemical model.

In this thesis I have studied several aspects of stochastic simulation of both well-stirred and spatially heterogenous systems. In the well-stirred case, a hybrid method is proposed that reduces the dimension and stiffness of a model. We also demonstrate how both a high performance implementation and a variance reduction technique based on quasi-Monte Carlo can reduce the computational cost to estimate the probability density of the system.

In the spatially dependent case, the use of unstructured, tetrahedral meshes to sample realizations of the stochastic process is proposed. Using such meshes, we then extend the reaction-diffusion framework to incorporate active transport of cellular cargo in a seamless manner. Finally, two multilevel methods for spatial stochastic simulation are considered. One of them is a space-time adaptive method combining exact stochastic, approximate stochastic and macroscopic modeling levels to reduce the simualation cost. The other method blends together mesoscale and microscale simulation methods to locally increase modeling resolution.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2011. 63 p.
Series
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 832
Keyword
stochastic simulation, chemical master equation, reaction-diffusion master equation, unstructured mesh, active transport, hybrid methods, URDME
National Category
Computational Mathematics
Research subject
Scientific Computing
Identifiers
urn:nbn:se:uu:diva-152098 (URN)978-91-554-8089-9 (ISBN)
Public defence
2011-06-10, Room 2446, Polacksbacken, Lägerhyddsvägen 2D, Uppsala, 10:15 (English)
Opponent
Supervisors
Projects
eSSENCE
Available from: 2011-05-19 Created: 2011-04-23 Last updated: 2012-01-26Bibliographically approved

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Hellander, AndreasLötstedt, Per

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