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Multiscale Stochastic Simulation of Reaction-Transport Processes: Applications in Molecular Systems Biology
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.
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 [en]
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: urn:nbn:se:uu:diva-152098ISBN: 978-91-554-8089-9OAI: oai:DiVA.org:uu-152098DiVA: diva2:412484
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
List of papers
1. Hybrid method for the chemical master equation
Open this publication in new window or tab >>Hybrid method for the chemical master equation
2007 (English)In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 227, 100-122 p.Article in journal (Refereed) Published
National Category
Computational Mathematics Biochemistry and Molecular Biology
Identifiers
urn:nbn:se:uu:diva-26755 (URN)10.1016/j.jcp.2007.07.020 (DOI)000251140100006 ()
Available from: 2007-10-26 Created: 2007-10-26 Last updated: 2011-11-30Bibliographically approved
2. CellMC: a multiplatform model compiler for the Cell Broadband Engine and x86
Open this publication in new window or tab >>CellMC: a multiplatform model compiler for the Cell Broadband Engine and x86
2010 (English)In: Bioinformatics, ISSN 1367-4803, E-ISSN 1460-2059, Vol. 26, 426-428 p.Article in journal (Refereed) Published
National Category
Software Engineering Biochemistry and Molecular Biology
Identifiers
urn:nbn:se:uu:diva-111276 (URN)10.1093/bioinformatics/btp662 (DOI)000274342800026 ()
Projects
eSSENCE
Available from: 2009-12-08 Created: 2009-12-08 Last updated: 2011-11-30Bibliographically approved
3. Efficient computation of transient solutions of the chemical master equation based on uniformization and quasi-Monte Carlo
Open this publication in new window or tab >>Efficient computation of transient solutions of the chemical master equation based on uniformization and quasi-Monte Carlo
2008 (English)In: Journal of Chemical Physics, ISSN 0021-9606, E-ISSN 1089-7690, Vol. 128, 154109:1-7 p.Article in journal (Refereed) Published
National Category
Computational Mathematics Biochemistry and Molecular Biology
Identifiers
urn:nbn:se:uu:diva-16105 (URN)10.1063/1.2897976 (DOI)000255228900011 ()
Available from: 2008-04-22 Created: 2008-04-22 Last updated: 2011-11-30Bibliographically approved
4. Simulation of stochastic reaction-diffusion processes on unstructured meshes
Open this publication in new window or tab >>Simulation of stochastic reaction-diffusion processes on unstructured meshes
2009 (English)In: SIAM Journal on Scientific Computing, ISSN 1064-8275, E-ISSN 1095-7197, Vol. 31, 1774-1797 p.Article in journal (Refereed) Published
National Category
Computational Mathematics Computer Science
Identifiers
urn:nbn:se:uu:diva-97689 (URN)10.1137/080721388 (DOI)000267746200008 ()
Available from: 2008-11-07 Created: 2008-11-07 Last updated: 2011-11-30Bibliographically approved
5. Incorporating active transport of cellular cargo in stochastic mesoscopic models of living cells
Open this publication in new window or tab >>Incorporating active transport of cellular cargo in stochastic mesoscopic models of living cells
2010 (English)In: Multiscale Modeling & simulation, ISSN 1540-3459, E-ISSN 1540-3467, Vol. 8, 1691-1714 p.Article in journal (Refereed) Published
National Category
Computational Mathematics Biochemistry and Molecular Biology
Identifiers
urn:nbn:se:uu:diva-131200 (URN)10.1137/100784709 (DOI)000285509300006 ()
Projects
eSSENCE
Available from: 2010-09-23 Created: 2010-09-27 Last updated: 2011-11-30Bibliographically approved
6. An adaptive algorithm for simulation of stochastic reaction-diffusion processes
Open this publication in new window or tab >>An adaptive algorithm for simulation of stochastic reaction-diffusion processes
2010 (English)In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 229, 343-360 p.Article in journal (Refereed) Published
National Category
Computational Mathematics Computer Science
Identifiers
urn:nbn:se:uu:diva-108918 (URN)10.1016/j.jcp.2009.09.030 (DOI)000272760500008 ()
Projects
eSSENCE
Available from: 2009-10-04 Created: 2009-10-04 Last updated: 2011-11-30Bibliographically approved
7. Coupled mesoscopic and microscopic simulation of stochastic reaction-diffusion processes in mixed dimensions
Open this publication in new window or tab >>Coupled mesoscopic and microscopic simulation of stochastic reaction-diffusion processes in mixed dimensions
2011 (English)Report (Other academic)
Series
Technical report / Department of Information Technology, Uppsala University, ISSN 1404-3203 ; 2011-005
National Category
Computational Mathematics Biochemistry and Molecular Biology
Identifiers
urn:nbn:se:uu:diva-152228 (URN)
Projects
eSSENCE
Available from: 2011-04-04 Created: 2011-04-27 Last updated: 2011-11-18Bibliographically approved

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