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Numerical Methods for Stochastic Modeling of Genes and Proteins
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)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Stochastic models of biochemical reaction networks are used for understanding the properties of molecular regulatory circuits in living cells. The state of the cell is defined by the number of copies of each molecular species in the model. The chemical master equation (CME) governs the time evolution of the the probability density function of the often high-dimensional state space. The CME is approximated by a partial differential equation (PDE), the Fokker-Planck equation and solved numerically. Direct solution of the CME rapidly becomes computationally expensive for increasingly complex biological models, since the state space grows exponentially with the number of dimensions. Adaptive numerical methods can be applied in time and space in the PDE framework, and error estimates of the approximate solutions are derived. A method for splitting the CME operator in order to apply the PDE approximation in a subspace of the state space is also developed. The performance is compared to the most widely spread alternative computational method.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis , 2007. , 42 p.
Series
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 358
Keyword [en]
master equation, Fokker-Planck equation, stochastic models, biochemical reaction networks
National Category
Computational Mathematics Biochemistry and Molecular Biology
Research subject
Scientific Computing
Identifiers
URN: urn:nbn:se:uu:diva-8293ISBN: 978-91-554-7009-8 (print)OAI: oai:DiVA.org:uu-8293DiVA: diva2:170939
Public defence
2007-11-30, Room 2446, Polacksbacken, Lägerhyddsvägen 2D, Uppsala, 13:15 (English)
Opponent
Supervisors
Available from: 2007-11-08 Created: 2007-11-08 Last updated: 2011-10-26Bibliographically approved
List of papers
1. Problems of high dimension in molecular biology
Open this publication in new window or tab >>Problems of high dimension in molecular biology
2003 (English)In: Proc. 19th GAMM Seminar Leipzig on High-dimensional problems: Numerical treatment and applications, Leipzig, Germany: Max Planck Institute for Mathematics in the Sciences , 2003, 21-30 p.Conference paper, Published paper (Refereed)
Place, publisher, year, edition, pages
Leipzig, Germany: Max Planck Institute for Mathematics in the Sciences, 2003
National Category
Biochemistry and Molecular Biology Computational Mathematics
Identifiers
urn:nbn:se:uu:diva-91875 (URN)
Available from: 2004-05-13 Created: 2004-05-13 Last updated: 2011-11-26Bibliographically approved
2. Conservative solution of the Fokker-Planck equation for stochastic chemical reactions
Open this publication in new window or tab >>Conservative solution of the Fokker-Planck equation for stochastic chemical reactions
2006 (English)In: BIT Numerical Mathematics, ISSN 0006-3835, E-ISSN 1572-9125, Vol. 46, S61-S83 p.Article in journal (Refereed) Published
National Category
Computational Mathematics Computer Science
Identifiers
urn:nbn:se:uu:diva-83864 (URN)10.1007/s10543-006-0082-z (DOI)000243196000007 ()
Available from: 2007-09-28 Created: 2007-09-28 Last updated: 2011-11-29Bibliographically approved
3. Fokker-Planck approximation of the master equation in molecular biology
Open this publication in new window or tab >>Fokker-Planck approximation of the master equation in molecular biology
2009 (English)In: Computing and Visualization in Science, ISSN 1432-9360, E-ISSN 1433-0369, Vol. 12, 37-50 p.Article in journal (Refereed) Published
National Category
Computational Mathematics Biochemistry and Molecular Biology
Identifiers
urn:nbn:se:uu:diva-26498 (URN)10.1007/s00791-006-0045-6 (DOI)
Available from: 2008-07-18 Created: 2008-07-18 Last updated: 2011-11-30Bibliographically approved
4. Partial approximation of the master equation by the Fokker-Planck equation
Open this publication in new window or tab >>Partial approximation of the master equation by the Fokker-Planck equation
2007 (English)In: Applied Parallel Computing: State of the Art in Scientific Computing, Berlin: Springer-Verlag , 2007, 637-646 p.Conference paper, Published paper (Refereed)
Place, publisher, year, edition, pages
Berlin: Springer-Verlag, 2007
Series
Lecture Notes in Computer Science, 4699
National Category
Computational Mathematics Biochemistry and Molecular Biology
Identifiers
urn:nbn:se:uu:diva-11547 (URN)10.1007/978-3-540-75755-9_77 (DOI)000250904900077 ()978-3-540-75754-2 (ISBN)
Available from: 2007-09-26 Created: 2007-09-26 Last updated: 2011-11-26Bibliographically approved
5. PDE and Monte Carlo approaches to solving the master equation applied to gene regulation
Open this publication in new window or tab >>PDE and Monte Carlo approaches to solving the master equation applied to gene regulation
2007 (English)Report (Other academic)
Series
Technical report / Department of Information Technology, Uppsala University, ISSN 1404-3203 ; 2007-028
National Category
Computational Mathematics Biochemistry and Molecular Biology
Identifiers
urn:nbn:se:uu:diva-11804 (URN)
Available from: 2007-10-20 Created: 2007-10-20 Last updated: 2011-11-18Bibliographically approved

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Citation style
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