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Conservative solution of the Fokker-Planck equation for stochastic chemical reactions
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)
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)
2006 (English)In: BIT Numerical Mathematics, ISSN 0006-3835, E-ISSN 1572-9125, Vol. 46, S61-S83 p.Article in journal (Refereed) Published
Place, publisher, year, edition, pages
2006. Vol. 46, S61-S83 p.
National Category
Computational Mathematics Computer Science
Identifiers
URN: urn:nbn:se:uu:diva-83864DOI: 10.1007/s10543-006-0082-zISI: 000243196000007OAI: oai:DiVA.org:uu-83864DiVA: diva2:111772
Available from: 2007-09-28 Created: 2007-09-28 Last updated: 2017-12-14Bibliographically approved
In thesis
1. Numerical Methods for Stochastic Modeling of Genes and Proteins
Open this publication in new window or tab >>Numerical Methods for Stochastic Modeling of Genes and Proteins
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
master equation, Fokker-Planck equation, stochastic models, biochemical reaction networks
National Category
Computational Mathematics Biochemistry and Molecular Biology
Research subject
Scientific Computing
Identifiers
urn:nbn:se:uu:diva-8293 (URN)978-91-554-7009-8 (ISBN)
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

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Ferm, LarsLötstedt, PerSjöberg, Paul

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