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Problems of high dimension in molecular biology
Uppsala University, Disciplinary Domain of Science and Technology, Biology, Department of Cell and Molecular Biology, Molecular 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. (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)
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. 21-30 p.
National Category
Biochemistry and Molecular Biology Computational Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-91875OAI: oai:DiVA.org:uu-91875DiVA: diva2:164742
Available from: 2004-05-13 Created: 2004-05-13 Last updated: 2011-11-26Bibliographically approved
In thesis
1. Intracellular Flows and Fluctuations
Open this publication in new window or tab >>Intracellular Flows and Fluctuations
2004 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Mathematical models are now gaining in importance for descriptions of biological processes. In this thesis, such models have been used to identify and analyze principles that govern bacterial protein synthesis under amino acid limitation. New techniques, that are generally applicable for analysis of intrinsic fluctuations in systems of chemical reactions, are also presented.

It is shown how multi-substrate reactions, such as protein synthesis, may display zero order kinetics below saturation, because an increase in one substrate pool is compensated by a decrease in another, so that the overall flow is unchanged. Under those conditions, metabolite pools display hyper sensitivity and large fluctuations, unless metabolite synthesis is carefully regulated. It is demonstrated that flow coupling in protein synthesis has consequences for transcriptional control of amino acid biosynthetic operons, accuracy of mRNA translation and the stringent response.

Flow coupling also determines the choices of synonymous codons in a number of cases. The reason is that tRNA isoacceptors, cognate to the same amino acid, often read different codons and become deacylated to very different degrees when their amino acid is limiting for protein synthesis. This was demonstrated theoretically and used to successfully predict the choices of control codons in ribosome mediated transcriptional attenuation and codon bias in stress response genes.

New tools for the analysis of internal fluctuations have been forged, most importantly, an efficient Monte Carlo algorithm for simulation of the Markov-process corresponding to the reaction-diffusion master equation. The algorithm makes it feasible to analyze stochastic kinetics in spatially extended systems. It was used to demonstrate that bi-stable chemical systems can display spontaneous domain separation also in three spatial dimensions. This analysis reveals geometrical constraints on biochemical memory circuits built from bistable systems. Further, biochemical applications of the Fokker-Planck equation and the Linear Noise Approximation have been explored.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2004. 63 p.
Series
Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1104-232X ; 988
Keyword
Molecular biology, mesoscopic, reaction-diffusion, protein synthesis, amino acid, flow, fluctuations, Molekylärbiologi
National Category
Biochemistry and Molecular Biology
Research subject
Molecular Biotechnology
Identifiers
urn:nbn:se:uu:diva-4291 (URN)91-554-5988-9 (ISBN)
Public defence
2004-06-03, Room B41, Uppsala Biomedical Centre, Husarg. 3, Uppsala, 10:00 (English)
Opponent
Supervisors
Available from: 2004-05-13 Created: 2004-05-13 Last updated: 2010-01-14Bibliographically approved
2. 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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Elf, JohanLötstedt, PerSjöberg, Paul

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