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Stochastic diffusion processes on Cartesian meshes
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.
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.
2016 (English)In: Journal of Computational and Applied Mathematics, ISSN 0377-0427, E-ISSN 1879-1778, Vol. 294, 1-11 p.Article in journal (Refereed) Published
Place, publisher, year, edition, pages
2016. Vol. 294, 1-11 p.
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-265731DOI: 10.1016/j.cam.2015.07.035ISI: 000364245700001OAI: oai:DiVA.org:uu-265731DiVA: diva2:866453
Available from: 2015-08-05 Created: 2015-11-02 Last updated: 2017-12-01Bibliographically approved
In thesis
1. Stochastic Simulation of Multiscale Reaction-Diffusion Models via First Exit Times
Open this publication in new window or tab >>Stochastic Simulation of Multiscale Reaction-Diffusion Models via First Exit Times
2016 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Mathematical models are important tools in systems biology, since the regulatory networks in biological cells are too complicated to understand by biological experiments alone. Analytical solutions can be derived only for the simplest models and numerical simulations are necessary in most cases to evaluate the models and their properties and to compare them with measured data.

This thesis focuses on the mesoscopic simulation level, which captures both, space dependent behavior by diffusion and the inherent stochasticity of cellular systems. Space is partitioned into compartments by a mesh and the number of molecules of each species in each compartment gives the state of the system. We first examine how to compute the jump coefficients for a discrete stochastic jump process on unstructured meshes from a first exit time approach guaranteeing the correct speed of diffusion. Furthermore, we analyze different methods leading to non-negative coefficients by backward analysis and derive a new method, minimizing both the error in the diffusion coefficient and in the particle distribution.

The second part of this thesis investigates macromolecular crowding effects. A high percentage of the cytosol and membranes of cells are occupied by molecules. This impedes the diffusive motion and also affects the reaction rates. Most algorithms for cell simulations are either derived for a dilute medium or become computationally very expensive when applied to a crowded environment. Therefore, we develop a multiscale approach, which takes the microscopic positions of the molecules into account, while still allowing for efficient stochastic simulations on the mesoscopic level. Finally, we compare on- and off-lattice models on the microscopic level when applied to a crowded environment.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2016. 53 p.
Series
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 1376
Keyword
computational systems biology, diffusion, first exit times, unstructured meshes, reaction-diffusion master equation, macromolecular crowding, excluded volume effects, finite element method, backward analysis, stochastic simulation
National Category
Computational Mathematics
Research subject
Scientific Computing with specialization in Numerical Analysis
Identifiers
urn:nbn:se:uu:diva-284085 (URN)978-91-554-9582-4 (ISBN)
Public defence
2016-06-10, ITC 2446, Lägerhyddsvägen 2, Uppsala, 10:15 (English)
Opponent
Supervisors
Funder
Swedish Research Council, 621- 2001-3148NIH (National Institute of Health), 1R01EB014877-01
Available from: 2016-05-19 Created: 2016-04-14 Last updated: 2016-06-01Bibliographically approved

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Meinecke, LinaLötstedt, Per

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