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Stochastic Simulation of Multiscale Reaction-Diffusion Models via First Exit Times
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.ORCID iD: 0000-0002-0415-7983
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 [en]
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: urn:nbn:se:uu:diva-284085ISBN: 978-91-554-9582-4 (print)OAI: oai:DiVA.org:uu-284085DiVA: diva2:921108
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
List of papers
1. Stochastic diffusion processes on Cartesian meshes
Open this publication in new window or tab >>Stochastic diffusion processes on Cartesian meshes
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
National Category
Computational Mathematics
Identifiers
urn:nbn:se:uu:diva-265731 (URN)10.1016/j.cam.2015.07.035 (DOI)000364245700001 ()
Available from: 2015-08-05 Created: 2015-11-02 Last updated: 2017-12-01Bibliographically approved
2. Simulation of stochastic diffusion via first exit times
Open this publication in new window or tab >>Simulation of stochastic diffusion via first exit times
2015 (English)In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 300, 862-886 p.Article in journal (Refereed) Published
National Category
Computational Mathematics
Identifiers
urn:nbn:se:uu:diva-264806 (URN)10.1016/j.jcp.2015.07.065 (DOI)000361573200043 ()
Available from: 2015-08-12 Created: 2015-10-19 Last updated: 2017-12-01Bibliographically approved
3. Analysis and design of jump coefficients in discrete stochastic diffusion models
Open this publication in new window or tab >>Analysis and design of jump coefficients in discrete stochastic diffusion models
2016 (English)In: SIAM Journal on Scientific Computing, ISSN 1064-8275, E-ISSN 1095-7197, Vol. 38, A55-A83 p.Article in journal (Refereed) Published
National Category
Computational Mathematics Biochemistry and Molecular Biology
Identifiers
urn:nbn:se:uu:diva-272192 (URN)10.1137/15M101110X (DOI)000371235600003 ()
Projects
UPMARCeSSENCE
Available from: 2016-01-06 Created: 2016-01-12 Last updated: 2017-11-30Bibliographically approved
4. Multiscale modeling of diffusion in a crowded environment
Open this publication in new window or tab >>Multiscale modeling of diffusion in a crowded environment
2017 (English)In: Bulletin of Mathematical Biology, ISSN 0092-8240, E-ISSN 1522-9602, Vol. 79, 2672-2695 p.Article in journal (Refereed) Published
National Category
Computational Mathematics
Identifiers
urn:nbn:se:uu:diva-283633 (URN)10.1007/s11538-017-0346-6 (DOI)
Funder
Swedish Research Council, 621-2001-3148NIH (National Institute of Health), 1R01EB014877-01
Available from: 2017-09-18 Created: 2016-04-13 Last updated: 2017-11-09Bibliographically approved
5. Excluded volume effects in on- and off-lattice reaction–diffusion models
Open this publication in new window or tab >>Excluded volume effects in on- and off-lattice reaction–diffusion models
2017 (English)In: IET Systems Biology, ISSN 1751-8849, E-ISSN 1751-8857, Vol. 11, 55-64 p.Article in journal (Refereed) Published
National Category
Computational Mathematics Signal Processing
Identifiers
urn:nbn:se:uu:diva-285216 (URN)10.1049/iet-syb.2016.0021 (DOI)000398811200001 ()28476973 (PubMedID)
Funder
Swedish Research Council, 621-2001-3148
Available from: 2016-11-01 Created: 2016-04-19 Last updated: 2017-05-19Bibliographically approved

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