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Stochastic Simulation of Reaction-Diffusion Processes
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.
2013 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Numerical simulation methods have become an important tool in the study of chemical reaction networks in living cells. Many systems can, with high accuracy, be modeled by deterministic ordinary differential equations, but other systems require a more detailed level of modeling. Stochastic models at either the mesoscopic level or the microscopic level can be used for cases when molecules are present in low copy numbers.

In this thesis we develop efficient and flexible algorithms for simulating systems at the microscopic level. We propose an improvement to the Green's function reaction dynamics algorithm, an efficient microscale method. Furthermore, we describe how to simulate interactions with complex internal structures such as membranes and dynamic fibers.

The mesoscopic level is related to the microscopic level through the reaction rates at the respective scale. We derive that relation in both two dimensions and three dimensions and show that the mesoscopic model breaks down if the discretization of space becomes too fine. For a simple model problem we can show exactly when this breakdown occurs.

We show how to couple the microscopic scale with the mesoscopic scale in a hybrid method. Using the fact that some systems only display microscale behaviour in parts of the system, we can gain computational time by restricting the fine-grained microscopic simulations to only a part of the system.

Finally, we have developed a mesoscopic method that couples simulations in three dimensions with simulations on general embedded lines. The accuracy of the method has been verified by comparing the results with purely microscopic simulations as well as with theoretical predictions.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2013. , 46 p.
Series
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 1042
Keyword [en]
stochastic simulation, microscale, mesoscale, Smoluchowski's equation, hybrid methods
National Category
Computational Mathematics Biochemistry and Molecular Biology
Research subject
Scientific Computing with specialization in Numerical Analysis
Identifiers
URN: urn:nbn:se:uu:diva-198522ISBN: 978-91-554-8667-9 (print)OAI: oai:DiVA.org:uu-198522DiVA: diva2:616667
Public defence
2013-06-05, Room 2446, Polacksbacken, Lägerhyddsvägen 2D, Uppsala, 10:15 (English)
Opponent
Supervisors
Projects
eSSENCE
Available from: 2013-05-14 Created: 2013-04-18 Last updated: 2013-08-30Bibliographically approved
List of papers
1. Flexible single molecule simulation of reaction-diffusion processes
Open this publication in new window or tab >>Flexible single molecule simulation of reaction-diffusion processes
2011 (English)In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 230, 3948-3965 p.Article in journal (Refereed) Published
National Category
Computational Mathematics Biochemistry and Molecular Biology
Identifiers
urn:nbn:se:uu:diva-149900 (URN)10.1016/j.jcp.2011.02.020 (DOI)000289597500017 ()
Projects
eSSENCE
Available from: 2011-02-19 Created: 2011-03-24 Last updated: 2013-05-06Bibliographically approved
2. Coupled mesoscopic and microscopic simulation of stochastic reaction-diffusion processes in mixed dimensions
Open this publication in new window or tab >>Coupled mesoscopic and microscopic simulation of stochastic reaction-diffusion processes in mixed dimensions
2012 (English)In: Multiscale Modeling & simulation, ISSN 1540-3459, E-ISSN 1540-3467, Vol. 10, 585-611 p.Article in journal (Refereed) Published
National Category
Computational Mathematics Biochemistry and Molecular Biology
Identifiers
urn:nbn:se:uu:diva-175073 (URN)10.1137/110832148 (DOI)000305949600010 ()
Projects
eSSENCE
Available from: 2012-05-29 Created: 2012-05-31 Last updated: 2017-12-07Bibliographically approved
3. Efficient sampling in event-driven algorithms for reaction-diffusion processes
Open this publication in new window or tab >>Efficient sampling in event-driven algorithms for reaction-diffusion processes
2013 (English)In: Communications in Computational Physics, ISSN 1815-2406, E-ISSN 1991-7120, Vol. 13, 958-984 p.Article in journal (Refereed) Published
National Category
Computational Mathematics
Identifiers
urn:nbn:se:uu:diva-181793 (URN)10.4208/cicp.271011.230312a (DOI)000322065200002 ()
Projects
eSSENCE
Available from: 2012-09-21 Created: 2012-09-28 Last updated: 2017-12-07Bibliographically approved
4. Reaction-diffusion master equation in the microscopic limit
Open this publication in new window or tab >>Reaction-diffusion master equation in the microscopic limit
2012 (English)In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, E-ISSN 1550-2376, Vol. 85, 042901:1-5 p.Article in journal (Refereed) Published
National Category
Computational Mathematics Biochemistry and Molecular Biology
Identifiers
urn:nbn:se:uu:diva-173986 (URN)10.1103/PhysRevE.85.042901 (DOI)000302409200005 ()
Projects
eSSENCE
Available from: 2012-04-03 Created: 2012-05-09 Last updated: 2017-12-07Bibliographically approved
5. Stochastic reaction–diffusion processes with embedded lower dimensional structures
Open this publication in new window or tab >>Stochastic reaction–diffusion processes with embedded lower dimensional structures
2012 (English)Report (Other academic)
Series
Technical report / Department of Information Technology, Uppsala University, ISSN 1404-3203 ; 2012-034
National Category
Computational Mathematics Biochemistry and Molecular Biology
Identifiers
urn:nbn:se:uu:diva-187336 (URN)
Projects
eSSENCE
Available from: 2012-12-05 Created: 2012-12-05 Last updated: 2013-05-06Bibliographically approved
6. Single molecule simulations in complex geometries with embedded dynamic one-dimensional structures
Open this publication in new window or tab >>Single molecule simulations in complex geometries with embedded dynamic one-dimensional structures
2013 (English)Report (Other academic)
Series
Technical report / Department of Information Technology, Uppsala University, ISSN 1404-3203 ; 2013-009
National Category
Computational Mathematics Biochemistry and Molecular Biology
Identifiers
urn:nbn:se:uu:diva-198504 (URN)
Projects
eSSENCE
Available from: 2013-04-16 Created: 2013-04-16 Last updated: 2013-05-06Bibliographically approved
7. Convergence of methods for coupling of microscopic and mesoscopic reaction-diffusion simulations
Open this publication in new window or tab >>Convergence of methods for coupling of microscopic and mesoscopic reaction-diffusion simulations
2013 (English)Report (Other academic)
Series
Technical report / Department of Information Technology, Uppsala University, ISSN 1404-3203 ; 2013-010
National Category
Computational Mathematics Biochemistry and Molecular Biology
Identifiers
urn:nbn:se:uu:diva-198521 (URN)
Projects
eSSENCE
Available from: 2013-04-18 Created: 2013-04-18 Last updated: 2013-05-21Bibliographically approved

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