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  • 1. Bani-Hashemian, Hossein
    et al.
    Hellander, Stefan
    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.
    Lötstedt, Per
    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.
    Efficient sampling in event-driven algorithms for reaction-diffusion processes2011Report (Other academic)
  • 2. Bani-Hashemian, Mohammad Hossein
    et al.
    Hellander, Stefan
    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.
    Lötstedt, Per
    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.
    Efficient sampling in event-driven algorithms for reaction-diffusion processes2013In: Communications in Computational Physics, ISSN 1815-2406, E-ISSN 1991-7120, Vol. 13, p. 958-984Article in journal (Refereed)
  • 3.
    Bouchnita, Anass
    et al.
    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, Computational Science.
    Hellander, Stefan
    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, Computational Science.
    Hellander, Andreas
    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, Computational Science.
    A 3D multiscale model to explore the role of EGFR overexpression in tumourigenesis2019In: Bulletin of Mathematical Biology, ISSN 0092-8240, E-ISSN 1522-9602, Vol. 81, p. 2323-2344Article in journal (Refereed)
  • 4. Flegg, Mark B.
    et al.
    Hellander, Stefan
    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.
    Erban, Radek
    Convergence of methods for coupling of microscopic and mesoscopic reaction-diffusion simulations2013Report (Other academic)
  • 5. Golkaram, Mahdi
    et al.
    Jang, Jiwon
    Hellander, Stefan
    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, Computational Science.
    Kosik, Kenneth S.
    Petzold, Linda R.
    The role of chromatin density in cell population heterogeneity during stem cell differentiation2017In: Scientific Reports, ISSN 2045-2322, E-ISSN 2045-2322, Vol. 7, p. 13307:1-11, article id 13307Article in journal (Refereed)
  • 6.
    Hellander, Andreas
    et al.
    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.
    Hellander, Stefan
    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.
    Lötstedt, Per
    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.
    Coupled mesoscopic and microscopic simulation of stochastic reaction-diffusion processes in mixed dimensions2011Report (Other academic)
  • 7.
    Hellander, Andreas
    et al.
    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.
    Hellander, Stefan
    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.
    Lötstedt, Per
    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.
    Coupled mesoscopic and microscopic simulation of stochastic reaction-diffusion processes in mixed dimensions2012In: Multiscale Modeling & simulation, ISSN 1540-3459, E-ISSN 1540-3467, Vol. 10, p. 585-611Article in journal (Refereed)
  • 8.
    Hellander, Stefan
    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.
    Single molecule simulations in complex geometries with embedded dynamic one-dimensional structures2013Report (Other academic)
  • 9.
    Hellander, Stefan
    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.
    Single molecule simulations in complex geometries with embedded dynamic one-dimensional structures2013In: Journal of Chemical Physics, ISSN 0021-9606, E-ISSN 1089-7690, Vol. 139, p. 014103:1-11Article in journal (Refereed)
  • 10.
    Hellander, Stefan
    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.
    Stochastic Simulation of Reaction-Diffusion Processes2013Doctoral 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.

    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, p. 3948-3965Article 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: 2017-12-11Bibliographically 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, p. 585-611Article 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, p. 958-984Article 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, p. 042901:1-5Article 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
  • 11.
    Hellander, Stefan
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Computational Science.
    Hellander, Andreas
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Computational Science.
    Petzold, Linda
    University of California, Department of Computer Science.
    Mesoscopic-microscopic spatial stochastic simulation with automatic system partitioning2017In: Journal of Chemical Physics, ISSN 0021-9606, E-ISSN 1089-7690, Vol. 147, no 23, article id 234101Article in journal (Refereed)
    Abstract [en]

    The reaction-diffusion master equation (RDME) is a model that allows for efficient on-lattice simulation of spatially resolved stochastic chemical kinetics. Compared to off-lattice hard-sphere simulations with Brownian dynamics or Green's function reaction dynamics, the RDME can be orders of magnitude faster if the lattice spacing can be chosen coarse enough. However, strongly diffusion-controlled reactions mandate a very fine mesh resolution for acceptable accuracy. It is common that reactions in the same model differ in their degree of diffusion control and therefore require different degrees of mesh resolution. This renders mesoscopic simulation inefficient for systems with multiscale properties. Mesoscopic-microscopic hybrid methods address this problem by resolving the most challenging reactions with a microscale, off-lattice simulation. However, all methods to date require manual partitioning of a system, effectively limiting their usefulness as "black-box" simulation codes. In this paper, we propose a hybrid simulation algorithm with automatic system partitioning based on indirect a priori error estimates. We demonstrate the accuracy and efficiency of the method on models of diffusion-controlled networks in 3D.

  • 12. Hellander, Stefan
    et al.
    Hellander, Andreas
    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, Computational Science.
    Petzold, Linda
    Reaction rates for mesoscopic reaction-diffusion kinetics2015In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, E-ISSN 1550-2376, Vol. 91, p. 023312:1-12, article id 023312Article in journal (Refereed)
  • 13.
    Hellander, Stefan
    et al.
    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.
    Hellander, Andreas
    Petzold, Linda
    Reaction-diffusion master equation in the microscopic limit2012In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, E-ISSN 1550-2376, Vol. 85, p. 042901:1-5Article in journal (Refereed)
  • 14.
    Hellander, Stefan
    et al.
    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.
    Lötstedt, Per
    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.
    Flexible single molecule simulation of reaction-diffusion processes2010Report (Other academic)
  • 15.
    Hellander, Stefan
    et al.
    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.
    Lötstedt, Per
    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.
    Flexible single molecule simulation of reaction-diffusion processes2011In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 230, p. 3948-3965Article in journal (Refereed)
  • 16.
    Wang, Siyang
    et al.
    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.
    Elf, Johan
    Uppsala University, Disciplinary Domain of Science and Technology, Biology, Department of Cell and Molecular Biology, Computational and Systems Biology. Uppsala University, Science for Life Laboratory, SciLifeLab.
    Hellander, Stefan
    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.
    Lötstedt, Per
    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.
    Stochastic reaction–diffusion processes with embedded lower dimensional structures2012Report (Other academic)
  • 17.
    Wang, Siyang
    et al.
    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.
    Elf, Johan
    Uppsala University, Disciplinary Domain of Science and Technology, Biology, Department of Cell and Molecular Biology, Computational and Systems Biology. Uppsala University, Science for Life Laboratory, SciLifeLab.
    Hellander, Stefan
    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.
    Lötstedt, Per
    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.
    Stochastic reaction–diffusion processes with embedded lower-dimensional structures2014In: Bulletin of Mathematical Biology, ISSN 0092-8240, E-ISSN 1522-9602, Vol. 76, p. 819-853Article in journal (Refereed)
1 - 17 of 17
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