uu.seUppsala University Publications

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Numerical Methods for Stochastic Modeling of Genes and ProteinsPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); 2007 (English)Doctoral thesis, comprehensive summary (Other academic)
##### Abstract [en]

##### 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 [en]

master equation, Fokker-Planck equation, stochastic models, biochemical reaction networks
##### National Category

Computational Mathematics Biochemistry and Molecular Biology
##### Research subject

Scientific Computing
##### Identifiers

URN: urn:nbn:se:uu:diva-8293ISBN: 978-91-554-7009-8 (print)OAI: oai:DiVA.org:uu-8293DiVA: diva2:170939
##### Public defence

2007-11-30, Room 2446, Polacksbacken, Lägerhyddsvägen 2D, Uppsala, 13:15 (English)
##### Opponent

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##### Supervisors

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#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt481",{id:"formSmash:j_idt481",widgetVar:"widget_formSmash_j_idt481",multiple:true});
Available from: 2007-11-08 Created: 2007-11-08 Last updated: 2011-10-26Bibliographically approved
##### List of papers

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.

1. Problems of high dimension in molecular biology$(function(){PrimeFaces.cw("OverlayPanel","overlay164742",{id:"formSmash:j_idt518:0:j_idt522",widgetVar:"overlay164742",target:"formSmash:j_idt518:0:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

2. Conservative solution of the Fokker-Planck equation for stochastic chemical reactions$(function(){PrimeFaces.cw("OverlayPanel","overlay111772",{id:"formSmash:j_idt518:1:j_idt522",widgetVar:"overlay111772",target:"formSmash:j_idt518:1:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

3. Fokker-Planck approximation of the master equation in molecular biology$(function(){PrimeFaces.cw("OverlayPanel","overlay54272",{id:"formSmash:j_idt518:2:j_idt522",widgetVar:"overlay54272",target:"formSmash:j_idt518:2:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

4. Partial approximation of the master equation by the Fokker-Planck equation$(function(){PrimeFaces.cw("OverlayPanel","overlay39316",{id:"formSmash:j_idt518:3:j_idt522",widgetVar:"overlay39316",target:"formSmash:j_idt518:3:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

5. PDE and Monte Carlo approaches to solving the master equation applied to gene regulation$(function(){PrimeFaces.cw("OverlayPanel","overlay39573",{id:"formSmash:j_idt518:4:j_idt522",widgetVar:"overlay39573",target:"formSmash:j_idt518:4:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

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