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Multiscale analysis of reaction networks
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Sbano, L. and Kirkilionis, Markus (2008) Multiscale analysis of reaction networks. In: Annual European Conference on Complex Systems, Dresden, Germany, OCT 01-06, 2007. Published in: Theory in Biosciences, Vol.127 (No.2). pp. 107-123. doi:10.1007/s12064-008-0036-x ISSN 1431-7613.
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Official URL: http://dx.doi.org/10.1007/s12064-008-0036-x
Abstract
In most natural sciences there is currently the insight that it is necessary to bridge gaps between different processes which can be observed on different scales. This is especially true in the field of chemical reactions where the different abilities to form bonds between different types of atoms and molecules create much of the properties we experience in our everyday life, especially in all biological activity. There are essentially two types of processes related to biochemical reaction networks, the interactions among molecules and interactions involving their conformational changes, so in a sense, their internal state. The first type of processes can be conveniently approximated by the so-called mass-action kinetics, but this is not necessarily so for the second kind: here molecular states do not define any kind of density or concentration. In this paper, we demonstrate the necessity to study reaction networks in a stochastic formulation for which we can construct a coherent approximation in terms of specific space-time scales and the number of particles. The continuum limit procedure naturally creates equations of Fokker-Planck type where the evolution of the concentration occurs on a slower time scale when compared to the evolution of the conformational changes, for example triggered by binding or unbinding events with other (typically smaller) molecules. We apply the asymptotic theory to derive the effective, i.e. macroscopic dynamics of a general biochemical reaction system. The theory can also be applied to other processes where entities can be described by finitely many internal states, with changes of states occurring by arrival of other entities described by a birth-death process.
Item Type: | Conference Item (UNSPECIFIED) | ||||
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Subjects: | Q Science > QD Chemistry Q Science > QH Natural history > QH301 Biology |
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Multiscale modeling, Biochemistry, Chemical reactions -- Mathematical models | ||||
Journal or Publication Title: | Theory in Biosciences | ||||
Publisher: | Springer | ||||
ISSN: | 1431-7613 | ||||
Official Date: | June 2008 | ||||
Dates: |
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Volume: | Vol.127 | ||||
Number: | No.2 | ||||
Number of Pages: | 17 | ||||
Page Range: | pp. 107-123 | ||||
DOI: | 10.1007/s12064-008-0036-x | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access | ||||
Funder: | Seventh Framework Programme (European Commission) (FP7) | ||||
Title of Event: | Annual European Conference on Complex Systems | ||||
Type of Event: | Conference | ||||
Location of Event: | Dresden, Germany | ||||
Date(s) of Event: | OCT 01-06, 2007 |
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