Title
Single-variable reaction systems: deterministic and stochastic models Single-variable reaction systems: deterministic and stochastic models
Author
Faculty/Department
Faculty of Pharmaceutical, Biomedical and Veterinary Sciences . Biomedical Sciences
Publication type
article
Publication
New York, N.Y. ,
Subject
Mathematics
Biology
Human medicine
Computer. Automation
Source (journal)
Mathematical biosciences. - New York, N.Y.
Volume/pages
227(2010) :2 , p. 105-116
ISSN
0025-5564
ISI
000282727200003
Carrier
E
Target language
English (eng)
Full text (Publishers DOI)
Affiliation
University of Antwerp
Abstract
Biochemical reaction networks are often described by deterministic models based on macroscopic rate equations. However, for small numbers of molecules, intrinsic noise can play a significant role and stochastic methods may thus be required. In this work, we analyze the differences and similarities between a class of macroscopic deterministic models and corresponding mesoscopic stochastic models. We derive expressions that provide a clear and intuitive view upon the behavior of the stochastic model. In particular, these expressions show the dependence of both the dynamics and the stationary distribution of the stochastic model on the number of molecules in the system. As expected, most properties of the stochastic model correspond well with those in the deterministic model if the number of molecules is large enough. However, for some properties, both models are inconsistent, even if the number of molecules in the stochastic model tends to infinity. Throughout this paper, we use a bistable autophosphorylation cycle as a running example. For such a bistable system, we give an explicit proof that the rate of convergence to the stationary distribution (or the second eigenvalue of the transition matrix) depends exponentially on the number of molecules. (C) 2010 Elsevier Inc. All rights reserved.
E-info
https://repository.uantwerpen.be/docman/iruaauth/4d5beb/4318341.pdf
http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000282727200003&DestLinkType=RelatedRecords&DestApp=ALL_WOS&UsrCustomerID=ef845e08c439e550330acc77c7d2d848
http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000282727200003&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=ef845e08c439e550330acc77c7d2d848
http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000282727200003&DestLinkType=CitingArticles&DestApp=ALL_WOS&UsrCustomerID=ef845e08c439e550330acc77c7d2d848
Handle