Kummer, U. (Ursula), Krajnc, Borut, Pahle, Jürgen, Green, Anne K., Dixon, C. Jane and Marhl, Marko (2005) Transition from stochastic to deterministic behavior in calcium oscillations. Biophysical Journal, Vol.89 (No.3). pp. 1603-1611. doi:10.1529/biophysj.104.057216 ISSN 0006-3495.

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Abstract

Simulation and modeling is becoming more and more important when studying complex biochemical systems. Most often, ordinary differential equations are employed for this purpose. However, these are only applicable when the numbers of participating molecules in the biochemical systems are large enough to be treated as concentrations. For smaller systems, stochastic simulations on discrete particle basis are more accurate. Unfortunately, there are no general rules for determining which method should be employed for exactly which problem to get the most realistic result. Therefore, we study the transition from stochastic to deterministic behavior in a widely studied system, namely the signal transduction via calcium, especially calcium oscillations. We observe that the transition occurs within a range of particle numbers, which roughly corresponds to the number of receptors and channels in the cell, and depends heavily on the attractive properties of the phase space of the respective systems dynamics. We conclude that the attractive properties of a system, expressed, e.g., by the divergence of the system, are a good measure for determining which simulation algorithm is appropriate in terms of speed and realism.

Item Type:	Journal Article
Subjects:	Q Science > QD Chemistry
Divisions:	Faculty of Science, Engineering and Medicine > Science > Life Sciences (2010- ) > Biological Sciences ( -2010)
Library of Congress Subject Headings (LCSH):	Calcium, Oscillating chemical reactions, Differential equations, Biochemistry -- Computer simulation, Biochemistry -- Mathematical models
Journal or Publication Title:	Biophysical Journal
Publisher:	Biophysical Society
ISSN:	0006-3495
Official Date:	September 2005
Dates:	Date Event September 2005 Published
Volume:	Vol.89
Number:	No.3
Page Range:	pp. 1603-1611
DOI:	10.1529/biophysj.104.057216
Status:	Peer Reviewed
Access rights to Published version:	Open Access (Creative Commons)
Funder:	Wellcome Trust (London, England), Klaus Tschira Foundation (KTF), Germany. Bundesministerium für Bildung und Forschung (BMBF)

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