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Biophys. J. BioFAST: First Published July 1, 2005. doi:10.1529/biophysj.104.057216
© 2005 by the Biophysical Society.

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Ursula Kummer
Jürgen Pahle
Anne K. Green
Marko Marhl
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BIOPHYSICAL THEORY AND MODELING

Transition from Stochastic to Deterministic Behaviour in Calcium Oscillations

Ursula Kummer 1*, Borut Krajnc 2, Jürgen Pahle 1, Anne K. Green 3, C. Jane Dixon 4 and Marko Marhl 2

1 EML Research
2 University of Maribor
3 University of Warwick
4 De Montfort University

* To whom correspondence should be addressed. E-mail: ursula.kummer{at}eml-r.villa-bosch.de.

Submitted on November 30, 2004
Revised on December 23, 2004
Accepted on 16 June 2005


  Abstract
Simulation and modeling is becoming more and more important when studying complex biochemical systems. Most often, ordinary differential equations (ODEs) 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 in order 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.

Key Words: bursting oscillations, calcium oscillations, deterministic simulations, stochastic simulations




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Copyright © 2005 by the Biophysical Society.