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Transition from stochastic to deterministic behavior in calcium oscillations

By U. (Ursula) Kummer, Borut Krajnc, Jürgen Pahle, Anne K. Green, C. Jane Dixon and Marko Marhl


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

Topics: QD
Publisher: Biophysical Society
Year: 2005
OAI identifier:

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  5. (1991). Aequorin measurements of cytoplasmic free calcium. In Cellular Calcium: A Practical Approach.
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  11. (1992). Calcium-mediated mechanisms in chemically induced cell death. doi
  12. (1998). Calcium: a life and death signal. doi
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  14. (1995). Chaos in intracellular Ca 21 oscillations in a new model for non-excitable cells. Cell Calcium. doi
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  16. (1993). Cytosolic calcium oscillators: critical discussion and stochastic modeling. doi
  17. (1995). Cytosolic free Ca 21 oscillations induced by diadenosine 59,5999-P1,P3-triphosphate and diadenosine 59,5999-P1,P4-tetraphosphate in single rat hepatocytes are indistinguishable from those induced by ADP and ATP respectively.
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  20. Evidence for two Ca 21-mobilizing purinoreceptors on rat hepatocytes.
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  22. (2003). Mechanism of melatonin-induced oscillations in the peroxidase-oxidase reaction. doi
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  24. (1999). Noiseinduced chaos.
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  26. (2003). On the role of stochastic channel behavior in intracellular Ca 21 dynamics. doi
  27. (2001). Probability-weighted dynamic Monte Carlo method for reaction kinetics simulations. doi
  28. (1998). Protein kinase C as a molecular machine for decoding calcium and diacylglycerol signals. doi
  29. (1994). Quantifying the closeness of fractal measures. doi
  30. (2004). Reading the patterns in living cells: the physics of Ca 21 signaling. doi
  31. (1986). Repetitive transient rises in cytoplasmic free calcium in hormonestimulated hepatocytes. doi
  32. (2000). Robustness in a model for calcium signal transduction dynamics.
  33. (2003). Sensitivity and flexibility of regular and chaotic calcium oscillations. doi
  34. (1998). Sensitivity of CaM kinase II to the frequency of Ca 21 oscillations. doi
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