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Statistical analysis of calcium oscillations

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Abstract

Calcium is an important and versatile second messenger in eukaryotic cells. External signals are often transmitted to intracellular targets by oscillations of the cytosolic calcium concentration. Recently, we have experimentally shown that these oscillations consist of sequences of random spikes and depend on spatial characteristics of cells. Here, we apply further statistical analysis to experimental data in order to describe the spike generating process and compare spontaneous and agonist-induced oscillations. It turns out that these oscillations exhibit a non-resonant behavior, and, consequently, regular spiking originates by array-enhanced coherent resonance. Moreover, we present a heuristic model based on the probability density of intervals between spikes that takes a positive feedback of a spike to its successor into account. The extended model is analyzed with respect to statistical properties and information content.

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References

  1. M. Bootman, T. Collins, C. Peppiatt, L. Prothero, L. MacKenzie, P. DeSmet, M. Travers, S. Tovey, J. Seo, M. Berridge, et al., Semin. Cell Dev. Biol. 12, 3 (2001)

    Article  Google Scholar 

  2. M. Berridge, P. Lipp, M. Bootman, Nature Rev. Mol. Cell Biol. 1, 11 (2000)

    Article  Google Scholar 

  3. M. Berridge, M. Bootman, P. Lipp, Nature 395, 645 (1998)

    Article  ADS  Google Scholar 

  4. M. Falcke, Adv. Phys. 53, 255 (2004)

    Article  ADS  Google Scholar 

  5. N. Woods, K. Cuthbertson, P. Cobbold, Nature 319, 600 (1986)

    Article  ADS  Google Scholar 

  6. A. Goldbeter, Biochemical Oscillations and Cellular Rhythms (Cambridge University Press, Cambridge, 1996)

  7. A. Skupin, H. Kettenmann, U. Winkler, M. Wartenberg, H. Sauer, S. Tovey, C. Taylor, M. Falcke, Biophys. J. 94, 2404 (2008)

    Article  Google Scholar 

  8. A. Skupin, M. Falcke, Gen. Inform. 19, 69 (2008)

    Google Scholar 

  9. R. Thul, M. Falcke, Phys Rev Lett 93, 188103 (2004)

    Article  ADS  Google Scholar 

  10. E. Finch, T. Turner, S. Goldin, Science 252, 443 (1991)

    Article  ADS  Google Scholar 

  11. J. Sneyd, S. Girard, D. Clapham, Bull. Math. Biol. 55, 315 (1993)

    MATH  Google Scholar 

  12. G. Dupont, A. Goldbeter, Theoretical insights into the origin of signal induced Ca2+ oscillations, p. 449, in [14] (1989)

  13. A. Goldbeter, G. Dupont, M. Berridge, Proc. Natl. Acad. Sci. USA 87, 1461 (1990)

    Article  ADS  Google Scholar 

  14. A. Goldbeter (ed.), Cell to Cell Signalling: From Experiments to Theoretical Models (Academic Press, London, 1989)

  15. G. DeYoung, J. Keizer, Proc. Natl. Acad. Sci. USA 89, 9895 (1992)

    Article  ADS  Google Scholar 

  16. B. Wilson, J. Pfeiffer, A. Smith, J. Oliver, J. Oberdorf, R. Wojcikiewicz, Mol. Biol. Cell 9, 1465 (1998)

    Google Scholar 

  17. I. Smith, I. Parker, Proc. Natl. Acad. Sci. USA 106, 6406 (2009)

    ADS  Google Scholar 

  18. T. Rahman, A. Skupin, M. Falcke, C. Taylor, Nature 458, 655 (2009)

    Article  ADS  Google Scholar 

  19. I. Smith, S. Witgen, I. Parker, Cell Calcium 45, 65 (2009)

    Article  Google Scholar 

  20. Y. Tateishi, M. Hattori, T. Nakayama, M. Iwai, H. Bannai, T. Nakamura, T. Michikawa, T. Inoue, K. Mikoshiba, J. Biol. Chem. 280, 6816 (2004)

    Article  Google Scholar 

  21. J. Marchant, N. Callamaras, I. Parker, EMBO J. 18, 5285 (1999)

    Article  Google Scholar 

  22. J. Marchant, I. Parker, EMBO J. 20, 65 (2001)

    Article  Google Scholar 

  23. M. Falcke, Building a wave - models of the puff-to-wave transition, Vol. 623 of Lecture Notes in Physics, Chap. 13 (Springer, Berlin Heidelberg New York, 2003), p. 253

  24. A. Skupin, M. Falcke, Chaos 19, 037111 (2009)

    Article  ADS  Google Scholar 

  25. T.A. Engel, B. Helbig, D.F. Russell, L. Schimansky-Geier, A.B. Neiman, Phys. Rev. E 80, 021919 (2009)

    Article  ADS  Google Scholar 

  26. U. Fano, Phys. Rev. 72, 26 (1947)

    Article  ADS  Google Scholar 

  27. J. Middleton, M. Chacron, B. Lindner, A. Longtin, Phys. Rev. E 68, 021920 (2003)

    Article  ADS  Google Scholar 

  28. T. Engel, L. Schimansky-Geier, A. Herz, S. Schreiber, I. Erchova, J. Neurophysiol. 100, 1576 (2008)t

    Article  Google Scholar 

  29. M. Abramowitz, A. Stegun, Handbook of Mathematical Functions (Dover Publication, New York, 1970)

  30. B. Lindner, J. Garcia-Ojalvo, A. Neimann, L. Schimansky-Geier, Phys. Rep. 392, 321 (2004)

    Article  ADS  Google Scholar 

  31. T. Schwalger, L. Schimansky-Geier, Phys. Rev. E 77, 031914 (2008)

    Article  ADS  Google Scholar 

  32. C. Gardiner, Handbook of Stochastic Methods (Springer, Berlin, 1985)

  33. R. Stratonovich, Topics in the Theory of Random Noise (Gordan and Breach, New York & London, 1963)

  34. C. Shannon, Bell Syst. Tech. J. 27, 379 (1948)

    MATH  MathSciNet  Google Scholar 

  35. I. Goychuk, P. Hänggi, Phys. Rev. E 61, 4272 (1999)

    Article  ADS  Google Scholar 

  36. A. Skupin, H. Kettenmann, M. Falcke, PLoS Comp. Biol. 6, e1000870 (2010)

    Article  Google Scholar 

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Skupin, A., Falcke, M. Statistical analysis of calcium oscillations. Eur. Phys. J. Spec. Top. 187, 231–240 (2010). https://doi.org/10.1140/epjst/e2010-01288-9

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  • DOI: https://doi.org/10.1140/epjst/e2010-01288-9

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