Transition from stochastic to deterministic behavior in calcium oscillations
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. ISSN 0006-3495
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Official URL: http://dx.doi.org/10.1529/biophysj.104.057216
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 > 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|
|Official Date:||September 2005|
|Page Range:||pp. 1603-1611|
|Access rights to Published version:||Open Access|
|Funder:||Wellcome Trust (London, England), Klaus Tschira Foundation (KTF), Germany. Bundesministerium für Bildung und Forschung (BMBF)|
1. D.T. Gillespie, Approximate accelerated stochastic simulation of chemically reacting systems, J. Chem. Phys. 115 (2001), pp. 1716–1733.
2. H. Resat, H.S. Wiley and D.A. Dixon, Probability-weighted dynamic Monte Carlo method for reaction kinetics simulations, J. Phys. Chem. B 105 (2001), pp. 11026–11034.
3. E.L. Haseltine and J.B. Rawlings, Approximate simulation of coupled fast and slow reactions for stochastic chemical kinetics, J. Chem. Phys. 117 (2002), pp. 6959–6969.
4. J. Puchalka and A.M. Kierzek, Bridging the gap between stochastic and deterministic regimes in the kinetic simulations of the biochemical reaction networks, Biophys. J. 86 (2004), pp. 1357–1372.
5. K. Vasudeva and U.S. Bhalla, Adaptive stochastic-deterministic chemical kinetic simulations, Bioinformatics 20 (2004), pp. 78–84.
6. L.F. Olsen, U. Kummer, A.L. Kindzelskii and H.R. Petty, A model of the oscillatory metabolism of activated neutrophils, Biophys. J. 84 (2003), pp. 69–81.
7. D. Gonze, J. Halloy and A. Goldbeter, Emergence of coherent oscillations in stochastic models for circadian rhythms, Phys. A 342 (2004), pp. 221–233.
8. M.J. Berridge, M.D. Bootman and P. Lipp, Calcium: a life and death signal, Nature 395 (1998), pp. 645–648.
9. W.H. Li, J. Llopis, M. Whitney, G. Zlokarnik and R. Tsien, Cell-permeant caged InsP3-ester shows that Ca2+ spike frequency can optimize gene expression, Nature 392 (1998), pp. 936–944.
10. R.E. Dolmetsch, K. Xu and R.S. Lewis, Calcium oscillations increase the efficiency and specificity of gene expression, Nature 392 (1998), pp. 933–936.
11. P. De Koninck and H. Schulman, Sensitivity of CaM kinase II to the frequency of Ca2+ oscillations, Science 279 (1998), pp. 227–230.
12. E. Oancea and T. Meyer, Protein kinase C as a molecular machine for decoding calcium and diacylglycerol signals, Cell 95 (1998), pp. 307–318.
13. N.M. Woods, K.S.R. Cuthbertson and P.H. Cobbold, Repetitive transient rises in cytoplasmic free calcium in hormone-stimulated hepatocytes, Nature 319 (1986), pp. 600–602.
14. C.J. Dixon, N.M. Woods, K.S.R. Cuthbertson and P.H. Cobbold, Evidence for two Ca2+-mobilizing purinoreceptors on rat hepatocytes, Biochem. J. 269 (1990), pp. 499–502.
15. A.Z. Larsen, L.F. Olsen and U. Kummer, On the encoding and decoding of calcium signals in hepatocytes, Biophys. Chem. 107 (2004), pp. 83–99.
16. G. Dupont, S. Swillens, C. Clair, T. Tordjmann and L. Combettes, Hierarchical organization of calcium signals in liver cells, Biochim. Biophys. Acta 1498 (2000), pp. 134–152.
17. S. Schuster, M. Marhl and T. Höfer, Modelling of simple and complex calcium oscillations, Eur. J. Biochem. 269 (2002), pp. 1333–1355.
18. P. Shen and R. Larter, Chaos in intracellular Ca2+ oscillations in a new model for non-excitable cells, Cell Calcium 17 (1995), pp. 225–232.
19. G. Houart, G. Dupont and A. Goldbeter, Bursting, chaos and birhythmicity originating from self-modulation of the inositol 1,4,5-triphosphate signal in a model for intracellular Ca2+ oscillations, Bull. Math. Biol. 61 (1999), pp. 507–530.
20. U. Kummer, L.F. Olsen, C.J. Dixon, A.K. Green, E. Bornberg-Bauer and G. Baier, Switching from simple to complex oscillations in calcium signaling, Biophys. J. 79 (2000), pp. 1188–1195.
21. M. Marhl, T. Haberichter, M. Brumen and R. Heinrich, Complex calcium oscillations and the role of mitochondria and cytosolic protein, Biosystems 57 (2000), pp. 75–86. Article | PDF (279 K) | View Record in Scopus | Cited By in Scopus (58)
22. M. Kraus and B. Wolf, Cytosolic calcium oscillators: critical discussion and stochastic modeling, Biol. Signals. 2 (1993), pp. 1–15.
23. K. Prank, U. Ahlvers, F. Baumgarte, H.G. Musmann, von zur Mühlen, C. Schöfl and G. Brabant, Methoden der medizinischer Informatik, Biometrie und Epidemiologie in der modernen Informationsgesellschaft. [in German] Jahrestagung der Deutschen Gesellschaft für Informatik, Biometrie und Epidemiologie, Bremen, Germany (1998).
24. M. Falcke, On the role of stochastic channel behavior in intracellular Ca2+ dynamics, Biophys. J. 84 (2003), pp. 42–56. Article | PDF (388 K) | View Record in Scopus | Cited By in Scopus (53)
25. M. Falcke, Reading the patterns in living cells: the physics of Ca2+ signaling, Adv. Phys. 53 (2004), pp. 255–440.
26. M. Falcke, Deterministic and stochastic models of intracellular Ca2+ waves, N. J. Phys. 5 (2003), pp. 1–28.
27. J.W. Shuai and P. Jung, Stochastic properties of Ca2+ release of inositol-1,4,5,-trisphosphate receptor clusters, Biophys. J. 83 (2002), pp. 87–97.
28. D.T. Gillespie, A general method for numerically simulating the stochastic time evolution of coupled chemical reactions, J. Comput. Phys. 22 (1976), pp.
29. C.J. Dixon, P.H. Cobbold and A.K. Green, Actions of ADP, but not ATP, on cytosolic free Ca2+ in single rat hepatocytes mimicked by 2-methylthioATP, Br. J. Pharmacol. 116 (1995), pp. 1979–1984.
30. P.H. Cobbold and J.A.C. Lee, Aequorin measurements of cytoplasmic free calcium. In: J.G. McCormack and P.H. Cobbold, Editors, Cellular Calcium: A Practical Approach, I.R.L. Press, Oxford, UK (1991), pp. 55–81.
31. H. Kantz, Quantifying the closeness of fractal measures, Phys. Rev. E 49 (1994), pp. 5091–5097.
32. N.T. Koussoulos, Spectral moments and the analysis of chaotic systems, Int. J. Bifur. & Chaos 11 (2001), pp. 2051–2059.
33. L.F. Olsen, A. Lunding and U. Kummer, Mechanism of melatonin-induced oscillations in the peroxidase-oxidase reaction, Arch. Biochem. Biophys. 410 (2003), pp. 287–295.
34. A.K. Green, P.H. Cobbold and C.J. Dixon, Cytosolic free Ca2+ oscillations induced by diadenosine 5′,5triple prime-P1,P3-triphosphate and diadenosine 5′,5triple prime-P1,P4-tetraphosphate in single rat hepatocytes are indistinguishable from those induced by ADP and ATP respectively, Biochem. J. 310 (1995), pp. 629–635.
35. P. Nicotera, G. Bellomo and S. Orrenius, Calcium-mediated mechanisms in chemically induced cell death, Annu. Rev. Pharmacol. Toxicol. 32 (1992), pp. 449–470.
36. M. Marhl and S. Schuster, Under what condition signal transduction pathways are highly flexible in response to external forcing? A case study on calcium oscillations, J. Theor. Biol. 224 (2003), pp. 491–501.
37. M. Perc and M. Marhl, Sensitivity and flexibility of regular and chaotic calcium oscillations, Biophys. Chem. 104 (2003), pp. 509–522.
38. J.B. Gao, C.C. Chen, S.K. Hwang and J.M. Liu, Noise-induced chaos, Int. J. Mod. Phys. B 13 (1999), pp. 3283–3305.
39. U. Kummer, G. Baier and L.F. Olsen, Robustness in a model for calcium signal transduction dynamics. In: J.S. Hofmeyr, J.M. Rohwer and J.L. Snoep, Editors, Proceedings of BTK2000: Animating the Cellular Map, Stellenbosch University Press, Stellenbosch, South Africa (2000), pp. 171–176.
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