Selective Regulation of Protein Activity by Complex Ca2+ Oscillations: A Theoretical Study

  • Beate Knoke
  • Marko Marhl
  • Stefan Schuster
Part of the Modeling and Simulation in Science, Engineering and Technology book series (MSSET)


Calcium oscillations play an important role in intracellular signal transduction. As a second messenger, Ca2+ represents a link between several input signals and several target processes in the cell. Whereas the frequency of simple Ca2+ oscillations enables a selective activation of a specific protein and herewith a particular process, the question arises of how at the same time two or more classes of proteins can be specifically regulated. The question is general and concerns the problem of how one second messenger can transmit more than one signal simultaneously (bow-tie structure of signalling). To investigate whether a complex Ca2+ signal like bursting, a succession of low-peak and high-peak oscillatory phases, could selectively activate different proteins, several bursting patterns with simplified square pulses were applied in a theoretical model. The results indicate that bursting Ca2+ oscillations allow a differential regulation of two different calcium-binding proteins, and hence, perform the desired function.


Bow-tie structure of signalling calcium oscillations bursting decoding 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Berridge, M.J., Bootman, M.D., Lipp, P.: Calcium–a life and death signal. Nature, 395, 645–648 (1998).CrossRefGoogle Scholar
  2. 2.
    Dupont, G., Swillens, S., Clair, C., Tordjmann, T., Combettes, L.: Hierarchical organization of calcium signals in hepatocytes: from experiments to models. Biochim. Biophys. Acta, 1498, 134–152 (2000).CrossRefGoogle Scholar
  3. 3.
    Falcke, M.: Reading the patterns in living cells—the physics of Ca2+signaling. Adv. Phys., 53, 255–440 (2004).CrossRefGoogle Scholar
  4. 4.
    Schuster, S., Marhl, M., Höfer, T.: Modelling of simple and complex calcium oscillations. From single-cell responses to intercellular signalling. FEBS J., 269, 1333–1355 (2002).Google Scholar
  5. 5.
    Goldbeter, A.: Biochemical Oscillations and Cellular Rhythms. Cambridge University Press, Cambridge (1996).zbMATHGoogle Scholar
  6. 6.
    De Koninck, P., Schulman, H.: Sensitivity of CaM kinase II to the frequency of Ca2+oscillations. Science, 279, 227–230 (1998).CrossRefGoogle Scholar
  7. 7.
    Kummer, U., Olsen, L.F., Dixon, C.J., Green, A.K., Bornberg-Bauer, E., Baier, G.: Switching from simple to complex oscillations in calcium signaling. Biophys. J., 79, 1188–1195 (2000).CrossRefGoogle Scholar
  8. 8.
    Dupont, G., Houart, G., De Koninck, P.: Sensitivity of CaM kinase II to the frequency of Ca2 +oscillations: a simple model. Cell Calcium, 34, 485–497 (2003).CrossRefGoogle Scholar
  9. 9.
    Dolmetsch, R.E., Lewis, R.S., Goodnow, C.C., Healy, J.I.: Differential activation of transcription factors induced by Ca2 +response amplitude and duration. Nature, 386, 855–858 (1997).CrossRefGoogle Scholar
  10. 10.
    Prank, K., Gabbiani, F., Brabant, G.: Coding ef?ciency and information rates in transmembrane signaling. Biosystems, 55, 15–22 (2000).CrossRefGoogle Scholar
  11. 11.
    Tompa, P., Toth-Boconadi, R., Friedrich, P.: Frequency decoding of fast calcium oscillations by calpain. Cell Calcium, 29, 161–170 (2001).CrossRefGoogle Scholar
  12. 12.
    Van Eldik, L.J., Watterson, D.M.: Calmodulin and Signal Transduction. Academic Press, London (1998).Google Scholar
  13. 13.
    Colbran, R.J.: Targeting of calcium/calmodulin-dependent protein kinase II. Biochem. J., 378, 1–16 (2004).CrossRefGoogle Scholar
  14. 14.
    Stull, J.T., Tansey, M.G., Tang, D.C., Word, R.A., Kamm, K.E.: Phosphorylation of myosin light chain kinase: a cellular mechanism for Ca2 +desensitization. Mol. Cell. Biochem., 127–128, 229–237 (1993).CrossRefGoogle Scholar
  15. 15.
    Webb, B.L.J., Hirst, S.J., Giembycz, M.A.: Protein kinase C isoenzymes: a review of their structure, regulation and role in regulating airways smooth muscle tone and mitogenesis. Brit. J. Pharmacol., 130, 1433–1452 (2000).CrossRefGoogle Scholar
  16. 16.
    Dixon, C.J., Woods, N.M., Cuthbertson, K.S.R., Cobbold, P.H.: Evidence for two Ca2 +mobilizing purinoceptors on rat hepatocytes. Biochem. J., 269, 499–502 (1990).Google Scholar
  17. 17.
    Dixon, C.J.: Evidence that 2-methylthioATP and 2-methylthioADP are both agonists at the rat hepatocyte P2Y1 receptor. Brit. J. Pharmacol., 130, 664–668 (2000).CrossRefGoogle Scholar
  18. 18.
    Izhikevich, E.M.: Neural excitability, spiking and bursting. Int. J. Bifurcat. Chaos, 10, 1171– 1266 (2000).zbMATHCrossRefMathSciNetGoogle Scholar
  19. 19.
    Borghans, J.A.M., Dupont, G., Goldbeter, A.: Complex intracellular calcium oscillations. A theoretical exploration of possible mechanisms. Biophys. Chem., 66, 25–41 (1997).CrossRefGoogle Scholar
  20. 20.
    Houart, G., Dupont, G., Goldbeter, A.: Bursting, chaos and birhythmicity originating from self-modulation of the inositol 1,4,5,-trisphosphate signal in a model for intracellular Ca2 +oscillations. Bull. Math. Biol., 61, 507–530 (1999).CrossRefGoogle Scholar
  21. 21.
    Marhl, M., Haberichter, T., Brumen, M., Heinrich, R.: Complex calcium oscillations and the role of mitochondria and cytosolic proteins. BioSystems, 57, 75–86 (2000).CrossRefGoogle Scholar
  22. 22.
    Perc, M., Marhl, M.: Different types of bursting calcium oscillations in non-excitable cells. Chaos Sol. Fract., 18, 759–773 (2003).zbMATHCrossRefMathSciNetGoogle Scholar
  23. 23.
    Larsen, A.Z., Kummer, U.: Information processing in calcium signal transduction. In: Falcke, M., Malchow, D. (Eds.) Understanding Calcium Dynamics: Experiments and Theory, Lecture Notes in Physics, Vol. 623. Springer, Berlin, pp. 153–178 (2003).Google Scholar
  24. 24.
    Rozi, A., Jia, Y.: A theoretical study of effects of cytosolic Ca2 +oscillations on activation of glycogen phosphorylase. Biophys. Chem., 106, 193–202 (2003).CrossRefGoogle Scholar
  25. 25.
    Larsen, A.Z., Olsen, L.F., Kummer, U.: On the encoding and decoding of calcium signals in hepatocytes. Biophys. Chem., 107, 83–99 (2004).CrossRefGoogle Scholar
  26. 26.
    Csete, M., Doyle, J.: Bow ties, metabolism and disease. Trends Biotechnol., 22, 446–450 (2004).CrossRefGoogle Scholar
  27. 27.
    Ma, H.W., Zeng, A.P.: The connectivity structure, giant strong component and centrality of metabolic networks. Bioinformatics, 19, 1423–1430 (2003).CrossRefGoogle Scholar
  28. 28.
    Somsen, O.J, Siderius, M., Bauer, F.F., Snoep, J.L., Westerhoff, H.V.: Selectivity in overlapping MAP kinase cascades. J. Theor. Biol., 218, 343–354 (2002).CrossRefMathSciNetGoogle Scholar
  29. 29.
    Li, Y.-X., Goldbeter, A.: Pulsatile signaling in intercellular communication. Biophys. J., 61, 161–171 (1992).Google Scholar
  30. 30.
    . Salazar, C., Politi, A., Höfer, T.: Decoding of calcium oscillations by phosphorylation cycles. Genome Informatics Series, 15, 50–51 (2004).Google Scholar
  31. 31.
    Gall, D., Baus, E., Dupont, G.: Activation of the liver glycogen phosphorylase by Ca2 +oscillations: a theoretical study. J. Theor. Biol., 207, 445–454 (2000).CrossRefGoogle Scholar
  32. 32.
    Shen, Y., Lee, Y.S., Soelaiman, S., Bergson, P., Lu, D., Chen, A., Beckingham, K., Grabarek, Z., Mrksich, M., Tang, W.-J.: Physiological calcium concentrations regulate calmodulin binding and catalysis of adenylyl cyclase exotoxins. EMBO J., 21, 6721–6732 (2002).CrossRefGoogle Scholar
  33. 33.
    Soelaiman, S., Wei, B.Q., Bergson, P., Lee, Y.-S., Shen, Y., Mrksich, M., Shoichet, B.K., Tang, W.-J.: Structure-based inhibitor discovery against adenylyl cyclase toxins from pathogenic bacteria that cause anthrax and whooping cough. J. Biol. Chem., 278, 25990– 25997 (2003).CrossRefGoogle Scholar
  34. 34.
    Falke, J.J., Drake, S.K., Hazard A.L., Peersen, O.B.: Molecular tuning of ion binding to calcium signaling proteins. Quart. Rev. Biophys., 27, 219–290 (1994).Google Scholar
  35. 35.
    Marhl, M., Schuster, S., Brumen, M., Heinrich, R.: Modelling oscillations of calcium and endoplasmatic reticulum transmembrane potential. Role of the signalling and buffering proteins and of the size of the Ca2 +sequestering ER subcompartments. Bioelectrochem. Bioenerg., 46, 79–90 (1998).CrossRefGoogle Scholar
  36. 36.
    Segel, I.H.: Enzyme Kinetics. Wiley, New York (1993).Google Scholar
  37. 37.
    Schuster, S., Knoke, B., Marhl, M.: Differential regulation of proteins by bursting calcium oscillations—a theoretical study. BioSystems, 81, 49–63 (2005).CrossRefGoogle Scholar
  38. 38.
    . Bezprozvanny, I., Watras, J., Ehrlich, B.E.: Bell-shaped calcium-response curves of Ins(1,4,5)P3-and calcium-gated channels from endoplasmic reticulum of cerebellum. Nature, 351, 751–754 (1991).CrossRefGoogle Scholar
  39. 39.
    De Young, G.W., Keizer, J.: A single-pool inositol 1,4,5-trisphosphate-receptor-based model for agonist-stimulated oscillations in Ca2 +concentration. Proc. Nat. Acad. Sci. USA, 89, 9895–9899 (1992).CrossRefGoogle Scholar
  40. 40.
    Ulmer, T.S., Soelaiman, S., Li, S., Klee, C.B., Tang, W.-J., Bax, A.: Calcium dependence of the interaction between calmodulin and anthrax edema factor. J. Biol. Chem., 278, 29261– 29266 (2003).CrossRefGoogle Scholar
  41. 41.
    Cho, M.J., Vaghy, P.L., Kondo, R., Lee, S.H., Davis, J.P., Rehl, R., Heo, W.D., Johnson, J.D.: Reciprocal regulation of mammalian nitric oxide synthase and calcineurin by plant calmodulin isoforms. Biochemistry, 37, 15593–15597 (1998).CrossRefGoogle Scholar
  42. 42.
    Lee, S.H., Kim, J.C., Lee, M.S., Heo, W.D., Seo, H.Y., Yoon, H.W., Hong, J.C., Lee, S.Y., Bahk, J.D., Hwang, I., Cho, M.J.: Identi?cation of a novel divergent calmodulin isoform from soybean which has differential ability to activate calmodulin-dependent enzymes. J. Biol. Chem., 270, 21806–21812 (1995).CrossRefGoogle Scholar
  43. 43.
    Lee, S.H., Seo, H.Y., Kim, J.C., Heo, W.D., Chung, W.S., Lee, K.J., Kim, M.C., Cheong, Y.H., Choi, J.Y., Lim, C.O., Cho, M.J.: Differential activation of NAD kinase by plant calmodulin isoforms. J. Biological Chemistry, 272, 9252–9259 (1997).CrossRefGoogle Scholar
  44. 44.
    Lee, S.H., Johnson, J.D., Walsh, M.P., van Lierop, J.E., Sutherland, C., Xu, A., Snedden, W.A., Kosk-Kosicka, D., Fromm, H., Narayanan, N., Cho, M.J.: Differential regulation of Ca2 +/calmodulin-dependent enzymes by plant calmodulin isoforms and free Ca2 +concentration. J. Biol. Chem., 350, 299–306 (2000).Google Scholar
  45. 45.
    Crawford, N.M., Guo, F.-Q.: New insights into nitric oxide metabolism and regulatory functions. Trends Plant Sci., 10, 195–200 (2005).CrossRefGoogle Scholar
  46. 46.
    del Rio, L.A., Corpasa, F.J., Barroso, J.B.: Nitric oxide and nitric oxide synthase activity in plants. Phytochemistry, 65, 783–792 (2004).CrossRefGoogle Scholar
  47. 47.
    . Weissman, B.A., Jones, C.L., Liu, Q., Gross, S.S.: Activation and inactivation of neuronal nitric oxide synthase: characterization of Ca2 +-dependent [125I]Calmodulin binding. Eur. J. Pharmacol., 435, 9–18 (2002).CrossRefGoogle Scholar
  48. 48.
    Delledonne, M., Xia, Y., Dixon, R.A., Lamb, C.: Nitric oxide functions as a signal in plant disease resistance. Nature, 394, 585–588 (1998).CrossRefGoogle Scholar
  49. 49.
    Durner, J., Wendehenne, D., Klessig, D.F.: Defense gene induction in tobacco by nitric oxide, cyclic GMP, and cyclic ADP-ribose. Proc. Nat. Acad. Sci. USA, 95, 10328–10333 (1998).CrossRefGoogle Scholar
  50. 50.
    Bouche, N., Yellin, A., Snedden, W.A., Fromm, H.: Plant-speci?c calmodulin-binding proteins. Annu. Rev. Plant Biol., 56, 435–466 (2005).CrossRefGoogle Scholar
  51. 51.
    White, P.J., Broadley, M.R.: Calcium in plants. Annals of Botany, 92, 487–511 (2003).CrossRefGoogle Scholar
  52. 52.
    Nimchuk, Z., Eulgem, T., Holt, B.F., Dangl, J.L.: Recognition and response in the plant immune system. Annu. Rev. Genet., 37, 579–609 (2003).CrossRefGoogle Scholar
  53. 53.
    Heo, W.D., Lee, S.H., Kim, M.C., Kim, J.C., Chung, W.S., Chun, H.J., Lee, K.J., Park, C.Y., Park, H.C., Choi, J.Y., Cho, M.J.: Involvement of speci?c calmodulin isoforms in salicylic acid-independent activation of plant disease resistance responses. Proc. Nat. Acad. Sci. USA, 96, 766–771 (1999).CrossRefGoogle Scholar
  54. 54.
    Berridge, M.J.: The AM and FM of calcium signalling. Nature, 386, 759–760 (1997).CrossRefGoogle Scholar
  55. 55.
    Marhl, M., Perc, M., Schuster, S.: Selective regulation of cellular processes via protein cascades acting as band-pass ?lters for time-limited oscillations. FEBS Lett., 579, 5461– 5465 (2005).Google Scholar
  56. 56.
    Marhl, M., Perc, M., Schuster, S.: A minimal model for decoding of time-limited Ca2+oscillations. Biophys. Chem., 120, 161–167 (2006).CrossRefGoogle Scholar

Copyright information

© springer 2007

Authors and Affiliations

  • Beate Knoke
    • 2
  • Marko Marhl
    • 1
  • Stefan Schuster
    • 2
  1. 1.Dept. of Bioinformatics, Faculty of Biology and PharmaceuticsFriedrich-Schiller University of JenaErnst-Abbe-Platz 2Germany
  2. 2.Dept. of Physics, Faculty of Education, University of Maribor, MariborUniversity of Maribor2000 MariborSlovenia

Personalised recommendations