BetaSys pp 505-538 | Cite as

Geometric and Electromagnetic Aspects of Fusion Pore Making

  • Darya Apushkinskaya
  • Evgeny Apushkinsky
  • Bernhelm Booß-BavnbekEmail author
  • Martin Koch
Part of the Systems Biology book series (SYSTBIOL, volume 2)


For regulated exocytosis, we model the morphology and dynamics of the making of the fusion pore or porosome as a cup-shaped lipoprotein structure (a dimple or pit) on the cytosol side of the plasma membrane. We describe the formation of the dimple by a free boundary problem. We discuss the various forces acting and analyse the magnetic character of the wandering electromagnetic field wave produced by intracellular spatially distributed pulsating (and well-observed) release and binding of Ca2+ ions anteceding the bilayer membrane vesicle fusion of exocytosis. Our approach explains the energy efficiency of the dimple formation prior to hemifusion and fusion pore and the observed flickering in secretion. It provides a frame to relate characteristic time length of exocytosis to the frequency, amplitude and direction of propagation of the underlying electromagnetic field wave. We sketch a comprehensive experimental programme to verify – or falsify – our mathematical and physical assumptions and conclusions where conclusive evidence still is missing for pancreatic β-cells.


Calcium oscillations Dimple formation Free boundary problems Fusion pore Lorentz force Maxwell equations Pancreatic β-cell Plasma membrane Regulated exocytosis 



The first author was partially supported by the Russian Foundation for Basic Research (grant no. 09-01-00729). The third author acknowledges the support by the Danish network Modeling, Estimation and Control of Biotechnological Systems (MECOBS). We four thank the referees for their thoughtful comments to and harsh criticism of a first draft and F. Pociot and J. Størling for their corrections and helpful suggestions which led to many improvements. Referees and colleagues went clearly beyond the call of duty, and we are indebted to them.


  1. 1.
    Alberts B et al (2002) Molecular biology of the cell, 4th edn. Garland Science, Taylor and Francis Group, New York, NY, p 757Google Scholar
  2. 2.
    Koch M et al (2007) Can single electrons initiate fusion of biological membranes? Biophys Rev Lett 2(1):23–31, Jan 2007CrossRefGoogle Scholar
  3. 3.
    Lentz BR et al (2000) Protein machines and lipid assemblies: current views of cell membrane fusion. Curr Opin Struct Biol 10:607–615PubMedCrossRefGoogle Scholar
  4. 4.
    Rorsman P, Renström E (2003) Insulin granule dynamics in pancreatic beta cells. Diabetologia 46:1029–1045PubMedCrossRefGoogle Scholar
  5. 5.
    Renström E, Rorsman P (2007) Regulation of insulin granule exocytosis. In: Seino S, Bell GI (eds) Pancreatic beta cell in health and disease, Springer, Tokyo, pp 146–176Google Scholar
  6. 6.
    Shillcock JC, Lipowsky R (2006) The computational route from bilayer membranes to vesicle fusion. J Phys Condens Matter 18:S1191–S1219CrossRefGoogle Scholar
  7. 7.
    Grodsky GM (1972) A threshold distribution hypothesis for packet storage of insulin and its mathematical modelling. J Clin Invest 51:2047–2059, Aug 1972PubMedCrossRefGoogle Scholar
  8. 8.
    Chen Y, Wang S, Sherman A (2008) Identifying the targets of the amplifying pathway for insulin secretion in pancreatic beta cells by kinetic modeling of granule exocytosis. Biophys J 95(5):2226–2241, Sept 2008PubMedCrossRefGoogle Scholar
  9. 9.
    Caflisch RE, Li B (2002) Analysis of island dynamics in epitaxial growth of thin films. Multiscale Model Sim 1(1):150–171CrossRefGoogle Scholar
  10. 10.
    Le Bris C (2006) Mathematical and numerical analysis for molecular simulation: accomplishments and challenges. In Sanz-Solé M. et al (eds) Proceedings of international congress mathematicians, Madrid 2006, Zürich, European Mathematical Society, p 1506Google Scholar
  11. 11.
    Bazalyi BV, Friedman A (2003) A free boundary problem for an elliptic-parabolic system: application to a model of tumor growth. Comm Partial Differ Equ 28(3–4):517–560Google Scholar
  12. 12.
    Bazalyi B, Friedman A (2003) Global existence and asymptotic stability for an elliptic-parabolic free boundary problem: an application to a model of tumor growth. Indiana Univ Math J 52(5):1265–1304CrossRefGoogle Scholar
  13. 13.
    Tao Y, Yoshida N, Guo Q (2004) Nonlinear analysis of a model of vascular tumor growth and treatment. Nonlinearity 17:867–895CrossRefGoogle Scholar
  14. 14.
    Tao Y, Chen M (2006) An elliptic-hyperbolic free boundary problem modelling cancer therapy. Nonlinearity 19:419–440CrossRefGoogle Scholar
  15. 15.
    Ni D, Shi H, Yin Y (2005) Theoretical analysis of adhering lipid vesicles with free edges. Colloids Surf B: Biointerfaces 46:162–168CrossRefGoogle Scholar
  16. 16.
    Pociot F, Størling J 18 March 2010 Letter to the authors.Google Scholar
  17. 17.
    Jackson JD (1999) Classical electrodynamics, 3rd edn. Wiley, New York, NYGoogle Scholar
  18. 18.
    Monck JR, Fernandez JM (1992) The exocytotic fusion pore. J Cell Biol 119(6):1395–1404, Dec 1992PubMedCrossRefGoogle Scholar
  19. 19.
    Rosenheck K (1998) Evaluation of the electrostatic field strength at the site of exocytosis in adrenal chromaffin cells. Biophys J 75:1237–1243, Sept 1998PubMedCrossRefGoogle Scholar
  20. 20.
    Kraus M, Wolf Bj, Wolf Be (1996) Crosstalk between cellular morphology and calcium oscillation patterns Insights from a stochastic computer model. Cell Calcium 19(6):461–472, June 1996PubMedCrossRefGoogle Scholar
  21. 21.
  22. 22.
    Salazar C, Politi AZ, Höfer T (2008) Decoding of calcium oscillations by phosphorylation cycles: analytic results. Biophys J 94:1203–1215, Feb 2008PubMedCrossRefGoogle Scholar
  23. 23.
    Jahn R, Lang T, Südhoff TC (2003) Membrane fusion. Cell 112:519–533, 21 Feb 2003PubMedCrossRefGoogle Scholar
  24. 24.
    Berridge MJ, Bootman MD, Roderick HL (2003) Ca2+ signaling: dynamics, homeostasis and remodeling. Nat Rev Mol Cell Biol 4:517–529PubMedCrossRefGoogle Scholar
  25. 25.
    Gaspers LD, Thomas AP (2005) Calcium signaling in liver. Cell Calcium 38:329–342PubMedCrossRefGoogle Scholar
  26. 26.
    Noske AB, Costin AJ, Morgan GP, Marsh BJ (2007) Expedited approaches to whole cell electron tomography and organelle mark-up in situ in high-pressure frozen pancreatic islets. J Struct Biol 161(3):298–313PubMedCrossRefGoogle Scholar
  27. 27.
  28. 28.
    Jensen KA (1957) Almen Kemi. CopenhagenGoogle Scholar
  29. 29.
    Frankel RB, Blakemore RP (eds) (1991) Iron biominerals - proceedings of a conference on iron biominerals, held July 31–August 1, 1989, at the University of New Hampshire, Durham, Plenum Press, New York, NYGoogle Scholar
  30. 30.
    Chandler DE, Heuser J (1979) Membrane fusion during secretion. J Cell Biol 83:91–108, Oct 1979PubMedCrossRefGoogle Scholar
  31. 31.
    Chandler DE, Heuser J (1980) Arrest of membrane fusion events in mast cells by quick–freezing. J Cell Biol 86(2):666–674, Aug 1980PubMedCrossRefGoogle Scholar
  32. 32.
    Curran MJ, Cohen FS, Chandler DE, Munson PJ, Zimmerberg J (1993) Exocytotic fusion pores exhibit semi–stable states. J Membrane Biol 133:61–75, Oct 1993CrossRefGoogle Scholar
  33. 33.
    Jena BP, Cho S-J, Jeremic A, Stromer MH, Abu-Hamdah R (2003) Stucture and composition of the fusion pore. Biophys J 84:1337–1343, Feb 2003PubMedCrossRefGoogle Scholar
  34. 34.
    Fernandez JM, Neher E, Gomperts BD (1984) Capacitance measurements reveal stepwise fusion events in degranulating mast cells. Nature 312:453–455PubMedCrossRefGoogle Scholar
  35. 35.
    Churchill RV (1958) Operational mathematics, 3rd edn. Mc Graw Hill, Boston, MAGoogle Scholar
  36. 36.
    Logan JD (2004) Applied partial differential equations, 2. edn. Undergraduate Texts in Mathematics, SpringerGoogle Scholar
  37. 37.
    Tipler PA (1991) Physics for Scientists and Engineers, 3. edn. Worth New York, NYGoogle Scholar
  38. 38.
    Friedman A (1982) Variational principles and free-boundary problems. Pure Appl math, John Wiley & Sons Inc.Google Scholar
  39. 39.
    Fasano A, Primicerio M (eds) (1983) Free boundary problems: theory and applications, vol 2. London, Pitman Books LtdGoogle Scholar
  40. 40.
    Caffarelli LA, Petrosyan A, Shahgholian H (2004) Regularity of a free boundary in parabolic potential theory. J Am Math Soc 17:827–869 (electronic)CrossRefGoogle Scholar
  41. 41.
    Blanchet A (2006) On the singular set of the parabolic obstacle problem. J Differ Equ 231:656–672CrossRefGoogle Scholar
  42. 42.
    Blanchet A, Dolbeault J, Monneau R (2006) On the continuity of the time derivative of the solution to the parabolic obstacle problem with variable coefficients. J Math Pures Appl (9) 85(3):371–414Google Scholar
  43. 43.
    Weiss GS (1999) Self-similar blow-up and Hausdorff dimension estimates for a class of parabolic free boundary problems. SIAM J Math Anal 30:623–644 (electronic)CrossRefGoogle Scholar
  44. 44.
    Blanchet A (2006) On the regularity of the free boundary in the parabolic obstacle problem. Application to American options. Nonlinear Anal 65:1362–1378CrossRefGoogle Scholar
  45. 45.
    Fridlyand LE, Tamarina N, Philipson LH (2003) Modeling the Ca2+ flux in pancreatic beta-cells: role of the plasma membrane and intracellular stores. Am J Physiol Endocrinol Metab 285:E138–E154PubMedGoogle Scholar
  46. 46.
    Henriksen JR, Ipsen JH (2004) Measurement of membrane elasticity by micro-pipette aspiration. Eur Phys J E 14:149–167PubMedCrossRefGoogle Scholar
  47. 47.
    Bicknese S, Periasamy N, Shohet SB, Verkman AS (1993) Cytoplasmic viscosity near the cell plasma membrane: measurement by evanescent field frequency-domain microfluorimetry. Biophys J 65:1272–1282, Sep 1993PubMedCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Darya Apushkinskaya
    • 1
  • Evgeny Apushkinsky
    • 2
  • Bernhelm Booß-Bavnbek
    • 3
    Email author
  • Martin Koch
    • 4
  1. 1.Department of MathematicsSaarland UniversitySaarbrückenGermany
  2. 2.Experimental Physics DepartmentSt. Petersburg State Polytechnical UniversitySt. PetersburgRussia
  3. 3.Department of Science, Systems and Models/IMFUFARoskilde UniversityRoskildeDenmark
  4. 4.Feldkraft Ltd.CopenhagenDenmark

Personalised recommendations