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Estimating the time course of pore expansion during the spike phase of exocytotic release in mast cells of the beige mouse

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Abstract

Our objective is to determine the time course of exocytotic fusion pore opening (P) in mast cells of the beige mouse from the measured efflux of the spike phase of exocytotic release (J). We show that a pore whose meridian or radius grows linearly with time cannot reproduce the efflux. We also show that a pore that opens very quickly [relative to the diffusivity of 5-hydroxytryptamine (5-HT)] and completely (P = π) also does not mimic the experimental efflux, and estimate maximum pore angles of 70(±20)°. We show that a larger class of opening functions reproduces the rising phase and part of the decay phase and calculate pore expansion rate, pore radius and pore angle, none of which can be readily measured. In the initial stages of the spike phase (50–200 ms) when the gel matrix has not expanded significantly, this model suggests that the pore radius increases exponentially with a time constant of 82(±62) ms with pore expansion reaching its maximum velocity of 20(±7) nm ms−1. We conclude that the release process is dynamic and suggest that the velocity of pore opening (V) and the diffusivity of 5-HT (D), in addition to the size of the vesicle (R, radius), vary with time. We discuss assumptions and improvements to the model and propose that this methodology is applicable for determining P from measured J in other endocrine cells and neurons when D within the secretory vesicle is much less than D within the pore neck.

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References

  • Albillos, A., G. Dernick, H. Horstman, W. Almers, G. Alvarez de Toledo and M. Lindau (1997). The exocytotic event in chromaffin cells revealed by patch amperometry. Nature 389, 509–512.

    Article  Google Scholar 

  • Alvarez de Toledo, G., R. Fernandez-Chacon and J. M. Fernandez (1993). Release of secretory products during transient vesicle fusion. Nature 363, 554–557.

    Article  Google Scholar 

  • Amatore, C., Y. Bouret and L. Midrier (1999). Time-resolved dynamics of vesicle membrane during individual exocytotic secretion events as extracted from amperometric monitoring of adrenaline exocytosis by chromaffin cells. Chem. Eur. J. 5, 2151–2162.

    Article  Google Scholar 

  • Amatore, C., Y. Bouret, E. R. Travis and R. M. Wightman (2000). Interplay between membrane dynamics, diffusion and swelling pressure governs individual vesicular exocytotic events during release of adrenaline by chromaffin cells. Biochimie 82, 481–496.

    Article  Google Scholar 

  • Bruns, D. and R. Jahn (1995). Real-time measurement of transmitter release from single synaptic vesicles. Nature 377, 62–65.

    Article  Google Scholar 

  • Bruns, D., D. Riedel, J. Klingauf and R. Jahn (2000). Quantal release of serotonin. Neuron 28, 205–220.

    Article  Google Scholar 

  • Chandler, D. E. and J. E. Heuser (1980). Arrest of membrane fusion events in mast cells by quick freezing. J. Cell Biol. 86, 666–674.

    Article  Google Scholar 

  • Chizmadzhev, Y. A., F. S. Cohen, A. Scherbakov and J. Zimmerberg (1995). Membrane mechanics can account for fusion pore dilation in stages. Biophys. J. 69, 2489–2500.

    Google Scholar 

  • Chizmadzhev, Y. A., P. I. Kuzmin, D. A. Kumenko, J. Zimmerberg and F. S. Cohen (2000). Dynamics of fusion pores connecting membranes of different tensions. Biophys. J. 78, 2241–2256.

    Google Scholar 

  • Crank, J. (1976). The Mathematics of Diffusion, Oxford: Oxford University Press.

    Google Scholar 

  • Curran, M. J., F. S. Cohen, D. E. Chandler, P. J. Munson and J. Zimmerberg (1993). Exocytotic fusion pores exhibit semi-stable states. J. Membr. Biol. 133, 61–75.

    Google Scholar 

  • Demmel, J. W., S. C. Eisenstat, J. R. Gilbert, X. S. Li and J. W. H. Liu (1999). A supernodal approach to sparse partial pivoting. SIAM J. Matrix Anal. Appl. 20, 720–755.

    Article  MathSciNet  MATH  Google Scholar 

  • Dvorak, A. M., I. Hammel and S. J. Galli (1987). Beige mouse mast cells generated in vitro: ultrastructural analysis of maturation induced by sodium butyrate and IgE-mediated antigen dependent degranulation. Int. Arch. Allergy Appl. Immunol. 82, 261–268.

    Google Scholar 

  • Fisher, R. J., J. Pevsner and R. D. Burgoyne (2001). Control of fusion pore dynamics during exocytosis by Munc18. Science 291, 875–878.

    Article  Google Scholar 

  • Friedman, A. (1964). Partial Differential Equations of Parabolic Type, Englewood Cliffs, NJ: Prentice-Hall.

    MATH  Google Scholar 

  • Graham, M. E. and R. D. Burgoyne (2000). Comparison of cysteine string protein (Csp) and mutant α-SNAP overexpression reveals a role for Csp in late steps of membrane fusion in dense-core granule exocytosis in adrenal chromaffin cells. J. Neurosci. 20, 1281–1289.

    Google Scholar 

  • Haller, M., C. Heinemann, R. H. Chow, R. Heidelberger and E. Neher (1998). Comparison of secretory responses as measured by membrane capacitance and by amperometry. Biophys. J. 74, 2100–2113.

    Google Scholar 

  • Isakov, V. (1998). Inverse Problems for Partial Differential Equations, New York: Spinger.

    MATH  Google Scholar 

  • Johnson, R. G., S. E. Carty, B. J. Fingerhood and A. Scarpa (1980). The internal pH of mast cell granules. FEBS Lett. 120, 75–79.

    Article  Google Scholar 

  • Jones, B. F. Jr (1963). Various methods for finding unknown coefficients in parabolic differential equations. Comm. Pure Appl. Math. 16, 33–44.

    MATH  MathSciNet  Google Scholar 

  • Khanin, R., H. Parnas and L. Segel (1994). Diffusion cannot govern the discharge of neurotransmitter at fast synapses. Biophys. J. 67, 966–972.

    Google Scholar 

  • Krizaj, D., M. E. Rice, R. A. Wardle and C. Nicholson (1996). Water compartmentalization and extracellular tortuosity after osmotic changes in cerebellum of Trachemys scripta. J. Physiol. 492, 887–896.

    Google Scholar 

  • Marszalek, P. E., B. Farrell and J. M. Fernandez (1996). Ion exchange gel regulates neurotransmitter release through the exocytotic fusion pore, in Organellar Ion Channels and Transporters, Vol. 51, D. E. Clapham and B. E. Ehrlich (Eds), New York: Rockefeller University Press, pp. 211–222.

    Google Scholar 

  • Marszalek, P. E., B. Farrell, P. Verdugo and J. M. Fernandez (1997a). Kinetics of release of serotonin from isolated secretory granules. I. Amperometric detection of serotonin from electroporated granules. Biophys. J. 73, 1160–1168.

    Google Scholar 

  • Marszalek, P. E., B. Farrell, P. Verdugo and J. M. Fernandez (1997b). Kinetics of release of serotonin from isolated secretory granules. II. Ion-exchange determines the diffusivity of serotonin. Biophys. J. 73, 1169–1183.

    Google Scholar 

  • Monck, J. R., A. F. Oberhauser and J. M. Fernandez (1991). Is swelling of the secretory granule matrix the force that dilates the exocytotic fusion pore? Biophys. J. 59, 39–47.

    Google Scholar 

  • Nanavati, C., V. S. Markin, A. F. Oberhauser and J. M. Fernandez (1992). The exocytotic fusion pore modeled as a lipidic pore. Biophys. J. 63, 1118–1132.

    Google Scholar 

  • Nielsen, E. H., P. Bytzer, J. Clausen and N. Chakravarty (1981). Electron microscopic study of the regeneration in vitro of rat peritoneal mast cells after histamine secretion. Cell Tissue Res. 216, 635–645.

    Article  Google Scholar 

  • Rabenstein, D. L., P. Bratt and J. Peng (1998). Quantitative characterization of the binding of histamine to heparin. Biochemistry 37, 14121–14127.

    Google Scholar 

  • Rabenstein, D. L., P. Bratt, T. D. Schierling, J. M. Robert and W. Guo (1992). The interaction of biological molecules with heparin and related glycosaminoglycans. 1. Identification of a specific binding site for histamine. J. Am. Chem. Soc. 114, 3728–3285.

    Article  Google Scholar 

  • Rusakov, D. A. and D. M. Kullmann (1998). Extrasynaptic glutamate diffusion in the hippocampus: ultrastructural constraints, uptake and receptor activation. J. Neurosci. 18, 3158–3170.

    Google Scholar 

  • Schroeder, T. J., R. Borges, J. M. Finnegan, K. Pihel, C. Amatore and R. M. Wightman (1996). Temporally resolved independent stages of individual exocytotic secretion events. Biophys. J. 70, 1061–1068.

    Google Scholar 

  • Schroeder, T. J., Jankowoski, K. T. Kawagoe, R. M. Wightman, C. Lefrou and C. Amatore (1992). Analysis of diffusional broadening of vesicular packets of catecholamines released from biological cells during exocytosis. Anal. Chem. 64, 3077–3083.

    Article  Google Scholar 

  • Spruce, A. E., L. J. Breckenridge, A. K. Lee and W. Almers (1990). Properties of the fusion pore that forms during exocytosis of a mast cell secretory vesicle. Neuron 4, 643–654.

    Article  Google Scholar 

  • Steyer, J. A., H. Horstmann and W. Almers (1997). Transport, docking and exocytosis of single secretory granules in live chromaffin cells. Nature 388, 474–478.

    Article  Google Scholar 

  • Stiles, J. R., D. Van Helden, T. M. Bartol Jr, E. E. Salpeter and M. M. Salpeter (1996). Miniature endplate current rise times <100 μs from improved dual recordings can be modeled with passive acetylcholine diffusion from a synaptic vesicle. Proc. Natl. Acad. Sci. 93, 5747–5752.

    Article  Google Scholar 

  • Urena, J. R., A. R. Fernandez-Chacon, A. R. Benot, G. Alvarez de Toledo and J. Lopez-Barneo (1994). Hypoxia induces voltage dependent Ca2+ entry and quantal secretion in carotid body glomus cells. Proc. Natl. Acad. Sci. 91, 10208–10211.

    Google Scholar 

  • Uvnas, B. and C-H. Aborg (1977). On the cation exchanger properties of rat mast cell granules and their storage of histamine. Acta Physiol. Scand. 100, 309–314.

    Google Scholar 

  • Uvnas, B., C-H. Aborg, L. Lyssarides and J. Thyberg (1985). Cation exchanger properties of isolated rat peritoneal mast cell granules. Acta. Physiol. Scand. 125, 25–31.

    Article  Google Scholar 

  • Yurt, R. W., R. W. Leid Jr, K. F. Austen and J. E. Silbert (1976). Native heparin from rat peritoneal mast cells. J. Biol. Chem. 252, 518–521.

    Google Scholar 

  • Zhou, Z. and S. Misler (1995a). Action potential-induced quantal secretion of catecholamines from rat adrenal chromaffin cells. J. Biol. Chem. 270, 3498–3505.

    Article  Google Scholar 

  • Zhou, Z. and S. Misler (1995b). Amperometric detection of stimulus-induced quantal release of catecholamines from cultured cervical ganglion neurons. Proc. Natl. Acad. Sci. 92, 6938–6942.

    Article  Google Scholar 

  • Zimmerberg, J., M. Curran, F. S. Cohen and M. Brodwick (1987). Simultaneous electrical and optical measurements show that membrane fusion precedes secretory granule swelling during exocytosis of beige mouse mast cells. Proc. Natl. Acad. Sci. 84, 1585–1589.

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Biochemistry and Cell Biology and Keck Center for Computational Biology, Rice University, 6100 S. Main, Houston, TX, 77005, USA

    Brenda Farrell

  2. Department of Computational & Applied Mathematics, Rice University, 6100 S. Main, Houston, TX, 77005, USA

    Steven J. Cox

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  1. Brenda Farrell
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Correspondence to Brenda Farrell.

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Farrell, B., Cox, S.J. Estimating the time course of pore expansion during the spike phase of exocytotic release in mast cells of the beige mouse. Bull. Math. Biol. 64, 979–1010 (2002). https://doi.org/10.1006/bulm.2002.0308

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  • DOI: https://doi.org/10.1006/bulm.2002.0308

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