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Mathematical analysis of a proposed mechanism for oscillatory insulin secretion in perifused HIT-15 cells

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Abstract

Oscillatory secretion of insulin has been observed in many different experimental preparations ranging from pancreatic islets to the whole pancreas. Here we examine the mathematical features underlying a possible model for oscillatory secretion from the perifused, insulin-secreting cell line, HIT-15. The model includes the kinetics of uptake of glucose by GLUT transporters, the rate of glucose metabolism within the cell, and the effect of glucose on the rate of insulin secretion. Putative feedback by insulin on the rate of glucose transport into the cells is treated phenomenologically and leads to insulin oscillations similar to those observed experimentally in HIT cells. The resulting set of ordinary differential equations is simplified by time-scale analysis to a two-variable set of ordinary differential equations. Because of this simplification we can explore, in great detail, the characteristics of the oscillations and their sensitivity to parameter variation using phase plane analysis.

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References

  • Alberts, B., B. Dennis, J. Lewis, M. Raff, K. Roberts and J. D. Watson. 1989.Molecular Biology of the Cell, second edition. New York: Garland.

    Google Scholar 

  • Atwater, I., P. Carroll and M. X. Li. 1989. Electrophysiology of the pancreatic B-cell. InMolecular and Cellular Biology of Diabetes Mellitus: Insulin Secretion, Volume I, pp.49–68, B. Draznin, S. Melmed and D. LeRoith (Eds). New York: Alan R. Liss, Inc.

    Google Scholar 

  • Bendayan, M. 1992. Association of secreted insulin with particular domains of the pancreatic B-cell plasma membrane: the actin rich microvilli.J. histochem. Cytochem.40, 327–331.

    Google Scholar 

  • Bergsten, M. and B. Hellman. 1993. Glucose-induced amplitude regulation of pulsatile insulin secretion from individual pancreatic islets.Diabetes 42, 670–674.

    Google Scholar 

  • Bergstrom, R. W., W. Y. Fujimoto, D. C. Teller and C. DeHaen. 1989. Oscillatory insulin secretion in perifused isolated rat islets.Am. J. physiol. 257 (Endocrinol. Metab. 20), E479-E485.

    Google Scholar 

  • Brandt, A. M., S. McCoid, H. M. Thomas, S. A. Baldwin, A. Davis, J. C. Parker, E. M. Gibbs and G. W. Gould. 1992. Analysis of the glucose transporter content of islet cell lines: implications for glucose-stimulated insulin release.Cell. Signal. 4, 641–650.

    Article  Google Scholar 

  • Chen, L., T. Alam, J. H. Johnson, S. Hughes, C. B. Newgard and R. H. Unger. 1990. Regulation of beta-cell glucose transporter gene expression.Proc. natl. Acad. Sci. U.S.A. 87, 4088–4092.

    Article  Google Scholar 

  • Chou, H. F. and E. Ipp. 1990. Pulsatile insulin secretion in isolated rat islets.Diabetes 39, 112–117.

    Google Scholar 

  • Chou, H. F., E. Ipp, R. R. Bowsher, N. Berman, C. Ezrin and S. Griffiths. 1991. Sustained pulsatile insulin secretion from adenomatous human beta-cells.Diabetes 40, 1453–1458.

    Google Scholar 

  • Chou, H. F., N. Berman and E. Ipp. 1992. Oscillations of lactate released from islets of Langerhans: evidence for oscillatory glycolysis in beta-cells.Am. J. Physiol. 262 (Endocrinol. Metab. 25), E800-E805.

    Google Scholar 

  • Cunningham, B. A. 1993. Characterization of oscillations in insulin secretion. M.Phil. thesis, Boston University Graduate School.

  • DeYoung, G. and J. Keizer. 1992. A single pool IP3-receptor-based model for agonist stimulated oscillations in Ca2+ concentration.Proc. natl. Acad. Sci. USA 89, 9895–9899.

    Article  Google Scholar 

  • Doedel, E. 1981. Auto: A program for the automatic bifurcation analysis of autonomous systems.Conq. Num. 30, 265–284.

    MATH  MathSciNet  Google Scholar 

  • Draznin, B., M. Goodman, J. W. Leitner and K. E. Sussman. 1986. Feedback inhibition of insulin on insulin secretion in isolated pancreatic islets.Endocrinology 118, 1054–1058.

    Google Scholar 

  • Edelstein-Keshet, L. 1988.Mathematical Models in Biology. New York: Random House.

    MATH  Google Scholar 

  • Epstein, I. 1983. Oscillations and chaos in chemical systems.Physica 7D, 47–58.

    Google Scholar 

  • Garfinkel, D., L. Garfinkel, M. D. Meglasson and F. M. Matschinsky. 1984. Computer modeling identifies glucokinase as glucose sensor of pancreatic beta-cells.Am. J. Physiol. 247, R527-R536.

    Google Scholar 

  • Harrison, S. A., E. D. Buxton and M. P. Czech. 1991. Suppressed intrinsic catalytic activity of GLUT-1 glucose transporters in insulin sensitive 3T3-L1 adipocytes.Proc. Natl. Acad. Sci., USA 88, 7839–7843.

    Article  Google Scholar 

  • Hedeskov, C. J. 1980. Mechanism of glucose-induced insulin secretion.Physiol. Rev. 60, 442–509.

    Google Scholar 

  • Hellman, B., E. Gylfe, N. Wesslen, A. Hallberg, E. Grapengiesser and A. Marcstrom. 1989. Plasma membrane associated ATP as regulator of the secretory activity of the pancreatic beta cell.Exp. Clin. Endocrinol. 93, 125–135.

    Article  Google Scholar 

  • Hill, T. 1977.Free Energy Transduction in Biology. New York: Academic Press.

    Google Scholar 

  • Kahaner, D. and D. Barnett. 1989.Plod, version 4.9.

  • Keizer, J. and G. DeYoung, 1994. Simplification of a reaslistic model of IP3-induced Ca2+ oscillations.J. Theor. Biol. 166, 431–442.

    Article  Google Scholar 

  • Lang, D. A., D. R. Matthews, M. Burnett and R. C. Turner. 1979. Cyclic oscillations of basal plasma glucose and insulin concentrations in human beings.New England J. Med. 301, 1023–1027.

    Article  Google Scholar 

  • Li, X.-Y. and J. Rinzel. 1994. Equations for InsP3 receptor-mediated [Ca3+]i oscillations derived from a detailed kinetic model: a Hodgkin-Huxley like formalism.J. Theor. Biol. 166, 461–473.

    Article  Google Scholar 

  • Maki, L. B. 1994. Analysis of theoretical models describingin vitro oscillations of insulin secretion. Ph.D. thesis, University of Califorhia, Davis.

    Google Scholar 

  • Maki, L. W. and J. E. Keizer. 1995. Analysis of possible mechanisms forin vitro oscillation of insulin secretion.Am. J. physiol. 268 (Cell Physiol. 37) C: 780–791.

    Google Scholar 

  • Matschinsky, F. M. 1990. Glucokinase as glucose sensor and metabolic signal generator in pancreatic beta-cells and hepatocytes.Diabetes 39, 647–652.

    Google Scholar 

  • Meglasson, M. D. and F. M. Matschinsky. 1984. New perspectives on pancreatic islet glucokinase.Am J. Physiol. 246 (Endocrinol. Metab. 9), E1-E13.

    Google Scholar 

  • Moore, W. J. 1972.Physical Chemistry, 4th edition. Englewood Cliffs: Prentice-Hall.

    Google Scholar 

  • Newgard, C. B., C. Quaade, S. D. Hughes and J. L. Milburn. 1990. Glucokinase and glucose transporter expression in liver and islets: implications for control of glucose homoeostasis.Biochem. Soc. trans. The Starved to Fed Transition 18, 851–853.

    Google Scholar 

  • Orci, L., B. Thorens, M. Ravazzola and H. F. Lodish. 1989. Localization of the pancreatic beta cell glucose transporter to specific plasma membrane domains.Science 245, 295–297.

    Google Scholar 

  • Shimizu, T., J. C. Parker, H. Najafi and F. M. Matschinsky. 1988. Control of glucose metabolism in pancreatic beta-cells by glucokinase, hexokinase, and phosphofructokinase.Diabetes 37, 1524–1530.

    Google Scholar 

  • Sturis, J., K. S. Polonsky and E. Mosekilde. 1991. Computer model for mechanisms underlying ultradian oscillations of insulin and glucose.Am. J. Physiol. 260 (Endocrinol. Metab. 23), E801-E809.

    Google Scholar 

  • Unger, R. H. 1991. Diabetic hyperglycemia: link to impaired glucose transport in pancreatic beta cells.Science 251, 1200–1205.

    Google Scholar 

  • Wardzala, L. J., S. W. Cushman and L. B. Salans. 1978. Mechanism of insulin action on glucose transport in the isolated rat adipose cell.J. Biol. Chem. 253, 8002–8005.

    Google Scholar 

  • Whitesell, R., A. Powers, D. Regen and N. Abumrad. 1991. Transport and metabolism of glucose in an insulin-secreting cell line βTC-1.Biochem. 30, 11560–11566.

    Article  Google Scholar 

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Authors and Affiliations

  1. Institute of theoretical dynamics, University of California, 95616, Davis, CA, U.S.A.

    Laura Weiss Maki & Joel Keizer

  2. Section of Neurobiology, Physiology and Behavior, University of California, 95616, Davis, CA, U.S.A.

    Laura Weiss Maki & Joel Keizer

  3. Department of Chemistry, University of California, 95616, Davis, CA, U.S.A.

    Laura Weiss Maki & Joel Keizer

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  1. Laura Weiss Maki
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  2. Joel Keizer
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Correspondence to Joel Keizer.

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Maki, L.W., Keizer, J. Mathematical analysis of a proposed mechanism for oscillatory insulin secretion in perifused HIT-15 cells. Bltn Mathcal Biology 57, 569–591 (1995). https://doi.org/10.1007/BF02460784

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  • DOI: https://doi.org/10.1007/BF02460784

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