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Study on bursting of pancreatic cells in codimension-2 bifurcation regions

Yang Zhuo-Qin Guan Ting-Ting Gan Chun-Biao Zhang Jiao-Ying

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Study on bursting of pancreatic cells in codimension-2 bifurcation regions

Yang Zhuo-Qin, Guan Ting-Ting, Gan Chun-Biao, Zhang Jiao-Ying
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  • Electrical activities of insulin secretion in pancreatic islets are characterized by bursts of action potentials. With a simple but representative Vries-Sherman model, we determine the regions of different types of bursting in two-parameter plane through the two-parameter bifurcation analysis of the fast subsystem. Moreover, fast/slow analysis is used to reveal topological types of bursting patterns for different values of the parameter Vm and transition mechanisms between them.
    [1]

    Chou H F, Ipp E 1990 Diabetes 39 112

    [2]
    [3]

    Longo E A, Tornheim K, Deeney J T, Varnum B A, Tillotson D, Prentki M, Corkey B E 1991 J. Biol. Chem. 266 9314

    [4]

    Omeara N M, Sturis J, Blackman J D, Byrne M M, Jaspan J B, Thistlethwaite J R, Polonsky K S 1993 Diabetes 42 855

    [5]
    [6]

    Bertram R, Butte M J, Kiemel T and Sherman A 1995 Bull. Math. Biol. 57 413

    [7]
    [8]
    [9]

    Rinzel J 1987 Lecture Notes in Biomathematics (New York: Springer-Verlag) p267

    [10]

    Izhikevich E M 2000 Int. J. Bifur. and Chaos 10 1171

    [11]
    [12]
    [13]

    Gao Z Y, Lu Q S 2007 Chin. Phys. 16 2479

    [14]
    [15]

    Yang Z Q, Lu Q S 2006 Chin. Phys. 15 518

    [16]
    [17]

    Xie Y, Xu J X, Kang Y M, Hu S J, Duan Y B 2003 Acta Phys. Sin. 52 1112 (in Chinese)[谢 勇、徐健学、康艳梅、胡三觉、段玉斌 2003 物理学报 52 1112]

    [18]

    Wu Y, Xu J X, He D H, Jin W Y 2005 Acta Phys. Sin. 54 3457(in Chinese)[吴 莹、徐健学、何岱海、靳伍银 2005 物理学报 54 3457]

    [19]
    [20]

    Wang B Y, Xu W, Xing Z C 2009 Acta Phys. Sin. 58 6590(in Chinese)[王宝燕、徐 伟、邢真慈 2009 物理学报 58 6590]

    [21]
    [22]

    Chay T R, Keizer J 1983 Biophys J. 42 181

    [23]
    [24]

    Atwater I, Dawson C M, Scott A, Eddlestone G, Rojas E 1980 Biochemistry and Biophysics of the Pancreatic -cell Thieme G (Ed) (New York: Verlag) p100

    [25]
    [26]
    [27]

    Keizer J, Smolen P 1991 Proc. Natl. Acad. Sci. USA 88 3897

    [28]
    [29]

    Keizer J, Magnus G 1989 Biophys. J. 56 229

    [30]
    [31]

    Vries G D, Sherman A 2000 J. Theor. Biol. 207 513

  • [1]

    Chou H F, Ipp E 1990 Diabetes 39 112

    [2]
    [3]

    Longo E A, Tornheim K, Deeney J T, Varnum B A, Tillotson D, Prentki M, Corkey B E 1991 J. Biol. Chem. 266 9314

    [4]

    Omeara N M, Sturis J, Blackman J D, Byrne M M, Jaspan J B, Thistlethwaite J R, Polonsky K S 1993 Diabetes 42 855

    [5]
    [6]

    Bertram R, Butte M J, Kiemel T and Sherman A 1995 Bull. Math. Biol. 57 413

    [7]
    [8]
    [9]

    Rinzel J 1987 Lecture Notes in Biomathematics (New York: Springer-Verlag) p267

    [10]

    Izhikevich E M 2000 Int. J. Bifur. and Chaos 10 1171

    [11]
    [12]
    [13]

    Gao Z Y, Lu Q S 2007 Chin. Phys. 16 2479

    [14]
    [15]

    Yang Z Q, Lu Q S 2006 Chin. Phys. 15 518

    [16]
    [17]

    Xie Y, Xu J X, Kang Y M, Hu S J, Duan Y B 2003 Acta Phys. Sin. 52 1112 (in Chinese)[谢 勇、徐健学、康艳梅、胡三觉、段玉斌 2003 物理学报 52 1112]

    [18]

    Wu Y, Xu J X, He D H, Jin W Y 2005 Acta Phys. Sin. 54 3457(in Chinese)[吴 莹、徐健学、何岱海、靳伍银 2005 物理学报 54 3457]

    [19]
    [20]

    Wang B Y, Xu W, Xing Z C 2009 Acta Phys. Sin. 58 6590(in Chinese)[王宝燕、徐 伟、邢真慈 2009 物理学报 58 6590]

    [21]
    [22]

    Chay T R, Keizer J 1983 Biophys J. 42 181

    [23]
    [24]

    Atwater I, Dawson C M, Scott A, Eddlestone G, Rojas E 1980 Biochemistry and Biophysics of the Pancreatic -cell Thieme G (Ed) (New York: Verlag) p100

    [25]
    [26]
    [27]

    Keizer J, Smolen P 1991 Proc. Natl. Acad. Sci. USA 88 3897

    [28]
    [29]

    Keizer J, Magnus G 1989 Biophys. J. 56 229

    [30]
    [31]

    Vries G D, Sherman A 2000 J. Theor. Biol. 207 513

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Publishing process
  • Received Date:  31 January 2011
  • Accepted Date:  02 March 2011
  • Published Online:  15 November 2011

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