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Synchronization of bursting activities in pancreatic islets when pancreatic β-cells are coupled together by gap junctions plays an important role in the insulin secretion. A minimal and generic phantom bursting model proposed by Bertram et al is employed to produce compound bursting synchronization with anti-phase spikes of two electrical coupling pancreatic β-cells, where the membrane exhibits a transition between a burst episode composed of a long burst and several short bursts and a relatively long rest state with large amplitude on both sides but small at the middle. Two different fast/slow analyses for the moderate and the slower slow variables in three-dimensional spaces are combined to highlight better how these two slow variables with different time scales commonly or separately result in complex dynamics of the compound bursting of the two electrical coupling β-cells. Especially for the compound bursting synchronization with anti-phase spikes, more is stressed on how varying coupling strengths lead to a change of the number of the short bursts within the burst episode of different compound bursting.
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Keywords:
- electrical coupling /
- slow variables with different time scales /
- compound bursting /
- fast/slow dynamic analysis
[1] Chay T R, Keizer J 1983 Biophys. J. 42 181
[2] Rinzel J Ordinary and Partial Differential Aligns (New York: Springer) pp304
[3] Rinzel J 1987 Mathematical Topics in Population Biology, Morphogenesis and Neurosciences. Lecture Notes in Mathematics (Berlin: Springer) pp267
[4] Gao Z Y, Lu Q S 2007 Chin. Phys. 16 2479
[5] 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 52 1112]
[6] 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 54 3457]
[7] Wang B Y, Xu W, Xing Z C 2009 Acta Phys. Sin. 90 5865 (in Chinese) [王宝燕, 徐伟, 邢真慈 2009 90 5865]
[8] Yang Z Q 2010 Acta Phys. Sin. (in Chinese) [杨卓琴 2010 59 5319]
[9] Yang Z Q, Guan T T, Gan C B, Zhang J Y 2011 Acta Phys. Sin. 60 110202 (in Chinese) [杨卓琴, 管亭亭, 甘春标, 张矫瑛 2011 60 110202]
[10] Wierschem K, Bertram R 2004 J. Theor. Biol. 228 513
[11] Bertram R, Satin L, Zhang M, Smolen P, Sherman A 2004 Biophys. J. 87 3074
[12] Bertram R, Satin L, Pedersen M G, Luciani D S, Sherman A 2007 Biophys. J. 92 1544
[13] Goel P, Sherman A 2009 Dyn. Sys. 8 1664
[14] Bertram R, Rhoadsa J, Cimbora W P 2008 Bull. Math. Biol. 70 1979
[15] Bertram R, Previte J, Sherman A, Kinard T A, Satin L S 2000 Biophys. J. 79 2880
[16] Sherman A, Rinzel J, Keizer J 1988 Biophys. J. 54 411
[17] Pedersen M G, Bertram R, Sherman A 2005 Biophys. J. 89 107
[18] Atwater I, Rosario L, Rojas E 1983 Cell Calcium 4 451
[19] Chay T R, Kang H S 1988 Biophys. J. 54 427
[20] Jo J, Kang H, Choi M Y, Koh D S 2005 Biophys. J. 89 1534
[21] Fendler B, Zhang M, Satin L, Bertram R 2009 Biophys. J. 97 722
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[1] Chay T R, Keizer J 1983 Biophys. J. 42 181
[2] Rinzel J Ordinary and Partial Differential Aligns (New York: Springer) pp304
[3] Rinzel J 1987 Mathematical Topics in Population Biology, Morphogenesis and Neurosciences. Lecture Notes in Mathematics (Berlin: Springer) pp267
[4] Gao Z Y, Lu Q S 2007 Chin. Phys. 16 2479
[5] 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 52 1112]
[6] 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 54 3457]
[7] Wang B Y, Xu W, Xing Z C 2009 Acta Phys. Sin. 90 5865 (in Chinese) [王宝燕, 徐伟, 邢真慈 2009 90 5865]
[8] Yang Z Q 2010 Acta Phys. Sin. (in Chinese) [杨卓琴 2010 59 5319]
[9] Yang Z Q, Guan T T, Gan C B, Zhang J Y 2011 Acta Phys. Sin. 60 110202 (in Chinese) [杨卓琴, 管亭亭, 甘春标, 张矫瑛 2011 60 110202]
[10] Wierschem K, Bertram R 2004 J. Theor. Biol. 228 513
[11] Bertram R, Satin L, Zhang M, Smolen P, Sherman A 2004 Biophys. J. 87 3074
[12] Bertram R, Satin L, Pedersen M G, Luciani D S, Sherman A 2007 Biophys. J. 92 1544
[13] Goel P, Sherman A 2009 Dyn. Sys. 8 1664
[14] Bertram R, Rhoadsa J, Cimbora W P 2008 Bull. Math. Biol. 70 1979
[15] Bertram R, Previte J, Sherman A, Kinard T A, Satin L S 2000 Biophys. J. 79 2880
[16] Sherman A, Rinzel J, Keizer J 1988 Biophys. J. 54 411
[17] Pedersen M G, Bertram R, Sherman A 2005 Biophys. J. 89 107
[18] Atwater I, Rosario L, Rojas E 1983 Cell Calcium 4 451
[19] Chay T R, Kang H S 1988 Biophys. J. 54 427
[20] Jo J, Kang H, Choi M Y, Koh D S 2005 Biophys. J. 89 1534
[21] Fendler B, Zhang M, Satin L, Bertram R 2009 Biophys. J. 97 722
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