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Volumn 8, Issue 4, 2009, Pages 1664-1693

The geometry of bursting in the dual oscillator model of pancreatic β-cells

Author keywords

Bursting; Calcium; Composite bifurcation diagram; Coupled oscillators; Dual oscillator model; Fast slow systems; Insulin; Oscillations; Pancreatic beta cells; Sliding bars

Indexed keywords

BIFURCATION DIAGRAM; COUPLED OSCILLATORS; DUAL OSCILLATOR MODEL; FAST-SLOW SYSTEM; FAST-SLOW SYSTEMS; OSCILLATOR MODEL;

EID: 77950907336     PISSN: None     EISSN: 15360040     Source Type: Journal    
DOI: 10.1137/08074427X     Document Type: Article
Times cited : (21)

References (31)
  • 1
    • 0034311437 scopus 로고    scopus 로고
    • Homoclinic bifurcations leading to the emergence of bursting oscillations in cell models
    • V. N. BELYKH, I. V. BELYKH, M. COLDING-JORGENSON, AND E. MOSEKILDE, Homoclinic bifurcations leading to the emergence of bursting oscillations in cell models, Eur. Phys. J., 3 (2000), pp. 205-219.
    • (2000) Eur. Phys. J. , vol.3 , pp. 205-219
    • Belykh, V.N.1    Belykh, I.V.2    Colding-Jorgenson, M.3    Mosekilde, E.4
  • 3
    • 52549090449 scopus 로고    scopus 로고
    • A phantom bursting mechanism for episodic bursting
    • R. BERTRAM, J. RHOADS, AND W. P. CIMBORA, A phantom bursting mechanism for episodic bursting, Bull. Math. Biol, 70 (2008), pp. 1979-1993.
    • (2008) Bull. Math. Biol , vol.70 , pp. 1979-1993
    • Bertram, R.1    Rhoads, J.2    Cimbora, W.P.3
  • 4
    • 10044256230 scopus 로고    scopus 로고
    • Calcium and glycolysis mediate multiple bursting modes in pancreatic islets
    • R. BERTRAM, L. SATIN, M. ZHANG, P. SMOLEN, AND A. SHERMAN, Calcium and glycolysis mediate multiple bursting modes in pancreatic islets, Biophys. J., 87 (2004), pp. 3074-3087.
    • (2004) Biophys. J. , vol.87 , pp. 3074-3087
    • Bertram, R.1    Satin, L.2    Zhang, M.3    Smolen, P.4    Sherman, A.5
  • 5
    • 3042708493 scopus 로고    scopus 로고
    • A calcium-based phantom bursting model for pancreatic β-cells
    • R. BERTRAM AND A. SHERMAN, A calcium-based phantom bursting model for pancreatic β-cells, Bull. Math. Biol., 66 (2004), pp. 1313-1344.
    • (2004) Bull. Math. Biol. , vol.66 , pp. 1313-1344
    • Bertram, R.1    Sherman, A.2
  • 6
    • 10044228389 scopus 로고    scopus 로고
    • Filtering of calcium transients by the endoplasmic reticulum in pancreatic β-cells
    • R. BERTRAM AND A. SHERMAN, Filtering of calcium transients by the endoplasmic reticulum in pancreatic β-cells, Biophys. J., 87 (2004), pp. 3775-3785.
    • (2004) Biophys. J. , vol.87 , pp. 3775-3785
    • Bertram, R.1    Sherman, A.2
  • 7
    • 84967387125 scopus 로고    scopus 로고
    • Negative calcium feedback: The road from Chay-Keizer
    • S. Coombes and P. Bressloff, eds., World Scientific, Singapore
    • R. BERTRAM AND A. SHERMAN, Negative calcium feedback: The road from Chay-Keizer, in Bursting: The Genesis of Rhythm in the Nervous System, S. Coombes and P. Bressloff, eds., World Scientific, Singapore, 2005, pp. 243-272.
    • (2005) Bursting: The Genesis of Rhythm in the Nervous System , pp. 243-272
    • Bertram, R.1    Sherman, A.2
  • 8
    • 35148816130 scopus 로고    scopus 로고
    • Metabolic and electrical oscillations: Partners in controlling pulsatile insulin secretion
    • R. BERTRAM, A. SHERMAN, AND L. SATIN, Metabolic and electrical oscillations: Partners in controlling pulsatile insulin secretion, Am. J. Physiol. Endocrinol. Met ab., 293 (2007), pp. 890-900.
    • (2007) Am. J. Physiol. Endocrinol. Metab. , vol.293 , pp. 890-900
    • Bertram, R.1    Sherman, A.2    Satin, L.3
  • 9
    • 0020957719 scopus 로고
    • Minimal model for membrane oscillations in the pancreatic β-cell
    • T. R. CHAY AND J. KEIZER., Minimal model for membrane oscillations in the pancreatic β-cell, Biophys. J., 42 (1983), pp. 181-190.
    • (1983) Biophys. J. , vol.42 , pp. 181-190
    • Chay, T.R.1    Keizer, J.2
  • 10
    • 0022037388 scopus 로고
    • Bursting, beating, and chaos in an excitable membrane model
    • T. R. CHAY AND J. RINZEL, Bursting, beating, and chaos in an excitable membrane model, Biophys. J., 47 (1985), pp. 357-366.
    • (1985) Biophys. J. , vol.47 , pp. 357-366
    • Chay, T.R.1    Rinzel, J.2
  • 11
    • 0019545985 scopus 로고
    • Voltage dependence of rhythmic plateau potentials of pancreatic islet cells
    • D. COOK, D. PORTE, AND W. CRILL, Voltage dependence of rhythmic plateau potentials of pancreatic islet cells, Am. J. Physiol., 240 (1981), pp. E290-E296.
    • (1981) Am. J. Physiol. , vol.240
    • Cook, D.1    Porte, D.2    Crill, W.3
  • 12
    • 0020620416 scopus 로고
    • Isolated islets of Langerhans have slow oscillations of electrical activity
    • D. L. COOK, Isolated islets of Langerhans have slow oscillations of electrical activity, Metabolism, 32 (1983), pp. 681-685.
    • (1983) Metabolism , vol.32 , pp. 681-685
    • Cook, D.L.1
  • 14
    • 34247603072 scopus 로고    scopus 로고
    • Rhythm of the β-cell oscillator is not governed by a single regulator: Multiple systems contribute to oscillatory behavior
    • E. HEART AND P.J. SMITH, Rhythm of the β-cell oscillator is not governed by a single regulator: Multiple systems contribute to oscillatory behavior, Am. J. Physiol., 292 (2007), pp. E1295-E1300.
    • (2007) Am. J. Physiol. , vol.292
    • Heart, E.1    Smith, P.J.2
  • 15
    • 0020046104 scopus 로고
    • Cyclic variations of glucose-induced electrical activity in pancreatic β-cells
    • J. C. HENQUIN, H. P. MEISSNER, AND W. SCHMEER, Cyclic variations of glucose-induced electrical activity in pancreatic β-cells, Pflügers Archiv., 393 (1982), pp. 322-327.
    • (1982) Pflügers Archiv. , vol.393 , pp. 322-327
    • Henquin, J.C.1    Meissner, H.P.2    Schmeer, W.3
  • 16
    • 35649001607 scopus 로고
    • A quantitative description of membrane current and its application to conduction and excitation in nerve
    • A. L. HODGKIN AND A. F. HUXLEY, A quantitative description of membrane current and its application to conduction and excitation in nerve, J. Physiol. (Lond.), 117 (1952), pp. 205-249.
    • (1952) J. Physiol. (Lond.) , vol.117 , pp. 205-249
    • Hodgkin, A.L.1    Huxley, A.F.2
  • 17
    • 28844453661 scopus 로고    scopus 로고
    • Glucose metabolism and oscillatory behavior of pancreatic islets
    • paper 051905
    • H. KANG, J. JO, H. J. KIM, M. Y. CHOI, S. W. RHEE, AND D. S. KOH, Glucose metabolism and oscillatory behavior of pancreatic islets, Phys. Rev. E, 72 (2005), paper 051905.
    • (2005) Phys. Rev. E , vol.72
    • Kang, H.1    Jo, J.2    Kim, H.J.3    Choi, M.Y.4    Rhee, S.W.5    Koh, D.S.6
  • 18
    • 0024323358 scopus 로고
    • ATP-sensitive potassium channel and bursting in the pancreatic beta-cell
    • J. KEIZER AND G. MAGNUS, ATP-sensitive potassium channel and bursting in the pancreatic beta-cell, Biophys. J., 56 (1989), pp. 229-242.
    • (1989) Biophys. J. , vol.56 , pp. 229-242
    • Keizer, J.1    Magnus, G.2
  • 20
    • 0034809769 scopus 로고    scopus 로고
    • Bifurcation structure of a model of bursting pancreatic cells
    • E. MOSEKILDE, B. LADING, S. YANCHUK, AND Y. MAISTRENKO, Bifurcation structure of a model of bursting pancreatic cells, BioSystems, 63 (2001), pp. 3-13.
    • (2001) BioSystems , vol.63 , pp. 3-13
    • Mosekilde, E.1    Lading, B.2    Yanchuk, S.3    Maistrenko, Y.4
  • 22
    • 34548017201 scopus 로고    scopus 로고
    • Phantom bursting is highly sensitive to noise and unlikely to account for slow bursting in beta-cells: Considerations in favor of metabolically driven oscillations
    • M. G. PEDERSEN, Phantom bursting is highly sensitive to noise and unlikely to account for slow bursting in beta-cells: Considerations in favor of metabolically driven oscillations, J. Theoret. Biol., 248 (2007), pp. 391-400.
    • (2007) J. Theoret. Biol. , vol.248 , pp. 391-400
    • Pedersen, M.G.1
  • 23
    • 23244441271 scopus 로고    scopus 로고
    • Intra- and inter-islet synchronization of metabolically driven insulin secretion
    • M. G. PEDERSEN, R. BERTRAM, AND A. SHERMAN, Intra- and inter-islet synchronization of metabolically driven insulin secretion, Biophys. J., 89 (2005), pp. 107-119.
    • (2005) Biophys. J. , vol.89 , pp. 107-119
    • Pedersen, M.G.1    Bertram, R.2    Sherman, A.3
  • 24
    • 0000117122 scopus 로고
    • Bursting oscillations in an excitable membrane model
    • B. D. Sleeman and R. J. Jarvis, eds., Springer-Verlag, New York
    • J. RINZEL, Bursting oscillations in an excitable membrane model, in Ordinary and Partial Differential Equations, B. D. Sleeman and R. J. Jarvis, eds., Springer-Verlag, New York, 1985, pp. 304-316.
    • (1985) Ordinary and Partial Differential Equations , pp. 304-316
    • Rinzel, J.1
  • 25
    • 0023461032 scopus 로고
    • Dissection of a model for neuronal parabolic bursting
    • J. RINZEL AND Y. S. LEE, Dissection of a model for neuronal parabolic bursting, J. Math. Biol., 25 (1987), pp. 653-675.
    • (1987) J. Math. Biol. , vol.25 , pp. 653-675
    • Rinzel, J.1    Lee, Y.S.2
  • 26
    • 0029784059 scopus 로고    scopus 로고
    • Contributions of modeling to understanding stimulus-secretion coupling in pancreatic β-cells
    • A. SHERMAN, Contributions of modeling to understanding stimulus-secretion coupling in pancreatic β-cells, Am. J. Physiol., 271 (1996), pp. E362-E372.
    • (1996) Am. J. Physiol. , vol.271
    • Sherman, A.1
  • 27
    • 0029031338 scopus 로고
    • A model for glycolytic oscillations based on skeletal muscle phosphofructokinase kinetics
    • P. SMOLEN, A model for glycolytic oscillations based on skeletal muscle phosphofructokinase kinetics, J. Theoret. Biol., 174 (1995), pp. 137-148.
    • (1995) J. Theoret. Biol. , vol.174 , pp. 137-148
    • Smolen, P.1
  • 28
    • 34249839599 scopus 로고
    • The transition from bursting to continuous spiking in excitable membrane models
    • D. TERMAN, The transition from bursting to continuous spiking in excitable membrane models, J. Nonlinear Sci., 2 (1992), pp. 135-182.
    • (1992) J. Nonlinear Sci. , vol.2 , pp. 135-182
    • Terman, D.1
  • 29
    • 0030756468 scopus 로고    scopus 로고
    • Are metabolic oscillations responsible for normal oscillatory insulin secretion?
    • K. TORNHEIM, Are metabolic oscillations responsible for normal oscillatory insulin secretion?, Diabetes, 46 (1997), pp. 1375-1380.
    • (1997) Diabetes , vol.46 , pp. 1375-1380
    • Tornheim, K.1
  • 30
    • 33646198964 scopus 로고    scopus 로고
    • Diffusion of calcium and metabolites in pancreatic islets: Killing oscillations with a pitchfork
    • K. TSANEVA-ATANASOVA, C. ZIMLIKI, R. BERTRAM, AND A. SHERMAN, Diffusion of calcium and metabolites in pancreatic islets: Killing oscillations with a pitchfork, Biophys. J., 90 (2006), pp. 3434-3446.
    • (2006) Biophys. J. , vol.90 , pp. 3434-3446
    • Tsaneva-Atanasova, K.1    Zimliki, C.2    Bertram, R.3    Sherman, A.4
  • 31
    • 44949266418 scopus 로고
    • Genesis of bursting oscillations in the Hindmarsh-Rose model and homoclinicity to a chaotic saddle
    • X.-J. WANG, Genesis of bursting oscillations in the Hindmarsh-Rose model and homoclinicity to a chaotic saddle, Phys. D, 62 (1993), pp. 263-274.
    • (1993) Phys. D , vol.62 , pp. 263-274
    • Wang, X.-J.1


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