A phantom bursting mechanism for episodic bursting

Bulletin of Mathematical Biology

Volumn 70, Issue 7, 2008, Pages 1979-1993

  Bertram, Richard ^a   Rhoads, Joseph ^a   Cimbora, Wendy P ^a  

^a FLORIDA STATE UNIVERSITY   (United States)

Author keywords

Beta cells; Bursting; Electrical oscillations; Endocrine cells; Neurons; Pancreatic islets

Indexed keywords

ACTION POTENTIAL; ALGORITHM; ANIMAL; ARTICLE; BIOLOGICAL MODEL; COMPUTER SIMULATION; CYTOLOGY; ELECTROPHYSIOLOGY; ENDOCRINE SYSTEM; HUMAN; KINETICS; NERVE CELL; PANCREAS ISLET; PHYSIOLOGY; STATISTICS;

ACTION POTENTIALS; ALGORITHMS; ANIMALS; COMPUTER SIMULATION; ELECTROPHYSIOLOGY; ENDOCRINE SYSTEM; HUMANS; ISLETS OF LANGERHANS; KINETICS; MODELS, BIOLOGICAL; MODELS, NEUROLOGICAL; NEURONS; STOCHASTIC PROCESSES;

EID: 52549090449     PISSN: 00928240     EISSN: 15229602     Source Type: Journal    
DOI: 10.1007/s11538-008-9335-0     Document Type: Article

References (33)

1. B.O. Alving 1986 Spontaneous activity in isolated somata of Aplysia pacemaker neurons J. Gen. Physiol. 51 29 45
2. + channel in pancreatic β-cells Cell Calcium 4 451 461
3. S.M. Baer T. Erneux J. Rinzel 1989 The slow passage through a Hopf bifurcation: delay, memory effects, and resonance SIAM J. Appl. Math. 49 55 71
4. R. Bertram A. Sherman 2004 A calcium-based phantom bursting model for pancreatic islets Bull. Math. Biol. 66 1313 1344
5. R. Bertram M. Butte T. Kiemel A. Sherman 1995 Topological and phenomenological classification of bursting oscillations Bull. Math. Biol. 57 413 439
6. R. Bertram J. Previte A. Sherman T.A. Kinard L.S. Satin 2000 The phantom burster model for pancreatic β-cells Biophys. J. 79 2880 2892
7. R. Bertram L. Satin M. Zhang P. Smolen A. Sherman 2004 Calcium and glycolysis mediate multiple bursting modes in pancreatic islets Biophys. J. 87 3074 3087
8. R. Bertram A. Sherman L.S. Satin 2007 Metabolic and electrical oscillations: partners in controlling pulsatile insulin secretion Am. J. Physiol. 293 E890 E900
9. T.R. Chay H.S. Kang 1988 Role of single-channel stochastic noise on bursting clusters of pancreatic β-cells Biophys. J. 54 427 435
10. T.R. Chay J. Keizer 1983 Minimal model for membrane oscillations in the pancreatic β-cell Biophys. J. 42 181 190
11. T.R. Chay J. Rinzel 1985 Bursting, beating, and chaos in an excitable membrane model Biophys. J. 47 357 366
12. Coombes, S., Bressloff, P.C. (Eds.), 2005. Bursting: The Genesis of Rhythm in the Nervous System. World Scientific, Singapore.
13. V. Crunelli J.S. Kelly N. Leresche M. Pirchio 1987 The ventral and dorsal lateral geniculate nucleus of the rat: intracellular recordings in vitro J. Physiol. (Lond.) 384 587 601
14. G. de Vries A. Sherman 2000 Channel sharing in pancreatic β-cells revisited: enhancement of emergent bursting by noise J. Theor. Biol. 207 513 530
15. P.M. Dean E.K. Mathews 1970 Glucose-induced electrical activity in pancreatic islet cells J. Physiol. 210 255 264
16. C.A. Del Negro C.-F. Hsiao S.H. Chandler A. Garfinkel 1998 Evidence for a novel bursting mechanism in rodent trigeminal neurons Biophys. J. 75 174 182
17. Ermentrout, G.B., 2002. Simulating, Analyzing, and Animating Dynamical Systems: A Guide to XPPAUT for Researchers and Students. SIAM, Philadelphia.
18. R.F. Fox 1997 Stochastic versions of the Hodgkin-Huxley equations Biophys. J. 72 2068 2074
19. J.C. Henquin H.P. Meissner W. Schmeer 1982 Cyclic variations of glucose-induced electrical activity in pancreatic B cells Pflügers Arch. 393 322 327
20. T.A. Kinard G. Vries A. Sherman L.S. Satin 1999 Modulation of the bursting properties of single mouse pancreatic β-cells by artificial conductances Biophys. J. 76 1423 1435
21. M.C. Kuehl-Kovarik W.A. Pouliot G.L. Halterman R.J. Handa F.E. Dubek K.M. Partin 2002 Episodic bursting activity and response to excitatory amino acids in acutely dissociated gonadotropin-releasing hormone neurons genetically targeted with green fluorescent protein J. Neurosci. 22 2313 2322
22. M.G. Pedersen 2007 Phantom bursting is highly sensitive to noise and unlikely to account for slow bursting in β-cells: considerations in favor of metabolically driven oscillations J. Theor. Biol. 248 391 400
23. Rinzel, J., 1985. Bursting oscillations in an excitable membrane model. In: Sleeman, B.D., Jarvis, R.J. (Eds.), Ordinary and Partial Differential Equations, Lecture Notes in Mathematics, pp. 304-316. Springer, New York.
24. Rinzel, J., 1987. A formal classification of bursting mechanisms in excitable systems. In: Teramoto, E., Yamaguti, M. (Eds.), Mathematical Topics in Population Biology, Morphogenesis and Neurosciences. Springer, Berlin.
25. Rinzel, J., Ermentrout, G.B., 1998. Analysis of neural excitability and oscillations. In: Koch, C., Segev, I. (Eds.), Methods in Neuronal Modeling: From Ions to Networks, pp. 251-291. MIT Press, Cambridge.
26. A. Sherman J. Rinzel J. Keizer 1988 Emergence of organized bursting in clusters of pancreatic β-cells by channel sharing Biophys. J. 54 411 425
27. P. Smolen D. Terman J. Rinzel 1993 Properties of a bursting model with two slow inhibitory variables SIAM J. Appl. Math. 53 861 892
28. S.S. Stojilkovic M. Kukuljan T. Iida E. Rojas K.J. Catt 1992 Integration of cytoplasmic calcium and membrane potential oscillations maintains calcium signaling in pituitary gonadotrophs Proc. Natl. Acad. Sci. 89 4081 4085
29. K.J. Suter J.-P. Wuarin B.N. Smith F.E. Dudek S.M. Moenter 2000 Whole-cell recordings from preoptic/hypothalamic slices reveal burst firing in gonadotropin-releasing hormone neurons identified with green fluorescent protein in transgenic mice Endocrinology 141 3731 3736
30. D. Terman 1992 The transition from bursting to continuous spiking in excitable membrane models J. Nonlinear Sci. 2 135 182
31. K. Tornheim 1997 Are metabolic oscillations responsible for normal oscillatory insulin secretion? Diabetes 46 1375 1380
32. R.K.S. Wong D.A. Prince 1981 Afterpotential generation in hippocampal pyramidal cells J. Neurophysiol. 45 86 97
33. 2+ dynamics of isolated mouse β-cells and islets: implications for mathematical models Biophys. J. 84 2852 2870