Negative calcium feedback: The road from Chay-Keizer

Bursting: The Genesis of Rhythm in the Nervous System

Volumn , Issue , 2005, Pages 19-48

  Bertram, Richard ^a   Sherman, Arthur ^b  

^a FLORIDA STATE UNIVERSITY   (United States)

^b NATIONAL INSTITUTES OF HEALTH   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84967387125     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1142/9789812703231_0002     Document Type: Chapter

References (45)

1. 2+ homeostasis in pancreatic β-cells, Diabetes. 51, 3245-3253, (2002).
2. F. M. Ashcroft, D. E. Harrison, and S. J. H. Ashcroft, Glucose induces closure of single potassium channels in isolated rat pancreatic β-cells, Nature. 312, 446-448, (1984).
3. F. M. Ashcroft and P. Rorsman, Type 2 diabetes mellitus: not quite exciting enough?, Human Mol. Gen. 13, R21-R31, (2004).
4. I. Atwater, C. M. Dawson, A. Scott, G. Eddlestone, and E. Rojas. The nature of the oscillatory behavior in electrical activity for pancreatic β-cell, Horm. Metab. Res. Suppl. 10, 100-7, (1980).
5. P. M. Beigelman, B. Ribalet, and I. Atwater, Electrical activity of mouse pancreatic beta-cells: II. Effects of glucose and arginine, J. Physiol. (Paris). 73, 201-217, (1977).
6. R. Bertram, M. J. Butte, T. Kiemel, and A. Sherman, Topological and phenomenological classification of bursting oscillations, Bull. Math. Biol. 57, 413-439, (1995).
7. R. Bertram, J. Previte, A. Sherman, T. A. Kinard, and L. S. Satin, The phantom burster model for pancreatic β-cells, Biophys. J. 79, 2880-2892, (2000).
8. R. Bertram, L. Satin, M. Zhang, P. Smolen, and A. Sherman, Calcium and glycolysis mediate multiple bursting modes in pancreatic islets, Biophys. J. 87, 3074-3087, (2004).
9. R. Bertram and A. Sherman, A calcium-based phantom bursting model for pancreatic islets, Bull. Math. Biol. 66, 1313-1344, (2004).
10. R. Bertram and A. Sherman, Filtering of calcium transients by the en doplasmic reticulum in pancreatic β-cells, Biophys. J. 87, 3775-3785, (2004).
11. R. J. Butera Jr., J. Rinzel, and J. C. Smith, Models of respiratory rhythm generation in the pre-Bötzinger complex. I. Bursting pacemaker neurons, J. Neurophysiol. 81, 382-397, (1999).
12. T. R. Chay, Electrical bursting and luminal calcium oscillation in excitable cell models, Biol. Cybern. 75, 419-431, (1996).
13. T. R. Chay, Effects of extracellular calcium on electrical bursting and intracellular and luminal calcium oscillations in insulin secreting pancreatic β-cells, Biophys. J. 73, 1673-1688, (1997).
14. T. R. Chay and D. L. Cook, Endogenous bursting patterns in excitable cells, Math. Biosci. 90, 139-153, (1988).
15. T. R. Chay and J. Keizer, Minimal model for membrane oscillations in the pancreatic β-cell, Biophys. J. 42, 181-190, (1983).
16. D. L. Cook, W. E. Crill, and D. Porte, Jr., Plateau potentials in pancreatic islet cells are voltage-dependent action potentials, Nature. 286, 404-406, (1980).
17. L. N. Cornelisse, W. J. J. M. Scheenen, W. J. H. Koopman, E. W. Roubos, and S. C. A. M. Gielen, Minimal model for intracellular calcium oscillations and electrical bursting in melanotrope cells of Xenopus Laevis, Neural Comput. 13, 113-137, (2000).
18. G. B. Ermentrout, Simulating, analyzing, and animating dynamical systems: A guide to XPPAUT for researchers and students. (SIAM Books, Philadelphia, 2002).
19. R. Fitz Hugh, Impulses and physiological states in theoretical models of nerve membrane, Biophys. J. 1, 445-466, (1961).
20. 2+ flux in pancreatic β-cells: role of the plasma membrane and intracellular stores, Am. J. Physiol. (Endocrinol. Metab.). 285, E138-E154, (2003).
21. 2+: Experimental and theoretical studies, J. Gen. Physiol. 120, 307-322, (2002).
22. + channels contributes to rhythmic firing of action potentials in mouse pancreatic cells, J. Gen. Physiol. 114, 759-769, (1999).
23. B. Hille, Ionic channels of excitable membranes. (Sinauer Associates, Sunderland, MA, 2001)
24. J. L. Hindmarsh and R. M. Rose, A model of neuronal bursting using three coupled first order differential equations, Proc. R. Soc. Lond. B. 221, 87-102, (1984).
25. 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, 500-544, (1952).
26. E. M. Izhikevich, Neural excitability, spiking, and bursting, Int. J. Bifur. Chaos. 10, 1171-1266, (2000).
27. J. Keizer and G. Magnus, ATP-sensitive potassium channel and bursting in the pancreatic cell, Biophys. J. 56, 229-242, (1989).
28. 2+ channels, Proc. Natl. Acad. Sei. USA. 88, 3897-3901, (1991).
29. Y.-X. Li, S. S. Stojilkovic, J. Keizer, and J. Rinzel, Sensing and refilling calcium stores in an excitable cell, Biophys. J. 72, 1080-1091, (1997).
30. E. K. Matthews and M. D. L. O’Connor, Dynamic oscillations in the membrane potential of pancreatic islet cells, J. Exp. Biol. 81, 75-91, (1979).
31. C. Morris and H. Lecar, Voltage oscillations in the barnacle giant muscle fiber, Biophys. J. 35, 193-213, (1981).
32. 2+ on bursting neurons, Biophys. J. 21, 217-237, (1978).
33. J. Rinzel. A formal classification of bursting mechanisms in excitable systems. In eds. E. Teramoto and M. Yamaguti, Mathematical Topics in Population Biology, Morphogenesis and Neurosciences, vol. 71, Lecture Notes in Biomathematics, pp. 267-281, Berlin, (1987). Springer Verlag.
34. 2+ by mathematical modeling. In eds. I. Atwater, E. Rojas, and B. Soria, Biophysics of the Pancreatic β-Cell, pp. 247-263. Plenum Publishing Co., New York and London, (1986).
35. J. Rinzel and Y. S. Lee. On different mechanisms for membrane potential bursting. In ed. H. G. Othmer, Nonlinear oscillations in biology and chemistry, vol. 66, Lecture Notes in Biomathematics, pp. 19-33, Berlin, (1985). Springer-Verlag.
36. A. Sherman. Calcium and membrane potential oscillations in pancreatic β-cells. In eds. H. G. Othmer, F. R. Adler, M. A. Lewis, and J. C. Dallon, Case Studies in Mathematical Modeling-Ecology, Physiology, and Cell Biology, pp. 199-217. Prentice-Hall, New Jersey, (1997).
37. P. R. Shorten and D. J. N. Wall, A Hodgkin-Huxley model exhibiting bursting oscillations, Bull. Math. Biol. 62, 695-715, (2000).
38. 2+ currents and bursting mechanisms for the mouse pancreatic β-cell, J. Membrane Biol. 127, 9-19, (1992).
39. P. Smolen and A. Sherman, Phase independent resetting in relaxation and bursting oscillators, J. Theor. Biol. 169, 339-348, (1994).
40. P. Smolen, D. Terman, and J. Rinzel, Properties of a bursting model with two slow inhibitory variables, SIAM J. Appl. Math. 53, 861-892, (1993).
41. J. Tabak, J. Rinzel, and M. J. O’Donovan, The role of activity dependent network depression in the expression and self-regulation of spontaneous activity in the developing spinal cord, J. Neurosci. 21, 8966-8978, (2001).
42. D. Terman, The transition from bursting to continuous spiking in excitable membrane models, J. Nonlinear Sci. 2, 135-182, (1992).
43. 2+ concentration resembling bursting electrical activity in single mouse islets of Langerhans, FEBS Lett. 259, 19-23, (1989).
44. B. van der Pol and J. van der Mark, The heartbeat considered as a relaxation oscillation, and an electrical model of the heart, Phil. Mag. 6, 763-775, (1928).
45. 2+ dynamics of isolated mouse β-cells and islets: Implications for mathematical models, Biophys. J. 84, 2852-2870, (2003).