Phase independent resetting in relaxation and bursting oscillators

Journal of Theoretical Biology

Volumn 169, Issue 4, 1994, Pages 339-348

  Smolen, Paul ^a   Sherman, Arthur ^a  

^a NATIONAL INSTITUTE OF DIABETES AND DIGESTIVE AND KIDNEY DISEASES   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; MEMBRANE POTENTIAL; OSCILLATION; PANCREAS ISLET BETA CELL; THEORETICAL STUDY;

BIOLOGICAL CLOCKS; ELECTROPHYSIOLOGY; HUMAN; ISLETS OF LANGERHANS; MATHEMATICS; MEMBRANE POTENTIALS; MODELS, BIOLOGICAL; TIME FACTORS;

EID: 0027936196     PISSN: 00225193     EISSN: 10958541     Source Type: Journal    
DOI: 10.1006/jtbi.1994.1156     Document Type: Review

References (32)

1. Bertram, R. (1993). A computational study of the effects of serotonin on a molluscan burster neuron. Biol. Cybernet. 69, 257-267.
2. Bertram, R. (1994) Reduced-system analysis of the effects of serotonin on a molluscan burster neuron. Biol. Cybernet. 70, 359-368.
3. Canavier, C., Clarke, J. & Byrne, J. (1991). Simulation of the bursting activity of neuron R15 in Aplysia: role of ionic currents, calcium balance, and modulatory transmitters. J. Neurophysiol. 66, 2107-2124.
4. Chay, T. R. & Keizer, J, (1983). Minimal model for membrane oscillations in the pancreatic 0-cell. Biophys. J. 42, 181-190.
5. Cook, D., Porte, D. & Crill, W. (1981). Voltage dependence of rhythmic plateau potentials of pancreatic islet cells. Am. J. Physiol. 240, E290-E296.
6. Cook, D. L., Satin, L. & Hopkins, W. (1991). Pancreatic 0-cells are bursting, but how? TINS 14, 411-414.
7. Coulter, D., Huguenard, J. & Prince, D. (1989). Calcium currents in rat thalamocortical relay neurons: kinetic properties of the transient low-threshold current. J. Physiol., Lond. 414, 587-604.
8. h and its possible role in thalamocortical oscillations. Neuro Report 4, 223-226.
9. Doedel, E. (1981). AUTO: A program for the automatic bifurcation analysis of autonomous systems. Congr. Num. 30, 265-284.
10. Eddlestone, G., Goncalves, A., Bangham, J. & Rojas, E. (1984). Electrical coupling between cells in islets of Langerhans in mouse. J. Membr. Biol. 77, 1-4.
11. Fitzhugh, R. (1961). Impulses and physiological states in theoretical models of nerve membrane. Biophys. J. 1, 445-466.
12. Gear, C. (1967). The numerical integration of ordinary differential equations. Math. Comput. 21, 146-156.
13. Glass, L. (1988). From Clocks to Chaos, 98-111. Princeton, NJ: Princeton University Press.
14. Hindmarsh, A. (1974). An ordinary differential equation solver. Report UCID-3000I, Lawrence Livermore Laboratory.
15. Hopkins, W., Satin, L. & Cook, D. (1991). Inactivation kinetics and pharmacology distinguish two calcium currents in mouse pancreatic 0-cells. J. Membr. Biol. 119, 229-239.
16. Kaczmarek, L. & Levitan, I. (1988). Neuromodulation: The Biochemical Control of Neuronal Excitability, 163-165. New York: Oxford University Press.
17. Keizer, J. & Magnus, G. (1989). ATP-sensitive potassium channels and bursting in the pancreatic 0-cell. Biophys. J. 56, 229-242.
18. 2+ channels. Proc, natn. Acad. Sei. U.S.A. 88, 3897-3901.
19. Lee, R. & Stein, R. (1981). Resetting of tremor by mechanical perturbations: A comparison of essential and parkinsonian tremor. Ann. Neurol. 10, 523-531.
20. McCormick, D., Huguenard, J. & Strowbridge, B. (1992). Determination of state-dependent processing in thalamus by single neuron properties and neuromodulators. In: Single Neuron Computation (Mc Kenna, T., ed.)278-279. San Diego, CA: Academic Press.
21. Pipeleers, D. (1992). Heterogeneity in pancreatic 0-cell population. Diabetes 41, 777-781.
22. Rinzel, J. (1985). Bursting oscillations in an excitable membrane model. In: Ordinary and Partial Differential Equations (Sleeman, B. & Jarvin, R., eds)304-316. New York: Springer-Verlag.
23. Rinzel, J. (1987). A formal classification of bursting mechanisms in excitable systems. In: Mathematical Topics in Population Biology, Morphogenesis and Neurosciences. Lecture Notes in Biomathematics, Vol. 71 (Teramoto, E. & Yamoguti, M., eds). New York: Springer-Verlag.
24. Rinzel, J. & Lee, Y. (1987). Dissection of a model for neuronal parabolic bursting. J. math. Biol. 25, 653-675.
25. Rorsman, P. & Trübe, G. (1985). Calcium and delayed potassium currents in mouse pancreatic 0-cells under voltage clamp conditions. J. Physiol., Lond. 374, 531-550.
26. 2+ oscillations due to bursting electrical activity in single pancreatic islets. Pflügers Arch. 418, 417-422.
27. Satin, L. & Cook, D. (1989). Calcium current inactivation in insulin-secreting cells is mediated by calcium influx and membrane depolarization. Pflügers Arch. 414, 1-10.
28. +-currents in isolated mouse pancreatic 0-cells. FEBS Lett. 261, 187-190.
29. 2+ currents and bursting mechanisms for the mouse pancreatic 0-cell. J. Membr. Biol. 127, 9-19.
30. Smolen, P., Rinzel, J, & Sherman, A. (1993a). Why pancreatic islets burst but single 0-cells do not: The heterogeneity hypothesis. Biophys. J. 64, 1668-1680.
31. Smolen, P., Terman, D. & Rinzel, J. (1993). Properties of a bursting model with two slow inhibitory variables. SIAM J. appl. Math. 53, 861-892.
32. 2+ concentration resembling bursting electrical activity in single mouse islets of Langerhans. FEBS Leu. 259, 19-23.