Dynamical systems theory in physiology

Journal of General Physiology

Volumn 138, Issue 1, 2011, Pages 13-19

  Sherman, Arthur ^a  

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

Author keywords

[No Author keywords available]

Indexed keywords

CALCIUM; GLUCOSE;

ANIMAL; CELL MEMBRANE; METABOLISM; NOTE; PANCREAS ISLET BETA CELL; PHYSIOLOGY;

ANIMALS; CALCIUM; CELL MEMBRANE; GLUCOSE; INSULIN-SECRETING CELLS;

EID: 79960251114     PISSN: 00221295     EISSN: 15407748     Source Type: Journal    
DOI: 10.1085/jgp.201110668     Document Type: Note

References (27)

1. Atwater, I., C.M. Dawson, A. Scott, G. Eddlestone, and E. Rojas. 1980. The nature of the oscillatory behavior in electrical activity for the pancreatic β-cell. In Biochemistry and Biophysics of the Pancreatic β-cell. G. Thieme, editor. Springer-Verlag, New York. 100-107.
2. Bertram, R., M.J. Butte, T. Kiemel, and A. Sherman. 1995. Topological and phenomenological classification of bursting oscillations. Bull. Math. Biol. 57:413-439.
3. 2+ dynamics underlying the glucose response of pancreatic β cells: a simulation study. J. Gen. Physiol. 138:21-37.
4. Cha, C.Y., E. Santos, A. Amano, T. Shimayoshi, and A. Noma. 2011b. Time-dependent changes in membrane excitability during glucoseinduced bursting activity in pancreatic β cells. J. Gen. Physiol. 138:39-47.
5. Chay, T.R. 1990. Bursting excitable cell models by a slow Ca2+ current. J. Theor. Biol. 142:305-315.
6. Chay, T.R., and J. Keizer. 1983. Minimal model for membrane oscillations in the pancreatic β-cell. Biophys. J. 42:181-190.
7. Cook, D.L., D. Porte Jr., and W.E. Crill. 1981. Voltage dependence of rhythmic plateau potentials of pancreatic islet cells. Am. J. Physiol. 240:E290-E296.
8. Ermentrout, G.B. 2002. Simulating, Analyzing, and Animating Dynamical Systems: A Guide to XPPAUT for Researchers and Students. SIAM Press, Philadelphia. 290 pp.
9. Fall, C.P., E.S. Marland, J.M. Wagner, and J.J. Tyson. 2002. Computational Cell Biology. Springer-Verlag, New York. 445 pp.
10. Fridlyand, L.E., N. Tamarina, and L.H. Philipson. 2003. Modeling of Ca2+ flux in pancreatic beta-cells: role of the plasma membrane and intracellular stores. Am. J. Physiol. Endocrinol. Metab. 285:E138-E154.
11. Gardner, T.S., C.R. Cantor, and J.J. Collins. 2000. Construction of a genetic toggle switch in Escherichia coli. Nature. 403:339-342.
12. Goel, P., and A. Sherman. 2009. The geometry of bursting in the dual oscillator model of pancreatic beta-cells. SIAM J. Appl. Dyn. Syst. 8:1664-1693.
13. Golubitsky, M., K. Josic, and T.J. Kaper. 2001. An unfolding theory approach to bursting in fast-slow systems. In Global Analysis of Dynamical Systems. H.W. Broer, B. Krauskopf, and G. Vegter, editors. Institute of Physics Publishing, London. 277-308.
14. Hodgkin, A.L., and A.F. Huxley. 1952. A quantitative description of membrane current and its application to conduction and excitation in nerve. J. Physiol. 117:500-544.
15. Izhikevich, E. 2010. Dynamical Systems in Neuroscience. The MIT Press, Cambridge, MA. 457 pp.
16. Keener, J., and J. Sneyd. 1998. Mathematical Physiology. Springer-Verlag, New York. 792 pp.
17. Keizer, J., and G. Magnus. 1989. ATP-sensitive potassium channel and bursting in the pancreatic beta cell. A theoretical study. Biophys. J. 56:229-242.
18. Rinzel, J. 1985. Bursting oscillations in an excitable membrane model. In Ordinary and Partial Differential Equations, Lecture Notes in Mathematics. B.D. Sleeman and R.J. Jarvis, editors. Springer, New York. 304-316.
19. Rinzel, J. 1987. A formal classification of bursting mechanisms in excitable systems. In Mathematical Topics in Population Biology, Morphogenesis, and Neurosciences. E. Teramoto and M. Yamaguti, editors. Springer-Verlag, New York. 267-281.
20. Rinzel, J., and G.B. Ermentrout. 1998. Analysis of neural excitability and oscillations. In Methods in Neuronal Modeling. C. Koch and I. Segev, editors. The MIT Press, Cambridge, MA. 251-291.
21. Rinzel, J., and Y.S. Lee. 1987. Dissection of a model for neuronal parabolic bursting. J. Math. Biol. 25:653-675.
22. Rinzel, J., T.R. Chay, D. Himmel, and I. Atwater. 1986. Prediction of the glucose-induced changes in membrane ionic permeability and cytosolic Ca2+ by mathematical modeling. Adv. Exp. Med. Biol. 211:247-263.
23. Stern, J.V., H.M. Osinga, A. LeBeau, and A. Sherman. 2008. Resetting behavior in a model of bursting in secretory pituitary cells: distinguishing plateaus from pseudo-plateaus. Bull. Math. Biol. 70:68-88.
24. Tabak, J., N. Toporikova, M.E. Freeman, and R. Bertram. 2007. Low dose of dopamine may stimulate prolactin secretion by increasing fast potassium currents. J. Comput. Neurosci. 22:211-222.
25. Tsaneva-Atanasova, K., H.M. Osinga, T. Riess, and A. Sherman. 2010. Full system bifurcation analysis of endocrine bursting models. J. Theor. Biol. 264:1133-1146.
26. Tyson, J.J., K.C. Chen, and B. Novak. 2003. Sniffers, buzzers, toggles and blinkers: dynamics of regulatory and signaling pathways in the cell. Curr. Opin. Cell Biol. 15:221-231.
27. Van Goor, F., Y.X. Li, and S.S. Stojilkovic. 2001. Paradoxical role of large-conductance calcium-activated K+ (BK) channels in controlling action potential-driven Ca2+ entry in anterior pituitary cells. J. Neurosci. 21:5902-5915.