Modelling the β-Cell Electrical Activity
A considerable body of quantitative information is emerging on the processes involved in stimulus-secretion by the β-cells of the islet of Langerhans. Many variables are involved and the relationships between them are complex. However, it is possible to quantify these relationships by producing mathematical models. Such models are based on simple physico-chemical principles and provide a convenient quantitative catalogue of relevant data. However in general they are non-linear and too complex for intuition alone to give the insight necessary to predict their properties. The alternative is to solve the equations numerically with the help of a computer. This approach has contributed to the quantitative description of for example purkinje fibres27,32, cardiac muscle13,3, epithelia22, bursting pacemaker neuron34 and a start has been made with the β-cell5,25,21,36.
KeywordsIntracellular Calcium Concentration Pancreatic Islet Cell Mouse Islet Potassium Conductance Calcium Efflux
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- 10.C.M. Dawson, P.C. Crogham, A.M. Scott, and J.A. Bangham, Potassium and rubidium permeability and potassium conductance of the β-cell membrane in mouse islets of Langerhans, Quart. J. Expt. Physiol. in press (1985).Google Scholar
- 11.C.M. Dawson, I. Atwater, and E. Rojas, The response of pancreatic β-cell membrane potential to potassium-induced calcium influx in the presence of glucose, Quart. J. Expt. Physiol. 69:819 (1984).Google Scholar
- 20.T.J.C. Jacob, J.A. Bangham, and G. Duncan, Characterisation of a cation channel on the apical surface of the frog lens epithelium, Quarterly J. Exp. Physiol. 70:403 (1985).Google Scholar
- 26.E.K. Matthews and Y. Sakamoto, Pancreatic islet cells: electrogenic and electrodiffusional control of membrane potential, J. Physiol. 246:439 (1975).Google Scholar
- 28.P. Meda, I. Atwater, A. Goncalves, A. Bangham, L. Orci, and E. Rojas, The topography of electrical synchrony among β-cells in the mouse islet of Langerhans, Quart. J. Exp. Physiol. 69:719 (1984).Google Scholar
- 31.H.P. Meissner and J.C. Henquin, The sodium pump of mouse pancreatic β-cells: electrogenic properties and activation by intracellular sodium, in: “Electrogenic Transport: fundamental principles and physiological implications”, M.P. Blaustein and M. Lieberman, eds., M. Raven Press, New York (1984).Google Scholar
- 36.J. Rinzel, Bursting oscillations in an excitable membrane model, in: “Proc. 8th Dundee Conf. on the Theory of Ordinary and Partial Differential Equations”, B.D. Sleeman, R.J. Jarvis and D.S. Jones, eds., Springer Press, (in press).Google Scholar
- 37.A.M. Scott, J.A. Bangham, C.M. Dawson, and P.C. Crogham, Insulin output, ion flux and electrical measurements show that mouse islets distinguish fast from slow changes of glucose concentration, Diabetologia 27:267A (1984).Google Scholar
- 40.I. Atwater, A.A. Goncalves and E. Rojas, Electrical Measurement of an Oscillating Potassium Permeability during the Glucose-Stimulated Burst Activity in Mouse Pancreatic β-cell, Biomed. Res., 3:645 (1982).Google Scholar