September 2, 2017

Download Analysis and Modeling of Neural Systems by George L. Gerstein (auth.), Frank H. Eeckman (eds.) PDF

By George L. Gerstein (auth.), Frank H. Eeckman (eds.)

ISBN-10: 146136793X

ISBN-13: 9781461367932

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3). 5 Summary We have outlined theories to account for the generation and synchronization of bursting oscillations in an ensemble of electrically excitable cells. 8-cells) we have chosen for illustration. We have employed mathematical concepts that also apply more generally and which have enabled us to identify the underlying qualitative structure of a class of models. 41 An essential feature in this type of bursting model, made transparent by our fast/slow dissection and phase space representation, is bistability for the spike-generating subsystem.

Bangham, J. , and Rojas, E. (1984) Electrical coupling between cells in islets of Langerhans in mouse J. Membrane BioI. 77, 1-14. [91 FitzHugh, R. (1961). Impulses and physiological states in theoretical models of nerve membrane. Biophys. J. 1,445-466. [10] Gray, C. M. and Singer, W. (1989). Stimulus-specific neuronal oscillations in orientation columns of cat visual cortex. Proc. Nati. Acad. Sci. USA 86, 1698-1702. [11] Henquin, J. C. and Meissner, H. P. (1984). Significance of ionic ftuxes and changes in membrane potential for stimulus-secretion coupling in pancreatic B-cells.

To complete the graphical representation we indicate, with the curve labeled S = 0, the values of V and S where, according to Eqn. 3, the growth rate of S balances its decay; above the curve, S is increasing, and below it, decreasing. This curve is called the S-nullcline. As an application of this representation, consider our model for bursting in the ,8-cell and suppose that the calcium removal rate kCa is glucose-sensitive (say, increasing with glucose). This parameter appears only in the equation for the slow variable, Eqn.

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