Graduate School in Nonlinear Science

Sponsored by the Danish Research Academy

MIDIT                               OFD                           CATS
Modelling, Nonlinear Dynamics       Optics and Fluid Dynamics     Chaos and Turbulence Studies
and Irreversible Thermodynamics     Risø National Laboratory      Niels Bohr Institute and 
Technical University of Denmark     Building 128                  Department of Chemistry
Building 321                        P.O. Box 49                   University of Copenhagen 
DK-2800 Lyngby                      DK-4000 Roskilde              DK-2100 Copenhagen Ø
Denmark                             Denmark                       Denmark


by Robert M. Miura
Department of Mathematics,
University of British Columbia
Vancouver, B.C.

MIDIT-seminar 459

Tuesday July 20, 1999, 15.00 h
at MIDIT, IMM Building 305, room 027

Abstract: Bursting electrical activity (BEA) in cells, e.g., neurons and pancreatic beta-cells, consists of alternating active and silent phases in which the membrane potential exhibits rapid oscillations and slow changes, respectively. In pancreatic beta-cells, BEA is related to the secretion of insulin which regulates blood glucose. Specifically, the rate of release of insulin from beta-cells as a function of glucose concentration is correlated to the plateau fraction, the ratio of the active phase duration to the total period of the BEA. This talk will summarize recent progress on the perturbation and computational analysis of different models for BEA in pancreatic beta-cells. The models are dynamical systems consisting of three nonlinear ordinary differential equations. The three ODEs are characterized as a two-dimensional fast subsystem coupled to a one-dimensional slow subsystem. A method will be outlined for computing the plateau fraction for a specific model as a model parameter is varied. Melnikov's method is used to locate the homoclinic bifurcation point for the fast subsystem. An extension of this method to other models will be described. The plateau fraction then can be compared with existing data and thus permits determination of a functional dependence between this model parameter and glucose concentration.