Effect of Na/Ca Exchange on Plateau Fraction and [Ca]i in Models for Bursting in Pancreatic Beta-Cells

Model Status

This is the original unchecked version of the model imported from the previous CellML model repository, 24-Jan-2006.

Model Structure

Pancreatic beta-cells have been the subject of both experimental and theoretical studies for several decades. One reason for this interest has been the essential role beta-cells play in glucose homeostasis - they are the only source of insulin that most cells require in order to take up and metabolise glucose, and impairment of beta-cell function contributes to diabetes. A major focus of theoretical work has been beta-cell dynamics, especially in the form of bursting electrical activity. The bursts consist of active phases of Ca²⁺-carrying action potentials alternating with silent phases of repolarisation and are accompanied by oscillations in cytosolic Ca²⁺, which drive pulses of insulin secretion. Hence [Ca²⁺]_i regulation is of great importance due to its role as a secondary messenger in the stimulus-secretion coupling. Several transport mechanisms at the level of the plasma membrane are involved in this regulation, including L-type Ca²⁺ channels, Ca²⁺-ATPases and the Na⁺/Ca²⁺ exchange. This antiporter couples the energy released by the influx of Na⁺ ions down their electrochemical to the efflux of Ca²⁺ from the cytosol. In pancreatic beta-cells the physiological role of the Na⁺/Ca²⁺ remains unclear, but data suggest that it can regulate the burst duration.

In their 1999 study, David Gall and Isabella Susa use mathematical modelling to explore the impact of the activity of this transporter, both on the [Ca²⁺]_i regulation and on the periodic bursting electrical activity. Specifically they tested the hypothesis that the Na⁺/Ca²⁺ exchange is able to modulate the plateau fraction, and hence the amount of insulin secreted. Gall and Susa tested this hypothesis by including I_Na/Ca in three single cell models differing in the identity of the slow variable controlling the bursting electrical activity (see the figure below). In addition, they examined a possible link between Na⁺/Ca²⁺ exchange activity and glucose metabolism, finding that Na⁺/Ca²⁺ exchange can provide a physiological mechanism to increase the plateau fraction as the glucose concentration is raised. The mathematical models have been translated into CellML descriptions which can be downloaded in various formats as described in .

The complete original paper reference is cited below:

Effect of Na/Ca Exchange on Plateau Fraction and [Ca²⁺]_i in Models for Bursting in Pancreatic Beta-Cells, David Gall and Isabella Susa, 1999, Biophysical Journal , 77, 45-53. (Full text and PDF versions of the article are available for Journal Members on the Biophysical Journal website.) PubMed ID: 10388739

Schematic diagram of the pancreatic beta-cell plasma membrane showing the ionic currents captured by the three single cell mathematical models.