Na/Ca Exchange in Models for Pancreatic Beta-Cells
Catherine
Lloyd
Auckland Bioengineering Institute, The University of Auckland
Model Status
This CellML model represents Model III from the published paper. The CellML matches the published equations and the model runs in OpenCell and COR but it does not replicate the published results.
Model Structure
ABSTRACT: In the presence of an insulinotropic glucose concentration, beta-cells, in intact pancreatic islets, exhibit periodic bursting electrical activity consisting of an alternation of active and silent phases. The fraction of time spent in the active phase over a period is called the plateau fraction and is correlated with the rate of insulin release. However, the mechanisms that regulate the plateau fraction remain unclear. In this paper we investigate the possible role of the plasma membrane Na+/Ca2+ exchange of the beta-cell in controlling the plateau fraction. We have extended different single-cell models to incorporate this Ca2+-activated electrogenic Ca2+ transporter. We find that the Na+/Ca2+ exchange can provide a physiological mechanism to increase the plateau fraction as the glucose concentration is raised. In addition, we show theoretically that the Na+/Ca2+ exchanger is a key regulator of the cytoplasmic calcium concentration in clusters of heterogeneous cells with gap-junctional electrical coupling.
The 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. PubMed ID: 10388739
cell schematic for the model
Schematic diagram of the pancreatic beta-cell plasma membrane showing the ionic currents captured by the three single cell mathematical models.
$\frac{d V}{d \mathrm{time}}=\frac{-(\mathrm{i\_K}+\mathrm{i\_Ca}+\mathrm{i\_K\_Ca}+\mathrm{i\_Na\_Ca})}{\mathrm{Cm}}$
$\mathrm{i\_K}=\mathrm{g\_K}n(V-\mathrm{V\_K})$
$\frac{d n}{d \mathrm{time}}=\mathrm{lamda}\frac{\mathrm{n\_infinity}-n}{\mathrm{tau\_n}}\mathrm{n\_infinity}=\frac{1.0}{1.0+e^{\frac{\mathrm{V\_n}-V}{\mathrm{S\_n}}}}\mathrm{tau\_n}=\frac{c}{e^{\frac{V-\mathrm{V\_}}{a}}+e^{\frac{\mathrm{V\_}-V}{b}}}$
$\mathrm{i\_Ca}=\mathrm{g\_Ca}\mathrm{m\_infinity}(V-\mathrm{V\_Ca})$
$\mathrm{m\_infinity}=\frac{1.0}{1.0+e^{\frac{\mathrm{V\_m}-V}{\mathrm{S\_m}}}}$
$\mathrm{i\_K\_Ca}=\mathrm{g\_K\_Ca}\frac{\mathrm{Ca\_i}}{\mathrm{K\_d}+\mathrm{Ca\_i}}(V-\mathrm{V\_K})$
$\mathrm{i\_Na\_Ca}=\mathrm{g\_Na\_Ca}\frac{\mathrm{Ca\_i}^{\mathrm{nH}}}{\mathrm{K\_1\_2}^{\mathrm{nH}}+\mathrm{Ca\_i}^{\mathrm{nH}}}(V-\mathrm{V\_Na\_Ca})\mathrm{V\_Na\_Ca}=\mathrm{RT\_F}3.0\ln (\frac{\mathrm{Na\_o}}{\mathrm{Na\_i}}-\ln \left(\frac{\mathrm{Ca\_o}}{\mathrm{Ca\_i}}\right))$
$\frac{d \mathrm{Ca\_i}}{d \mathrm{time}}=f(-\mathrm{alpha}(\mathrm{i\_Ca}-2.0\mathrm{i\_Na\_Ca})-\mathrm{k\_Ca}\mathrm{Ca\_i})+\mathrm{k\_rel}(\mathrm{Ca\_ret}-\mathrm{Ca\_i})-\mathrm{k\_pump}\mathrm{Ca\_i}\frac{d \mathrm{Ca\_ret}}{d \mathrm{time}}=\mathrm{k\_rel}(\mathrm{Ca\_ret}-\mathrm{Ca\_i})+\mathrm{k\_pump}\mathrm{Ca\_i}$
calcium dynamics
electrophysiology
Pancreatic Beta-Cell
na/ca exchanger
beta cell
Catherine Lloyd
Isabella
Susa
Autumn
Cuellar
A
keyword
10388739
Corrected dV/dt equation in membrane component.
Effect of Na/Ca Exchange on Plateau Fraction and [Ca]i in Models for Bursting in Pancreatic Beta-Cells (Model C)
The University of Auckland, Auckland Bioengineering Institute
Added publication date information.
1999-07-01
The Gall and Susa 1999 model of Na/Ca exchange in Model III for
pancreatic beta-cells.
Pancreatic Beta-Cell
Added more metadata.
2002-07-18
The University of Auckland
Auckland Bioengineering Institute
Catherine
Lloyd
May
David
Gall
2002-07-18
c.lloyd@auckland.ac.nz
This is the CellML description of Gall and Susa's 1999 model of Na/Ca exchange in Model III for pancreatic beta-cells.
2002-04-10
Effect of Na/Ca Exchange on Plateau Fraction and [Ca]i in Models for Bursting in Pancreatic Beta-Cells
77
45
53
Catherine
Lloyd
May
Biophysical Journal
2003-04-09
Catherine
Lloyd
May