Fridlyand, Tamarina, Philipson, 2003

Model Status

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

Model Structure

An increase in the concentration of intracellular free calcium ([Ca²⁺]_i) is an essential signal for the initiation of insulin secretion in pancreatic beta-cells. This increase is primarily due to the opening of Ca²⁺ channels in the plasma membrane in response to glucose. Glucose metabolism leads to an increase in the cytosolic ATP:ADP ratio, which in turn causes the ATP-sensitive potassium channels to close. The beta-cell membrane becomes depolarised, Ca²⁺ channels open, and Ca²⁺ enters the cell. These events underlie the glucose-induced electrical activity, which in pancreatic islets, consists of Ca²⁺-dependent action potentials.

There is an abundance of literature that describes beta-cell electrical activity and its relationship to [Ca²⁺]_i. Complex and cyclic spike-burst activity, and corresponding [Ca²⁺]_i oscillations in pancreatic islets and beta-cell clusters are induced in response to a rise in extracellular glucose concentration. Intermediate glucose concentrations induce both fast and slow oscillations. The authors of this current study: Fridlyand, Tamarina and Philipson, have previously studied slow and fast [Ca²⁺]_i oscillations in islets in response to a variety of conditions. However, the experimental results were complex, and precise understanding was limited by the large number of channels and pumps in the beta-cell plasma membrane that were simultaneously working.

In order to better understand the molecular mechanisms underlying this behaviour, in this publication Fridlyand et al. have developed a mathematical model of the Ca²⁺ fluxes in pancreatic beta-cells. Several other mathematical models of glucose-induced insulin secretion, with corresponding descriptions of glucose transport, metabolism and ion regulation, have been published. These include:

However, most of these models are focused on describing one specific phenomenon. They only include a very limited set of channels and pumps, and therefore it is difficult to apply them to a another situation. In addition, since their publication, new experimental data has become available, and these new findings should be included in a theoretical model. For this reason Fridlyand et al. have developed the new mathematical model described here (see the raw CellML description of the Fridlyand et al. 2003 model in ). They have adopted the more complex style of modelling that has previously been used successfully to describe the electrophysiology of cardiac myocytes and other cell types (for example in Human Atrial Cell Model, Nygren et al. 1998 and in Modelling Interval-Force Relations in Cardiac Muscle, Rice et al., 2000).

Their new model includes a wider range of channels and pumps, as well as endoplasmic reticulum (ER) Ca²⁺ sequestration mechanisms (see the figure below). Using this model they were able to simulate whole cell electrical activity and [Ca²⁺]_i, free calcium in the ER ([Ca²⁺]_ER), intracellular Na⁺ ([Na⁺]_i), cytosolic ATP ([ATP]_i), and inositol triphosphate ([IP₃]_i) concentrations. However, they acknowledge that this model does not consider metabolic processes or insulin secretion.

The complete original paper reference is cited below:

Modeling of Ca²⁺ flux in pancreatic beta-cells: role of the plasma membrane and intracellular stores, Leonid E. Fridlyand, Natalia Tamarina, and Louis H. Philipson, 2003, American Journal of Physiology , 285, E138-E154. (Full text (HTML) and PDF versions of the article are available on the American Jounal of Physiology website.) PubMed ID: 12644446

Schematic representation of currents and ion fluxes, through the plasma membrane and the endoplasmic reticulum membrane, which have been included in the whole beta-cell mathematical model.