Pedersen, Bertram, Sherman, 2005

Model Structure

Insulin secretion from pancreatic beta-cells is known to be pulsatile, with a period of 5-10 milliseconds. It has been suggested that this pulsatile behaviour stems from oscillations in the glycolysis pathway, mediated by the enzyme phosphofructokinase (PFK). In turn, this rhythmical enzymatic behaviour induces periodic activity of ATP-dependent potassium channels (K(ATP)-channels) in the plasma membrane. Insulin pulsatility is impaired in diabetic patients, which are also relatively insulin insensitive. Target tissues, such as the liver, are more sensitive to pulsatile insulin than to constant levels, and therefore an improved understanding of the mechanisms underlying pulsatile insulin secretion is important in the search for a potential therapeutic treatment for diabetes.

The link between metabolism and calcium ion influx leading to insulin secretion is provided by the electrical activity of the beta-cells, which has a characteristic behaviour known as bursting. A burst consists of an active phase of spiking followed by a silent phase of membrane repolarisation. During the active burst calcium ions diffuse into the cell through voltage-gated calcium channels, and the subsequent rise in the cytosolic calcium concentration results in the secretion of insulin (see diagram below).

In the paper described here, Pedersen et al. present a mathematical model of metabolically driven insulin secretion. This model is based on one which has been published previously by Bertram et al. (2004), which has also been described in CellML and can be found in the model repository. Model simulation data indicate that electrical coupling is sufficient to synchronise electrical bursting activity and metabolic oscillations.

Schematic diagram of the pathways described by the mathematical model. Extracellular glucose (Ge) enters the pancreatic beta-cell through GLUT-2 transporters in the plasma membrane, and is subsequently broken down through a series of enzyme-catalysed reactions in the glycolysis pathway. The metabolic products of the glycolysis pathway feed into the mitchondria, the site of aerobic respiration, where they are used to produce ATP. ATP represents the common substrate, linking the metabolic (glycolysis) and electrical (membrane potential) components of the mathematical model by regulating the flow of potassium ions through the K(ATP)-channels in the plasma membrane. In turn, these control regulate the membrane potential and calcium ion flow leading to insulin secretion. Insulin acts to lower the plasma glucose concentration though the functions of the liver (represented by a dashed line).

The complete original paper reference is cited below:

Intra- and inter-islet synchronization of metabolically driven insulin secretion, Morten Gram Pedersen, Richard Bertram, and Arthur Sherman, 2005, Biophysical Journal , 89, 107-119. (Full text and PDF versions of the article are available to journal subscribers on the Biophysical Journal website.) PubMed ID: 15834002

The authors highlight that the original model code can be downloaded here. The CellML translation of this model represents the core model and it will run in the PCEnv software. However the pulsatile behaviour of the model, as published in the original paper can not be recreated. To achieve these results I suspect several cell models have to be run simultaneously, generating many bursts which are clustered together into what is termed compound bursting.