A Calciumbased Phantom Bursting Model for Pancreatic Islets
Model Status
This model is has consistent units and has been verified as valid CellML by ValidateCellML. It is currently unsuitably constrained and can not be solved.
Model Structure
Pancreatic betacells are located in clusters within the pancreas called the islets of Langerhans. Betacells secrete the hormone insulin in response to elevated blood glucose levels, and in doing so, they play an essential role in glucose homeostasis. When betacells fail to function properly, this can lead to pathologies such as type II diabetes.
Insulin secretion is oscillatory, and it is inphase with oscillations in the free cytosolic calcium concentration ([Ca^{2+}]_{i}), and theses Ca^{2+} oscillations reflect a bursting pattern in the betacell electrical activity. Electrical bursting consists of periodic active phases of cell firing (excitation) followed by silent phases of hyperpolarisation (rest). These oscillations can be divided into three categories:

Fast bursting, which has a period between 2 and 5 seconds and which often occurs in single cells and in islets where acetylcholine is present;

Medium bursting, which has a period of 10 to 60 seconds and which occurs in islets where there is a stimulatory glucose concentration; and

Slow bursting, which has a period of 2 to 4 minutes and which occurs in single cells and in islets.
The first mathematical models of betacells were developed to describe medium bursting, and the first models to address the variability in betacell oscillations were developed by Chay in 1995 and 1997 (see Extracellular and Intracellular Calcium Effects on Pancreatic Beta Cells, Chay, 1997 for more details). In these models the main mechanism for oscillations was variation in the Ca^{2+} concentration in the ER, which directly or indirectly modulates one or more Ca^{2+}dependent channels. In the Bertram and Sherman model described here the authors analyse in detail how the ER exerts its affects using a phantom bursting model (see the figure below).
The phantom bursting model is a general paradigm for temporal plasticity in bursting in betacells in which bursting is driven by the interaction of two slow variables with disparate time constants (see The Phantom Burster Model for Pancreatic BetaCells, 2000 for more details). There are three potential slow variables which could drive the phantom bursting in vivo:

cytosolic Ca^{2+} concentration;

ER Ca^{2+} concentration;

and the ADP to ATP ratio.
The complete original paper reference is cited below:
A Calciumbased Phantom Bursting Model for Pancreatic Islets, Richard Bertram and Arthur Sherman, 2004, Bulletin of Mathematical Biology , 66, 13131344. (Full text (HTML) and PDF versions of the article are available to subscribers on the Bulletin of Mathematical Biology website.) PubMed ID: 15294427
A schematic diagram of the ionic currents and fluxes across the ER and the cell surface membranes, which are described by the mathematical model. 