Bertram, Smolen, Sherman, Mears, Atwater, Martin, Soria, 1995
Model Status
This model can not be solved as it is overconstrained. ValidateCellML verifies this model as valid CellML but detects unit inconsistencies.
Model Structure
The endocrine portion of the pancreas (the islets of Langerhans) synthesises and secretes several hormones, including insulin. Insulin secretion is triggered by an increase in blood glucose or by parasympathetic stimulation, and it is decreased by sympathetic input. Increases in insulin secretion usually correlate with increases in free cytosolic Ca2+ concentration ([Ca2+]i), and in turn, [Ca2+]i is largely determined by the electrical activity of the cell. When exposed to a threshold concentration of glucose, pancreatic beta-cells exhibit a complicated pattern of electrical activity. Bursts of action potential spikes (the "active" phase) are observed, separated by a "silent" phase of membrane repolarisation. At even higher glucose concentrations, continuous action potentials are seen.
Cholinergic drugs enhance glucose-induced insulin secretion. In their 1995 mathematical model, Richard Bertram, Paul Smolen, Arthur Sherman, David Mears, Illani Atwater, Franz Martin and Bernat Soria account for the cholinergic effects on membrane potential and cytosolic Ca2+. They believe that the mechanism underlying the muscarinic-induced depolarisation of the beta-cell is a calcium release-activated current (CRAC). This current is activated by the depletion of Ca2+ stores in the endoplasmic reticulum (ER), and it is carried by Na+ and K+.
Their mathematical model incorporates six ionic currents: two fast calcium currents (ICaf and ICas), one of which (ICas) inactivates slowly.; a delayed rectifying potassium current (IK); and an ATP activated potassium current (IK(ATP)). These currents allow independent bursting to occur. An additional CRAC current (ICRAC) provides direct feedback from the ER to the cell membrane. Additional equations account for the calcium handling and a calcium-activated potassium current (IK(Ca)) (see the figure below).
The complete original paper reference is cited below:
A Role for Calcium Release-Activated Current (CRAC) in Cholinergic Modulation of Electrical Activity in Pancreatic Beta-Cells, Richard Bertram, Paul Smolen, Arthur Sherman, David Mears, Illani Atwater, Franz Martin and Bernat Soria, 1995, Biophysical Journal , 68, 2323-2332. PubMed ID: 7647236
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