Calcium and Glycolysis Mediate Multiple Bursting Modes in Pancreatic Islets

Model Status

This model has been rebuilt and coded by translating the authors original XPPAUT .ode file, which can be found at http://www.math.fsu.edu/~bertram/software/islet/BJ_04a.ode . This file runs in PCEnv and is able to produce the expected output for a few cycles, after which the output degenerates. This model has been parameterised for the 'compound bursting' model.

ValidateCellML detects unit inconsistencies and absent initial value definitions within this model.

Model Structure

Secretion of insulin from pancreatic islets is oscillatory and multimodal. These oscillations occur over a fairly broad range of time scales:

• Fast oscillations have a period of tens of seconds and they are in phase with the intracellular free calcium concentration ([Ca²⁺]_i) of beta-cells, the insulin-secreting cells of the islet.

• The second component of the oscillatory insulin signal has a period of 5-10 milliseconds and it is known to play some physiological role which is lost in patients with type II diabetes.

• Even slower ultradian rhythms with a period of 2 hours, and circadian rhythms with a period of about 24 hours, have also been observed.

In mouse islets, Ca²⁺ oscillations are driven by bursting electrical activity at stimulatory glucose levels. It is though that when Ca²⁺ enters the cell during an action potential, the increase in [Ca²⁺]_i provides negative feedg onto the membrane through the activation of K⁺ channels, in turn leading to membrane hyperpolarisation and ending bursting electrical activity. After cytosolic Ca²⁺ has been cleared by the action of ATP-drive calcium pumps (Ca²⁺ ATPases) in the plasma membrane and in the ER membrane, an active spiking phase restarts. Thus Ca²⁺ may act directly to activate Ca²⁺-activated K⁺ channels, or indirectly by lowering the ratio of ATP to ADP (through the action of the Ca²⁺ ATPases), which in turn activates ATP-sensitive K⁺ channels. The interaction of these mechanisms is analysed in more detail in The Phantom Burster Model for Pancreatic Beta-Cells, Bertram et al., 2000, and A Calcium-based Phantom Bursting Model for Pancreatic Islets, Bertram and Sherman, 2004

An alternative theory is that electrical activity is exclusively driven by slow oscillations in glycolysis due to the allosteric enzyme phosphofructokinase (PFK). Glycolytic products serve as substrates for mitochondrial metabolism, so their rhythmical synthesis is likely to lead to oscillations in the ATP to ADP ratio which then drives bursting activity through their effects on beta-cell ATP-sensitive K⁺ channels.

In this current study, Bertram et al. analyse these two mechanisms for insulin oscillations in pancreatic islets. They demonstrate via a mathematical model that they are not mutually exclusive but instead they can cooperate to produce rhythmical insulin secretion. The mathematical model (see the figure below) is based in part on an earlier model for Ca²⁺-dependent bursting (Bertram and Sherman, 2004), which has been extended to include glycolytic components.

The article has bee published online adhead of print. To view this article as a PDF, please follow the link below:

Calcium and Glycolysis Mediate Multiple Bursting Modes in Pancreatic Islets, Richard Bertram, Leslie Satin, Min Zhang, Paul Smolen, and Arthur Sherman, 2004, Biophysical Journal PubMed ID: 15347584

A schematic diagram of the ionic currents and fluxes across the ER and the cell surface membranes which are described by the mathematical model.