Bertram, Satin, Zhang, Smolen, Sherman, 2004
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 COR and produces the expected output. This model has been parameterised for the 'glycolytic bursting' model. Some equations have inconsistent magnitudes due to the fact that time is defined in milliseconds, yet flux is defined in micromolar per second.
ABSTRACT: Pancreatic islets of Langerhans produce bursts of electrical activity when exposed to stimulatory glucose levels. These bursts often have a regular repeating pattern, with a period of 10-60 s. In some cases, however, the bursts are episodic, clustered into bursts of bursts, which we call compound bursting. Consistent with this are recordings of free Ca2+ concentration, oxygen consumption, mitochondrial membrane potential, and intraislet glucose levels that exhibit very slow oscillations, with faster oscillations superimposed. We describe a new mathematical model of the pancreatic beta-cell that can account for these multimodal patterns. The model includes the feedback of cytosolic Ca2+ onto ion channels that can account for bursting, and a metabolic subsystem that is capable of producing slow oscillations driven by oscillations in glycolysis. This slow rhythm is responsible for the slow mode of compound bursting in the model. We also show that it is possible for glycolytic oscillations alone to drive a very slow form of bursting, which we call "glycolytic bursting." Finally, the model predicts that there is bistability between stationary and oscillatory glycolysis for a range of parameter values. We provide experimental support for this model prediction. Overall, the model can account for a diversity of islet behaviors described in the literature over the past 20 years.
Calcium and Glycolysis Mediate Multiple Bursting Modes in Pancreatic Islets, Richard Bertram, Leslie Satin, Min Zhang, Paul Smolen, and Arthur Sherman, 2004, Biophysical Journal, 87, 3074-3087. 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.|