Complex bursting in pancreatic islets: a potential glycolytic mechanism
Ethan
Choi
Auckland Bioengineering Institute, The University of Auckland
Model Status
This model has been built with the differential expressions in Wierschem's 2004 paper and also the XPPAUT code from Richard Bertram. This file is known to run in PCEnv and COR, however the model works in milliseconds, and must be run for at least 600000 time units or more (to simulate 10 minutes) and could not be changed to portray minutes instead. Due to the large iterations, and large point density required to run the model, problems were found in PCEnv and COR where the model would crash or not display properly giving an memory exceded error. Current parameterization of the model replicates Figure 9 of the paper. The initial conditions for all variables were provided in the Bertram code (given as V=-66, n=0, c=0.17, ATP=2.4, ADP=0.05) however these figures still required a warmup period for the functions so they were changed by running the model to steady state then cloning to the output to better replicate the figures from the paper.
Model Structure
ABSTRACT: The electrical activity of insulin-secreting pancreatic islets of Langerhans is characterized by bursts of action potentials. Most often this bursting is periodic, but in some cases it is modulated by an underlying slower rhythm. We suggest that the modulatory rhythm for this complex bursting pattern is due to oscillations in glycolysis, while the bursting itself is generated by some other slow process. To demonstrate this hypothesis, we couple a minimal model of glycolytic oscillations to a minimal model for activity-dependent bursting in islets. We show that the combined model can reproduce several complex bursting patterns from mouse islets published in the literature, and we illustrate how these complex oscillations are produced through the use of a fast/slow analysis.
Complex bursting in pancreatic islets: a potential glycolytic mechanism, Wierschem, Bertram, 2004, Journal of Theoretical Biology
, 228, 513-521. PubMed ID: 15178199
Model Diagram
Schematic diagram of the composite model.
$\mathrm{phi}=\mathrm{ATP}(1+k\mathrm{ADP})^{2}\frac{d \mathrm{ATP}}{d \mathrm{time}}=\frac{v-\mathrm{phi}}{1000\mathrm{tau\_c}}\frac{d \mathrm{ADP}}{d \mathrm{time}}=\frac{\mathrm{phi}-\mathrm{eta}\mathrm{ADP}}{1000\mathrm{tau\_c}}$
$\frac{d V}{d \mathrm{time}}=\frac{-(\mathrm{I\_Ca}+\mathrm{I\_K}+\mathrm{I\_KCa}+\mathrm{I\_KATP})}{\mathrm{C\_m}}$
$\mathrm{I\_Ca}=\mathrm{g\_Ca\_}\mathrm{m\_infinity}(V-\mathrm{V\_Ca})\mathrm{m\_infinity}=\frac{1}{1+e^{\frac{\mathrm{v\_m}-V}{\mathrm{s\_m}}}}$
$\mathrm{I\_K}=\mathrm{g\_K\_}n(V-\mathrm{V\_K})$
$\mathrm{omega}=\frac{1}{1+\frac{\mathrm{k\_D}}{c}}\mathrm{I\_KCa}=\mathrm{g\_KCa\_}\mathrm{omega}(V-\mathrm{V\_K})$
$\mathrm{I\_KATP}=\frac{(V-\mathrm{V\_K})\mathrm{g\_KATP\_}}{\mathrm{ATP}}$
$\mathrm{n\_infinity}=\frac{1}{1+e^{\frac{\mathrm{v\_n}-V}{\mathrm{s\_n}}}}\frac{d n}{d \mathrm{time}}=\frac{\mathrm{n\_infinity}-n}{\mathrm{tau\_n}}$
$\frac{d c}{d \mathrm{time}}=\mathrm{J\_mem}$
$\mathrm{J\_mem}=-f(\mathrm{alpha}\mathrm{I\_Ca}+\mathrm{k\_c}c)$
Complex bursting in pancreatic islets: a potential glycolytic mechanism513521228BurstingMetabolismBeta-cellGlycolysisInsulinCalcium DynamicskeywordJournal of Theoretical Biologypancreatic beta cellRichardBertrammcho099@aucklanduni.ac.nz15178199KeolaWierschem2009-12-162009-12-16bdf15100000400000EthanChoiAuckland Bioengineering InstituteThe University of Auckland