Enhancement Of Emergent Bursting In Pancreatic Beta-Cells
Catherine
Lloyd
Auckland Bioengineering Institute, The University of Auckland
Model Status
This model has been validated and is known to run in OpenCell and COR to recreate the published results (figure 1). The paper by Devries and Sherman describes several different parameter sets including single cell and two cell sets, and also describes a deterministic and a stochastic model. This CellML model uses equations 1-3 and the parameters given in table 1 for the single cell deterministic model. For this particular model lambda = 0.9. Note there is a unit inconsistency in the equation for V, but our attempts to balance the units for this equation resulted in a model which no longer worked.
Model Structure
ABSTRACT: Secretion of insulin by electrically coupled populations of pancreatic beta -cells is governed by bursting electrical activity. Isolated beta -cells, however, exhibit atypical bursting or continuous spike activity. We study bursting as an emergent property of the population, focussing on interactions among the subclass of spiking cells. These are modelled by equipping the fast subsystem with a saddle-node-loop bifurcation, which makes it monostable. Such cells can only spike tonically or remain silent when isolated, but can be induced to burst with weak diffusive coupling. With stronger coupling, the cells revert to tonic spiking. We demonstrate that the addition of noise dramatically increases, via a phenomenon like stochastic resonance, the coupling range over which bursting is seen.
The original paper reference is cited below:
Channel Sharing in Pancreatic Beta-Cells Revisited: Enhancement of Emergent Bursting by Noise, Gerda De Vries and Arthur Sherman, 2000,
The Journal Of Theoretical Biology
, 207, 513-530. PubMed ID: 11093836
diagram of the model
A schematic representation of the four transmembrane currents captured by the De Vries and Sherman 2000 pancreatic beta-cell model.
$\frac{d V}{d \mathrm{time}}=\frac{-(\mathrm{i\_Ca}+\mathrm{i\_K}+\mathrm{i\_K\_ATP}+\mathrm{i\_s})}{\mathrm{tau}}$
$\mathrm{i\_Ca}=\mathrm{g\_Ca}\mathrm{m\_infinity}(V-\mathrm{V\_Ca})$
$\mathrm{m\_infinity}=\frac{1.0}{1.0+e^{\frac{\mathrm{V\_m}-V}{\mathrm{theta\_m}}}}$
$\mathrm{i\_K}=\mathrm{g\_K}n(V-\mathrm{V\_K})$
$\frac{d n}{d \mathrm{time}}=\frac{\mathrm{lambda}(\mathrm{n\_infinity}-n)}{\mathrm{tau}}\mathrm{n\_infinity}=\frac{1.0}{1.0+e^{\frac{\mathrm{V\_n}-V}{\mathrm{theta\_n}}}}$
$\mathrm{i\_s}=\mathrm{g\_s}s(V-\mathrm{V\_K})$
$\frac{d s}{d \mathrm{time}}=\frac{\mathrm{s\_infinity}-s}{\mathrm{tau\_s}}\mathrm{s\_infinity}=\frac{1.0}{1.0+e^{\frac{\mathrm{V\_s}-V}{\mathrm{theta\_s}}}}$
$\mathrm{i\_K\_ATP}=\mathrm{g\_K\_ATP}p(V-\mathrm{V\_K})$
2000-12-21The University of Auckland, Bioengineering Institute
Added publication date information.
This is the CellML description of De Vries and Sherman's 2000 mathematical model of channel sharing in pancreatic beta cells.ArthurSherman
De Vries and Sherman's 2000 mathematical model of channel sharing in pancreatic beta cells.
Pancreatic Beta-CellJames Lawson
Added more metadata.
Catherine LloydChannel Sharing in Pancreatic Beta-Cells Revisited: Enhancement of Emergent Bursting by Noise2075135302002-05-09T00:00:00+00:00keyword10000060000100calcium dynamicselectrophysiologybeta cellpancreasJournal of theoretical BiologyThis model has been validated and is known to run in PCEnv. The paper by Devries and Sherman describes several different parameter sets including single cell and two cell sets, and also describes a deterministic and a stochastic model. This file uses the equations and parameters given for the single cell deterministic model. c.lloyd@auckland.ac.nzGerdaDe Vries2002-07-18AutumnCuellarA11093836Auckland Bioengineering InstituteThe University of AucklandCatherineLloydMayCatherineLloydMay2003-04-09