The phantom burster model for pancreatic beta-cells
Catherine
Lloyd
Auckland Bioengineering Institute, University of Auckland
Model Status
This model has been rebuilt according to the author's original XPPAUT code, which can be found here. This version of the CellML model represents the fast bursting model where gs1=20. The model replicates figure 2 in the published paper. The model runs in both PCEnv and COR and the units are consistent.
Model Structure
ABSTRACT: Pancreatic beta-cells exhibit bursting oscillations with a wide range of periods. Whereas periods in isolated cells are generally either a few seconds or a few minutes, in intact islets of Langerhans they are intermediate (10-60 s). We develop a mathematical model for beta-cell electrical activity capable of generating this wide range of bursting oscillations. Unlike previous models, bursting is driven by the interaction of two slow processes, one with a relatively small time constant (1-5 s) and the other with a much larger time constant (1-2 min). Bursting on the intermediate time scale is generated without need for a slow process having an intermediate time constant, hence phantom bursting. The model suggests that isolated cells exhibiting a fast pattern may nonetheless possess slower processes that can be brought out by injecting suitable exogenous currents. Guided by this, we devise an experimental protocol using the dynamic clamp technique that reliably elicits islet-like, medium period oscillations from isolated cells. Finally, we show that strong electrical coupling between a fast burster and a slow burster can produce synchronized medium bursting, suggesting that islets may be composed of cells that are intrinsically either fast or slow, with few or none that are intrinsically medium.
The original paper reference is cited below:
The phantom burster model for pancreatic beta-cells, Richard Bertram, Joseph Previte, Arthur Sherman, Tracie A. Kinard and Leslie S. Satin, 2000,
Biophysical Journal, 79, 2880-2892. PubMed ID: 11106596
cell schematic for the model
Schematic diagram of the pancreatic beta-cell plasma membrane showing the ionic currents captured by the phantom burster model.
$\frac{d V}{d \mathrm{time}}=\frac{-(\mathrm{ICa}+\mathrm{IK}+\mathrm{Il}+\mathrm{Is1}+\mathrm{Is2})}{\mathrm{Cm}}$
$\mathrm{minf}=\frac{1}{1+e^{\frac{\mathrm{Vm}-V}{\mathrm{sm}}}}\mathrm{ICa}=\mathrm{gCa}\mathrm{minf}(V-\mathrm{VCa})$
$\mathrm{IK}=\mathrm{gK}n(V-\mathrm{VK})\frac{d n}{d \mathrm{time}}=\frac{\mathrm{lambda}(\mathrm{ninf}-n)}{\mathrm{taun}\times 1}\mathrm{ninf}=\frac{1}{1+e^{\frac{\mathrm{Vn}-V}{\mathrm{sn}}}}\mathrm{taun}=\frac{\mathrm{tnbar}}{1+e^{\frac{V-\mathrm{Vn}}{\mathrm{sn}}}}$
$\mathrm{Is1}=\mathrm{gs1}\mathrm{s1}(V-\mathrm{VK})\mathrm{s1inf}=\frac{1}{1+e^{\frac{\mathrm{Vs1}-V}{\mathrm{ss1}}}}\frac{d \mathrm{s1}}{d \mathrm{time}}=\frac{\mathrm{s1inf}-\mathrm{s1}}{\mathrm{taus1}\times 1}$
$\mathrm{Is2}=\mathrm{gs2}\mathrm{s2}(V-\mathrm{VK})\mathrm{s2inf}=\frac{1}{1+e^{\frac{\mathrm{Vs2}-V}{\mathrm{ss2}}}}\frac{d \mathrm{s2}}{d \mathrm{time}}=\frac{\mathrm{s2inf}-\mathrm{s2}}{\mathrm{taus2}\times 1}$
$\mathrm{Il}=\mathrm{gl}(V-\mathrm{Vl})$
Joseph
Previte
James
Lawson
Richard
Added more metadata.
Autumn
Cuellar
A
James
Lawson
Richard
2002-07-18
2009-05-15T16:10:00+12:00
Fixed errors detected by ValidateCellML, including connection duplication and namespace mixing.
The Bertram et al 2000 phantom burster model for pancreatic beta-cells.
pancreatic beta-cell
keyword
calcium dynamics
electrophysiology
beta cell
pancreas
1000
2000-12
Tracie
Kinard
A
The Phantom Burster Model for Pancreatic Beta Cells (fast bursting model)
The University of Auckland, Bioengineering Institute
11106596
James Lawson
This is the CellML description of Bertram et al's 2000 phantom burster model for pancreatic beta-cells.
100
10000
0.001
2003-04-09
Arthur
Sherman
Biophysical Journal
The University of Auckland
The Bioengineering Institute
j.lawson@auckland.ac.nz
Richard
Bertram
Catherine Lloyd
Added publication date information.
5000
100000
0.001
bdf15
2007-08-08T00:00:00+00:00
This model has been rebuilt according to the author's original XPPAUT code, which can be found at http://www.math.fsu.edu/~bertram/software/islet/BJ_04a.ode . Unfortunately the model is still unable to produce the correct output. This file is known to run in PCEnv.
Catherine
Lloyd
May
The Phantom Burster Model for Pancreatic Beta Cells
79
2880
2892
Leslie
Satin
S