The Phantom Burster Model For Pancreatic Beta-Cells
Catherine
Lloyd
Bioengineering Institute, University of Auckland
Model Status
This is the original unchecked version of the model imported from the previous
CellML model repository, 24-Jan-2006.
Model Structure
Pancreatic beta-cells have been the subject of both experimental and theoretical studies for several decades. One reason for this interest has been the essential role beta-cells play in glucose homeostasis - they are the only source of insulin that most cells require in order to take up and metabolise glucose, and impairment of beta-cell function contributes to diabetes. A major focus of theoretical work has been beta-cell dynamics, especially in the form of bursting electrical activity. The bursts consist of active phases of Ca2+-carrying action potentials alternating with silent phases of repolarisation and are accompanied by oscillations in cytosolic Ca2+, which drive pulses of insulin secretion.
Experimentally, electrical activity in beta-cells is studied in two distinct preparations: islets of Langerhans, which are microorgans containing thousands of endocrine cells, and isolated cells. 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 seconds). In their 2000 publication, Richard Bertram, Joseph Previte, Arthur Sherman, Tracie A. Kinard and Leslie S. Satin develop a mathematical model for beta-cell electrical activity capable of generating this wide range of bursting oscillations. Unlike previously published models, bursting is driven by the interaction of two slow processes (Is1 and Is2 in below), one with a relatively small time constant (1-5 seconds) and the other with a much larger time constant (1-2 minutes). Bursting on the intermediate time scale is generated without the need for a slow process having an intermediate time constant, hence phantom bursting. This mathematical model has been translated into a CellML description which can be downloaded in various formats as described in .
The complete 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. (Full text and PDF versions of the article are available for Journal Members on the Biophysical Journal website.) 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.
$\frac{d V}{d \mathrm{time}}=\frac{-(\mathrm{i\_Ca}+\mathrm{i\_K}+\mathrm{i\_s1}+\mathrm{i\_s2}+\mathrm{i\_L})}{\mathrm{Cm}}$
$\mathrm{i\_Ca}=\mathrm{g\_Ca}\mathrm{m\_infinity}(V-\mathrm{V\_Ca})$
$\mathrm{m\_infinity}=\frac{1.0}{1.0+e^{\frac{-22.0-V}{7.5}}}$
$\mathrm{i\_K}=\mathrm{g\_K}n(V-\mathrm{V\_K})$
$\frac{d n}{d \mathrm{time}}=\frac{\mathrm{n\_infinity}-n}{\mathrm{tau\_n}}\mathrm{n\_infinity}=\frac{1.0}{1.0+e^{\frac{-9.0-V}{10.0}}}\mathrm{tau\_n}=\frac{8.3}{1.0+e^{\frac{V+9.0}{10.0}}}$
$\mathrm{i\_s1}=\mathrm{g\_s1}\mathrm{s1}(V-\mathrm{V\_K})$
$\frac{d \mathrm{s1}}{d \mathrm{time}}=\frac{\mathrm{s1\_infinity}-\mathrm{s1}}{\mathrm{tau\_s1}}\mathrm{s1\_infinity}=\frac{1.0}{1.0+e^{\frac{-40.0-V}{0.5}}}$
$\mathrm{i\_s2}=\mathrm{g\_s2}\mathrm{s2}(V-\mathrm{V\_K})$
$\frac{d \mathrm{s2}}{d \mathrm{time}}=\frac{\mathrm{s2\_infinity}-\mathrm{s2}}{\mathrm{tau\_s2}}\mathrm{s2\_infinity}=\frac{1.0}{1.0+e^{\frac{-42.0-V}{0.4}}}$
$\mathrm{i\_L}=\mathrm{g\_L}(V-\mathrm{V\_L})$
The University of Auckland, Bioengineering Institute
Autumn
Cuellar
A
The Bertram et al 2000 phantom burster model for pancreatic beta-cells.
pancreatic beta-cell
c.lloyd@auckland.ac.nz
Catherine
Lloyd
May
Added more metadata.
The University of Auckland
The Bioengineering Institute
2000-12
This is the CellML description of Bertram et al's 2000 phantom burster model for pancreatic beta-cells.
Richard
Bertram
Catherine
Lloyd
May
Biophysical Journal
Arthur
Sherman
2002-04-10
Joseph
Previte
Tracie
Kinard
A
11106596
keyword
calcium dynamics
The Phantom Burster Model for Pancreatic Beta Cells
79
2880
2892
Added publication date information.
Catherine Lloyd
Leslie
Satin
S
2002-07-18
2003-04-09