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 medium bursting model where gs1=7. The model replicates figure 3 in the published paper (please note you need to run the model for at least 100 seconds to get past the initial unstable stage). 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.
$\frac{d V}{d \mathrm{time}}=\frac{-(\mathrm{ICa}+\mathrm{IK}+\mathrm{Il}+\mathrm{Is1}+\mathrm{Is2})}{\mathrm{Cm}}$
$\mathrm{minf}=\frac{1}{1+e^{\frac{\mathrm{Vm}-V}{\mathrm{sm}}}}\mathrm{ICa}=\mathrm{gCa}\mathrm{minf}(V-\mathrm{VCa})$
$\mathrm{IK}=\mathrm{gK}n(V-\mathrm{VK})\frac{d n}{d \mathrm{time}}=\frac{\mathrm{lambda}(\mathrm{ninf}-n)}{\mathrm{taun}\times 1}\mathrm{ninf}=\frac{1}{1+e^{\frac{\mathrm{Vn}-V}{\mathrm{sn}}}}\mathrm{taun}=\frac{\mathrm{tnbar}}{1+e^{\frac{V-\mathrm{Vn}}{\mathrm{sn}}}}$
$\mathrm{Is1}=\mathrm{gs1}\mathrm{s1}(V-\mathrm{VK})\mathrm{s1inf}=\frac{1}{1+e^{\frac{\mathrm{Vs1}-V}{\mathrm{ss1}}}}\frac{d \mathrm{s1}}{d \mathrm{time}}=\frac{\mathrm{s1inf}-\mathrm{s1}}{\mathrm{taus1}\times 1}$
$\mathrm{Is2}=\mathrm{gs2}\mathrm{s2}(V-\mathrm{VK})\mathrm{s2inf}=\frac{1}{1+e^{\frac{\mathrm{Vs2}-V}{\mathrm{ss2}}}}\frac{d \mathrm{s2}}{d \mathrm{time}}=\frac{\mathrm{s2inf}-\mathrm{s2}}{\mathrm{taus2}\times 1}$
$\mathrm{Il}=\mathrm{gl}(V-\mathrm{Vl})$
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