gating variable of voltage-dependent potassium current
calcium uptake of the endoplasmic reticulum by SERCA pumps
calcium release-activated nonselective cation current
concentration of extracellular potassium
concentration of calcium in endoplasmic reticulum
concentration of free intracellular calcium
reversal potential of calcium release-activated nonselective cation current
maximum conductance coefficient of calcium release-activated nonselective cation current
fraction of open IP3-activated calcium channels
current-voltage relationship of sodium current
maximum conductance of delayed rectifier potassium current
concentration of free extracellular calcium
half-maximal pump activity of plasma membrane calcium pumps
reversal potential of non-selective cation current
half maximal pump activity of SERCA pumps
voltage-independent component of calcium-dependent potassium current
fraction of free calcium in endoplasmic reticulum
slope of voltage-dependent calcium current at half-maximum potential
maximum endoplasmic reticulum calcium permeability through open IP3-activated channels
affinity constant of voltage-dependent small conductance calcium-activated potassium current
fraction of ATP-sensitive potassium channels open
concentration of intracellular potassium
reversal potential of sodium-calcium exchanger
half-activation endoplasmic reticulum calcium concentration level of calcium release-activated nonselective cation current
calcium leak current out of the endoplasmic reticulum
affinity constant of intracellular IP3 to IP3 receptor
affinity constant of intracellular calcium to IP3 receptor
maximum conductance of sodium-calcium exchange current
current-voltage relationship of voltage-dependent calcium current
voltage-dependent small conductance calcium-activated potassium current
half activation intracellular calcium concentration of IP3 metabolism
maximum conductance of voltage-dependent small conductance calcium-activated potassium current
maximum conductance of inward sodium current
<documentation xmlns="http://cellml.org/tmp-documentation"> <articleinfo> Modelling Ca2+ Flux in Pancreatic Beta-cells <author> <firstname>Catherine</firstname> <surname>Lloyd</surname> <affiliation> <shortaffil>Bioengineering Institute, University of Auckland</shortaffil> </affiliation> </author> </articleinfo> Model Status This is the original unchecked version of the model imported from the previous CellML model repository, 24-Jan-2006. <sect1 id="sec_structure"> Model Structure An increase in the concentration of intracellular free calcium ([Ca <superscript>2+</superscript> ] <subscript>i</subscript> ) is an essential signal for the initiation of insulin secretion in pancreatic beta-cells. This increase is primarily due to the opening of Ca <superscript>2+</superscript> channels in the plasma membrane in response to glucose. Glucose metabolism leads to an increase in the cytosolic ATP:ADP ratio, which in turn causes the ATP-sensitive potassium channels to close. The beta-cell membrane becomes depolarised, Ca <superscript>2+</superscript> channels open, and Ca <superscript>2+</superscript> enters the cell. These events underlie the glucose-induced electrical activity, which in pancreatic islets, consists of Ca <superscript>2+</superscript> -dependent action potentials. There is an abundance of literature that describes beta-cell electrical activity and its relationship to [Ca <superscript>2+</superscript> ] <subscript>i</subscript> . Complex and cyclic spike-burst activity, and corresponding [Ca <superscript>2+</superscript> ] <subscript>i</subscript> oscillations in pancreatic islets and beta-cell clusters are induced in response to a rise in extracellular glucose concentration. Intermediate glucose concentrations induce both fast and slow oscillations. The authors of this current study: Fridlyand, Tamarina and Philipson, have previously studied slow and fast [Ca <superscript>2+</superscript> ] <subscript>i</subscript> oscillations in islets in response to a variety of conditions. However, the experimental results were complex, and precise understanding was limited by the large number of channels and pumps in the beta-cell plasma membrane that were simultaneously working. In order to better understand the molecular mechanisms underlying this behaviour, in this publication Fridlyand et al. have developed a mathematical model of the Ca <superscript>2+</superscript> fluxes in pancreatic beta-cells. Several other mathematical models of glucose-induced insulin secretion, with corresponding descriptions of glucose transport, metabolism and ion regulation, have been published. These include: Extracellular and Intracellular Calcium Effects on Pancreatic Beta Cells, Chay, 1997 ; Na <superscript>+</superscript> /Ca <superscript>2+</superscript> Exchange in Models for Pancreatic Beta-Cells, Gall and Susa, 1999 ; and The Phantom Burster Model for Pancreatic Beta-Cells, Bertram et al. , 2000 . However, most of these models are focused on describing one specific phenomenon. They only include a very limited set of channels and pumps, and therefore it is difficult to apply them to a another situation. In addition, since their publication, new experimental data has become available, and these new findings should be included in a theoretical model. For this reason Fridlyand et al. have developed the new mathematical model described here (see the raw CellML description of the Fridlyand et al. 2003 model in ). They have adopted the more complex style of modelling that has previously been used successfully to describe the electrophysiology of cardiac myocytes and other cell types (for example in Human Atrial Cell Model, Nygren et al. 1998 and in Modelling Interval-Force Relations in Cardiac Muscle, Rice et al. , 2000 ). Their new model includes a wider range of channels and pumps, as well as endoplasmic reticulum (ER) Ca <superscript>2+</superscript> sequestration mechanisms (see below). Using this model they were able to simulate whole cell electrical activity and [Ca <superscript>2+</superscript> ] <subscript>i</subscript> , free calcium in the ER ([Ca <superscript>2+</superscript> ] <subscript>ER</subscript> ), intracellular Na <superscript>+</superscript> ([Na <superscript>+</superscript> ] <subscript>i</subscript> ), cytosolic ATP ([ATP] <subscript>i</subscript> ), and inositol triphosphate ([IP <subscript>3</subscript> ] <subscript>i</subscript> ) concentrations. However, they acknowledge that this model does not consider metabolic processes or insulin secretion. The complete original paper reference is cited below: Modeling of Ca <superscript>2+</superscript> flux in pancreatic beta-cells: role of the plasma membrane and intracellular stores , Leonid E. Fridlyand, Natalia Tamarina, and Louis H. Philipson, 2003, American Journal of Physiology , 285, E138-E154. ( Full text (HTML) and PDF versions of the article are available on the American Jounal of Physiology website.) PubMed ID: 12644446 <informalfigure float="0" id="fig_cell_diagram"> <mediaobject> <imageobject> <objectinfo> cell diagram </objectinfo> <imagedata fileref="fridlyand_2003.png" /> </imageobject> </mediaobject> Schematic representation of currents and ion fluxes, through the plasma membrane and the endoplasmic reticulum membrane, which have been included in the whole beta-cell mathematical model. </informalfigure> </sect1> </documentation>
Fridlyand et al's 2003 mathematical model of Ca2+ fluxes in pancreatic beta-cells.
calcium affinity constant of sodium-calcium exchange current
steady-state value of gating variable of voltage-dependent potassium current
rate constant of permanent ATP consumption
concentration of intracellular nucleotides
maximum conductance of voltage-dependent calcium current
current coefficient of sodium-potassium pump
half-activation potential of voltage-dependent calcium current
maximum conductance of ATP-dependent potassium current
voltage-independent component of non-selective cation current
coefficient of calcium sequestration rate
half-activation potential of voltage-dependent potassium current
maximum plasma membrane calcium pump current
calcium leak permeability out of the endoplasmic reticulum
rate constant of calcium-dependent ATP consumption