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The Phantom Burster Model for Pancreatic Beta Cells
The CellML code.
<!-- FILE : bertram_model_2000.xml
CREATED : 10th April 2002
LAST MODIFIED : 9th April 2003
AUTHOR : Catherine Lloyd
Bioengineering Institute
The University of Auckland
MODEL STATUS : This model conforms to the CellML 1.0 Specification released on
10th August 2001, and the 16/01/2002 CellML Metadata 1.0 Specification.
DESCRIPTION : This file contains a CellML description of Bertram et al's
2000 phantom burster model for pancreatic beta-cells.
CHANGES:
18/07/2002 - CML - Added more metadata.
09/04/2003 - AAC - Added publication date information.
-->
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<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>The Phantom Burster Model For Pancreatic Beta-Cells</title>
<author>
<firstname>Catherine</firstname>
<surname>Lloyd</surname>
<affiliation>
<shortaffil>Bioengineering Institute, University of Auckland</shortaffil>
</affiliation>
</author>
</articleinfo>
<section id="sec_status">
<title>Model Status</title>
<para>
This is the original unchecked version of the model imported from the previous
CellML model repository, 24-Jan-2006.
</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
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 Ca<superscript>2+</superscript>-carrying action potentials alternating with silent phases of repolarisation and are accompanied by oscillations in cytosolic Ca<superscript>2+</superscript>, which drive pulses of insulin secretion.
</para>
<para>
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 (I<subscript>s1</subscript> and I<subscript>s2</subscript> in <xref linkend="fig_cell_diagram" /> 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 <xref linkend="sec_download_this_model" />.
</para>
<para>
The complete original paper reference is cited below:
</para>
<para>
<ulink url="http://www.biophysj.org/cgi/content/abstract/79/6/2880">The Phantom Burster Model for Pancreatic beta-Cells</ulink>, Richard Bertram, Joseph Previte, Arthur Sherman, Tracie A. Kinard and Leslie S. Satin, 2000, <ulink url="http://www.biophysj.org/">
<emphasis>Biophysical Journal</emphasis>
</ulink>, 79, 2880-2892. (<ulink url="http://www.biophysj.org/cgi/content/full/79/6/2880">Full text</ulink> and <ulink url="http://www.biophysj.org/cgi/reprint/79/6/2880.pdf">PDF</ulink> versions of the article are available for Journal Members on the Biophysical Journal website.) <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=11106596&dopt=Abstract">PubMed ID: 11106596</ulink>
</para>
<informalfigure float="0" id="fig_cell_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>cell schematic for the model</title>
</objectinfo>
<imagedata fileref="../images/bertram_model_2000/cell_diagram.gif" />
</imageobject>
</mediaobject>
<caption>Schematic diagram of the pancreatic beta-cell plasma membrane showing the ionic currents captured by the phantom burster model.</caption>
</informalfigure>
</sect1>
</article>
</documentation>
<!--
Below, we define some additional units for association with variables and
constants within the model. The identifiers are fairly self-explanatory.
-->
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<unit units="second" multiplier="60.0" />
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CREATED : 10th April 2002
LAST MODIFIED : 9th April 2003
AUTHOR : Catherine Lloyd
Bioengineering Institute
The University of Auckland
MODEL STATUS : This model conforms to the CellML 1.0 Specification released on
10th August 2001, and the 16/01/2002 CellML Metadata 1.0 Specification.
DESCRIPTION : This file contains a CellML description of Bertram et al's
2000 phantom burster model for pancreatic beta-cells.
CHANGES:
18/07/2002 - CML - Added more metadata.
09/04/2003 - AAC - Added publication date information.
-->
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<article>
<articleinfo>
<title>The Phantom Burster Model For Pancreatic Beta-Cells</title>
<author>
<firstname>Catherine</firstname>
<surname>Lloyd</surname>
<affiliation>
<shortaffil>Bioengineering Institute, University of Auckland</shortaffil>
</affiliation>
</author>
</articleinfo>
<section id="sec_status">
<title>Model Status</title>
<para>
This is the original unchecked version of the model imported from the previous
CellML model repository, 24-Jan-2006.
</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
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 Ca<superscript>2+</superscript>-carrying action potentials alternating with silent phases of repolarisation and are accompanied by oscillations in cytosolic Ca<superscript>2+</superscript>, which drive pulses of insulin secretion.
</para>
<para>
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 (I<subscript>s1</subscript> and I<subscript>s2</subscript> in <xref linkend="fig_cell_diagram" /> 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 <xref linkend="sec_download_this_model" />.
</para>
<para>
The complete original paper reference is cited below:
</para>
<para>
<ulink url="http://www.biophysj.org/cgi/content/abstract/79/6/2880">The Phantom Burster Model for Pancreatic beta-Cells</ulink>, Richard Bertram, Joseph Previte, Arthur Sherman, Tracie A. Kinard and Leslie S. Satin, 2000, <ulink url="http://www.biophysj.org/">
<emphasis>Biophysical Journal</emphasis>
</ulink>, 79, 2880-2892. (<ulink url="http://www.biophysj.org/cgi/content/full/79/6/2880">Full text</ulink> and <ulink url="http://www.biophysj.org/cgi/reprint/79/6/2880.pdf">PDF</ulink> versions of the article are available for Journal Members on the Biophysical Journal website.) <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=11106596&dopt=Abstract">PubMed ID: 11106596</ulink>
</para>
<informalfigure float="0" id="fig_cell_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>cell schematic for the model</title>
</objectinfo>
<imagedata fileref="../images/bertram_model_2000/cell_diagram.gif" />
</imageobject>
</mediaobject>
<caption>Schematic diagram of the pancreatic beta-cell plasma membrane showing the ionic currents captured by the phantom burster model.</caption>
</informalfigure>
</sect1>
</article>
</documentation>
<!--
Below, we define some additional units for association with variables and
constants within the model. The identifiers are fairly self-explanatory.
-->
<units name="minute">
<unit units="second" multiplier="60.0" />
</units>
<units name="picoA">
<unit units="ampere" prefix="pico" />
</units>
<units name="femtoF">
<unit units="farad" prefix="femto" />
</units>
<units name="millivolt">
<unit units="volt" prefix="milli" />
</units>
<units name="picoS">
<unit units="siemens" prefix="pico" />
</units>
<!--
The "environment" component is used to declare variables that are used by
all or most of the other components, in this case just "time".
-->
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<variable units="second" public_interface="out" name="time" />
</component>
<component name="membrane">
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<variable units="second" public_interface="in" name="time" />
<variable units="picoA" public_interface="in" name="i_Ca" />
<variable units="picoA" public_interface="in" name="i_K" />
<variable units="picoA" public_interface="in" name="i_s1" />
<variable units="picoA" public_interface="in" name="i_s2" />
<variable units="picoA" public_interface="in" name="i_L" />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="membrane_voltage_diff_eq">
<eq />
<apply>
<diff />
<bvar>
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<ci> V </ci>
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<apply>
<minus />
<apply>
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<ci> i_Ca </ci>
<ci> i_K </ci>
<ci> i_s1 </ci>
<ci> i_s2 </ci>
<ci> i_L </ci>
</apply>
</apply>
<ci> Cm </ci>
</apply>
</apply>
</math>
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<variable units="second" public_interface="in" private_interface="out" name="time" />
<variable units="millivolt" public_interface="in" private_interface="out" name="V" />
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<ci> g_Ca </ci>
<ci> m_infinity </ci>
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<ci> V </ci>
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</math>
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<variable units="millivolt" public_interface="in" name="V" />
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<ci> V </ci>
<ci> V_K </ci>
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<variable units="millivolt" public_interface="in" name="V" />
<variable units="second" public_interface="in" name="time" />
<math xmlns="http://www.w3.org/1998/Math/MathML">
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<apply>
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<ci> s1 </ci>
</apply>
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<apply id="s1_infinity_calculation">
<eq />
<ci> s1_infinity </ci>
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</apply>
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