- Author:
- pmr2.import <nobody@models.cellml.org>
- Date:
- 2009-06-17 12:34:39+12:00
- Desc:
- committing version02 of bertram_smolen_sherman_mears_atwater_martin_soria_1995
- Permanent Source URI:
- https://models.physiomeproject.org/workspace/bertram_smolen_sherman_mears_atwater_martin_soria_1995/rawfile/476262654da8a1eaa77dd8f47c75baa95de63b32/bertram_smolen_sherman_mears_atwater_martin_soria_1995.cellml
<?xml version='1.0' encoding='utf-8'?>
<!-- FILE : bertram_model_1995.xml
CREATED : 6th May 2002
LAST MODIFIED : 20th April 2005
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 16/1/02 CellML Metadata 1.0 Specification.
DESCRIPTION : This file contains a CellML description of Bertram et al's
1995 model for a modulatory role for CRAC in islet electrical activity.
CHANGES:
22/07/2002 - CML - Added more metadata.
09/04/2003 - AAC - Added publication date information.
20/05/2005 - PJV - Modified mathml id to be unique
--><model xmlns="http://www.cellml.org/cellml/1.0#" xmlns:cmeta="http://www.cellml.org/metadata/1.0#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bqs="http://www.cellml.org/bqs/1.0#" xmlns:cellml="http://www.cellml.org/cellml/1.0#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" cmeta:id="bertram_smolen_sherman_mears_atwater_martin_soria_1995_version01" name="bertram_smolen_sherman_mears_atwater_martin_soria_1995_version01">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>Modulatory Role for CRAC in Pancreatic Beta-Cell Electrical Activity</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 model can not be solved as it is overconstrained. ValidateCellML verifies this model as valid CellML but detects unit inconsistencies.
</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
The endocrine portion of the pancreas (the islets of Langerhans) synthesises and secretes several hormones, including insulin. Insulin secretion is triggered by an increase in blood glucose or by parasympathetic stimulation, and it is decreased by sympathetic input. Increases in insulin secretion usually correlate with increases in free cytosolic Ca<superscript>2+</superscript> concentration ([Ca<superscript>2+</superscript>]<subscript>i</subscript>), and in turn, [Ca<superscript>2+</superscript>]<subscript>i</subscript> is largely determined by the electrical activity of the cell. When exposed to a threshold concentration of glucose, pancreatic beta-cells exhibit a complicated pattern of electrical activity. Bursts of action potential spikes (the "active" phase) are observed, separated by a "silent" phase of membrane repolarisation. At even higher glucose concentrations, continuous action potentials are seen.
</para>
<para>
Cholinergic drugs enhance glucose-induced insulin secretion. In their 1995 mathematical model, Richard Bertram, Paul Smolen, Arthur Sherman, David Mears, Illani Atwater, Franz Martin and Bernat Soria account for the cholinergic effects on membrane potential and cytosolic Ca<superscript>2+</superscript>. They believe that the mechanism underlying the muscarinic-induced depolarisation of the beta-cell is a calcium release-activated current (CRAC). This current is activated by the depletion of Ca<superscript>2+</superscript> stores in the endoplasmic reticulum (ER), and it is carried by Na<superscript>+</superscript> and K<superscript>+</superscript>.
</para>
<para>
Their mathematical model incorporates six ionic currents: two fast calcium currents (I<subscript>Caf</subscript> and I<subscript>Cas</subscript>), one of which (I<subscript>Cas</subscript>) inactivates slowly.; a delayed rectifying potassium current (I<subscript>K</subscript>); and an ATP activated potassium current (I<subscript>K(ATP)</subscript>). These currents allow independent bursting to occur. An additional CRAC current (I<subscript>CRAC</subscript>) provides direct feedback from the ER to the cell membrane. Additional equations account for the calcium handling and a calcium-activated potassium current (I<subscript>K(Ca)</subscript>) (see <xref linkend="fig_cell_diagram"/> below).
</para>
<para>
The complete original paper reference is cited below:
</para>
<para>
<ulink url="http://www.biophysj.org/cgi/content/abstract/68/6/2323">A Role for Calcium Release-Activated Current (CRAC) in Cholinergic Modulation of Electrical Activity in Pancreatic Beta-Cells</ulink>, Richard Bertram, Paul Smolen, Arthur Sherman, David Mears, Illani Atwater, Franz Martin and Bernat Soria, 1995, <ulink url="http://biophysj.org/">
<emphasis>Biophysical Journal</emphasis>
</ulink>, 68, 2323-2332. <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=7647236&dopt=Abstract">PubMed ID: 7647236</ulink>
</para>
<para>
The raw CellML description of the model can be downloaded in various formats as described in <xref linkend="sec_download_this_model"/>
</para>
<informalfigure float="0" id="fig_cell_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>diagram of the cellular model</title>
</objectinfo>
<imagedata fileref="bertram_1995.png"/>
</imageobject>
</mediaobject>
</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="millisecond">
<unit units="second" prefix="milli"/>
</units>
<units name="per_millisecond">
<unit units="millisecond" exponent="-1"/>
</units>
<units name="micromolar_per_millisecond">
<unit units="micromolar"/>
<unit units="millisecond" exponent="-1"/>
</units>
<units name="micromolar_per_millisecond_picoA">
<unit units="micromolar"/>
<unit units="millisecond" exponent="-1"/>
<unit units="picoA" exponent="-1"/>
</units>
<units name="millivolt">
<unit units="volt" prefix="milli"/>
</units>
<units name="micromolar">
<unit units="mole" prefix="micro"/>
<unit units="litre" exponent="-1"/>
</units>
<units name="micromolar_3">
<unit units="micromolar" exponent="3"/>
</units>
<units name="picoS">
<unit units="siemens" prefix="pico"/>
</units>
<units name="picoA">
<unit units="ampere" prefix="pico"/>
</units>
<units name="femtoF">
<unit units="farad" prefix="femto"/>
</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".
-->
<component name="environment">
<variable units="millisecond" public_interface="out" name="time"/>
</component>
<component name="membrane">
<variable units="millivolt" public_interface="out" name="V"/>
<variable units="femtoF" name="Cm" initial_value="6158.0"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="picoA" public_interface="in" name="i_K"/>
<variable units="picoA" public_interface="in" name="i_K_Ca"/>
<variable units="picoA" public_interface="in" name="i_K_ATP"/>
<variable units="picoA" public_interface="in" name="i_CRAC"/>
<variable units="picoA" public_interface="in" name="i_Ca_f"/>
<variable units="picoA" public_interface="in" name="i_Ca_s"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="membrane_voltage_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> V </ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci> i_K </ci>
<ci> i_K_Ca </ci>
<ci> i_K_ATP </ci>
<ci> i_Ca_f </ci>
<ci> i_Ca_s </ci>
<ci> i_CRAC </ci>
</apply>
</apply>
<ci> Cm </ci>
</apply>
</apply>
</math>
</component>
<component name="delayed_rectifier_K_channel_current">
<variable units="picoA" public_interface="out" name="i_K"/>
<variable units="millivolt" public_interface="out" name="V_K" initial_value="-70.0"/>
<variable units="picoS" name="g_K" initial_value="3900.0"/>
<variable units="millisecond" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<variable units="dimensionless" private_interface="in" name="n"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_K_calculation">
<eq/>
<ci> i_K </ci>
<apply>
<times/>
<ci> g_K </ci>
<ci> n </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> V_K </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="delayed_rectifier_K_channel_current_n_gate">
<variable units="dimensionless" public_interface="out" name="n"/>
<variable units="dimensionless" name="n_infinity"/>
<variable units="millisecond" name="tau_n"/>
<variable units="millivolt" name="Vn" initial_value="-15.0"/>
<variable units="millivolt" name="Sn" initial_value="6.0"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
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<diff/>
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</bvar>
<ci> n </ci>
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<apply>
<divide/>
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<minus/>
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<ci> n </ci>
</apply>
<ci> tau_n </ci>
</apply>
</apply>
<apply id="n_infinity_calculation">
<eq/>
<ci> n_infinity </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
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<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci> Vn </ci>
<ci> V </ci>
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<ci> Sn </ci>
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</apply>
</apply>
</apply>
</apply>
<apply id="tau_n_calculation">
<eq/>
<ci> tau_n </ci>
<apply>
<divide/>
<cn cellml:units="millisecond"> 4.86 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 15.0 </cn>
</apply>
<cn cellml:units="millivolt"> 6.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="K_ATP_channel_current">
<variable units="picoA" public_interface="out" name="i_K_ATP"/>
<variable units="picoS" name="g_K_ATP" initial_value="150.0"/>
<variable units="millivolt" public_interface="in" name="V_K"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="millivolt" public_interface="in" name="V"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_K_ATP_calculation">
<eq/>
<ci> i_K_ATP </ci>
<apply>
<times/>
<ci> g_K_ATP </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> V_K </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="fast_Ca_channel_current">
<variable units="picoA" public_interface="out" name="i_Ca_f"/>
<variable units="millivolt" public_interface="out" name="V_Ca" initial_value="100.0"/>
<variable units="picoS" name="g_Ca_f" initial_value="810.0"/>
<variable units="millisecond" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<variable units="dimensionless" private_interface="in" name="m_f_infinity"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_Ca_f_calculation">
<eq/>
<ci> i_Ca_f </ci>
<apply>
<times/>
<ci> g_Ca_f </ci>
<ci> m_f_infinity </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> V_Ca </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="fast_Ca_channel_current_m_f_gate">
<variable units="dimensionless" public_interface="out" name="m_f_infinity"/>
<variable units="millivolt" name="Vm_f" initial_value="-20.0"/>
<variable units="millivolt" name="Sm_f" initial_value="7.5"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="fast_Ca_channel_current_m_f_gate_infinity_calculation">
<eq/>
<ci> m_f_infinity </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci> Vm_f </ci>
<ci> V </ci>
</apply>
<ci> Sm_f </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="slow_Ca_channel_current">
<variable units="picoA" public_interface="out" name="i_Ca_s"/>
<variable units="picoS" name="g_Ca_s" initial_value="510.0"/>
<variable units="millisecond" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<variable units="millivolt" public_interface="in" name="V_Ca"/>
<variable units="dimensionless" private_interface="in" name="m_s_infinity"/>
<variable units="dimensionless" private_interface="in" name="j"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_Ca_s_calculation">
<eq/>
<ci> i_Ca_s </ci>
<apply>
<times/>
<ci> g_Ca_s </ci>
<ci> j </ci>
<ci> m_s_infinity </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> V_Ca </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="slow_Ca_channel_current_m_s_gate">
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<variable units="millivolt" name="Sm_s" initial_value="10.0"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="m_s_infinity_calculation">
<eq/>
<ci> m_s_infinity </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
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<ci> V </ci>
</apply>
<ci> Sm_s </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="slow_Ca_channel_current_j_gate">
<variable units="dimensionless" public_interface="out" name="j"/>
<variable units="dimensionless" name="j_infinity"/>
<variable units="millivolt" name="Vj" initial_value="-53.0"/>
<variable units="millisecond" name="tau_j"/>
<variable units="millivolt" name="Sj" initial_value="-2.0"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="j_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> j </ci>
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<apply>
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<apply>
<minus/>
<ci> j_infinity </ci>
<ci> j </ci>
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<ci> tau_j </ci>
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<apply id="j_infinity_calculation">
<eq/>
<ci> j_infinity </ci>
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<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
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<ci> V </ci>
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<ci> Sj </ci>
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<apply id="tau_j_calculation">
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<ci> tau_j </ci>
<apply>
<divide/>
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<exp/>
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<divide/>
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<cn cellml:units="millivolt"> 4.0 </cn>
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<apply>
<exp/>
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<divide/>
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<minus/>
<apply>
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<ci> V </ci>
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<cn cellml:units="millivolt"> 4.0 </cn>
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<cn cellml:units="dimensionless"> 1500.0 </cn>
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<component name="Ca_activated_K_current">
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<variable units="picoS" name="g_K_Ca" initial_value="1200.0"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millivolt" public_interface="in" name="V_K"/>
<variable units="micromolar" public_interface="in" name="Ca_i"/>
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<variable units="dimensionless" public_interface="out" name="P_leak"/>
<variable units="dimensionless" public_interface="out" name="P_ip3"/>
<variable units="dimensionless" public_interface="out" name="O_infinity"/>
<variable units="micromolar" public_interface="out" name="Ca_er"/>
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<variable units="dimensionless" name="b_infinity"/>
<variable units="dimensionless" name="h_infinity"/>
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<apply>
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Bertram et al's 1995 model for a modulatory role for CRAC in islet
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