- Author:
- rcai987 <devnull@localhost>
- Date:
- 2015-02-05 13:16:31+13:00
- Desc:
- Added annotations to marhl_schuster_brumen_heinrich_2007.cellml
- Permanent Source URI:
- http://models.cellml.org/workspace/marhl_schuster_brumen_heinrich_1997/rawfile/f3c330b66be95896c0f2c14c40e69c44b078cd2c/marhl_schuster_brumen_heinrich_1997.cellml
<?xml version='1.0'?>
<!-- FILE : marhl_model_1997.xml
CREATED : 21st January 2004
LAST MODIFIED : 21st January 2004
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 Marhl et al's
1997 model of the interrelations between calcium oscillations and ER membrane potential oscillations.
CHANGES:
-->
<model cmeta:id="marhl_schuster_brumen_heinrich_1997_version01" name="marhl_schuster_brumen_heinrich_1997_version01" xmlns="http://www.cellml.org/cellml/1.0#" xmlns:bqs="http://www.cellml.org/bqs/1.0#" xmlns:cellml="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:dcterms="http://purl.org/dc/terms/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>Modelling the Interellations Between Calcium Oscillations and ER Membrane Potential Oscillations</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>
Oscillations in the cytosolic calcium concentration ([Ca<superscript>2+</superscript>]<subscript>i</subscript>), in the form of repetitive spikes, may be stimulated by hormones or neurotransmitters in a variety of cell types, including hepatocytes, oocytes, cardiomyocytes and fibroblasts. It is generally accepted that the mechanism underlying these calcium oscillations is related to the calcium-induced calcium release (CICR) mechanism. Often, secondary messengers such as inositol 1,4,5-trisphosphate (IP<subscript>3</subscript>) are also involved. Calcium oscillations play a role in the regulation of cell excretion, muscle contraction, activation of mammalian oocytes, call signalling and other cellular activities.
</para>
<para>
Calcium oscillations and their underlying molecular mechanisms have been the subject of interest for several mathematical models, including:
</para>
<itemizedlist>
<listitem>
<para>
<ulink url="${HTML_EXMPL_LI_MODEL}">Li and Rinzel, IP3-Mediated Ca<superscript>2+</superscript> Oscillations - A Simplified Model, 1994</ulink>;</para>
</listitem>
<listitem>
<para>
<ulink url="${HTML_EXMPL_FRIEL_MODEL}">D. Friel, [Ca<superscript>2+</superscript>]<subscript>i</subscript> Oscillations in in Sympathetic Neurons, 1995</ulink>;</para>
</listitem>
<listitem>
<para>
<ulink url="${HTML_EXMPL_CHAY_MODEL}">Chay <emphasis>et al.</emphasis>, Intracellular Calcium Spikes in Non-Excitable Cells, 1995</ulink>; and</para>
</listitem>
<listitem>
<para>
<ulink url="${HTML_EXMPL_KEIZER_MODEL}">Keizer and Levine, RyR Adaptation and Ca<superscript>2+</superscript> Oscillations, 1996</ulink>.</para>
</listitem>
</itemizedlist>
<para>
In the Marhl <emphasis>et al.</emphasis> 1997 publication described here, the authors present an electrochemical model which accounts for intracellular calcium oscillations and their interrelations with oscillations of the potential difference across the membrane of the endoplasmic reticulum (ER) or other inracellular calium stores (see <xref linkend="fig_cell_diagram"/> below). The model shows tht when a calcium buffering system such as calmodulin is included, calcium oscillations can arise without a permanent influx of calium into the cell.
</para>
<para>
The model has been described here in CellML (the raw CellML description of the Marhl <emphasis>et al.</emphasis> 1997 model 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>
Modelling the interellations between calcium oscillations and ER membrane potential oscillations, Marko Marhl, Stefan Schuster, Milan Brumen, and Reinhart Heinrich, 1997, <emphasis>Biophysical Chemistry</emphasis>, 63, 221-239. <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=12362939&dopt=Abstract">PubMed ID: 12362939</ulink>
</para>
<informalfigure float="0" id="fig_cell_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>cell diagram</title>
</objectinfo>
<imagedata fileref="marhl_1997.png"/>
</imageobject>
</mediaobject>
<caption>Schematic diagram of the model system.</caption>
</informalfigure>
</sect1>
</article>
</documentation>
<units name="micromolar">
<unit prefix="micro" units="mole"/>
<unit exponent="-1" units="litre"/>
</units>
<units name="millivolt">
<unit prefix="milli" units="volt"/>
</units>
<units name="flux">
<unit units="micromolar"/>
<unit exponent="-1" units="second"/>
</units>
<units name="first_order_rate_constant">
<unit exponent="-1" units="second"/>
</units>
<units name="second_order_rate_constant">
<unit exponent="-1" units="micromolar"/>
<unit exponent="-1" units="second"/>
</units>
<units name="cm2">
<unit exponent="2" prefix="centi" units="metre"/>
</units>
<units name="micromolar_per_volt_second">
<unit units="micromolar"/>
<unit exponent="-1" units="volt"/>
<unit exponent="-1" units="second"/>
</units>
<units name="microS_per_cm2">
<unit prefix="micro" units="siemens"/>
<unit exponent="-2" prefix="centi" units="metre"/>
</units>
<units name="joule_per_kelvin_mole">
<unit units="joule"/>
<unit exponent="-1" units="kelvin"/>
<unit exponent="-1" units="mole"/>
</units>
<units name="coulomb_per_millimole">
<unit exponent="-1" units="coulomb"/>
<unit prefix="milli" units="mole"/>
</units>
<component name="environment">
<variable name="time" public_interface="out" units="second"/>
</component>
<component cmeta:id="id_000000008" name="free_protein_calcium_binding_sites">
<variable cmeta:id="id_000000009" name="CaPr" public_interface="out" units="micromolar"/>
<variable cmeta:id="id_000000010" name="Pr" public_interface="out" units="micromolar"/>
<variable cmeta:id="id_000000011" name="Pr_tot" public_interface="in" units="micromolar"/>
<variable name="k_plus" public_interface="in" units="second_order_rate_constant"/>
<variable name="k_minus" public_interface="in" units="first_order_rate_constant"/>
<variable name="time" public_interface="in" units="second"/>
<variable cmeta:id="id_000000001" name="Ca_cyt" public_interface="in" units="micromolar"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="Pr_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Pr </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> k_minus </ci>
<ci> CaPr </ci>
</apply>
<apply>
<times/>
<ci> k_plus </ci>
<ci> Ca_cyt </ci>
<ci> Pr </ci>
</apply>
</apply>
</apply>
<apply id="CaPr_calculation">
<eq/>
<ci> CaPr </ci>
<apply>
<minus/>
<ci> Pr_tot </ci>
<ci> Pr </ci>
</apply>
</apply>
</math>
</component>
<component cmeta:id="id_000000002" name="cytosolic_calcium">
<variable cmeta:id="id_000000003" name="Ca_cyt" public_interface="out" units="micromolar"/>
<variable name="k_plus" public_interface="in" units="second_order_rate_constant"/>
<variable name="k_minus" public_interface="in" units="first_order_rate_constant"/>
<variable name="Pr" public_interface="in" units="micromolar"/>
<variable name="CaPr" public_interface="in" units="micromolar"/>
<variable name="J_ch" public_interface="in" units="flux"/>
<variable cmeta:id="id_000000016" name="J_leak" public_interface="in" units="flux"/>
<variable cmeta:id="id_000000020" name="J_pump" public_interface="in" units="flux"/>
<variable name="time" public_interface="in" units="second"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="Ca_cyt_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Ca_cyt </ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<ci> J_ch </ci>
<ci> J_leak </ci>
<apply>
<times/>
<ci> k_minus </ci>
<ci> CaPr </ci>
</apply>
</apply>
<apply>
<plus/>
<ci> J_pump </ci>
<apply>
<times/>
<ci> k_plus </ci>
<ci> Ca_cyt </ci>
<ci> Pr </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="id_000000004" name="ER_calcium">
<variable cmeta:id="id_000000005" name="Ca_ER" public_interface="out" units="micromolar"/>
<variable cmeta:id="id_000000006" initial_value="45.0" name="Ca_tot" units="micromolar"/>
<variable name="rho" public_interface="in" units="dimensionless"/>
<variable cmeta:id="id_000000013" name="Pr" public_interface="in" units="micromolar"/>
<variable cmeta:id="id_000000012" name="Pr_tot" public_interface="in" units="micromolar"/>
<variable cmeta:id="id_000000007" name="Ca_cyt" public_interface="in" units="micromolar"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="Ca_ER_eq">
<eq/>
<ci> Ca_ER </ci>
<apply>
<divide/>
<apply>
<minus/>
<ci> Ca_tot </ci>
<apply>
<plus/>
<ci> Ca_cyt </ci>
<apply>
<minus/>
<ci> Pr_tot </ci>
<ci> Pr </ci>
</apply>
</apply>
</apply>
<ci> rho </ci>
</apply>
</apply>
</math>
</component>
<component name="potential_difference">
<variable name="delta_psi" public_interface="out" units="millivolt"/>
<variable name="a" units="micromolar"/>
<variable name="b" units="micromolar"/>
<variable name="c" units="micromolar"/>
<variable initial_value="5.0E3" name="C_tot" units="micromolar"/>
<variable initial_value="3.89E3" name="A_tot" units="micromolar"/>
<variable name="rho" public_interface="in" units="dimensionless"/>
<variable name="R" public_interface="in" units="joule_per_kelvin_mole"/>
<variable name="T" public_interface="in" units="kelvin"/>
<variable name="F" public_interface="in" units="coulomb_per_millimole"/>
<variable cmeta:id="id_000000034" name="Ca_cyt" public_interface="in" units="micromolar"/>
<variable cmeta:id="id_000000014" name="Pr" public_interface="in" units="micromolar"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="delta_psi_calculation">
<eq/>
<ci> delta_psi </ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
<ci> F </ci>
</apply>
<apply>
<ln/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<ci> b </ci>
</apply>
<apply>
<power/>
<apply>
<minus/>
<apply>
<power/>
<ci> b </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 4.0 </cn>
<ci> a </ci>
<ci> c </ci>
</apply>
</apply>
<cn cellml:units="dimensionless"> 0.5 </cn>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> a </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="a_calculation">
<eq/>
<ci> a </ci>
<apply>
<times/>
<ci> rho </ci>
<apply>
<minus/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> Ca_cyt </ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> Pr </ci>
</apply>
<ci> A_tot </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="b_calculation">
<eq/>
<ci> b </ci>
<apply>
<plus/>
<apply>
<minus/>
<ci> C_tot </ci>
<ci> A_tot </ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<apply>
<minus/>
<ci> Ca_cyt </ci>
<ci> Pr </ci>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<power/>
<ci> rho </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="c_calculation">
<eq/>
<ci> c </ci>
<apply>
<times/>
<ci> rho </ci>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> Ca_cyt </ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> Pr </ci>
</apply>
</apply>
<ci> C_tot </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="id_000000031" name="calcium_reversal_potential">
<variable cmeta:id="id_000000030" name="E_Ca" public_interface="out" units="millivolt"/>
<variable name="R" public_interface="in" units="joule_per_kelvin_mole"/>
<variable name="T" public_interface="in" units="kelvin"/>
<variable name="F" public_interface="in" units="coulomb_per_millimole"/>
<variable cmeta:id="id_000000033" name="Ca_cyt" public_interface="in" units="micromolar"/>
<variable cmeta:id="id_000000032" name="Ca_ER" public_interface="in" units="micromolar"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="E_Ca_calculation">
<eq/>
<ci> E_Ca </ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> F </ci>
</apply>
</apply>
<apply>
<ln/>
<apply>
<divide/>
<ci> Ca_ER </ci>
<ci> Ca_cyt </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="id_000000027" name="flux_through_the_channels">
<variable name="J_ch" public_interface="out" units="flux"/>
<variable initial_value="6.16E-3" name="S" units="cm2"/>
<variable cmeta:id="id_000000025" name="g_Ca" units="microS_per_cm2"/>
<variable cmeta:id="id_000000026" initial_value="100.0" name="g_Ca_max" units="microS_per_cm2"/>
<variable name="k_ch" units="micromolar_per_volt_second"/>
<variable cmeta:id="id_000000028" initial_value="5.0" name="K_Ca" units="micromolar"/>
<variable initial_value="5.84E-11" name="Vcyt" units="litre"/>
<variable name="F" public_interface="in" units="coulomb_per_millimole"/>
<variable cmeta:id="id_000000029" name="E_Ca" public_interface="in" units="millivolt"/>
<variable name="delta_psi" public_interface="in" units="millivolt"/>
<variable name="Ca_cyt" public_interface="in" units="micromolar"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="J_ch_calculation">
<eq/>
<ci> J_ch </ci>
<apply>
<times/>
<ci> k_ch </ci>
<apply>
<minus/>
<ci> E_Ca </ci>
<ci> delta_psi </ci>
</apply>
</apply>
</apply>
<apply id="k_ch_calculation">
<eq/>
<ci> k_ch </ci>
<apply>
<divide/>
<ci> g_Ca </ci>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> F </ci>
<ci> Vcyt </ci>
</apply>
</apply>
</apply>
<apply id="g_Ca_calculation">
<eq/>
<ci> g_Ca </ci>
<apply>
<divide/>
<apply>
<times/>
<ci> g_Ca_max </ci>
<ci> S </ci>
<apply>
<power/>
<apply>
<divide/>
<ci> Ca_cyt </ci>
<ci> K_Ca </ci>
</apply>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<power/>
<apply>
<divide/>
<ci> Ca_cyt </ci>
<ci> K_Ca </ci>
</apply>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="id_000000021" name="calcium_pump">
<variable cmeta:id="id_000000022" name="J_pump" public_interface="out" units="flux"/>
<variable cmeta:id="id_000000023" initial_value="76.0" name="k_pump" units="first_order_rate_constant"/>
<variable name="Ca_cyt" public_interface="in" units="micromolar"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="J_pump_calculation">
<eq/>
<ci> J_pump </ci>
<apply>
<times/>
<ci> k_pump </ci>
<ci> Ca_cyt </ci>
</apply>
</apply>
</math>
</component>
<component cmeta:id="id_000000019" name="leak_flux">
<variable cmeta:id="id_000000017" name="J_leak" public_interface="out" units="flux"/>
<variable cmeta:id="id_000000018" initial_value="10.0" name="k_leak" units="micromolar_per_volt_second"/>
<variable name="E_Ca" public_interface="in" units="millivolt"/>
<variable name="delta_psi" public_interface="in" units="millivolt"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="J_leak_calculation">
<eq/>
<ci> J_leak </ci>
<apply>
<times/>
<ci> k_leak </ci>
<apply>
<minus/>
<ci> E_Ca </ci>
<ci> delta_psi </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="model_parameters">
<variable cmeta:id="id_000000024" initial_value="600.0" name="Pr_tot" public_interface="out" units="micromolar"/>
<variable cmeta:id="id_000000015" initial_value="8.3143" name="R" public_interface="out" units="joule_per_kelvin_mole"/>
<variable initial_value="310.0" name="T" public_interface="out" units="kelvin"/>
<variable initial_value="96.4867" name="F" public_interface="out" units="coulomb_per_millimole"/>
<variable initial_value="0.01" name="rho" public_interface="out" units="dimensionless"/>
<variable initial_value="0.1" name="k_plus" public_interface="out" units="second_order_rate_constant"/>
<variable initial_value="0.5" name="k_minus" public_interface="out" units="first_order_rate_constant"/>
</component>
<connection>
<map_components component_1="free_protein_calcium_binding_sites" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="cytosolic_calcium" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="free_protein_calcium_binding_sites" component_2="cytosolic_calcium"/>
<map_variables variable_1="Pr" variable_2="Pr"/>
<map_variables variable_1="Ca_cyt" variable_2="Ca_cyt"/>
<map_variables variable_1="CaPr" variable_2="CaPr"/>
</connection>
<connection>
<map_components component_1="free_protein_calcium_binding_sites" component_2="model_parameters"/>
<map_variables variable_1="Pr_tot" variable_2="Pr_tot"/>
<map_variables variable_1="k_plus" variable_2="k_plus"/>
<map_variables variable_1="k_minus" variable_2="k_minus"/>
</connection>
<connection>
<map_components component_1="cytosolic_calcium" component_2="calcium_reversal_potential"/>
<map_variables variable_1="Ca_cyt" variable_2="Ca_cyt"/>
</connection>
<connection>
<map_components component_1="cytosolic_calcium" component_2="flux_through_the_channels"/>
<map_variables variable_1="J_ch" variable_2="J_ch"/>
<map_variables variable_1="Ca_cyt" variable_2="Ca_cyt"/>
</connection>
<connection>
<map_components component_1="cytosolic_calcium" component_2="calcium_pump"/>
<map_variables variable_1="J_pump" variable_2="J_pump"/>
<map_variables variable_1="Ca_cyt" variable_2="Ca_cyt"/>
</connection>
<connection>
<map_components component_1="cytosolic_calcium" component_2="leak_flux"/>
<map_variables variable_1="J_leak" variable_2="J_leak"/>
</connection>
<connection>
<map_components component_1="cytosolic_calcium" component_2="model_parameters"/>
<map_variables variable_1="k_plus" variable_2="k_plus"/>
<map_variables variable_1="k_minus" variable_2="k_minus"/>
</connection>
<connection>
<map_components component_1="calcium_reversal_potential" component_2="model_parameters"/>
<map_variables variable_1="R" variable_2="R"/>
<map_variables variable_1="T" variable_2="T"/>
<map_variables variable_1="F" variable_2="F"/>
</connection>
<connection>
<map_components component_1="calcium_reversal_potential" component_2="ER_calcium"/>
<map_variables variable_1="Ca_ER" variable_2="Ca_ER"/>
</connection>
<connection>
<map_components component_1="flux_through_the_channels" component_2="calcium_reversal_potential"/>
<map_variables variable_1="E_Ca" variable_2="E_Ca"/>
</connection>
<connection>
<map_components component_1="flux_through_the_channels" component_2="potential_difference"/>
<map_variables variable_1="delta_psi" variable_2="delta_psi"/>
</connection>
<connection>
<map_components component_1="flux_through_the_channels" component_2="model_parameters"/>
<map_variables variable_1="F" variable_2="F"/>
</connection>
<connection>
<map_components component_1="ER_calcium" component_2="cytosolic_calcium"/>
<map_variables variable_1="Ca_cyt" variable_2="Ca_cyt"/>
</connection>
<connection>
<map_components component_1="ER_calcium" component_2="free_protein_calcium_binding_sites"/>
<map_variables variable_1="Pr" variable_2="Pr"/>
</connection>
<connection>
<map_components component_1="ER_calcium" component_2="model_parameters"/>
<map_variables variable_1="rho" variable_2="rho"/>
<map_variables variable_1="Pr_tot" variable_2="Pr_tot"/>
</connection>
<connection>
<map_components component_1="leak_flux" component_2="calcium_reversal_potential"/>
<map_variables variable_1="E_Ca" variable_2="E_Ca"/>
</connection>
<connection>
<map_components component_1="leak_flux" component_2="potential_difference"/>
<map_variables variable_1="delta_psi" variable_2="delta_psi"/>
</connection>
<connection>
<map_components component_1="potential_difference" component_2="model_parameters"/>
<map_variables variable_1="R" variable_2="R"/>
<map_variables variable_1="T" variable_2="T"/>
<map_variables variable_1="F" variable_2="F"/>
<map_variables variable_1="rho" variable_2="rho"/>
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