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Multiple Modes of Calcium-induced Calcium Release in Sympathetic Neurons I: Attenuation of Endoplasmic Reticulum Ca2+ Accumulation at Low [Ca2+]i during Weak Depolarisation
The CellML code.
<!-- FILE : albrecht_model_2001.xml
CREATED : 25th March 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 16/1/02 CellML Metadata 1.0 Specification.
DESCRIPTION : This file contains a CellML description of Albrecht et al's
2001 model of calcium-induced calcium release in sympathetic neurons.
CHANGES:
18/07/2002 - CML - Added more metadata.
09/04/2003 - AAC - Added publication date information.
-->
<model xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:cellml="http://www.cellml.org/cellml/1.0#" xmlns:bqs="http://www.cellml.org/bqs/1.0#" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:cmeta="http://www.cellml.org/metadata/1.0#" xmlns="http://www.cellml.org/cellml/1.0#" cmeta:id="albrecht_colegrove_hongpaisan_pivovarova_andrews_friel_2001_version01" name="albrecht_colegrove_hongpaisan_pivovarova_andrews_friel_2001_version01">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>Multiple Modes of Calcium-induced Calcium Release in Sympathetic Neurons</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 is consistently represented within the CellML but contains sets of algebraic equations that prevent the model from being solved in currently available software - 03/08.
</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
Calcium is an important signalling ion, and changes in Ca<superscript>2+</superscript> concentration ([Ca<superscript>2+</superscript>]) regulate diverse processes in many cellular compartments. In excitable cells, depolarisation-induced Ca<superscript>2+</superscript> entry increases [Ca<superscript>2+</superscript>]<subscript>i</subscript>, leading to secondary changes in [Ca<superscript>2+</superscript>] within organelles such as mitochondria and ER that regulate specific Ca<superscript>2+</superscript>-sensitive targets within these organelles. Although mitochondria accumulate Ca<superscript>2+</superscript> in response to depolarisation-evoked [Ca<superscript>2+</superscript>]<subscript>i</subscript> elevations (see <ulink url="${HTML_EXMPL_COLEGROVE_MODEL}">The Colegrove <emphasis>et al</emphasis> Model Of Mitochondrial Ca<superscript>2+</superscript> Uptake And Release, 2000</ulink>), the ER has been described as either a Ca<superscript>2+</superscript> source or sink. Different modes of net ER Ca<superscript>2+</superscript> transport are expected to have very different effects on cytoplasmic and intraluminal Ca<superscript>2+</superscript> signals and on the processes they regulate.
</para>
<para>
In their 2001 model, Meredith A. Albrecht, Stephen L. Colegrove, Jarin Hongpaisan, Natalia B. Pivovarova, S. Brian Andrews and David D. Friel have examined the relationship between changes in [Ca<superscript>2+</superscript>]<subscript>i</subscript> and [Ca<superscript>2+</superscript>]<subscript>ER</subscript> during weak depolarisation in sympathetic neurons. The total Ca<superscript>2+</superscript> flux during the recovery phase following membrane depolarisation was divided into four components (see <xref linkend="fig_cell_diagram" /> below). One representing net Ca<superscript>2+</superscript> extrusion across the plasma membrane (J<subscript>extru</subscript>), one representing Ca<superscript>2+</superscript> entry through voltage-gated Ca<superscript>2+</superscript> channels (J<subscript>ICa</subscript>), one representing ER Ca<superscript>2+</superscript> uptake via a Ca<superscript>2+</superscript> ATPase (J<subscript>SERCA</subscript>) and one representing passive ER Ca<superscript>2+</superscript> release. 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.jgp.org/cgi/content/abstract/118/1/83">Multiple Modes of Calcium-induced Calcium Release in Sympathetic Neurons I: Attenuation of Endoplasmic Reticulum Ca<superscript>2+</superscript> Accumulation at Low [Ca<superscript>2+</superscript>]<subscript>i</subscript> during Weak Depolarisation</ulink>, Meredith A. Albrecht, Stephen L. Colegrove, Jarin Hongpaisan, Natalia B. Pivovarova, S. Brian Andrews and David D. Friel, 2001, <ulink url="http://www.jgp.org/">
<emphasis>The Journal Of General Physiology</emphasis>
</ulink>, 118, 83-100. (<ulink url="http://www.jgp.org/cgi/content/full/118/1/83">Full text</ulink> and <ulink url="http://www.jgp.org/cgi/reprint/118/1/83.pdf">PDF</ulink> versions of the article are available for Journal Members on the JGP website.) <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=11429446&dopt=Abstract">PubMed ID: 11429446</ulink>
</para>
<informalfigure float="0" id="fig_cell_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>cell schematic for the model</title>
</objectinfo>
<imagedata fileref="../images/albrecht_model_2001/cell_diagram.gif" />
</imageobject>
</mediaobject>
<caption>Schematic of the model indicating Ca<superscript>2+</superscript> compartmentation in the extracellular matrix, cytosol and the ER and pathways for Ca<superscript>2+</superscript> ion movement between the compartments.</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="per_second">
<unit units="second" exponent="-1" />
</units>
<units name="millivolt">
<unit units="volt" prefix="milli" />
</units>
<units name="millimolar">
<unit units="mole" prefix="milli" />
<unit units="litre" exponent="-1" />
</units>
<units name="micromolar">
<unit units="mole" prefix="micro" />
<unit units="litre" exponent="-1" />
</units>
<units name="nanomolar">
<unit units="mole" prefix="nano" />
<unit units="litre" exponent="-1" />
</units>
<units name="nanomolar_per_second">
<unit units="nanomolar" />
<unit units="second" exponent="-1" />
</units>
<units name="micromolar_per_second">
<unit units="micromolar" />
<unit units="second" exponent="-1" />
</units>
<units name="micro_litre">
<unit units="litre" prefix="micro" />
</units>
<units name="coulomb_per_millimole">
<unit units="coulomb" />
<unit units="mole" prefix="milli" exponent="-1" />
</units>
<units name="picoA">
<unit units="ampere" 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".
-->
<component name="environment">
<variable units="second" public_interface="out" name="time" />
</component>
<component name="total_cytoplasmic_Ca_flux">
<variable units="nanomolar_per_second" public_interface="out" name="J_ICa" />
<variable units="micro_litre" public_interface="out" name="v_i" />
<variable units="dimensionless" public_interface="out" name="k_i" />
<variable units="coulomb_per_millimole" name="F" initial_value="96.5" />
<variable units="picoA" name="I_Ca" />
<variable units="second" public_interface="in" name="time" />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="J_ICa_calculation">
<eq />
<ci> J_ICa </ci>
<apply>
<divide />
<ci> I_Ca </ci>
<apply>
<times />
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> F </ci>
<ci> v_i </ci>
<ci> k_i </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="Ca_extrusion_across_the_plasma_membrane">
<variable units="nanomolar_per_second" public_interface="out" name="J_pm" />
<variable units="nanomolar_per_second" name="J_extru" />
<variable units="per_second" name="k_leak" initial_value="0.00000015" />
<variable units="nanomolar_per_second" name="Vmax_extru" initial_value="25.0" />
<variable units="nanomolar" name="EC50_extru" initial_value="386.0" />
<variable units="dimensionless" name="n_extru" initial_value="2.4" />
<variable units="millimolar" name="Ca_o" initial_value="2.0" />
<variable units="nanomolar_per_second" public_interface="in" name="J_ICa" />
<variable units="nanomolar" public_interface="in" name="Ca_i" />
<variable units="second" public_interface="in" name="time" />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="J_pm_calculation">
<eq />
<ci> J_pm </ci>
<apply>
<plus />
<ci> J_extru </ci>
<ci> J_ICa </ci>
</apply>
</apply>
<apply id="J_extru_calculation">
<eq />
<ci> J_extru </ci>
<apply>
<plus />
<apply>
<times />
<ci> k_leak </ci>
<apply>
<minus />
<ci> Ca_i </ci>
<ci> Ca_o </ci>
</apply>
</apply>
<apply>
<divide />
<ci> Vmax_extru </ci>
<apply>
<plus />
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<power />
<apply>
<divide />
<ci> EC50_extru </ci>
<ci> Ca_i </ci>
</apply>
<ci> n_extru </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="Ca_uptake_by_SR_Ca_ATPase">
<variable units="nanomolar_per_second" public_interface="out" name="J_SERCA" />
<variable units="nanomolar_per_second" name="Vmax_SERCA" initial_value="70.0" />
<variable units="nanomolar" name="EC50_SERCA" initial_value="700.0" />
<variable units="dimensionless" name="n_SERCA" initial_value="1.0" />
<variable units="nanomolar" public_interface="in" name="Ca_i" />
<variable units="second" public_interface="in" name="time" />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="J_SERCA_calculation">
<eq />
<ci> J_SERCA </ci>
<apply>
<divide />
<ci> Vmax_SERCA </ci>
<apply>
<plus />
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<power />
<apply>
<divide />
<ci> EC50_SERCA </ci>
<ci> Ca_i </ci>
</apply>
<ci> n_SERCA </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="ER_Ca_release">
<variable units="nanomolar_per_second" public_interface="out" name="J_ER" />
<variable units="per_second" name="P_ER" />
<variable units="per_second" name="P_basal" initial_value="0.0000178" />
<variable units="per_second" name="Pmax_RyR" initial_value="0.0009" />
<variable units="micromolar" name="EC50_RyR" initial_value="1.0" />
<variable units="dimensionless" name="n_RyR" initial_value="1.0" />
<variable units="nanomolar_per_second" name="J_release" />
<variable units="nanomolar_per_second" public_interface="in" name="J_SERCA" />
<variable units="nanomolar" public_interface="in" name="Ca_i" />
<variable units="nanomolar" public_interface="in" name="Ca_ER" />
<variable units="second" public_interface="in" name="time" />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="J_release_calculation">
<eq />
<ci> J_release </ci>
<apply>
<times />
<ci> P_ER </ci>
<apply>
<minus />
<ci> Ca_i </ci>
<ci> Ca_ER </ci>
</apply>
</apply>
</apply>
<apply id="J_ER_calculation">
<eq />
<ci> J_ER </ci>
<apply>
<plus />
<ci> J_SERCA </ci>
<ci> J_release </ci>
</apply>
</apply>
<apply id="P_ER_calculation">
<eq />
<ci> P_ER </ci>
<apply>
<plus />
<ci> P_basal </ci>
<apply>
<divide />
<ci> Pmax_RyR </ci>
<apply>
<plus />
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<power />
<apply>
<divide />
<ci> EC50_RyR </ci>
<ci> Ca_i </ci>
</apply>
<ci> n_RyR </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="cytoplasmic_calcium">
<variable units="nanomolar" public_interface="out" name="Ca_i" />
<variable units="nanomolar_per_second" name="J_i" />
<variable units="nanomolar_per_second" public_interface="in" name="J_ER" />
<variable units="nanomolar_per_second" public_interface="in" name="J_pm" />
<variable units="second" public_interface="in" name="time" />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="Ca_i_diff_eq">
<eq />
<apply>
<diff />
<bvar>
<ci> time </ci>
</bvar>
<ci> Ca_i </ci>
</apply>
<apply>
<minus />
<ci> J_i </ci>
</apply>
</apply>
<apply id="J_i_calculation">
<eq />
<ci> J_i </ci>
<apply>
<plus />
<ci> J_pm </ci>
<ci> J_ER </ci>
</apply>
</apply>
</math>
</component>
<component name="intraluminal_calcium">
<variable units="nanomolar" public_interface="out" name="Ca_ER" />
<variable units="micro_litre" name="v_ER" />
<variable units="dimensionless" name="k_ER" />
<variable units="dimensionless" name="gamma_ER" initial_value="0.01" />
<variable units="nanomolar" public_interface="in" name="Ca_i" />
<variable units="micro_litre" public_interface="in" name="v_i" />
<variable units="dimensionless" public_interface="in" name="k_i" />
<variable units="nanomolar_per_second" public_interface="in" name="J_ER" />
<variable units="nanomolar_per_second" public_interface="in" name="J_SERCA" />
<variable units="second" public_interface="in" name="time" />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="Ca_ER_diff_eq">
<eq />
<apply>
<diff />
<bvar>
<ci> time </ci>
</bvar>
<ci> Ca_ER </ci>
</apply>
<apply>
<divide />
<ci> J_ER </ci>
<ci> gamma_ER </ci>
</apply>
</apply>
<apply id="gamma_ER_calculation">
<eq />
<ci> gamma_ER </ci>
<apply>
<divide />
<apply>
<times />
<ci> v_ER </ci>
<ci> k_ER </ci>
</apply>
<apply>
<times />
<ci> v_i </ci>
<ci> k_i </ci>
</apply>
</apply>
</apply>
</math>
</component>
<connection>
<map_components component_2="environment" component_1="total_cytoplasmic_Ca_flux" />
<map_variables variable_2="time" variable_1="time" />
</connection>
<connection>
<map_components component_2="environment" component_1="Ca_extrusion_across_the_plasma_membrane" />
<map_variables variable_2="time" variable_1="time" />
</connection>
<connection>
<map_components component_2="environment" component_1="Ca_uptake_by_SR_Ca_ATPase" />
<map_variables variable_2="time" variable_1="time" />
</connection>
<connection>
<map_components component_2="environment" component_1="ER_Ca_release" />
<map_variables variable_2="time" variable_1="time" />
</connection>
<connection>
<map_components component_2="environment" component_1="cytoplasmic_calcium" />
<map_variables variable_2="time" variable_1="time" />
</connection>
<connection>
<map_components component_2="environment" component_1="intraluminal_calcium" />
<map_variables variable_2="time" variable_1="time" />
</connection>
<connection>
<map_components component_2="Ca_extrusion_across_the_plasma_membrane" component_1="total_cytoplasmic_Ca_flux" />
<map_variables variable_2="J_ICa" variable_1="J_ICa" />
</connection>
<connection>
<map_components component_2="intraluminal_calcium" component_1="total_cytoplasmic_Ca_flux" />
<map_variables variable_2="v_i" variable_1="v_i" />
<map_variables variable_2="k_i" variable_1="k_i" />
</connection>
<connection>
<map_components component_2="cytoplasmic_calcium" component_1="Ca_extrusion_across_the_plasma_membrane" />
<map_variables variable_2="Ca_i" variable_1="Ca_i" />
<map_variables variable_2="J_pm" variable_1="J_pm" />
</connection>
<connection>
<map_components component_2="cytoplasmic_calcium" component_1="Ca_uptake_by_SR_Ca_ATPase" />
<map_variables variable_2="Ca_i" variable_1="Ca_i" />
</connection>
<connection>
<map_components component_2="ER_Ca_release" component_1="Ca_uptake_by_SR_Ca_ATPase" />
<map_variables variable_2="J_SERCA" variable_1="J_SERCA" />
</connection>
<connection>
<map_components component_2="intraluminal_calcium" component_1="Ca_uptake_by_SR_Ca_ATPase" />
<map_variables variable_2="J_SERCA" variable_1="J_SERCA" />
</connection>
<connection>
<map_components component_2="cytoplasmic_calcium" component_1="ER_Ca_release" />
<map_variables variable_2="J_ER" variable_1="J_ER" />
<map_variables variable_2="Ca_i" variable_1="Ca_i" />
</connection>
<connection>
<map_components component_2="intraluminal_calcium" component_1="ER_Ca_release" />
<map_variables variable_2="J_ER" variable_1="J_ER" />
<map_variables variable_2="Ca_ER" variable_1="Ca_ER" />
</connection>
<connection>
<map_components component_2="intraluminal_calcium" component_1="cytoplasmic_calcium" />
<map_variables variable_2="Ca_i" variable_1="Ca_i" />
</connection>
<rdf:RDF>
<rdf:Bag rdf:about="rdf:#b3085f8f-f712-4d81-a1eb-21d56a1f3b02">
<rdf:li>neuron</rdf:li>
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<rdf:Description rdf:about="#albrecht_colegrove_hongpaisan_pivovarova_andrews_friel_2001_version01">
<dc:title>
Multiple modes of calcium-induced calcium release in sympathetic
neurons.
</dc:title>
<cmeta:bio_entity>sympathetic neuron</cmeta:bio_entity>
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<vCard:FN>Catherine Lloyd</vCard:FN>
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Added more metadata.
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Added publication date information.
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<vCard:Orgname>The University of Auckland</vCard:Orgname>
<vCard:Orgunit>The Bioengineering Institute</vCard:Orgunit>
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<dc:creator rdf:resource="rdf:#1596a452-45c6-4b36-930a-4c66659ae396" />
<rdf:value>
This is the CellML description of Albrecht et al's 2001 model of
calcium-induced calcium release in sympathetic neurons.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#ea4f9a05-8f82-402d-819a-c9f4803bbd7c">
<dcterms:W3CDTF>2002-07-18</dcterms:W3CDTF>
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<bqs:Pubmed_id>11429446</bqs:Pubmed_id>
<bqs:JournalArticle rdf:resource="rdf:#2499a6ef-7249-4f66-ae43-90f0f8f69688" />
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<rdf:Description rdf:about="rdf:#352ec194-dd29-4354-915b-152dc29972ba">
<vCard:Given>Natalia</vCard:Given>
<vCard:Family>Pivovarova</vCard:Family>
<vCard:Other>B</vCard:Other>
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<rdf:Description rdf:about="rdf:#65f06961-a13c-4922-addd-d5e9f9001de7">
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<rdf:Description rdf:about="rdf:#54a35be8-f6f1-4d4e-aefe-d57139e9e101">
<dc:title>Journal of General Physiology</dc:title>
</rdf:Description>
<rdf:Description rdf:about="rdf:#a7df0830-da20-4607-a0e7-04dc9ac6a87b">
<vCard:Given>Catherine</vCard:Given>
<vCard:Family>Lloyd</vCard:Family>
<vCard:Other>
CREATED : 25th March 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 16/1/02 CellML Metadata 1.0 Specification.
DESCRIPTION : This file contains a CellML description of Albrecht et al's
2001 model of calcium-induced calcium release in sympathetic neurons.
CHANGES:
18/07/2002 - CML - Added more metadata.
09/04/2003 - AAC - Added publication date information.
-->
<model xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:cellml="http://www.cellml.org/cellml/1.0#" xmlns:bqs="http://www.cellml.org/bqs/1.0#" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:cmeta="http://www.cellml.org/metadata/1.0#" xmlns="http://www.cellml.org/cellml/1.0#" cmeta:id="albrecht_colegrove_hongpaisan_pivovarova_andrews_friel_2001_version01" name="albrecht_colegrove_hongpaisan_pivovarova_andrews_friel_2001_version01">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>Multiple Modes of Calcium-induced Calcium Release in Sympathetic Neurons</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 is consistently represented within the CellML but contains sets of algebraic equations that prevent the model from being solved in currently available software - 03/08.
</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
Calcium is an important signalling ion, and changes in Ca<superscript>2+</superscript> concentration ([Ca<superscript>2+</superscript>]) regulate diverse processes in many cellular compartments. In excitable cells, depolarisation-induced Ca<superscript>2+</superscript> entry increases [Ca<superscript>2+</superscript>]<subscript>i</subscript>, leading to secondary changes in [Ca<superscript>2+</superscript>] within organelles such as mitochondria and ER that regulate specific Ca<superscript>2+</superscript>-sensitive targets within these organelles. Although mitochondria accumulate Ca<superscript>2+</superscript> in response to depolarisation-evoked [Ca<superscript>2+</superscript>]<subscript>i</subscript> elevations (see <ulink url="${HTML_EXMPL_COLEGROVE_MODEL}">The Colegrove <emphasis>et al</emphasis> Model Of Mitochondrial Ca<superscript>2+</superscript> Uptake And Release, 2000</ulink>), the ER has been described as either a Ca<superscript>2+</superscript> source or sink. Different modes of net ER Ca<superscript>2+</superscript> transport are expected to have very different effects on cytoplasmic and intraluminal Ca<superscript>2+</superscript> signals and on the processes they regulate.
</para>
<para>
In their 2001 model, Meredith A. Albrecht, Stephen L. Colegrove, Jarin Hongpaisan, Natalia B. Pivovarova, S. Brian Andrews and David D. Friel have examined the relationship between changes in [Ca<superscript>2+</superscript>]<subscript>i</subscript> and [Ca<superscript>2+</superscript>]<subscript>ER</subscript> during weak depolarisation in sympathetic neurons. The total Ca<superscript>2+</superscript> flux during the recovery phase following membrane depolarisation was divided into four components (see <xref linkend="fig_cell_diagram" /> below). One representing net Ca<superscript>2+</superscript> extrusion across the plasma membrane (J<subscript>extru</subscript>), one representing Ca<superscript>2+</superscript> entry through voltage-gated Ca<superscript>2+</superscript> channels (J<subscript>ICa</subscript>), one representing ER Ca<superscript>2+</superscript> uptake via a Ca<superscript>2+</superscript> ATPase (J<subscript>SERCA</subscript>) and one representing passive ER Ca<superscript>2+</superscript> release. 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.jgp.org/cgi/content/abstract/118/1/83">Multiple Modes of Calcium-induced Calcium Release in Sympathetic Neurons I: Attenuation of Endoplasmic Reticulum Ca<superscript>2+</superscript> Accumulation at Low [Ca<superscript>2+</superscript>]<subscript>i</subscript> during Weak Depolarisation</ulink>, Meredith A. Albrecht, Stephen L. Colegrove, Jarin Hongpaisan, Natalia B. Pivovarova, S. Brian Andrews and David D. Friel, 2001, <ulink url="http://www.jgp.org/">
<emphasis>The Journal Of General Physiology</emphasis>
</ulink>, 118, 83-100. (<ulink url="http://www.jgp.org/cgi/content/full/118/1/83">Full text</ulink> and <ulink url="http://www.jgp.org/cgi/reprint/118/1/83.pdf">PDF</ulink> versions of the article are available for Journal Members on the JGP website.) <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=11429446&dopt=Abstract">PubMed ID: 11429446</ulink>
</para>
<informalfigure float="0" id="fig_cell_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>cell schematic for the model</title>
</objectinfo>
<imagedata fileref="../images/albrecht_model_2001/cell_diagram.gif" />
</imageobject>
</mediaobject>
<caption>Schematic of the model indicating Ca<superscript>2+</superscript> compartmentation in the extracellular matrix, cytosol and the ER and pathways for Ca<superscript>2+</superscript> ion movement between the compartments.</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="per_second">
<unit units="second" exponent="-1" />
</units>
<units name="millivolt">
<unit units="volt" prefix="milli" />
</units>
<units name="millimolar">
<unit units="mole" prefix="milli" />
<unit units="litre" exponent="-1" />
</units>
<units name="micromolar">
<unit units="mole" prefix="micro" />
<unit units="litre" exponent="-1" />
</units>
<units name="nanomolar">
<unit units="mole" prefix="nano" />
<unit units="litre" exponent="-1" />
</units>
<units name="nanomolar_per_second">
<unit units="nanomolar" />
<unit units="second" exponent="-1" />
</units>
<units name="micromolar_per_second">
<unit units="micromolar" />
<unit units="second" exponent="-1" />
</units>
<units name="micro_litre">
<unit units="litre" prefix="micro" />
</units>
<units name="coulomb_per_millimole">
<unit units="coulomb" />
<unit units="mole" prefix="milli" exponent="-1" />
</units>
<units name="picoA">
<unit units="ampere" 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".
-->
<component name="environment">
<variable units="second" public_interface="out" name="time" />
</component>
<component name="total_cytoplasmic_Ca_flux">
<variable units="nanomolar_per_second" public_interface="out" name="J_ICa" />
<variable units="micro_litre" public_interface="out" name="v_i" />
<variable units="dimensionless" public_interface="out" name="k_i" />
<variable units="coulomb_per_millimole" name="F" initial_value="96.5" />
<variable units="picoA" name="I_Ca" />
<variable units="second" public_interface="in" name="time" />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="J_ICa_calculation">
<eq />
<ci> J_ICa </ci>
<apply>
<divide />
<ci> I_Ca </ci>
<apply>
<times />
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> F </ci>
<ci> v_i </ci>
<ci> k_i </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="Ca_extrusion_across_the_plasma_membrane">
<variable units="nanomolar_per_second" public_interface="out" name="J_pm" />
<variable units="nanomolar_per_second" name="J_extru" />
<variable units="per_second" name="k_leak" initial_value="0.00000015" />
<variable units="nanomolar_per_second" name="Vmax_extru" initial_value="25.0" />
<variable units="nanomolar" name="EC50_extru" initial_value="386.0" />
<variable units="dimensionless" name="n_extru" initial_value="2.4" />
<variable units="millimolar" name="Ca_o" initial_value="2.0" />
<variable units="nanomolar_per_second" public_interface="in" name="J_ICa" />
<variable units="nanomolar" public_interface="in" name="Ca_i" />
<variable units="second" public_interface="in" name="time" />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="J_pm_calculation">
<eq />
<ci> J_pm </ci>
<apply>
<plus />
<ci> J_extru </ci>
<ci> J_ICa </ci>
</apply>
</apply>
<apply id="J_extru_calculation">
<eq />
<ci> J_extru </ci>
<apply>
<plus />
<apply>
<times />
<ci> k_leak </ci>
<apply>
<minus />
<ci> Ca_i </ci>
<ci> Ca_o </ci>
</apply>
</apply>
<apply>
<divide />
<ci> Vmax_extru </ci>
<apply>
<plus />
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<power />
<apply>
<divide />
<ci> EC50_extru </ci>
<ci> Ca_i </ci>
</apply>
<ci> n_extru </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="Ca_uptake_by_SR_Ca_ATPase">
<variable units="nanomolar_per_second" public_interface="out" name="J_SERCA" />
<variable units="nanomolar_per_second" name="Vmax_SERCA" initial_value="70.0" />
<variable units="nanomolar" name="EC50_SERCA" initial_value="700.0" />
<variable units="dimensionless" name="n_SERCA" initial_value="1.0" />
<variable units="nanomolar" public_interface="in" name="Ca_i" />
<variable units="second" public_interface="in" name="time" />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="J_SERCA_calculation">
<eq />
<ci> J_SERCA </ci>
<apply>
<divide />
<ci> Vmax_SERCA </ci>
<apply>
<plus />
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<power />
<apply>
<divide />
<ci> EC50_SERCA </ci>
<ci> Ca_i </ci>
</apply>
<ci> n_SERCA </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="ER_Ca_release">
<variable units="nanomolar_per_second" public_interface="out" name="J_ER" />
<variable units="per_second" name="P_ER" />
<variable units="per_second" name="P_basal" initial_value="0.0000178" />
<variable units="per_second" name="Pmax_RyR" initial_value="0.0009" />
<variable units="micromolar" name="EC50_RyR" initial_value="1.0" />
<variable units="dimensionless" name="n_RyR" initial_value="1.0" />
<variable units="nanomolar_per_second" name="J_release" />
<variable units="nanomolar_per_second" public_interface="in" name="J_SERCA" />
<variable units="nanomolar" public_interface="in" name="Ca_i" />
<variable units="nanomolar" public_interface="in" name="Ca_ER" />
<variable units="second" public_interface="in" name="time" />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="J_release_calculation">
<eq />
<ci> J_release </ci>
<apply>
<times />
<ci> P_ER </ci>
<apply>
<minus />
<ci> Ca_i </ci>
<ci> Ca_ER </ci>
</apply>
</apply>
</apply>
<apply id="J_ER_calculation">
<eq />
<ci> J_ER </ci>
<apply>
<plus />
<ci> J_SERCA </ci>
<ci> J_release </ci>
</apply>
</apply>
<apply id="P_ER_calculation">
<eq />
<ci> P_ER </ci>
<apply>
<plus />
<ci> P_basal </ci>
<apply>
<divide />
<ci> Pmax_RyR </ci>
<apply>
<plus />
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<power />
<apply>
<divide />
<ci> EC50_RyR </ci>
<ci> Ca_i </ci>
</apply>
<ci> n_RyR </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="cytoplasmic_calcium">
<variable units="nanomolar" public_interface="out" name="Ca_i" />
<variable units="nanomolar_per_second" name="J_i" />
<variable units="nanomolar_per_second" public_interface="in" name="J_ER" />
<variable units="nanomolar_per_second" public_interface="in" name="J_pm" />
<variable units="second" public_interface="in" name="time" />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="Ca_i_diff_eq">
<eq />
<apply>
<diff />
<bvar>
<ci> time </ci>
</bvar>
<ci> Ca_i </ci>
</apply>
<apply>
<minus />
<ci> J_i </ci>
</apply>
</apply>
<apply id="J_i_calculation">
<eq />
<ci> J_i </ci>
<apply>
<plus />
<ci> J_pm </ci>
<ci> J_ER </ci>
</apply>
</apply>
</math>
</component>
<component name="intraluminal_calcium">
<variable units="nanomolar" public_interface="out" name="Ca_ER" />
<variable units="micro_litre" name="v_ER" />
<variable units="dimensionless" name="k_ER" />
<variable units="dimensionless" name="gamma_ER" initial_value="0.01" />
<variable units="nanomolar" public_interface="in" name="Ca_i" />
<variable units="micro_litre" public_interface="in" name="v_i" />
<variable units="dimensionless" public_interface="in" name="k_i" />
<variable units="nanomolar_per_second" public_interface="in" name="J_ER" />
<variable units="nanomolar_per_second" public_interface="in" name="J_SERCA" />
<variable units="second" public_interface="in" name="time" />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="Ca_ER_diff_eq">
<eq />
<apply>
<diff />
<bvar>
<ci> time </ci>
</bvar>
<ci> Ca_ER </ci>
</apply>
<apply>
<divide />
<ci> J_ER </ci>
<ci> gamma_ER </ci>
</apply>
</apply>
<apply id="gamma_ER_calculation">
<eq />
<ci> gamma_ER </ci>
<apply>
<divide />
<apply>
<times />
<ci> v_ER </ci>
<ci> k_ER </ci>
</apply>
<apply>
<times />
<ci> v_i </ci>
<ci> k_i </ci>
</apply>
</apply>
</apply>
</math>
</component>
<connection>
<map_components component_2="environment" component_1="total_cytoplasmic_Ca_flux" />
<map_variables variable_2="time" variable_1="time" />
</connection>
<connection>
<map_components component_2="environment" component_1="Ca_extrusion_across_the_plasma_membrane" />
<map_variables variable_2="time" variable_1="time" />
</connection>
<connection>
<map_components component_2="environment" component_1="Ca_uptake_by_SR_Ca_ATPase" />
<map_variables variable_2="time" variable_1="time" />
</connection>
<connection>
<map_components component_2="environment" component_1="ER_Ca_release" />
<map_variables variable_2="time" variable_1="time" />
</connection>
<connection>
<map_components component_2="environment" component_1="cytoplasmic_calcium" />
<map_variables variable_2="time" variable_1="time" />
</connection>
<connection>
<map_components component_2="environment" component_1="intraluminal_calcium" />
<map_variables variable_2="time" variable_1="time" />
</connection>
<connection>
<map_components component_2="Ca_extrusion_across_the_plasma_membrane" component_1="total_cytoplasmic_Ca_flux" />
<map_variables variable_2="J_ICa" variable_1="J_ICa" />
</connection>
<connection>
<map_components component_2="intraluminal_calcium" component_1="total_cytoplasmic_Ca_flux" />
<map_variables variable_2="v_i" variable_1="v_i" />
<map_variables variable_2="k_i" variable_1="k_i" />
</connection>
<connection>
<map_components component_2="cytoplasmic_calcium" component_1="Ca_extrusion_across_the_plasma_membrane" />
<map_variables variable_2="Ca_i" variable_1="Ca_i" />
<map_variables variable_2="J_pm" variable_1="J_pm" />
</connection>
<connection>
<map_components component_2="cytoplasmic_calcium" component_1="Ca_uptake_by_SR_Ca_ATPase" />
<map_variables variable_2="Ca_i" variable_1="Ca_i" />
</connection>
<connection>
<map_components component_2="ER_Ca_release" component_1="Ca_uptake_by_SR_Ca_ATPase" />
<map_variables variable_2="J_SERCA" variable_1="J_SERCA" />
</connection>
<connection>
<map_components component_2="intraluminal_calcium" component_1="Ca_uptake_by_SR_Ca_ATPase" />
<map_variables variable_2="J_SERCA" variable_1="J_SERCA" />
</connection>
<connection>
<map_components component_2="cytoplasmic_calcium" component_1="ER_Ca_release" />
<map_variables variable_2="J_ER" variable_1="J_ER" />
<map_variables variable_2="Ca_i" variable_1="Ca_i" />
</connection>
<connection>
<map_components component_2="intraluminal_calcium" component_1="ER_Ca_release" />
<map_variables variable_2="J_ER" variable_1="J_ER" />
<map_variables variable_2="Ca_ER" variable_1="Ca_ER" />
</connection>
<connection>
<map_components component_2="intraluminal_calcium" component_1="cytoplasmic_calcium" />
<map_variables variable_2="Ca_i" variable_1="Ca_i" />
</connection>
<rdf:RDF>
<rdf:Bag rdf:about="rdf:#b3085f8f-f712-4d81-a1eb-21d56a1f3b02">
<rdf:li>neuron</rdf:li>
<rdf:li>electrophysiology</rdf:li>
</rdf:Bag>
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<rdf:Description rdf:about="#albrecht_colegrove_hongpaisan_pivovarova_andrews_friel_2001_version01">
<dc:title>
Multiple modes of calcium-induced calcium release in sympathetic
neurons.
</dc:title>
<cmeta:bio_entity>sympathetic neuron</cmeta:bio_entity>
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<rdf:Description rdf:about="rdf:#1596a452-45c6-4b36-930a-4c66659ae396">
<vCard:FN>Catherine Lloyd</vCard:FN>
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<rdf:value>
Added more metadata.
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Added publication date information.
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<cmeta:modifier rdf:resource="rdf:#63304634-e12e-4b35-b11e-9bba0fb6e951" />
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<vCard:Orgname>The University of Auckland</vCard:Orgname>
<vCard:Orgunit>The Bioengineering Institute</vCard:Orgunit>
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<dc:creator rdf:resource="rdf:#1596a452-45c6-4b36-930a-4c66659ae396" />
<rdf:value>
This is the CellML description of Albrecht et al's 2001 model of
calcium-induced calcium release in sympathetic neurons.
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<dcterms:W3CDTF>2002-07-18</dcterms:W3CDTF>
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<vCard:Given>Natalia</vCard:Given>
<vCard:Family>Pivovarova</vCard:Family>
<vCard:Other>B</vCard:Other>
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<dc:title>Journal of General Physiology</dc:title>
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<vCard:Given>Catherine</vCard:Given>
<vCard:Family>Lloyd</vCard:Family>
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