<?xml version='1.0' encoding='utf-8'?>
<!-- FILE : albrecht_model_2002.xml
CREATED : 21st 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
2002 model of differential regulation of ER Ca2+ uptake and release rates.
CHANGES:
18/07/2002 - CML - Added more metadata.
09/04/2003 - AAC - Added publication date information.
--><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="albrecht_colegrove_friel_2002_version01" name="albrecht_colegrove_friel_2002_version01">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>Differential Regulation of ER Ca2+ Uptake and Release Rates Accounts for Multiple Modes of Ca2+-induced Ca2+ Release</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>
<para>
ValidateCellML found unit inconsistencies in this model
</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="${HTML_EXMPL_COLEGROVE_MODEL}">The Colegrove <emphasis>et al</emphasis> Model Of Mitochondrial Ca<superscript>2+</superscript> Uptake And Release, 2000</ulink>), the ER is also an important component in Ca<superscript>2+</superscript> signalling in virtually all non-muscle cells, and it has been described as either a Ca<superscript>2+</superscript> source or sink. Different modes of net ER Ca<superscript>2+</superscript> transport are expected to have very different effects on cytoplasmic and intraluminal Ca<superscript>2+</superscript> signals and on the processes they regulate (see <ulink url="${HTML_EXMPL_ALBRECHT_MODEL1}">The Albrecht <emphasis>et al</emphasis> Model Of Multiple Modes of Ca<superscript>2+</superscript>-induced Ca<superscript>2+</superscript> Release in Sympathetic Neurons, 2001</ulink>).
</para>
<para>
In a follow up study to their 2001 paper, Meredith A. Albrecht, Stephen L. Colegrove and David D. Friel have examined how differential regulation of ER Ca<superscript>2+</superscript> uptake and release rates accounts for multiple modes of Ca<superscript>2+</superscript>-induced Ca<superscript>2+</superscript> release. Three different macroscopic Ca<superscript>2+</superscript> fluxes were modelled: J<subscript>SERCA</subscript>, the rate of Ca<superscript>2+</superscript> uptake via SR Ca-ATPases; J<subscript>ICa</subscript>, the total cytoplasmic Ca<superscript>2+</superscript> flux when SR Ca-ATPases are inhibited; and J<subscript>pm</subscript>, the rate of Ca<superscript>2+</superscript> extrusion across the plasma membrane. One additional flux J<subscript>release</subscript> was calculated from the difference between J<subscript>ICa</subscript> and J<subscript>pm</subscript> (see <xref linkend="fig_cell_diagram"/> below). 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/119/3/211">Differential Regulation of ER Ca<superscript>2+</superscript> Uptake and Release Rates Accounts for Multiple Modes of Ca<superscript>2+</superscript>-induced Ca<superscript>2+</superscript> Release</ulink>, Meredith A. Albrecht, Stephen L. Colegrove and David D. Friel, 2002, <ulink url="http://www.jgp.org/">
<emphasis>The Journal Of General Physiology</emphasis>
</ulink>, 119, 211-233. (<ulink url="http://www.jgp.org/cgi/content/full/119/3/211">Full text</ulink> and <ulink url="http://www.jgp.org/cgi/reprint/119/3/211.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=11865019&dopt=Abstract">PubMed ID: 11865019</ulink>
</para>
<informalfigure float="0" id="fig_cell_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>cell schematic for the model</title>
</objectinfo>
<imagedata fileref="albrecht_2002.png"/>
</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="micro"/>
<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="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="nanomolar" name="Ca_ER_init"/>
<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="per_second" public_interface="in" name="P_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>
<times/>
<ci> J_ER </ci>
<apply>
<divide/>
<apply>
<times/>
<ci> v_i </ci>
<ci> k_i </ci>
</apply>
<apply>
<times/>
<ci> v_ER </ci>
<ci> k_ER </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="Ca_ER_init_calculation">
<eq/>
<ci> Ca_ER_init </ci>
<apply>
<plus/>
<ci> Ca_i </ci>
<apply>
<divide/>
<apply>
<times/>
<ci> J_SERCA </ci>
<ci> Ca_i </ci>
</apply>
<apply>
<times/>
<ci> P_ER </ci>
<apply>
<divide/>
<ci> Ca_i </ci>
<ci> v_i </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</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_pm" 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="dimensionless" public_interface="in" name="k_i"/>
<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>
<times/>
<apply>
<power/>
<ci> k_i </ci>
<cn cellml:units="dimensionless"> -1.0 </cn>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci> k_leak_pm </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>
</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="2146.0"/>
<variable units="micromolar" name="EC50_SERCA" initial_value="30.3"/>
<variable units="dimensionless" name="n_SERCA" initial_value="2.5"/>
<variable units="dimensionless" public_interface="in" name="k_i"/>
<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>
<times/>
<ci> k_i </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>
</apply>
</math>
</component>
<component name="ER_Ca_release">
<variable units="nanomolar_per_second" public_interface="out" name="J_ER"/>
<variable units="per_second" public_interface="out" name="P_ER"/>
<variable units="per_second" name="P_basal" initial_value="0.009"/>
<variable units="per_second" name="Pmax_RyR" initial_value="0.05"/>
<variable units="nanomolar" name="EC50_RyR" initial_value="2641.0"/>
<variable units="dimensionless" name="n_RyR" initial_value="0.96"/>
<variable units="nanomolar_per_second" name="J_release"/>
<variable units="nanomolar_per_second" public_interface="in" name="J_SERCA"/>
<variable units="micro_litre" public_interface="in" name="v_i"/>
<variable units="dimensionless" public_interface="in" name="k_i"/>
<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>
<divide/>
<apply>
<times/>
<ci> P_ER </ci>
<apply>
<minus/>
<ci> Ca_i </ci>
<ci> Ca_ER </ci>
</apply>
</apply>
<apply>
<times/>
<ci> v_i </ci>
<ci> k_i </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_v_i_calculation">
<eq/>
<ci> P_ER </ci>
<apply>
<times/>
<ci> v_i </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>
</apply>
</math>
</component>
<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="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="Ca_extrusion_across_the_plasma_membrane" component_1="cytoplasmic_calcium"/>
<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="Ca_uptake_by_SR_Ca_ATPase" component_1="cytoplasmic_calcium"/>
<map_variables variable_2="Ca_i" variable_1="Ca_i"/>
</connection>
<connection>
<map_components component_2="ER_Ca_release" component_1="cytoplasmic_calcium"/>
<map_variables variable_2="Ca_i" variable_1="Ca_i"/>
<map_variables variable_2="J_ER" variable_1="J_ER"/>
</connection>
<connection>
<map_components component_2="intraluminal_calcium" component_1="cytoplasmic_calcium"/>
<map_variables variable_2="Ca_i" variable_1="Ca_i"/>
</connection>
<connection>
<map_components component_2="ER_Ca_release" component_1="intraluminal_calcium"/>
<map_variables variable_2="Ca_ER" variable_1="Ca_ER"/>
<map_variables variable_2="J_ER" variable_1="J_ER"/>
<map_variables variable_2="P_ER" variable_1="P_ER"/>
</connection>
<connection>
<map_components component_2="Ca_uptake_by_SR_Ca_ATPase" component_1="intraluminal_calcium"/>
<map_variables variable_2="J_SERCA" variable_1="J_SERCA"/>
</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="Ca_extrusion_across_the_plasma_membrane" component_1="total_cytoplasmic_Ca_flux"/>
<map_variables variable_2="J_ICa" variable_1="J_ICa"/>
<map_variables variable_2="k_i" variable_1="k_i"/>
</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="ER_Ca_release" 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="Ca_uptake_by_SR_Ca_ATPase" component_1="total_cytoplasmic_Ca_flux"/>
<map_variables variable_2="k_i" variable_1="k_i"/>
</connection>
<rdf:RDF>
<rdf:Bag rdf:about="rdf:#8d6d8ff2-88c9-4e05-851b-737fcc458f9d">
<rdf:li>neuron</rdf:li>
<rdf:li>electrophysiology</rdf:li>
<rdf:li>calcium dynamics</rdf:li>
<rdf:li>er</rdf:li>
</rdf:Bag>
<rdf:Seq rdf:about="rdf:#10a6f2e1-447d-4bf2-ae2b-f4417adc8871">
<rdf:li rdf:resource="rdf:#e3ea6eca-928f-451b-9cd1-ca013e677550"/>
<rdf:li rdf:resource="rdf:#2c9fddfb-d78f-424c-a603-c5be16f70ce8"/>
<rdf:li rdf:resource="rdf:#90813684-7a7b-468e-a041-3ff09dbba116"/>
</rdf:Seq>
<rdf:Description rdf:about="rdf:#ac2a32d9-fbca-4912-aee9-ad8260bbcd91">
<vCard:Given>Catherine</vCard:Given>
<vCard:Family>Lloyd</vCard:Family>
<vCard:Other>May</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="">
<dc:publisher>The University of Auckland, Bioengineering Institute</dc:publisher>
<cmeta:comment rdf:resource="rdf:#b9e90e28-b72c-45e4-9849-9331052e90ae"/>
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<cmeta:modification rdf:resource="rdf:#6e35936f-2c34-4b29-9d02-a49e7f850df3"/>
<cmeta:modification rdf:resource="rdf:#24b0e4e2-b175-4156-8d6e-f70c3806c172"/>
<cmeta:modification rdf:resource="rdf:#4d873d62-ff2e-436d-ba16-9c4d05218d24"/>
</rdf:Description>
<rdf:Description rdf:about="#albrecht_colegrove_friel_2002_version01">
<dc:title>
Differential regulation of ER Ca2+ uptake and release.
</dc:title>
<cmeta:bio_entity>sympathetic neuron</cmeta:bio_entity>
<cmeta:comment rdf:resource="rdf:#8c76b646-2c23-42de-a543-f65e73c9c8db"/>
<bqs:reference rdf:resource="rdf:#16c21c1f-b111-4f11-a1ce-97429d7f213b"/>
<bqs:reference rdf:resource="rdf:#3685de9e-447a-404b-b4a7-fcfc718d872d"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#8905d384-47da-4f96-bcf1-715e354d64fd">
<vCard:Given>Stephen</vCard:Given>
<vCard:Family>Colegrove</vCard:Family>
<vCard:Other>L</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#90813684-7a7b-468e-a041-3ff09dbba116">
<rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
<vCard:N rdf:resource="rdf:#d5e9e357-b7fb-460f-9c9a-6b96524d37d9"/>
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<rdf:type rdf:resource="http://imc.org/vCard/3.0#internet"/>
<rdf:value>c.lloyd@auckland.ac.nz</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#a72eecbd-8b6e-4c2d-8769-359866ae4502">
<dcterms:W3CDTF>2002-07-18</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="rdf:#0590c7c2-1c63-4565-8bcb-f111bb4b34a0">
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