- Author:
- Hanne <Hanne@hanne-nielsens-macbook.local>
- Date:
- 2009-12-09 13:05:23+13:00
- Desc:
- Added images in ai and svg format, removed non pub med references
- Permanent Source URI:
- http://models.cellml.org/workspace/marhl_haberichter_brumen_heinrich_2000/rawfile/141fc9ec0432165423639ac1d5b6e31aedb6363b/marhl_haberichter_brumen_heinrich_2000.cellml
<?xml version='1.0' encoding='utf-8'?>
<!-- FILE : marhl_model_2000.xml
CREATED : 4th April 2002
LAST MODIFIED : 9th April 2003
AUTHOR : Catherine Lloyd
Bioengineering Institute
The University of Auckland
MODEL STATUS : This model conforms to the CellML 1.0 Specification released on
10th August 2001, and the 16/1/02 CellML Metadata 1.0 Specification.
DESCRIPTION : This file contains a CellML description of Marhl et al's
2000 model of Ca2+ oscillations and the role of mitochondria and cytosolic proteins.
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="marhl_haberichter_brumen_heinrich_2000_version01" name="marhl_haberichter_brumen_heinrich_2000_version01">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>Complex Calcium Oscillations and the Role of Mitochondria and Cytosolic Proteins</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>
Calcium oscillations play a vital role in intracellular signalling in several different cell types. Since they were discovered in the 1980s, many experimental works and theoretical studies explaining the mechanisms underlying these oscillations have been published (for example see <ulink url="${HTML_EXMPL_LI_MODEL}">The Li and Rinzel Model, 1994</ulink>). It is generally agreed that the endoplasmic reticulum (ER) represents the main calcium store in the cell, but more recently it has been recognised that the mitochondria also play an important role in intracellular calcium signalling.
</para>
<para>
In their 2000 model, Marko Marhl, Thomas Haberichter, Milan Brumen and Reinhart Heinrich provided a new possible explanation of complex intracellular calcium oscillations based on calcium exchange between different calcium stores in the cell (see <xref linkend="fig_cell_diagram"/> below). In addition to the ER, representing the main Ca<superscript>2+</superscript> store in the cell, they also consider Ca<superscript>2+</superscript> sequestration in mitochondria and the Ca<superscript>2+</superscript> binding to cytosolic proteins. They show how complex intracellular calcium oscillations can be explained by the specific Ca<superscript>2+</superscript> kinetics of the three intracellular stores: the ER, mitochondria and the cytosolic Ca<superscript>2+</superscript> binding proteins. Their model produces simple calcium oscillations, bursting and chaos. Their 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>
Complex calcium oscillations and the role of mitochondria and cytosolic proteins, Marko Marhl, Thomas Haberichter, Milan Brumen and Reinhart Heinrich, 2000, <<emphasis>Biosystems</emphasis>, 57, 75-86. <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=11004387&dopt=Abstract">PubMed ID: 11004387</ulink>
</para>
<informalfigure float="0" id="fig_cell_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>cell schematic for the model</title>
</objectinfo>
<imagedata fileref="marhl_2000.png"/>
</imageobject>
</mediaobject>
<caption>Schematic presentation of the model sysytem.</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="micromolar">
<unit units="mole" prefix="micro"/>
<unit units="litre" exponent="-1"/>
</units>
<units name="flux">
<unit units="micromolar"/>
<unit units="second" exponent="-1"/>
</units>
<units name="first_order_rate_constant">
<unit units="second" exponent="-1"/>
</units>
<units name="second_order_rate_constant">
<unit units="micromolar" exponent="-1"/>
<unit units="second" exponent="-1"/>
</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_calcium">
<variable units="micromolar" name="Ca_tot" initial_value="90.0"/>
<variable units="dimensionless" public_interface="in" name="rho_ER"/>
<variable units="dimensionless" public_interface="in" name="beta_ER"/>
<variable units="dimensionless" public_interface="in" name="rho_m"/>
<variable units="dimensionless" public_interface="in" name="beta_m"/>
<variable units="micromolar" public_interface="in" name="Ca_cyt"/>
<variable units="micromolar" public_interface="in" name="Ca_ER"/>
<variable units="micromolar" public_interface="in" name="Ca_m"/>
<variable units="micromolar" public_interface="in" name="Ca_Pr"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="Ca_tot_calculation">
<eq/>
<ci> Ca_tot </ci>
<apply>
<plus/>
<ci> Ca_cyt </ci>
<apply>
<times/>
<apply>
<divide/>
<ci> rho_ER </ci>
<ci> beta_ER </ci>
</apply>
<ci> Ca_ER </ci>
</apply>
<apply>
<times/>
<apply>
<divide/>
<ci> rho_m </ci>
<ci> beta_m </ci>
</apply>
<ci> Ca_m </ci>
</apply>
<ci> Ca_Pr </ci>
</apply>
</apply>
</math>
</component>
<component name="total_protein">
<variable units="micromolar" public_interface="out" name="Ca_Pr"/>
<variable units="micromolar" public_interface="out" name="Pr"/>
<variable units="micromolar" name="Pr_tot" initial_value="120.0"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="Pr_tot_calculation">
<eq/>
<ci> Pr_tot </ci>
<apply>
<plus/>
<ci> Pr </ci>
<ci> Ca_Pr </ci>
</apply>
</apply>
</math>
</component>
<component name="cytosolic_calcium">
<variable units="micromolar" public_interface="out" name="Ca_cyt"/>
<variable units="second_order_rate_constant" name="k_plus" initial_value="0.1"/>
<variable units="first_order_rate_constant" name="k_minus" initial_value="0.01"/>
<variable units="micromolar" public_interface="in" name="Pr"/>
<variable units="micromolar" public_interface="in" name="Ca_Pr"/>
<variable units="flux" public_interface="in" name="J_ch"/>
<variable units="flux" public_interface="in" name="J_leak"/>
<variable units="flux" public_interface="in" name="J_pump"/>
<variable units="flux" public_interface="in" name="J_out"/>
<variable units="flux" public_interface="in" name="J_in"/>
<variable units="second" public_interface="in" name="time"/>
<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>
<ci> J_out </ci>
<apply>
<times/>
<ci> k_minus </ci>
<ci> Ca_Pr </ci>
</apply>
</apply>
<apply>
<plus/>
<ci> J_pump </ci>
<ci> J_in </ci>
<apply>
<times/>
<ci> k_plus </ci>
<ci> Ca_cyt </ci>
<ci> Pr </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="ER_calcium">
<variable units="micromolar" public_interface="out" name="Ca_ER"/>
<variable units="dimensionless" public_interface="out" name="rho_ER" initial_value="0.01"/>
<variable units="dimensionless" public_interface="out" name="beta_ER" initial_value="0.0025"/>
<variable units="flux" public_interface="in" name="J_ch"/>
<variable units="flux" public_interface="in" name="J_leak"/>
<variable units="flux" public_interface="in" name="J_pump"/>
<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/>
<apply>
<divide/>
<ci> beta_ER </ci>
<ci> rho_ER </ci>
</apply>
<apply>
<minus/>
<ci> J_pump </ci>
<apply>
<plus/>
<ci> J_ch </ci>
<ci> J_leak </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="mitochondrial_calcium">
<variable units="micromolar" public_interface="out" name="Ca_m"/>
<variable units="dimensionless" public_interface="out" name="rho_m" initial_value="0.01"/>
<variable units="dimensionless" public_interface="out" name="beta_m" initial_value="0.0025"/>
<variable units="flux" public_interface="in" name="J_in"/>
<variable units="flux" public_interface="in" name="J_out"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="Ca_m_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Ca_m </ci>
</apply>
<apply>
<times/>
<apply>
<divide/>
<ci> beta_m </ci>
<ci> rho_m </ci>
</apply>
<apply>
<minus/>
<ci> J_in </ci>
<ci> J_out </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="ATP_dependent_Ca_uptake_into_the_ER">
<variable units="flux" public_interface="out" name="J_pump"/>
<variable units="first_order_rate_constant" name="k_pump" initial_value="20.0"/>
<variable units="micromolar" public_interface="in" name="Ca_cyt"/>
<variable units="second" public_interface="in" name="time"/>
<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 name="Ca_efflux_from_the_ER">
<variable units="flux" public_interface="out" name="J_ch"/>
<variable units="first_order_rate_constant" name="k_ch" initial_value="4100.0"/>
<variable units="micromolar" name="K1" initial_value="5.0"/>
<variable units="micromolar" public_interface="in" name="Ca_cyt"/>
<variable units="micromolar" 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_ch_calculation">
<eq/>
<ci> J_ch </ci>
<apply>
<times/>
<ci> k_ch </ci>
<apply>
<divide/>
<apply>
<power/>
<ci> Ca_cyt </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci> K1 </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply>
<power/>
<ci> Ca_cyt </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
</apply>
<apply>
<minus/>
<ci> Ca_ER </ci>
<ci> Ca_cyt </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="Ca_leak_flux_from_the_ER">
<variable units="flux" public_interface="out" name="J_leak"/>
<variable units="first_order_rate_constant" name="k_leak" initial_value="0.05"/>
<variable units="micromolar" public_interface="in" name="Ca_cyt"/>
<variable units="micromolar" 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_leak_calculation">
<eq/>
<ci> J_leak </ci>
<apply>
<times/>
<ci> k_leak </ci>
<apply>
<minus/>
<ci> Ca_ER </ci>
<ci> Ca_cyt </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="mitochondrial_Ca_uptake">
<variable units="flux" public_interface="out" name="J_in"/>
<variable units="second_order_rate_constant" name="k_in" initial_value="300.0"/>
<variable units="micromolar" name="K2" initial_value="0.8"/>
<variable units="micromolar" public_interface="in" name="Ca_cyt"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="J_in_calculation">
<eq/>
<ci> J_in </ci>
<apply>
<times/>
<ci> k_in </ci>
<apply>
<divide/>
<apply>
<power/>
<ci> Ca_cyt </ci>
<cn cellml:units="dimensionless"> 8.0 </cn>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci> K2 </ci>
<cn cellml:units="dimensionless"> 8.0 </cn>
</apply>
<apply>
<power/>
<ci> Ca_cyt </ci>
<cn cellml:units="dimensionless"> 8.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="mitochondrial_Ca_release">
<variable units="flux" public_interface="out" name="J_out"/>
<variable units="first_order_rate_constant" name="k_out" initial_value="125.0"/>
<variable units="first_order_rate_constant" name="k_m" initial_value="0.00625"/>
<variable units="micromolar" name="K3" initial_value="5.0"/>
<variable units="micromolar" public_interface="in" name="Ca_cyt"/>
<variable units="micromolar" public_interface="in" name="Ca_m"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="J_out_calculation">
<eq/>
<ci> J_out </ci>
<apply>
<times/>
<apply>
<plus/>
<apply>
<times/>
<ci> k_out </ci>
<apply>
<divide/>
<apply>
<power/>
<ci> Ca_cyt </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci> K3 </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply>
<power/>
<ci> Ca_cyt </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
</apply>
</apply>
<ci> k_m </ci>
</apply>
<ci> Ca_m </ci>
</apply>
</apply>
</math>
</component>
<connection>
<map_components component_2="environment" component_1="total_calcium"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="total_protein"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="cytosolic_calcium"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="ER_calcium"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="mitochondrial_calcium"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="ATP_dependent_Ca_uptake_into_the_ER"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="Ca_efflux_from_the_ER"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="Ca_leak_flux_from_the_ER"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="mitochondrial_Ca_uptake"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="mitochondrial_Ca_release"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="ER_calcium" component_1="total_calcium"/>
<map_variables variable_2="rho_ER" variable_1="rho_ER"/>
<map_variables variable_2="beta_ER" variable_1="beta_ER"/>
<map_variables variable_2="Ca_ER" variable_1="Ca_ER"/>
</connection>
<connection>
<map_components component_2="mitochondrial_calcium" component_1="total_calcium"/>
<map_variables variable_2="rho_m" variable_1="rho_m"/>
<map_variables variable_2="beta_m" variable_1="beta_m"/>
<map_variables variable_2="Ca_m" variable_1="Ca_m"/>
</connection>
<connection>
<map_components component_2="cytosolic_calcium" component_1="total_calcium"/>
<map_variables variable_2="Ca_cyt" variable_1="Ca_cyt"/>
</connection>
<connection>
<map_components component_2="total_protein" component_1="total_calcium"/>
<map_variables variable_2="Ca_Pr" variable_1="Ca_Pr"/>
</connection>
<connection>
<map_components component_2="total_protein" component_1="cytosolic_calcium"/>
<map_variables variable_2="Ca_Pr" variable_1="Ca_Pr"/>
<map_variables variable_2="Pr" variable_1="Pr"/>
</connection>
<connection>
<map_components component_2="ATP_dependent_Ca_uptake_into_the_ER" component_1="cytosolic_calcium"/>
<map_variables variable_2="Ca_cyt" variable_1="Ca_cyt"/>
<map_variables variable_2="J_pump" variable_1="J_pump"/>
</connection>
<connection>
<map_components component_2="Ca_efflux_from_the_ER" component_1="cytosolic_calcium"/>
<map_variables variable_2="Ca_cyt" variable_1="Ca_cyt"/>
<map_variables variable_2="J_ch" variable_1="J_ch"/>
</connection>
<connection>
<map_components component_2="Ca_leak_flux_from_the_ER" component_1="cytosolic_calcium"/>
<map_variables variable_2="Ca_cyt" variable_1="Ca_cyt"/>
<map_variables variable_2="J_leak" variable_1="J_leak"/>
</connection>
<connection>
<map_components component_2="mitochondrial_Ca_release" component_1="cytosolic_calcium"/>
<map_variables variable_2="Ca_cyt" variable_1="Ca_cyt"/>
<map_variables variable_2="J_out" variable_1="J_out"/>
</connection>
<connection>
<map_components component_2="mitochondrial_Ca_uptake" component_1="cytosolic_calcium"/>
<map_variables variable_2="Ca_cyt" variable_1="Ca_cyt"/>
<map_variables variable_2="J_in" variable_1="J_in"/>
</connection>
<connection>
<map_components component_2="ATP_dependent_Ca_uptake_into_the_ER" component_1="ER_calcium"/>
<map_variables variable_2="J_pump" variable_1="J_pump"/>
</connection>
<connection>
<map_components component_2="Ca_efflux_from_the_ER" component_1="ER_calcium"/>
<map_variables variable_2="Ca_ER" variable_1="Ca_ER"/>
<map_variables variable_2="J_ch" variable_1="J_ch"/>
</connection>
<connection>
<map_components component_2="Ca_leak_flux_from_the_ER" component_1="ER_calcium"/>
<map_variables variable_2="Ca_ER" variable_1="Ca_ER"/>
<map_variables variable_2="J_leak" variable_1="J_leak"/>
</connection>
<connection>
<map_components component_2="mitochondrial_Ca_release" component_1="mitochondrial_calcium"/>
<map_variables variable_2="Ca_m" variable_1="Ca_m"/>
<map_variables variable_2="J_out" variable_1="J_out"/>
</connection>
<connection>
<map_components component_2="mitochondrial_Ca_uptake" component_1="mitochondrial_calcium"/>
<map_variables variable_2="J_in" variable_1="J_in"/>
</connection>
<rdf:RDF>
<rdf:Bag rdf:about="rdf:#a3cd0a8d-7520-490f-a0de-85204d064f73">
<rdf:li>calcium dynamics</rdf:li>
<rdf:li>electrophysiology</rdf:li>
<rdf:li>mitochondria</rdf:li>
<rdf:li>oscillator</rdf:li>
</rdf:Bag>
<rdf:Seq rdf:about="rdf:#918348d1-2e8a-44ff-a480-fea01f35c99f">
<rdf:li rdf:resource="rdf:#13a4596c-df9b-4b0f-bf61-16b26cb9b805"/>
<rdf:li rdf:resource="rdf:#3473e1b4-dc45-450b-81df-371c72596376"/>
<rdf:li rdf:resource="rdf:#a0959cd9-8e4a-4308-95d6-0258dd9b9c37"/>
<rdf:li rdf:resource="rdf:#62fdc3aa-0065-4775-8a7a-64d80e71325b"/>
</rdf:Seq>
<rdf:Description rdf:about="">
<dc:publisher>
The University of Auckland, Bioengineering Institute
</dc:publisher>
<cmeta:modification rdf:resource="rdf:#0dd49186-b00b-4b9a-82e8-a3b1ef2ebeb5"/>
<cmeta:modification rdf:resource="rdf:#2b2c10d0-275e-432b-979f-24d8b72139e6"/>
<dcterms:created rdf:resource="rdf:#61835721-9e5f-401f-8a13-681c4788e39e"/>
<dc:creator rdf:resource="rdf:#7ab1934e-2d33-458a-94dc-07c8ae55359a"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#e7678806-38af-4487-8ea9-db9fbd85d250">
<vCard:Given>Catherine</vCard:Given>
<vCard:Family>Lloyd</vCard:Family>
<vCard:Other>May</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#c6e4ecca-6605-4d0a-83ee-990976943d4a">
<dc:subject rdf:resource="rdf:#85b236f8-da84-4531-9983-9b08fc8eafa0"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#85b236f8-da84-4531-9983-9b08fc8eafa0">
<bqs:subject_type>keyword</bqs:subject_type>
<rdf:value rdf:resource="rdf:#a3cd0a8d-7520-490f-a0de-85204d064f73"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#0dd49186-b00b-4b9a-82e8-a3b1ef2ebeb5">
<dcterms:modified rdf:resource="rdf:#b0273982-81de-4787-96b1-6adc53e450e6"/>
<rdf:value>
Added more metadata.
</rdf:value>
<cmeta:modifier rdf:resource="rdf:#7bde58e6-98fb-4f43-b526-3d0901db4ac8"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#9c5d8eef-f870-4a3e-97c5-778e1199cb20">
<vCard:Given>Reinhart</vCard:Given>
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A mathematical model of Ca2+ oscillations and the role of mitochondria
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Complex calcium oscillations and the role of mitochondria and cytosolic proteins
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