- Author:
- pmr2.import <nobody@models.cellml.org>
- Date:
- 2009-06-17 14:14:31+12:00
- Desc:
- committing version01 of friel_1995
- Permanent Source URI:
- https://models.cellml.org/workspace/friel_1995/rawfile/8c93002fa3036af4e88773d613eac92566212041/friel_1995.cellml
<?xml version='1.0' encoding='utf-8'?>
<!-- FILE : friel_model_1995.xml
CREATED : 2nd 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 D.D. Friel's 1995 model of Ca2+ oscillations in sympathetic neurons.
CHANGES:
22/07/2002 - 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="friel_1995_version01" name="friel_1995_version01">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>[Ca2+]i Oscillations 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 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>
[Ca<superscript>2+</superscript>]<subscript>i</subscript> oscillations have been described in a variety of cells. They appear to be controlled by multiple mechanisms. In some excitable cells, oscillations reflect periodic depolarisation and increased Ca<superscript>2+</superscript> entry across the plasma membrane. In others, oscillations are dominated by Ca<superscript>2+</superscript> uptake and release by internal stores.
</para>
<para>
In his 1995 mathematical model, David D. Friel has studied caffeine-induced [Ca<superscript>2+</superscript>]<subscript>i</subscript> oscillations in sympathetic neurons. In this cell type, oscillations reflect both Ca<superscript>2+</superscript> transport across the plasma membrane and uptake and release by internal stores. This model builds on previous work by examining the net fluxes of Ca<superscript>2+</superscript> across the plasma membrane and between the cytosol and the intracellular store, and by presenting a quantitative model that addresses how these fluxes can together account for a periodic steady state.
</para>
<para>
The model defines four Ca<superscript>2+</superscript> fluxes (see <xref linkend="fig_cell_diagram"/> below): two are passive leaks - one representing Ca<superscript>2+</superscript> entry into the cell (J<subscript>L1</subscript>) and one representing Ca<superscript>2+</superscript> release from the intracellular store into the cytosol (J<subscript>L2</subscript>). The other two Ca<superscript>2+</superscript> fluxes are driven against an electrochemical gradient by pumps; J<subscript>P1</subscript> represents Ca<superscript>2+</superscript> extrusion from the cytosol and J<subscript>P2</subscript> represents Ca<superscript>2+</superscript> uptake into the intracellular store from the cytosol. 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.biophysj.org/cgi/content/abstract/68/5/1752">[Ca<superscript>2+</superscript>]<subscript>i</subscript> Oscillations In Sympathetic Neurons</ulink>, David D. Friel, 1995, <ulink url="http://www.biophysj.org/">
<emphasis>Biophysical Journal</emphasis>
</ulink>, 68, 1752-1766. <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=7612818&dopt=Abstract">PubMed ID: 7612818</ulink>
</para>
<informalfigure float="0" id="fig_cell_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>cell schematic for the model</title>
</objectinfo>
<imagedata fileref="friel_1995.png"/>
</imageobject>
</mediaobject>
<caption>Schematic of the model indicating Ca<superscript>2+</superscript> compartmentalization in the extracellular matrix, cytosol and the mitochondrial matrix 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="nanomolar">
<unit units="mole" prefix="nano"/>
<unit units="litre" exponent="-1"/>
</units>
<units name="micromolar">
<unit units="mole" prefix="micro"/>
<unit units="litre" exponent="-1"/>
</units>
<units name="nanomolar_per_second">
<unit units="nanomolar"/>
<unit units="second" exponent="-1"/>
</units>
<units name="micro_litre">
<unit units="litre" prefix="micro"/>
</units>
<units name="micro_litre_per_second">
<unit units="micro_litre"/>
<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="cytosolic_Ca_uptake">
<variable units="per_second" public_interface="out" name="K_L1" initial_value="0.000005"/>
<variable units="micro_litre_per_second" name="k_L1"/>
<variable units="nanomolar_per_second" name="J_L1"/>
<variable units="nanomolar" public_interface="in" name="Ca_o"/>
<variable units="micro_litre" public_interface="in" name="v_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_L1_calculation">
<eq/>
<ci> J_L1 </ci>
<apply>
<times/>
<ci> k_L1 </ci>
<apply>
<minus/>
<ci> Ca_i </ci>
<ci> Ca_o </ci>
</apply>
</apply>
</apply>
<apply id="K_L1_calculation">
<eq/>
<ci> K_L1 </ci>
<apply>
<divide/>
<ci> k_L1 </ci>
<ci> v_i </ci>
</apply>
</apply>
</math>
</component>
<component name="cytosolic_Ca_release">
<variable units="per_second" public_interface="out" name="K_P1" initial_value="0.132"/>
<variable units="nanomolar_per_second" name="J_P1"/>
<variable units="micro_litre_per_second" name="k_P1"/>
<variable units="micro_litre" public_interface="in" name="v_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_P1_calculation">
<eq/>
<ci> J_P1 </ci>
<apply>
<times/>
<ci> k_P1 </ci>
<ci> Ca_i </ci>
</apply>
</apply>
<apply id="K_P1_calculation">
<eq/>
<ci> K_P1 </ci>
<apply>
<divide/>
<ci> k_P1 </ci>
<ci> v_i </ci>
</apply>
</apply>
</math>
</component>
<component name="internal_store_Ca_release">
<variable units="per_second" public_interface="out" name="K_L2"/>
<variable units="nanomolar_per_second" name="J_L2"/>
<variable units="micro_litre_per_second" name="k_L2"/>
<variable units="per_second" name="K_L2_0" initial_value="0.054"/>
<variable units="per_second" name="K_L2_1" initial_value="2.4"/>
<variable units="micromolar" name="Kd_Ca" initial_value="0.23"/>
<variable units="dimensionless" name="n" initial_value="3.8"/>
<variable units="nanomolar" public_interface="in" name="Ca_i"/>
<variable units="nanomolar" public_interface="in" name="Ca_s"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="J_L2_calculation">
<eq/>
<ci> J_L2 </ci>
<apply>
<times/>
<ci> k_L2 </ci>
<apply>
<minus/>
<ci> Ca_i </ci>
<ci> Ca_s </ci>
</apply>
</apply>
</apply>
<apply id="K_L2_calculation">
<eq/>
<ci> K_L2 </ci>
<apply>
<divide/>
<apply>
<plus/>
<ci> K_L2_0 </ci>
<ci> K_L2_1 </ci>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<power/>
<apply>
<divide/>
<ci> Kd_Ca </ci>
<ci> Ca_i </ci>
</apply>
<ci> n </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="internal_store_Ca_uptake">
<variable units="per_second" public_interface="out" name="K_P2" initial_value="3.78"/>
<variable units="micro_litre_per_second" name="k_P2"/>
<variable units="nanomolar_per_second" name="J_P2"/>
<variable units="micro_litre" public_interface="in" name="v_s"/>
<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_P2_calculation">
<eq/>
<ci> J_P2 </ci>
<apply>
<times/>
<ci> k_P2 </ci>
<ci> Ca_i </ci>
</apply>
</apply>
<apply id="K_P2_calculation">
<eq/>
<ci> K_P2 </ci>
<apply>
<divide/>
<ci> k_P2 </ci>
<ci> v_s </ci>
</apply>
</apply>
</math>
</component>
<component name="cytosolic_calcium">
<variable units="nanomolar" public_interface="out" name="Ca_i"/>
<variable units="nanomolar" public_interface="out" name="Ca_o"/>
<variable units="micro_litre" public_interface="out" name="v_i"/>
<variable units="nanomolar" public_interface="out" name="Ca_i_ss"/>
<variable units="dimensionless" name="gamma" initial_value="0.24"/>
<variable units="per_second" public_interface="in" name="K_L1"/>
<variable units="per_second" public_interface="in" name="K_P1"/>
<variable units="per_second" public_interface="in" name="K_L2"/>
<variable units="per_second" public_interface="in" name="K_P2"/>
<variable units="micro_litre" public_interface="in" name="v_s"/>
<variable units="nanomolar" public_interface="in" name="Ca_s"/>
<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>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<apply>
<plus/>
<ci> K_L1 </ci>
<ci> K_P1 </ci>
<apply>
<times/>
<ci> gamma </ci>
<apply>
<plus/>
<ci> K_L2 </ci>
<ci> K_P2 </ci>
</apply>
</apply>
</apply>
</apply>
<ci> Ca_i </ci>
</apply>
<apply>
<times/>
<ci> gamma </ci>
<ci> K_L2 </ci>
<ci> Ca_s </ci>
</apply>
<apply>
<times/>
<ci> K_L1 </ci>
<ci> Ca_o </ci>
</apply>
</apply>
</apply>
<apply id="Ca_i_ss_calculation">
<eq/>
<ci> Ca_i_ss </ci>
<apply>
<divide/>
<ci> Ca_o </ci>
<apply>
<divide/>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> K_P1 </ci>
</apply>
<ci> K_L1 </ci>
</apply>
</apply>
</apply>
<apply id="gamma_calculation">
<eq/>
<ci> gamma </ci>
<apply>
<divide/>
<ci> v_i </ci>
<ci> v_s </ci>
</apply>
</apply>
</math>
</component>
<component name="internal_store_calcium">
<variable units="nanomolar" public_interface="out" name="Ca_s"/>
<variable units="micro_litre" public_interface="out" name="v_s"/>
<variable units="nanomolar" public_interface="out" name="Ca_s_ss"/>
<variable units="nanomolar" public_interface="in" name="Ca_i"/>
<variable units="nanomolar" public_interface="in" name="Ca_i_ss"/>
<variable units="per_second" public_interface="in" name="K_L2"/>
<variable units="per_second" public_interface="in" name="K_P2"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="Ca_s_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Ca_s </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<apply>
<plus/>
<ci> K_L2 </ci>
<ci> K_P2 </ci>
</apply>
<ci> Ca_i </ci>
</apply>
<apply>
<times/>
<ci> K_L2 </ci>
<ci> Ca_s </ci>
</apply>
</apply>
</apply>
<apply id="Ca_s_ss_calculation">
<eq/>
<ci> Ca_s_ss </ci>
<apply>
<divide/>
<ci> Ca_i_ss </ci>
<apply>
<divide/>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> K_P2 </ci>
</apply>
<ci> K_L2 </ci>
</apply>
</apply>
</apply>
</math>
</component>
<connection>
<map_components component_2="environment" component_1="cytosolic_Ca_uptake"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="cytosolic_Ca_release"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="internal_store_Ca_release"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="internal_store_Ca_uptake"/>
<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="internal_store_calcium"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="cytosolic_calcium" component_1="cytosolic_Ca_uptake"/>
<map_variables variable_2="K_L1" variable_1="K_L1"/>
<map_variables variable_2="Ca_i" variable_1="Ca_i"/>
<map_variables variable_2="Ca_o" variable_1="Ca_o"/>
<map_variables variable_2="v_i" variable_1="v_i"/>
</connection>
<connection>
<map_components component_2="cytosolic_calcium" component_1="cytosolic_Ca_release"/>
<map_variables variable_2="K_P1" variable_1="K_P1"/>
<map_variables variable_2="Ca_i" variable_1="Ca_i"/>
<map_variables variable_2="v_i" variable_1="v_i"/>
</connection>
<connection>
<map_components component_2="cytosolic_calcium" component_1="internal_store_Ca_release"/>
<map_variables variable_2="K_L2" variable_1="K_L2"/>
<map_variables variable_2="Ca_i" variable_1="Ca_i"/>
</connection>
<connection>
<map_components component_2="internal_store_calcium" component_1="internal_store_Ca_release"/>
<map_variables variable_2="K_L2" variable_1="K_L2"/>
<map_variables variable_2="Ca_s" variable_1="Ca_s"/>
</connection>
<connection>
<map_components component_2="internal_store_calcium" component_1="internal_store_Ca_uptake"/>
<map_variables variable_2="K_P2" variable_1="K_P2"/>
<map_variables variable_2="v_s" variable_1="v_s"/>
</connection>
<connection>
<map_components component_2="cytosolic_calcium" component_1="internal_store_Ca_uptake"/>
<map_variables variable_2="K_P2" variable_1="K_P2"/>
<map_variables variable_2="Ca_i" variable_1="Ca_i"/>
</connection>
<connection>
<map_components component_2="internal_store_calcium" component_1="cytosolic_calcium"/>
<map_variables variable_2="Ca_i" variable_1="Ca_i"/>
<map_variables variable_2="Ca_i_ss" variable_1="Ca_i_ss"/>
<map_variables variable_2="v_s" variable_1="v_s"/>
<map_variables variable_2="Ca_s" variable_1="Ca_s"/>
</connection>
<rdf:RDF>
<rdf:Bag rdf:about="rdf:#38593c84-2b8a-4e76-9f16-2450acbdce46">
<rdf:li>calcium dynamics</rdf:li>
<rdf:li>sympathetic</rdf:li>
<rdf:li>electrophysiology</rdf:li>
<rdf:li>neuron</rdf:li>
</rdf:Bag>
<rdf:Description rdf:about="rdf:#a523d839-d741-4ac6-8d0d-a940a448694b">
<vCard:Given>Catherine</vCard:Given>
<vCard:Family>Lloyd</vCard:Family>
<vCard:Other>May</vCard:Other>
</rdf:Description>
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<bqs:Person rdf:resource="rdf:#0d6247e7-8a49-4371-a91d-0f1b62e4519b"/>
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<rdf:Description rdf:about="rdf:#783f94d7-a602-4efe-a009-70789daf65c9">
<dcterms:modified rdf:resource="rdf:#097b3f66-46c3-4f5d-8533-55b2f977180f"/>
<rdf:value>
Added publication date information.
</rdf:value>
<cmeta:modifier rdf:resource="rdf:#91828417-0569-4499-b066-fc8c6af1379b"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#370c9a52-4b33-4c61-a3d0-795baa44bf25">
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<rdf:value>
Added more metadata.
</rdf:value>
<cmeta:modifier rdf:resource="rdf:#f360b3e3-ad5a-4519-b3cf-c28fd8addb44"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#364d5d63-5b8f-4d5b-b27d-874df4234b04">
<dc:creator rdf:resource="rdf:#67948363-0da2-4b6d-9fcc-0d233741ddd2"/>
<dc:title>
[Ca2+]i oscillations in sympathetic neurons: an experimental test of a theoretical model
</dc:title>
<bqs:volume>68</bqs:volume>
<bqs:first_page>1752</bqs:first_page>
<bqs:Journal rdf:resource="rdf:#d0e39266-dde4-4a8a-81c5-66d11b4e003e"/>
<dcterms:issued rdf:resource="rdf:#1b72924c-01df-4725-b754-69fa4f3496d8"/>
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</rdf:Description>
<rdf:Description rdf:about="rdf:#209e8eea-1e47-4185-b87d-d3704e8d95f7">
<vCard:Given>David</vCard:Given>
<vCard:Family>Friel</vCard:Family>
<vCard:Other>D</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#59e4443d-4c3b-40eb-a8ab-b9029bd9ea90">
<dcterms:W3CDTF>2002-04-02</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="rdf:#1b72924c-01df-4725-b754-69fa4f3496d8">
<dcterms:W3CDTF>1995-05</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="rdf:#404066de-08f8-46f1-937e-9d554b7d5480">
<bqs:Pubmed_id>7612818</bqs:Pubmed_id>
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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:#097b3f66-46c3-4f5d-8533-55b2f977180f">
<dcterms:W3CDTF>2003-04-09</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="#friel_1995_version01">
<dc:title>
A Model Of Calcium Oscillations in Sympathetic Neurons
</dc:title>
<cmeta:bio_entity>Sympathetic Neuron</cmeta:bio_entity>
<cmeta:comment rdf:resource="rdf:#c0ab5e71-5262-443b-aba7-7db714a2affe"/>
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<rdf:Description rdf:about="rdf:#aac2b6ce-2e80-4cb5-b672-8a1c263e01e4">
<vCard:Given>Autumn</vCard:Given>
<vCard:Family>Cuellar</vCard:Family>
<vCard:Other>A</vCard:Other>
</rdf:Description>
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<dc:creator rdf:resource="rdf:#1442df3c-4a09-4214-9c05-42c0a1765b54"/>
<rdf:value>
This is the CellML description of David Friel's 1995 model of calcium
oscillations in sympathetic neurons.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#f360b3e3-ad5a-4519-b3cf-c28fd8addb44">
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