<?xml version="1.0"?>
<!-- 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#" cmeta:id="friel_1995" name="friel_1995">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>[Ca2+]i oscillations in sympathetic neurons: an experimental test of a theoretical model</title>
<author>
<firstname>Catherine</firstname>
<surname>Lloyd</surname>
<affiliation>
<shortaffil>Auckland Bioengineering Institute, The University of Auckland</shortaffil>
</affiliation>
</author>
</articleinfo>
<section id="sec_status">
<title>Model Status</title>
<para>
This CellML model runs in OpenCell and COR but unfortuntately does not recreate the published figures. Specifically the model has been parameterised with the values provided in the caption of figure 4. However the CellML model does not spontaneously oscillate. This may be due to there being incorrect initial concentrations of intracellular and sub-space calcium, which are not specified in the paper.
</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
ABSTRACT: [Ca2+]i oscillations have been described in a variety of cells. This study focuses on caffeine-induced [Ca2+]i oscillations in sympathetic neurons. Previous work has shown that these oscillations require Ca2+ entry from the extracellular medium and Ca(2+)-induced Ca2+ release from a caffeine- and ryanodine-sensitive store. The aim of the study was to understand the mechanism responsible for the oscillations. As a starting point, [Ca2+]i relaxations were examined after membrane depolarization and exposure to caffeine. For both stimuli, post-stimulus relaxations could be described by the sum of two decaying exponential functions, consistent with a one-pool system in which Ca2+ transport between compartments is regulated by linear Ca2+ pumps and leaks. After modifying the store to include a [Ca2+]i-sensitive leak, the model also exhibits oscillations such as those observed experimentally. The model was tested by comparing measured and predicted net Ca2+ fluxes during the oscillatory cycle. Three independent fluxes were measured, describing the rates of 1) Ca2+ entry across the plasma membrane, 2) Ca2+ release by the internal store, and 3) Ca2+ extrusion across the plasma membrane and uptake by the internal store. Starting with estimates of the model parameters deduced from post-stimulus relaxations and the rapid upstroke, a set of parameter values was found that provides a good description of [Ca2+]i throughout the oscillatory cycle. With the same parameter values, there was also good agreement between the measured and simulated net fluxes. Thus, a one-pool model with a single [Ca2+]i-sensitive Ca2+ permeability is adequate to account for many of the quantitative properties of steady-state [Ca2+]i oscillations in sympathetic neurons. Inactivation of the intracellular Ca2+ permeability, cooperative nonlinear Ca2+ uptake and extrusion mechanisms, and functional links between plasma membrane Ca2+ transport and the internal store are not required.
</para>
<para>
The original paper reference is cited below:
</para>
<para>
[Ca2+]i oscillations in sympathetic neurons: an experimental test of a theoretical model, David D. Friel, 1995, <emphasis>Biophysical Journal</emphasis>, 68, 1752-1766. <ulink url="http://www.ncbi.nlm.nih.gov/pubmed/7612818">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>
<units name="per_second">
<unit exponent="-1" units="second"/>
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<units name="nanomolar">
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<units name="picolitre_per_second">
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<units name="picolitre_nanomolar_per_second">
<unit units="picolitre"/>
<unit units="nanomolar"/>
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<component name="environment">
<variable name="time" public_interface="out" units="second"/>
</component>
<component name="rate_constants">
<variable name="kappa_L1" public_interface="out" units="per_second"/>
<variable initial_value="0.132" name="kappa_P1" public_interface="out" units="per_second"/>
<variable name="kappa_L2" public_interface="out" units="per_second"/>
<variable initial_value="3.78" name="kappa_P2" public_interface="out" units="per_second"/>
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<variable initial_value="3" name="n" units="dimensionless"/>
<variable name="time" public_interface="in" units="second"/>
<variable name="Ca_i" public_interface="in" units="nanomolar"/>
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<apply id="kappa_L2_calculation"><eq/><ci>kappa_L2</ci><apply><plus/><ci>kappa_L2_0</ci><apply><divide/><ci>kappa_L2_1</ci><apply><plus/><cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn><apply><power/><apply><divide/><ci>Kd_Ca</ci><ci>Ca_i</ci></apply><ci>n</ci></apply></apply></apply></apply></apply>
<apply id="Kd_Ca_calculation">
<eq/>
<ci> Kd_Ca </ci>
<piecewise>
<piece>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="micromolar"> 1.0 </cn>
<apply>
<and/>
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<ci> time </ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="second"> 0 </cn>
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<apply>
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<ci> time </ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="second"> 60 </cn>
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<otherwise>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="micromolar"> 0.5 </cn>
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</math>
</component>
<component name="cytosolic_calcium">
<variable initial_value="100.0" name="Ca_i" public_interface="out" units="nanomolar"/>
<variable initial_value="1000000.0" name="Ca_o" public_interface="out" units="nanomolar"/>
<variable name="Ca_i_ss" public_interface="out" units="nanomolar"/>
<variable initial_value="0.24" name="gamma" public_interface="out" units="dimensionless"/>
<variable name="kappa_L1" public_interface="in" units="per_second"/>
<variable name="kappa_P1" public_interface="in" units="per_second"/>
<variable name="kappa_L2" public_interface="in" units="per_second"/>
<variable name="kappa_P2" public_interface="in" units="per_second"/>
<variable name="Ca_s" public_interface="in" units="nanomolar"/>
<variable name="time" public_interface="in" units="second"/>
<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>kappa_L1</ci><ci>kappa_P1</ci><apply><times/><ci>gamma</ci><apply><plus/><ci>kappa_L2</ci><ci>kappa_P2</ci></apply></apply></apply></apply><ci>Ca_i</ci></apply><apply><times/><ci>gamma</ci><ci>kappa_L2</ci><ci>Ca_s</ci></apply><apply><times/><ci>kappa_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>
<plus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless"> 1.0 </cn>
<apply>
<divide/>
<ci> kappa_P1 </ci>
<ci> kappa_L1 </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="subspace_calcium">
<variable initial_value="10.0" name="Ca_s" public_interface="out" units="nanomolar"/>
<variable name="Ca_s_ss" public_interface="out" units="nanomolar"/>
<variable name="Ca_i" public_interface="in" units="nanomolar"/>
<variable name="Ca_i_ss" public_interface="in" units="nanomolar"/>
<variable name="kappa_L2" public_interface="in" units="per_second"/>
<variable name="kappa_P2" public_interface="in" units="per_second"/>
<variable name="time" public_interface="in" units="second"/>
<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> kappa_L2 </ci>
<ci> kappa_P2 </ci>
</apply>
<ci> Ca_i </ci>
</apply>
<apply>
<times/>
<ci> kappa_L2 </ci>
<ci> Ca_s </ci>
</apply>
</apply>
</apply>
<apply id="Ca_s_ss_calculation">
<eq/>
<ci> Ca_s_ss </ci>
<apply>
<times/>
<ci> Ca_i_ss </ci>
<apply>
<plus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless"> 1.0 </cn>
<apply>
<divide/>
<ci> kappa_P2 </ci>
<ci> kappa_L2 </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<connection>
<map_components component_1="rate_constants" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="cytosolic_calcium" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="subspace_calcium" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="cytosolic_calcium" component_2="rate_constants"/>
<map_variables variable_1="kappa_L1" variable_2="kappa_L1"/>
<map_variables variable_1="kappa_L2" variable_2="kappa_L2"/>
<map_variables variable_1="kappa_P1" variable_2="kappa_P1"/>
<map_variables variable_1="kappa_P2" variable_2="kappa_P2"/>
<map_variables variable_1="Ca_i" variable_2="Ca_i"/>
</connection>
<connection>
<map_components component_1="subspace_calcium" component_2="rate_constants"/>
<map_variables variable_1="kappa_L2" variable_2="kappa_L2"/>
<map_variables variable_1="kappa_P2" variable_2="kappa_P2"/>
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<connection>
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<map_variables variable_1="Ca_i" variable_2="Ca_i"/>
<map_variables variable_1="Ca_i_ss" variable_2="Ca_i_ss"/>
<map_variables variable_1="Ca_s" variable_2="Ca_s"/>
</connection>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"><rdf:Description rdf:about="rdf:#38593c84-2b8a-4e76-9f16-2450acbdce46"><rdf:_4 xml:lang="en">neuron</rdf:_4><rdf:_5 xml:lang="en">neurobiology</rdf:_5><rdf:type><rdf:Description rdf:about="http://www.w3.org/1999/02/22-rdf-syntax-ns#Bag"/></rdf:type><rdf:_3 xml:lang="en">electrophysiology</rdf:_3><rdf:_2 xml:lang="en">sympathetic</rdf:_2><rdf:_1 xml:lang="en">calcium dynamics</rdf:_1></rdf:Description><rdf:Description rdf:about="rdf:#404066de-08f8-46f1-937e-9d554b7d5480"><JournalArticle xmlns="http://www.cellml.org/bqs/1.0#"><rdf:Description rdf:about="rdf:#364d5d63-5b8f-4d5b-b27d-874df4234b04"/></JournalArticle><Pubmed_id xmlns="http://www.cellml.org/bqs/1.0#" xml:lang="en">7612818</Pubmed_id></rdf:Description><rdf:Description rdf:about="rdf:#1b72924c-01df-4725-b754-69fa4f3496d8"><W3CDTF xmlns="http://purl.org/dc/terms/" xml:lang="en">1995-05</W3CDTF></rdf:Description><rdf:Description rdf:about="rdf:#cf2f6d31-4136-41fb-9590-2d8ada1b579c"><Orgunit xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">Auckland Bioengineering Institute</Orgunit><Orgname xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">The University of Auckland</Orgname></rdf:Description><rdf:Description rdf:about="rdf:#209e8eea-1e47-4185-b87d-d3704e8d95f7"><Family xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">Friel</Family><Given xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">David</Given><Other xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">D</Other></rdf:Description><rdf:Description rdf:about="rdf:#1442df3c-4a09-4214-9c05-42c0a1765b54"><FN xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">Catherine Lloyd</FN></rdf:Description><rdf:Description rdf:about="rdf:#acac6a63-a306-4fe0-beb7-c549e7998a2d"><Family xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">Lloyd</Family><Given xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">Catherine</Given><Other xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">May</Other></rdf:Description><rdf:Description rdf:about="rdf:#783f94d7-a602-4efe-a009-70789daf65c9"><modified xmlns="http://purl.org/dc/terms/"><rdf:Description rdf:about="rdf:#097b3f66-46c3-4f5d-8533-55b2f977180f"/></modified><cmeta:modifier><rdf:Description rdf:about="rdf:#91828417-0569-4499-b066-fc8c6af1379b"/></cmeta:modifier><rdf:value xml:lang="en">
Added publication date information.
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This is the CellML description of David Friel's 1995 model of calcium
oscillations in sympathetic neurons.
</rdf:value><creator xmlns="http://purl.org/dc/elements/1.1/"><rdf:Description rdf:about="rdf:#1442df3c-4a09-4214-9c05-42c0a1765b54"/></creator></rdf:Description><rdf:Description rdf:about="#friel_1995"><simulation xmlns="http://www.cellml.org/metadata/simulation/1.0#"><rdf:Description rdf:nodeID="n1"/></simulation><cmeta:comment><rdf:Description rdf:about="rdf:#c0ab5e71-5262-443b-aba7-7db714a2affe"/></cmeta:comment><cmeta:bio_entity xml:lang="en">Sympathetic Neuron</cmeta:bio_entity><title xmlns="http://purl.org/dc/elements/1.1/" xml:lang="en">
A Model Of Calcium Oscillations in Sympathetic Neurons
</title><reference xmlns="http://www.cellml.org/bqs/1.0#"><rdf:Description rdf:about="rdf:#9d759697-4299-4616-b8fb-d7c18b622781"/></reference><reference xmlns="http://www.cellml.org/bqs/1.0#"><rdf:Description rdf:about="rdf:#404066de-08f8-46f1-937e-9d554b7d5480"/></reference></rdf:Description><rdf:Description rdf:about="rdf:#d0e39266-dde4-4a8a-81c5-66d11b4e003e"><title xmlns="http://purl.org/dc/elements/1.1/" xml:lang="en">Biophysical Journal</title></rdf:Description><rdf:Description rdf:about="rdf:#370c9a52-4b33-4c61-a3d0-795baa44bf25"><modified xmlns="http://purl.org/dc/terms/"><rdf:Description rdf:about="rdf:#330f494b-128e-4382-b84f-7063551353bb"/></modified><cmeta:modifier><rdf:Description rdf:about="rdf:#f360b3e3-ad5a-4519-b3cf-c28fd8addb44"/></cmeta:modifier><rdf:value xml:lang="en">
Added more metadata.
</rdf:value></rdf:Description><rdf:Description rdf:about="rdf:#364d5d63-5b8f-4d5b-b27d-874df4234b04"><issued xmlns="http://purl.org/dc/terms/"><rdf:Description rdf:about="rdf:#1b72924c-01df-4725-b754-69fa4f3496d8"/></issued><Journal xmlns="http://www.cellml.org/bqs/1.0#"><rdf:Description rdf:about="rdf:#d0e39266-dde4-4a8a-81c5-66d11b4e003e"/></Journal><title xmlns="http://purl.org/dc/elements/1.1/" xml:lang="en">
[Ca2+]i oscillations in sympathetic neurons: an experimental test of a theoretical model
</title><first_page xmlns="http://www.cellml.org/bqs/1.0#" xml:lang="en">1752</first_page><last_page xmlns="http://www.cellml.org/bqs/1.0#" xml:lang="en">1766</last_page><volume xmlns="http://www.cellml.org/bqs/1.0#" xml:lang="en">68</volume><creator xmlns="http://purl.org/dc/elements/1.1/"><rdf:Description rdf:about="rdf:#67948363-0da2-4b6d-9fcc-0d233741ddd2"/></creator></rdf:Description><rdf:Description rdf:about="rdf:#9d759697-4299-4616-b8fb-d7c18b622781"><subject xmlns="http://purl.org/dc/elements/1.1/"><rdf:Description rdf:about="rdf:#fdb08dac-74db-4f52-9895-16f933ba43e5"/></subject></rdf:Description><rdf:Description rdf:about="rdf:#aac2b6ce-2e80-4cb5-b672-8a1c263e01e4"><Family xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">Cuellar</Family><Given xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">Autumn</Given><Other xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">A</Other></rdf:Description><rdf:Description rdf:about=""><publisher xmlns="http://purl.org/dc/elements/1.1/" xml:lang="en">
The University of Auckland, Auckland Bioengineering Institute
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