- Author:
- Hanne <Hanne@hanne-nielsens-macbook.local>
- Date:
- 2009-12-11 16:28:18+13:00
- Desc:
- Addedi mages in ai and svg format
- Permanent Source URI:
- http://models.cellml.org/workspace/ostby_oyehaug_einevoll_nagelhus_plahte_zeuthen_voipio_lloyd_ottersen_omholt_2008/rawfile/fd7761840aba6f0f537c2c3fbd7de7136230ef47/ostby_oyehaug_einevoll_nagelhus_plahte_zeuthen_voipio_lloyd_ottersen_omholt_2008.cellml
<?xml version='1.0' encoding='utf-8'?>
<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#" xmlns:ns7="http://www.cellml.org/metadata/simulation/1.0#" name="ostby_model_2008" cmeta:id="ostby_model_2008">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>Astrocytic processes explaining neural activity-induced shrinkage of extraneuronal space</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 cellML model is known to run in PCEnv and COR to recreate the published results. The units have been checked and they are consistent. A PCEnv session is also available for this model.
</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
Neural activity triggers the release of neurotransmitters and ions from the neurons which, in turn, alters the ionic composition of the extracellular space (ECS) surrounding the neurons and astrocytes. Although the changes associated with ion flux have been well characterised - namely a 30 percent shrinkage of the ECS, and a corresponding swelling of the surrounding astrocytes - the mechanisms underlying these features have remained relatively elusive. However, a better understanding of astrocyte function and synaptic transmission provides a considerable incentive for researchers to further investigate this area.
</para>
<para>
In the study described here, Ivar Ostby <emphasis>et al.</emphasis> have produced a mathematical model to replicate the characteristics of the neuronal activity and the associated shrinkage of the ECS (this model is represented in the schematic diagram below). Ion transfer across the cell surface membrane occurs via the Na+/K+ ATPase pump as well as through ion channels (Na+, K+ and Cl-) and via the Na+/K+/Cl-/HCO3- cotransporters. Transmembrane water transport occurs though specialised channels called aquaporins (AQP4). The current model emphasises the importance of the Na+/K+/Cl- cotransporter, in particular, for achieving a realistic level of ECS shrinkage.
</para>
<informalfigure float="0" id="fig_reaction_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>model diagram</title>
</objectinfo>
<imagedata fileref="ostby_2008.png"/>
</imageobject>
</mediaobject>
<caption>Schematic diagram of the model. In the excited state there is an exchange of sodium and potassium ions across the neuron membrane and the cotransporters in the astrocyte are active.</caption>
</informalfigure>
</sect1>
</article>
</documentation>
<rdf:RDF>
<rdf:Description rdf:about="wi">
<dc:title>wi</dc:title>
<dcterms:alternative>ratio of astrocyte volume to astrocyte area</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<rdf:RDF>
<rdf:Description rdf:about="wo">
<dc:title>w_tot</dc:title>
<dcterms:alternative>ECS volume to area ratio</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<rdf:RDF>
<rdf:Description rdf:about="N_Nai">
<dc:title>N_Nai</dc:title>
<dcterms:alternative>number of sodium ions in the astrocyte</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<rdf:RDF>
<rdf:Description rdf:about="N_Ki">
<dc:title>N_Ki</dc:title>
<dcterms:alternative>number of potassium ions in the astrocyte</dcterms:alternative>
</rdf:Description>
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<rdf:RDF>
<rdf:Description rdf:about="N_HCO3i">
<dc:title>N_HCO3i</dc:title>
<dcterms:alternative>number of bicarbonate ions in the astrocyte</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
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<rdf:Description rdf:about="N_Cli">
<dc:title>N_Cli</dc:title>
<dcterms:alternative>number of chloride ions in the astrocyte</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
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<dc:title>N_Nao</dc:title>
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</rdf:Description>
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<rdf:RDF>
<rdf:Description rdf:about="N_Ko">
<dc:title>N_Ko</dc:title>
<dcterms:alternative>number of potassium ions in the extracellular space</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<rdf:RDF>
<rdf:Description rdf:about="N_HCO3o">
<dc:title>N_HCO3o</dc:title>
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</rdf:Description>
</rdf:RDF>
<rdf:RDF>
<rdf:Description rdf:about="N_Clo">
<dc:title>N_Clo</dc:title>
<dcterms:alternative>number of chloride ions in the extracellular space</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<rdf:RDF>
<rdf:Description rdf:about="J_NaKATPase">
<dc:title>J_NaKATPase</dc:title>
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</rdf:Description>
</rdf:RDF>
<rdf:RDF>
<rdf:Description rdf:about="I_K">
<dc:title>I_K</dc:title>
<dcterms:alternative>voltage-dependent potassium current</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<rdf:RDF>
<rdf:Description rdf:about="I_Cl">
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</rdf:Description>
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<unit units="coulomb"/>
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<component name="environment">
<variable units="second" public_interface="out" name="time" cmeta:id="environment_time"/>
</component>
<component name="wi">
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<variable units="cm_per_millimolar_second" public_interface="in" name="Lp"/>
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<variable units="millimolar" public_interface="in" name="Ko"/>
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<variable units="micrometre" public_interface="in" name="wi"/>
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<variable units="per_ohm_cm2" public_interface="in" name="gNa"/>
<variable units="volt" public_interface="in" name="ENa"/>
<variable units="volt" public_interface="in" name="Vm"/>
<variable units="mole_per_cm2_second" public_interface="in" name="J_NaKATPase"/>
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<ci>time</ci>
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<ci>N_Nai</ci>
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<ci>dN_Nai_dt</ci>
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<times/>
<cn cellml:units="cm2_millimolar_micrometre_per_mol">1e10</cn>
<apply>
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<times/>
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<divide/>
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<minus/>
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<times/>
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<ci>J_NaKATPase</ci>
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<cn cellml:units="cm2_millimolar_micrometre_per_mol">1e10</cn>
<cn cellml:units="dimensionless">2</cn>
<ci>J_NaKATPase</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="N_HCO3o">
<variable units="millimolar_micrometre" public_interface="out" name="N_HCO3o" initial_value="0.432552"/>
<variable units="dimensionless" public_interface="in" name="theta_NBC"/>
<variable units="millimolar_micrometre_per_second" public_interface="in" name="J_NBC"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>N_HCO3o</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>theta_NBC</ci>
<ci>J_NBC</ci>
</apply>
</apply>
</math>
</component>
<component name="N_Clo">
<variable units="millimolar_micrometre" public_interface="out" name="N_Clo"/>
<variable units="millimolar_micrometre" public_interface="in" name="N_Ko"/>
<variable units="millimolar_micrometre" public_interface="in" name="N_Nao"/>
<variable units="millimolar_micrometre" public_interface="in" name="N_HCO3o"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>N_Clo</ci>
<apply>
<minus/>
<apply>
<plus/>
<ci>N_Nao</ci>
<ci>N_Ko</ci>
</apply>
<ci>N_HCO3o</ci>
</apply>
</apply>
</math>
</component>
<component name="Nernst_potentials">
<variable units="volt" public_interface="out" name="ENa"/>
<variable units="volt" public_interface="out" name="EK"/>
<variable units="volt" public_interface="out" name="ECl"/>
<variable units="kelvin" public_interface="in" name="T"/>
<variable units="J_per_mol_K" public_interface="in" name="R"/>
<variable units="C_per_mol" public_interface="in" name="F"/>
<variable units="millimolar" public_interface="in" name="Nao"/>
<variable units="millimolar" public_interface="in" name="Ko"/>
<variable units="millimolar" public_interface="in" name="Clo"/>
<variable units="millimolar" public_interface="in" name="Nai"/>
<variable units="millimolar" public_interface="in" name="Ki"/>
<variable units="millimolar" public_interface="in" name="Cli"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>ENa</ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">1</cn>
<ci>F</ci>
</apply>
</apply>
<apply>
<ln/>
<apply>
<divide/>
<ci>Nao</ci>
<ci>Nai</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>EK</ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">1</cn>
<ci>F</ci>
</apply>
</apply>
<apply>
<ln/>
<apply>
<divide/>
<ci>Ko</ci>
<ci>Ki</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>ECl</ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
</apply>
<ci>F</ci>
</apply>
</apply>
<apply>
<ln/>
<apply>
<divide/>
<ci>Clo</ci>
<ci>Cli</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="J_KCC1">
<variable units="millimolar_micrometre_per_second" public_interface="out" name="J_KCC1"/>
<variable units="per_ohm_cm2" name="gKCC1" initial_value="1e-6"/>
<variable units="dimensionless" name="ft"/>
<variable units="kelvin" public_interface="in" name="T"/>
<variable units="J_per_mol_K" public_interface="in" name="R"/>
<variable units="C_per_mol" public_interface="in" name="F"/>
<variable units="millimolar" public_interface="in" name="Ko"/>
<variable units="millimolar" public_interface="in" name="Ki"/>
<variable units="millimolar" public_interface="in" name="Clo"/>
<variable units="millimolar" public_interface="in" name="Cli"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>J_KCC1</ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="cm2_millimolar_micrometre_per_mol">1e10</cn>
<ci>gKCC1</ci>
<ci>ft</ci>
</apply>
<ci>F</ci>
</apply>
<ci>R</ci>
<ci>T</ci>
</apply>
<ci>F</ci>
</apply>
<apply>
<ln/>
<apply>
<divide/>
<apply>
<times/>
<ci>Ko</ci>
<ci>Clo</ci>
</apply>
<apply>
<times/>
<ci>Ki</ci>
<ci>Cli</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>ft</ci>
<piecewise>
<piece>
<cn cellml:units="dimensionless">1</cn>
<apply>
<and/>
<apply>
<geq/>
<ci>time</ci>
<cn cellml:units="second">10</cn>
</apply>
<apply>
<lt/>
<ci>time</ci>
<cn cellml:units="second">20</cn>
</apply>
</apply>
</piece>
<otherwise>
<cn cellml:units="dimensionless">0</cn>
</otherwise>
</piecewise>
</apply>
</math>
</component>
<component name="J_NBC">
<variable units="millimolar_micrometre_per_second" public_interface="out" name="J_NBC"/>
<variable units="per_ohm_cm2" public_interface="out" name="gNBC" initial_value="9.03e-5"/>
<variable units="volt" public_interface="in" name="Vm"/>
<variable units="volt" public_interface="in" name="ENBC"/>
<variable units="C_per_mol" public_interface="in" name="F"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>J_NBC</ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="cm2_millimolar_micrometre_per_mol">1e10</cn>
<ci>gNBC</ci>
</apply>
<ci>F</ci>
</apply>
<apply>
<minus/>
<ci>Vm</ci>
<ci>ENBC</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="J_NKCC1">
<variable units="millimolar_micrometre_per_second" public_interface="out" name="J_NKCC1"/>
<variable units="per_ohm_cm2" name="gNKCC1" initial_value="5.54e-6"/>
<variable units="dimensionless" name="ft"/>
<variable units="kelvin" public_interface="in" name="T"/>
<variable units="J_per_mol_K" public_interface="in" name="R"/>
<variable units="C_per_mol" public_interface="in" name="F"/>
<variable units="millimolar" public_interface="in" name="Ko"/>
<variable units="millimolar" public_interface="in" name="Nai"/>
<variable units="millimolar" public_interface="in" name="Nao"/>
<variable units="millimolar" public_interface="in" name="Ki"/>
<variable units="millimolar" public_interface="in" name="Clo"/>
<variable units="millimolar" public_interface="in" name="Cli"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>J_NKCC1</ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="cm2_millimolar_micrometre_per_mol">1e10</cn>
<ci>gNKCC1</ci>
<ci>ft</ci>
</apply>
<ci>F</ci>
</apply>
<ci>R</ci>
<ci>T</ci>
</apply>
<ci>F</ci>
</apply>
<apply>
<ln/>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<divide/>
<ci>Nao</ci>
<ci>Nai</ci>
</apply>
<ci>Ko</ci>
</apply>
<ci>Ki</ci>
</apply>
<apply>
<power/>
<apply>
<divide/>
<ci>Clo</ci>
<ci>Cli</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>ft</ci>
<piecewise>
<piece>
<cn cellml:units="dimensionless">1</cn>
<apply>
<and/>
<apply>
<geq/>
<ci>time</ci>
<cn cellml:units="second">10</cn>
</apply>
<apply>
<lt/>
<ci>time</ci>
<cn cellml:units="second">20</cn>
</apply>
</apply>
</piece>
<otherwise>
<cn cellml:units="dimensionless">0</cn>
</otherwise>
</piecewise>
</apply>
</math>
</component>
<component name="ENBC">
<variable units="volt" public_interface="out" name="ENBC"/>
<variable units="dimensionless" name="zNBC" initial_value="-1"/>
<variable units="kelvin" public_interface="in" name="T"/>
<variable units="J_per_mol_K" public_interface="in" name="R"/>
<variable units="C_per_mol" public_interface="in" name="F"/>
<variable units="millimolar" public_interface="in" name="HCO3o"/>
<variable units="millimolar" public_interface="in" name="Nai"/>
<variable units="millimolar" public_interface="in" name="Nao"/>
<variable units="millimolar" public_interface="in" name="HCO3i"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>ENBC</ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
<apply>
<times/>
<ci>zNBC</ci>
<ci>F</ci>
</apply>
</apply>
<apply>
<ln/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<divide/>
<ci>Nao</ci>
<ci>Nai</ci>
</apply>
<apply>
<power/>
<ci>HCO3o</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<power/>
<ci>HCO3i</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="membrane">
<variable units="volt" public_interface="out" name="Vm"/>
<variable units="C_per_mol" public_interface="in" name="F"/>
<variable units="mole_per_cm2_second" public_interface="in" name="J_NaKATPase"/>
<variable units="volt" public_interface="in" name="ENa"/>
<variable units="volt" public_interface="in" name="EK"/>
<variable units="volt" public_interface="in" name="ECl"/>
<variable units="volt" public_interface="in" name="ENBC"/>
<variable units="per_ohm_cm2" public_interface="in" name="gNa"/>
<variable units="per_ohm_cm2" public_interface="in" name="gK"/>
<variable units="per_ohm_cm2" public_interface="in" name="gCl"/>
<variable units="per_ohm_cm2" public_interface="in" name="gNBC"/>
<variable units="dimensionless" public_interface="in" name="theta_NBC"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>Vm</ci>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<ci>gNa</ci>
<ci>ENa</ci>
</apply>
<apply>
<times/>
<ci>gK</ci>
<ci>EK</ci>
</apply>
<apply>
<times/>
<ci>gCl</ci>
<ci>ECl</ci>
</apply>
<apply>
<times/>
<ci>theta_NBC</ci>
<ci>gNBC</ci>
<ci>ENBC</ci>
</apply>
</apply>
<apply>
<times/>
<ci>J_NaKATPase</ci>
<ci>F</ci>
</apply>
</apply>
<apply>
<plus/>
<ci>gNa</ci>
<ci>gK</ci>
<ci>gCl</ci>
<apply>
<times/>
<ci>theta_NBC</ci>
<ci>gNBC</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="J_NaKATPase">
<variable units="mole_per_cm2_second" public_interface="out" name="J_NaKATPase"/>
<variable units="mole_per_cm2_second" name="Pmax" initial_value="1.4207e-10"/>
<variable units="millimolar" name="K_Nai" initial_value="10"/>
<variable units="millimolar" name="K_Ko" initial_value="1.5"/>
<variable units="millimolar" public_interface="in" name="Nai"/>
<variable units="millimolar" public_interface="in" name="Ko"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>J_NaKATPase</ci>
<apply>
<divide/>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci>Pmax</ci>
<apply>
<power/>
<ci>Nai</ci>
<cn cellml:units="dimensionless">1.5</cn>
</apply>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci>Nai</ci>
<cn cellml:units="dimensionless">1.5</cn>
</apply>
<apply>
<power/>
<ci>K_Nai</ci>
<cn cellml:units="dimensionless">1.5</cn>
</apply>
</apply>
</apply>
<ci>Ko</ci>
</apply>
<apply>
<plus/>
<ci>Ko</ci>
<ci>K_Ko</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="I_K">
<variable units="millimolar_micrometre_per_second" public_interface="out" name="I_K"/>
<variable units="per_ohm_cm2" public_interface="in" name="gK"/>
<variable units="volt" public_interface="in" name="EK"/>
<variable units="volt" public_interface="in" name="Vm"/>
<variable units="C_per_mol" public_interface="in" name="F"/>
<variable units="per_mole" public_interface="in" name="nA"/>
<variable units="C" public_interface="in" name="elementary_charge"/>
<variable units="mole_per_cm2_second" public_interface="in" name="J_NaKATPase"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>I_K</ci>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="cm2_millimolar_micrometre_per_mol">1e10</cn>
<cn cellml:units="dimensionless">2</cn>
<ci>J_NaKATPase</ci>
<ci>F</ci>
</apply>
<apply>
<times/>
<ci>elementary_charge</ci>
<ci>nA</ci>
</apply>
</apply>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="cm2_millimolar_micrometre_per_mol">1e10</cn>
<ci>gK</ci>
</apply>
<apply>
<times/>
<ci>elementary_charge</ci>
<ci>nA</ci>
</apply>
</apply>
<apply>
<minus/>
<ci>Vm</ci>
<ci>EK</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="I_Cl">
<variable units="millimolar_micrometre_per_second" public_interface="out" name="I_Cl"/>
<variable units="per_ohm_cm2" public_interface="in" name="gCl"/>
<variable units="volt" public_interface="in" name="ECl"/>
<variable units="volt" public_interface="in" name="Vm"/>
<variable units="per_mole" public_interface="in" name="nA"/>
<variable units="C" public_interface="in" name="elementary_charge"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>I_Cl</ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="cm2_millimolar_micrometre_per_mol">1e10</cn>
<ci>gCl</ci>
</apply>
<apply>
<times/>
<ci>elementary_charge</ci>
<ci>nA</ci>
</apply>
</apply>
<apply>
<minus/>
<ci>Vm</ci>
<ci>ECl</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="I_Na">
<variable units="millimolar_micrometre_per_second" public_interface="out" name="I_Na"/>
<variable units="per_ohm_cm2" public_interface="in" name="gNa"/>
<variable units="volt" public_interface="in" name="ENa"/>
<variable units="volt" public_interface="in" name="Vm"/>
<variable units="C_per_mol" public_interface="in" name="F"/>
<variable units="per_mole" public_interface="in" name="nA"/>
<variable units="C" public_interface="in" name="elementary_charge"/>
<variable units="mole_per_cm2_second" public_interface="in" name="J_NaKATPase"/>
<variable units="millimolar_micrometre_per_second" public_interface="in" name="J_NBC"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>I_Na</ci>
<apply>
<minus/>
<ci>J_NBC</ci>
<apply>
<plus/>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="cm2_millimolar_micrometre_per_mol">1e10</cn>
<ci>gNa</ci>
</apply>
<apply>
<times/>
<ci>elementary_charge</ci>
<ci>nA</ci>
</apply>
</apply>
<apply>
<minus/>
<ci>Vm</ci>
<ci>ENa</ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="cm2_millimolar_micrometre_per_mol">1e10</cn>
<cn cellml:units="dimensionless">3</cn>
<ci>J_NaKATPase</ci>
<ci>F</ci>
</apply>
<apply>
<times/>
<ci>elementary_charge</ci>
<ci>nA</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="model_parameters">
<variable units="millimolar" public_interface="out" name="Nai"/>
<variable units="millimolar" public_interface="out" name="Ki"/>
<variable units="millimolar" public_interface="out" name="Cli"/>
<variable units="millimolar" public_interface="out" name="HCO3i"/>
<variable units="millimolar" public_interface="out" name="Nao"/>
<variable units="millimolar" public_interface="out" name="Ko"/>
<variable units="millimolar" public_interface="out" name="Clo"/>
<variable units="millimolar" public_interface="out" name="HCO3o"/>
<variable units="J_per_mol_K" public_interface="out" name="R" initial_value="8.315"/>
<variable units="C_per_mol" public_interface="out" name="F" initial_value="9.649e4"/>
<variable units="kelvin" public_interface="out" name="T" initial_value="300"/>
<variable units="per_ohm_cm2" public_interface="out" name="gNa" initial_value="1.314e-4"/>
<variable units="per_ohm_cm2" public_interface="out" name="gK" initial_value="0.004"/>
<variable units="per_ohm_cm2" public_interface="out" name="gCl" initial_value="8.797e-5"/>
<variable units="C" public_interface="out" name="elementary_charge" initial_value="1.6e-19"/>
<variable units="per_mole" public_interface="out" name="nA" initial_value="6.0221415e23"/>
<variable units="millimolar_micrometre" public_interface="out" name="Xi" initial_value="12.41"/>
<variable units="micrometre_millimolar_per_second" public_interface="out" name="kc" initial_value="7.35e-2"/>
<variable units="dimensionless" public_interface="out" name="theta_NBC" initial_value="1"/>
<variable units="dimensionless" public_interface="out" name="theta_NKCC1" initial_value="1"/>
<variable units="dimensionless" public_interface="out" name="theta_KCC1" initial_value="1"/>
<variable units="cm_per_millimolar_second" public_interface="out" name="Lp" initial_value="2.1e-4"/>
<variable units="dimensionless" public_interface="out" name="y"/>
<variable units="second" public_interface="in" name="time"/>
<variable units="millimolar_micrometre" public_interface="in" name="N_Ki"/>
<variable units="millimolar_micrometre" public_interface="in" name="N_Ko"/>
<variable units="millimolar_micrometre" public_interface="in" name="N_Nai"/>
<variable units="millimolar_micrometre" public_interface="in" name="N_Nao"/>
<variable units="millimolar_micrometre" public_interface="in" name="N_Cli"/>
<variable units="millimolar_micrometre" public_interface="in" name="N_Clo"/>
<variable units="millimolar_micrometre" public_interface="in" name="N_HCO3i"/>
<variable units="millimolar_micrometre" public_interface="in" name="N_HCO3o"/>
<variable units="micrometre" public_interface="in" name="wi"/>
<variable units="micrometre" public_interface="in" name="wo"/>
<variable units="second" name="t0" initial_value="10"/>
<variable units="second" name="t1" initial_value="20"/>
<variable units="second" name="t2" initial_value="30"/>
<variable units="dimensionless" name="alpha" initial_value="2"/>
<variable units="dimensionless" name="beta" initial_value="14"/>
<variable units="second" name="deltaT"/>
<variable units="dimensionless" name="gamma_alpha_beta"/>
<variable units="dimensionless" name="gamma_alpha"/>
<variable units="dimensionless" name="gamma_beta"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>y</ci>
<piecewise>
<piece>
<apply>
<times/>
<apply>
<divide/>
<ci>gamma_alpha_beta</ci>
<apply>
<times/>
<ci>gamma_alpha</ci>
<ci>gamma_beta</ci>
</apply>
</apply>
<apply>
<power/>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<apply>
<minus/>
<ci>time</ci>
<ci>t0</ci>
</apply>
<ci>deltaT</ci>
</apply>
</apply>
<apply>
<minus/>
<ci>beta</ci>
<cn cellml:units="dimensionless">1</cn>
</apply>
</apply>
<apply>
<power/>
<apply>
<divide/>
<apply>
<minus/>
<ci>time</ci>
<ci>t0</ci>
</apply>
<ci>deltaT</ci>
</apply>
<apply>
<minus/>
<ci>alpha</ci>
<cn cellml:units="dimensionless">1</cn>
</apply>
</apply>
</apply>
<apply>
<and/>
<apply>
<geq/>
<ci>time</ci>
<ci>t0</ci>
</apply>
<apply>
<leq/>
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