- Author:
- Hanne <Hanne@hanne-nielsens-macbook.local>
- Date:
- 2010-04-09 10:10:57+12:00
- Desc:
- Added svg diagram to session file, I_Na and I_K work but don't highlight
- Permanent Source URI:
- http://models.cellml.org/workspace/ostby_oyehaug_einevoll_nagelhus_plahte_zeuthen_voipio_lloyd_ottersen_omholt_2008/rawfile/4373dafe39dac33919b11a61a2180f92a4a943a9/ostby_oyehaug_einevoll_nagelhus_plahte_zeuthen_voipio_lloyd_ottersen_omholt_2008.cellml
<?xml version="1.0"?>
<model xmlns="http://www.cellml.org/cellml/1.0#" xmlns:cmeta="http://www.cellml.org/metadata/1.0#" xml:base="" cmeta:id="ostby_model_2008" name="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 xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="wi">
<dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">wi</dc:title>
<dcterms:alternative xmlns:dcterms="http://purl.org/dc/terms/">ratio of astrocyte volume to astrocyte area</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="wo">
<dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">w_tot</dc:title>
<dcterms:alternative xmlns:dcterms="http://purl.org/dc/terms/">ECS volume to area ratio</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="N_Nai">
<dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">N_Nai</dc:title>
<dcterms:alternative xmlns:dcterms="http://purl.org/dc/terms/">number of sodium ions in the astrocyte</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="N_Ki">
<dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">N_Ki</dc:title>
<dcterms:alternative xmlns:dcterms="http://purl.org/dc/terms/">number of potassium ions in the astrocyte</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="N_HCO3i">
<dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">N_HCO3i</dc:title>
<dcterms:alternative xmlns:dcterms="http://purl.org/dc/terms/">number of bicarbonate ions in the astrocyte</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="N_Cli">
<dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">N_Cli</dc:title>
<dcterms:alternative xmlns:dcterms="http://purl.org/dc/terms/">number of chloride ions in the astrocyte</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="N_Nao">
<dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">N_Nao</dc:title>
<dcterms:alternative xmlns:dcterms="http://purl.org/dc/terms/">number of sodium ions in the extracellular space</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="N_Ko">
<dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">N_Ko</dc:title>
<dcterms:alternative xmlns:dcterms="http://purl.org/dc/terms/">number of potassium ions in the extracellular space</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="N_HCO3o">
<dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">N_HCO3o</dc:title>
<dcterms:alternative xmlns:dcterms="http://purl.org/dc/terms/">number of bicarbonate ions in the extracellular space</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="N_Clo">
<dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">N_Clo</dc:title>
<dcterms:alternative xmlns:dcterms="http://purl.org/dc/terms/">number of chloride ions in the extracellular space</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="J_NaKATPase">
<dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">J_NaKATPase</dc:title>
<dcterms:alternative xmlns:dcterms="http://purl.org/dc/terms/">sodium-potassium ATPase pump</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="I_K">
<dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">I_K</dc:title>
<dcterms:alternative xmlns:dcterms="http://purl.org/dc/terms/">voltage-dependent potassium current</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="I_Cl">
<dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">I_Cl</dc:title>
<dcterms:alternative xmlns:dcterms="http://purl.org/dc/terms/">voltage-dependent chloride current</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="I_Na">
<dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">I_Na</dc:title>
<dcterms:alternative xmlns:dcterms="http://purl.org/dc/terms/">voltage-dependent sodium current</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<units name="millisecond">
<unit prefix="milli" units="second"/>
</units>
<units name="picoampere">
<unit prefix="pico" units="ampere"/>
</units>
<units name="millimole">
<unit prefix="milli" units="mole"/>
</units>
<units name="millimole_per_cm2">
<unit units="millimole"/>
<unit exponent="-2" prefix="centi" units="metre"/>
</units>
<units name="millimolar">
<unit prefix="milli" units="mole"/>
<unit exponent="-1" units="litre"/>
</units>
<units name="millimolar_micrometre">
<unit units="millimolar"/>
<unit prefix="micro" units="metre"/>
</units>
<units name="millimolar_micrometre_per_second">
<unit units="millimolar"/>
<unit prefix="micro" units="metre"/>
<unit exponent="-1" units="second"/>
</units>
<units name="per_millimolar">
<unit exponent="-1" units="millimolar"/>
</units>
<units name="mole_per_cm2_second">
<unit units="mole"/>
<unit exponent="-2" prefix="centi" units="metre"/>
<unit exponent="-1" units="second"/>
</units>
<units name="millimole_per_cm2_second">
<unit prefix="milli" units="mole"/>
<unit exponent="-2" prefix="centi" units="metre"/>
<unit exponent="-1" units="second"/>
</units>
<units name="micrometre_per_millimolar_second">
<unit prefix="micro" units="metre"/>
<unit exponent="-1" units="millimolar"/>
<unit exponent="-1" units="second"/>
</units>
<units name="micrometre_millimolar_per_second">
<unit prefix="micro" units="metre"/>
<unit units="millimolar"/>
<unit exponent="-1" units="second"/>
</units>
<units name="micrometre_per_centimetre">
<unit prefix="micro" units="metre"/>
<unit exponent="-1" prefix="centi" units="metre"/>
</units>
<units name="cm_per_millimolar_second">
<unit prefix="centi" units="metre"/>
<unit exponent="-1" units="millimolar"/>
<unit exponent="-1" units="second"/>
</units>
<units name="cm2_millimolar_micrometre_per_mol">
<unit exponent="2" prefix="centi" units="metre"/>
<unit units="millimolar"/>
<unit prefix="micro" units="metre"/>
<unit exponent="-1" units="mole"/>
</units>
<units name="millimole_per_cm2_millisecond">
<unit prefix="milli" units="mole"/>
<unit exponent="-2" prefix="centi" units="metre"/>
<unit exponent="-1" prefix="milli" units="second"/>
</units>
<units name="first_order_rate_constant">
<unit exponent="-1" units="millisecond"/>
</units>
<units name="per_ohm_cm2">
<unit exponent="-1" units="ohm"/>
<unit exponent="-2" prefix="centi" units="metre"/>
</units>
<units name="micrometre">
<unit prefix="micro" units="metre"/>
</units>
<units name="micrometre_per_millimolar">
<unit prefix="micro" units="metre"/>
<unit exponent="-1" units="millimolar"/>
</units>
<units name="cm2">
<unit exponent="2" prefix="centi" units="metre"/>
</units>
<units name="cm3">
<unit exponent="3" prefix="centi" units="metre"/>
</units>
<units name="J_per_mol_K">
<unit units="joule"/>
<unit exponent="-1" units="mole"/>
<unit exponent="-1" units="kelvin"/>
</units>
<units name="C">
<unit units="coulomb"/>
</units>
<units name="per_mole">
<unit exponent="-1" units="mole"/>
</units>
<units name="C_per_mol">
<unit units="coulomb"/>
<unit exponent="-1" units="mole"/>
</units>
<units name="C_per_cm2">
<unit units="coulomb"/>
<unit exponent="-2" prefix="centi" units="metre"/>
</units>
<units name="C_per_cm2_s">
<unit units="coulomb"/>
<unit exponent="-2" prefix="centi" units="metre"/>
<unit exponent="-1" units="second"/>
</units>
<component name="environment">
<variable cmeta:id="environment_time" name="time" public_interface="out" units="second"/>
</component>
<component name="wi">
<variable initial_value="0.061" name="wi" public_interface="out" units="micrometre"/>
<variable name="Lp" public_interface="in" units="cm_per_millimolar_second"/>
<variable name="Xi" public_interface="in" units="millimolar_micrometre"/>
<variable name="Nao" public_interface="in" units="millimolar"/>
<variable name="Ko" public_interface="in" units="millimolar"/>
<variable name="Clo" public_interface="in" units="millimolar"/>
<variable name="HCO3o" public_interface="in" units="millimolar"/>
<variable name="Nai" public_interface="in" units="millimolar"/>
<variable name="Ki" public_interface="in" units="millimolar"/>
<variable name="Cli" public_interface="in" units="millimolar"/>
<variable name="HCO3i" public_interface="in" units="millimolar"/>
<variable name="time" public_interface="in" units="second"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>wi</ci>
</apply>
<apply>
<times/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="micrometre_per_centimetre">1</cn>
<ci>Lp</ci>
<apply>
<minus/>
<apply>
<plus/>
<ci>Nai</ci>
<ci>Ki</ci>
<ci>Cli</ci>
<ci>HCO3i</ci>
<apply>
<divide/>
<ci>Xi</ci>
<ci>wi</ci>
</apply>
</apply>
<apply>
<plus/>
<ci>Nao</ci>
<ci>Ko</ci>
<ci>Clo</ci>
<ci>HCO3o</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="wo">
<variable name="wo" public_interface="out" units="micrometre"/>
<variable initial_value="0.0879" name="w_tot" units="micrometre"/>
<variable name="wi" public_interface="in" units="micrometre"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>wo</ci>
<apply>
<minus/>
<ci>w_tot</ci>
<ci>wi</ci>
</apply>
</apply>
</math>
</component>
<component name="N_Nai">
<variable initial_value="0.99796" name="N_Nai" public_interface="out" units="millimolar_micrometre"/>
<variable name="dN_Nai_dt" public_interface="out" units="millimolar_micrometre_per_second"/>
<variable name="gNa" public_interface="in" units="per_ohm_cm2"/>
<variable name="ENa" public_interface="in" units="volt"/>
<variable name="Vm" public_interface="in" units="volt"/>
<variable name="J_NaKATPase" public_interface="in" units="mole_per_cm2_second"/>
<variable name="F" public_interface="in" units="C_per_mol"/>
<variable name="theta_NKCC1" public_interface="in" units="dimensionless"/>
<variable name="J_NKCC1" public_interface="in" units="millimolar_micrometre_per_second"/>
<variable name="theta_NBC" public_interface="in" units="dimensionless"/>
<variable name="J_NBC" public_interface="in" units="millimolar_micrometre_per_second"/>
<variable name="time" public_interface="in" units="second"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>N_Nai</ci>
</apply>
<ci>dN_Nai_dt</ci>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>dN_Nai_dt</ci>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<ci>theta_NKCC1</ci>
<ci>J_NKCC1</ci>
</apply>
<apply>
<times/>
<ci>theta_NBC</ci>
<ci>J_NBC</ci>
</apply>
</apply>
<apply>
<times/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="cm2_millimolar_micrometre_per_mol">1e10</cn>
<apply>
<plus/>
<apply>
<times/>
<apply>
<divide/>
<ci>gNa</ci>
<ci>F</ci>
</apply>
<apply>
<minus/>
<ci>Vm</ci>
<ci>ENa</ci>
</apply>
</apply>
<apply>
<times/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">3</cn>
<ci>J_NaKATPase</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="N_Ki">
<variable initial_value="5.52782" name="N_Ki" public_interface="out" units="millimolar_micrometre"/>
<variable name="dN_Ki_dt" public_interface="out" units="millimolar_micrometre_per_second"/>
<variable name="gK" public_interface="in" units="per_ohm_cm2"/>
<variable name="EK" public_interface="in" units="volt"/>
<variable name="Vm" public_interface="in" units="volt"/>
<variable name="J_NaKATPase" public_interface="in" units="mole_per_cm2_second"/>
<variable name="F" public_interface="in" units="C_per_mol"/>
<variable name="theta_NKCC1" public_interface="in" units="dimensionless"/>
<variable name="J_NKCC1" public_interface="in" units="millimolar_micrometre_per_second"/>
<variable name="theta_KCC1" public_interface="in" units="dimensionless"/>
<variable name="J_KCC1" public_interface="in" units="millimolar_micrometre_per_second"/>
<variable name="time" public_interface="in" units="second"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>N_Ki</ci>
</apply>
<ci>dN_Ki_dt</ci>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>dN_Ki_dt</ci>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<ci>theta_NKCC1</ci>
<ci>J_NKCC1</ci>
</apply>
<apply>
<times/>
<ci>theta_KCC1</ci>
<ci>J_KCC1</ci>
</apply>
<apply>
<times/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="cm2_millimolar_micrometre_per_mol">1e10</cn>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
<ci>J_NaKATPase</ci>
</apply>
</apply>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="cm2_millimolar_micrometre_per_mol">1e10</cn>
<ci>gK</ci>
</apply>
<ci>F</ci>
</apply>
<apply>
<minus/>
<ci>Vm</ci>
<ci>EK</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="N_HCO3i">
<variable initial_value="0.58804" name="N_HCO3i" public_interface="out" units="millimolar_micrometre"/>
<variable name="dN_HCO3i_dt" public_interface="out" units="millimolar_micrometre_per_second"/>
<variable name="theta_NBC" public_interface="in" units="dimensionless"/>
<variable name="J_NBC" public_interface="in" units="millimolar_micrometre_per_second"/>
<variable name="time" public_interface="in" units="second"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>N_HCO3i</ci>
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<ci>dN_HCO3i_dt</ci>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>dN_HCO3i_dt</ci>
<apply>
<times/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
<ci>theta_NBC</ci>
<ci>J_NBC</ci>
</apply>
</apply>
</math>
</component>
<component name="N_Cli">
<variable initial_value="0.32879" name="N_Cli" public_interface="out" units="millimolar_micrometre"/>
<variable name="dN_Ki_dt" public_interface="in" units="millimolar_micrometre_per_second"/>
<variable name="dN_Nai_dt" public_interface="in" units="millimolar_micrometre_per_second"/>
<variable name="dN_HCO3i_dt" public_interface="in" units="millimolar_micrometre_per_second"/>
<variable name="time" public_interface="in" units="second"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>N_Cli</ci>
</apply>
<apply>
<plus/>
<ci>dN_Ki_dt</ci>
<ci>dN_Nai_dt</ci>
<ci>dN_HCO3i_dt</ci>
</apply>
</apply>
</math>
</component>
<component name="N_Nao">
<variable cmeta:id="N_Nao_N_Nao" initial_value="4.301041" name="N_Nao" public_interface="out" units="millimolar_micrometre"/>
<variable name="y" public_interface="in" units="dimensionless"/>
<variable name="kc" public_interface="in" units="micrometre_millimolar_per_second"/>
<variable name="gNa" public_interface="in" units="per_ohm_cm2"/>
<variable name="ENa" public_interface="in" units="volt"/>
<variable name="Vm" public_interface="in" units="volt"/>
<variable name="J_NaKATPase" public_interface="in" units="mole_per_cm2_second"/>
<variable name="F" public_interface="in" units="C_per_mol"/>
<variable name="theta_NKCC1" public_interface="in" units="dimensionless"/>
<variable name="J_NKCC1" public_interface="in" units="millimolar_micrometre_per_second"/>
<variable name="theta_NBC" public_interface="in" units="dimensionless"/>
<variable name="J_NBC" public_interface="in" units="millimolar_micrometre_per_second"/>
<variable name="time" public_interface="in" units="second"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>N_Nao</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="cm2_millimolar_micrometre_per_mol">1e10</cn>
<apply>
<plus/>
<apply>
<times/>
<apply>
<divide/>
<ci>gNa</ci>
<ci>F</ci>
</apply>
<apply>
<minus/>
<ci>Vm</ci>
<ci>ENa</ci>
</apply>
</apply>
<apply>
<times/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">3</cn>
<ci>J_NaKATPase</ci>
</apply>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci>theta_NKCC1</ci>
<ci>J_NKCC1</ci>
</apply>
<apply>
<times/>
<ci>theta_NBC</ci>
<ci>J_NBC</ci>
</apply>
<apply>
<times/>
<ci>kc</ci>
<ci>y</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="N_Ko">
<variable cmeta:id="N_Ko_N_Ko" initial_value="0.0807" name="N_Ko" public_interface="out" units="millimolar_micrometre"/>
<variable name="y" public_interface="in" units="dimensionless"/>
<variable name="kc" public_interface="in" units="micrometre_millimolar_per_second"/>
<variable name="gK" public_interface="in" units="per_ohm_cm2"/>
<variable name="EK" public_interface="in" units="volt"/>
<variable name="Vm" public_interface="in" units="volt"/>
<variable name="J_NaKATPase" public_interface="in" units="mole_per_cm2_second"/>
<variable name="F" public_interface="in" units="C_per_mol"/>
<variable name="theta_NKCC1" public_interface="in" units="dimensionless"/>
<variable name="J_NKCC1" public_interface="in" units="millimolar_micrometre_per_second"/>
<variable name="theta_KCC1" public_interface="in" units="dimensionless"/>
<variable name="J_KCC1" public_interface="in" units="millimolar_micrometre_per_second"/>
<variable name="time" public_interface="in" units="second"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>N_Ko</ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="cm2_millimolar_micrometre_per_mol">1e10</cn>
<ci>gK</ci>
</apply>
<ci>F</ci>
</apply>
<apply>
<minus/>
<ci>Vm</ci>
<ci>EK</ci>
</apply>
</apply>
<apply>
<times/>
<ci>kc</ci>
<ci>y</ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci>theta_NKCC1</ci>
<ci>J_NKCC1</ci>
</apply>
<apply>
<times/>
<ci>theta_KCC1</ci>
<ci>J_KCC1</ci>
</apply>
<apply>
<times/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="cm2_millimolar_micrometre_per_mol">1e10</cn>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
<ci>J_NaKATPase</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="N_HCO3o">
<variable initial_value="0.432552" name="N_HCO3o" public_interface="out" units="millimolar_micrometre"/>
<variable name="theta_NBC" public_interface="in" units="dimensionless"/>
<variable name="J_NBC" public_interface="in" units="millimolar_micrometre_per_second"/>
<variable name="time" public_interface="in" units="second"/>
<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 xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
</apply>
<ci>theta_NBC</ci>
<ci>J_NBC</ci>
</apply>
</apply>
</math>
</component>
<component name="N_Clo">
<variable name="N_Clo" public_interface="out" units="millimolar_micrometre"/>
<variable name="N_Ko" public_interface="in" units="millimolar_micrometre"/>
<variable name="N_Nao" public_interface="in" units="millimolar_micrometre"/>
<variable name="N_HCO3o" public_interface="in" units="millimolar_micrometre"/>
<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 name="ENa" public_interface="out" units="volt"/>
<variable name="EK" public_interface="out" units="volt"/>
<variable name="ECl" public_interface="out" units="volt"/>
<variable name="T" public_interface="in" units="kelvin"/>
<variable name="R" public_interface="in" units="J_per_mol_K"/>
<variable name="F" public_interface="in" units="C_per_mol"/>
<variable name="Nao" public_interface="in" units="millimolar"/>
<variable name="Ko" public_interface="in" units="millimolar"/>
<variable name="Clo" public_interface="in" units="millimolar"/>
<variable name="Nai" public_interface="in" units="millimolar"/>
<variable name="Ki" public_interface="in" units="millimolar"/>
<variable name="Cli" public_interface="in" units="millimolar"/>
<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 xmlns:cellml="http://www.cellml.org/cellml/1.0#" 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 xmlns:cellml="http://www.cellml.org/cellml/1.0#" 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 xmlns:cellml="http://www.cellml.org/cellml/1.0#" 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 cmeta:id="J_KCC1_J_KCC1" name="J_KCC1" public_interface="out" units="millimolar_micrometre_per_second"/>
<variable initial_value="1e-6" name="gKCC1" units="per_ohm_cm2"/>
<variable name="ft" units="dimensionless"/>
<variable name="T" public_interface="in" units="kelvin"/>
<variable name="R" public_interface="in" units="J_per_mol_K"/>
<variable name="F" public_interface="in" units="C_per_mol"/>
<variable name="Ko" public_interface="in" units="millimolar"/>
<variable name="Ki" public_interface="in" units="millimolar"/>
<variable name="Clo" public_interface="in" units="millimolar"/>
<variable name="Cli" public_interface="in" units="millimolar"/>
<variable name="time" public_interface="in" units="second"/>
<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 xmlns:cellml="http://www.cellml.org/cellml/1.0#" 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 xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<apply>
<and/>
<apply>
<geq/>
<ci>time</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="second">10</cn>
</apply>
<apply>
<lt/>
<ci>time</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="second">20</cn>
</apply>
</apply>
</piece>
<otherwise>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0</cn>
</otherwise>
</piecewise>
</apply>
</math>
</component>
<component name="J_NBC">
<variable cmeta:id="J_NBC_J_NBC" name="J_NBC" public_interface="out" units="millimolar_micrometre_per_second"/>
<variable initial_value="9.03e-5" name="gNBC" public_interface="out" units="per_ohm_cm2"/>
<variable name="Vm" public_interface="in" units="volt"/>
<variable name="ENBC" public_interface="in" units="volt"/>
<variable name="F" public_interface="in" units="C_per_mol"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>J_NBC</ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" 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 cmeta:id="J_NKCC1_J_NKCC1" name="J_NKCC1" public_interface="out" units="millimolar_micrometre_per_second"/>
<variable initial_value="5.54e-6" name="gNKCC1" units="per_ohm_cm2"/>
<variable name="ft" units="dimensionless"/>
<variable name="T" public_interface="in" units="kelvin"/>
<variable name="R" public_interface="in" units="J_per_mol_K"/>
<variable name="F" public_interface="in" units="C_per_mol"/>
<variable name="Ko" public_interface="in" units="millimolar"/>
<variable name="Nai" public_interface="in" units="millimolar"/>
<variable name="Nao" public_interface="in" units="millimolar"/>
<variable name="Ki" public_interface="in" units="millimolar"/>
<variable name="Clo" public_interface="in" units="millimolar"/>
<variable name="Cli" public_interface="in" units="millimolar"/>
<variable name="time" public_interface="in" units="second"/>
<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 xmlns:cellml="http://www.cellml.org/cellml/1.0#" 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 xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>ft</ci>
<piecewise>
<piece>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<apply>
<and/>
<apply>
<geq/>
<ci>time</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="second">10</cn>
</apply>
<apply>
<lt/>
<ci>time</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="second">20</cn>
</apply>
</apply>
</piece>
<otherwise>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0</cn>
</otherwise>
</piecewise>
</apply>
</math>
</component>
<component name="ENBC">
<variable name="ENBC" public_interface="out" units="volt"/>
<variable initial_value="-1" name="zNBC" units="dimensionless"/>
<variable name="T" public_interface="in" units="kelvin"/>
<variable name="R" public_interface="in" units="J_per_mol_K"/>
<variable name="F" public_interface="in" units="C_per_mol"/>
<variable name="HCO3o" public_interface="in" units="millimolar"/>
<variable name="Nai" public_interface="in" units="millimolar"/>
<variable name="Nao" public_interface="in" units="millimolar"/>
<variable name="HCO3i" public_interface="in" units="millimolar"/>
<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 xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<power/>
<ci>HCO3i</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="membrane">
<variable cmeta:id="membrane_Vm" name="Vm" public_interface="out" units="volt"/>
<variable name="F" public_interface="in" units="C_per_mol"/>
<variable name="J_NaKATPase" public_interface="in" units="mole_per_cm2_second"/>
<variable name="ENa" public_interface="in" units="volt"/>
<variable name="EK" public_interface="in" units="volt"/>
<variable name="ECl" public_interface="in" units="volt"/>
<variable name="ENBC" public_interface="in" units="volt"/>
<variable name="gNa" public_interface="in" units="per_ohm_cm2"/>
<variable name="gK" public_interface="in" units="per_ohm_cm2"/>
<variable name="gCl" public_interface="in" units="per_ohm_cm2"/>
<variable name="gNBC" public_interface="in" units="per_ohm_cm2"/>
<variable name="theta_NBC" public_interface="in" units="dimensionless"/>
<variable name="time" public_interface="in" units="second"/>
<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 cmeta:id="J_NaKATPase_J_NaKATPase" name="J_NaKATPase" public_interface="out" units="mole_per_cm2_second"/>
<variable initial_value="1.4207e-10" name="Pmax" units="mole_per_cm2_second"/>
<variable initial_value="10" name="K_Nai" units="millimolar"/>
<variable initial_value="1.5" name="K_Ko" units="millimolar"/>
<variable name="Nai" public_interface="in" units="millimolar"/>
<variable name="Ko" public_interface="in" units="millimolar"/>
<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 xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1.5</cn>
</apply>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci>Nai</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1.5</cn>
</apply>
<apply>
<power/>
<ci>K_Nai</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" 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 cmeta:id="I_K_I_K" name="I_K" public_interface="out" units="millimolar_micrometre_per_second"/>
<variable name="gK" public_interface="in" units="per_ohm_cm2"/>
<variable name="EK" public_interface="in" units="volt"/>
<variable name="Vm" public_interface="in" units="volt"/>
<variable name="F" public_interface="in" units="C_per_mol"/>
<variable name="nA" public_interface="in" units="per_mole"/>
<variable name="elementary_charge" public_interface="in" units="C"/>
<variable name="J_NaKATPase" public_interface="in" units="mole_per_cm2_second"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>I_K</ci>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<times/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="cm2_millimolar_micrometre_per_mol">1e10</cn>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" 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 xmlns:cellml="http://www.cellml.org/cellml/1.0#" 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 cmeta:id="I_Cl_I_Cl" name="I_Cl" public_interface="out" units="millimolar_micrometre_per_second"/>
<variable name="gCl" public_interface="in" units="per_ohm_cm2"/>
<variable name="ECl" public_interface="in" units="volt"/>
<variable name="Vm" public_interface="in" units="volt"/>
<variable name="nA" public_interface="in" units="per_mole"/>
<variable name="elementary_charge" public_interface="in" units="C"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>I_Cl</ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" 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 cmeta:id="I_Na_I_Na" name="I_Na" public_interface="out" units="millimolar_micrometre_per_second"/>
<variable name="gNa" public_interface="in" units="per_ohm_cm2"/>
<variable name="ENa" public_interface="in" units="volt"/>
<variable name="Vm" public_interface="in" units="volt"/>
<variable name="F" public_interface="in" units="C_per_mol"/>
<variable name="nA" public_interface="in" units="per_mole"/>
<variable name="elementary_charge" public_interface="in" units="C"/>
<variable name="J_NaKATPase" public_interface="in" units="mole_per_cm2_second"/>
<variable name="J_NBC" public_interface="in" units="millimolar_micrometre_per_second"/>
<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 xmlns:cellml="http://www.cellml.org/cellml/1.0#" 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 xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="cm2_millimolar_micrometre_per_mol">1e10</cn>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" 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 name="Nai" public_interface="out" units="millimolar"/>
<variable name="Ki" public_interface="out" units="millimolar"/>
<variable name="Cli" public_interface="out" units="millimolar"/>
<variable name="HCO3i" public_interface="out" units="millimolar"/>
<variable name="Nao" public_interface="out" units="millimolar"/>
<variable name="Ko" public_interface="out" units="millimolar"/>
<variable name="Clo" public_interface="out" units="millimolar"/>
<variable name="HCO3o" public_interface="out" units="millimolar"/>
<variable initial_value="8.315" name="R" public_interface="out" units="J_per_mol_K"/>
<variable initial_value="9.649e4" name="F" public_interface="out" units="C_per_mol"/>
<variable initial_value="300" name="T" public_interface="out" units="kelvin"/>
<variable initial_value="1.314e-4" name="gNa" public_interface="out" units="per_ohm_cm2"/>
<variable initial_value="0.004" name="gK" public_interface="out" units="per_ohm_cm2"/>
<variable initial_value="8.797e-5" name="gCl" public_interface="out" units="per_ohm_cm2"/>
<variable initial_value="1.6e-19" name="elementary_charge" public_interface="out" units="C"/>
<variable initial_value="6.0221415e23" name="nA" public_interface="out" units="per_mole"/>
<variable initial_value="12.41" name="Xi" public_interface="out" units="millimolar_micrometre"/>
<variable initial_value="7.35e-2" name="kc" public_interface="out" units="micrometre_millimolar_per_second"/>
<variable initial_value="1" name="theta_NBC" public_interface="out" units="dimensionless"/>
<variable initial_value="1" name="theta_NKCC1" public_interface="out" units="dimensionless"/>
<variable initial_value="1" name="theta_KCC1" public_interface="out" units="dimensionless"/>
<variable initial_value="2.1e-4" name="Lp" public_interface="out" units="cm_per_millimolar_second"/>
<variable name="y" public_interface="out" units="dimensionless"/>
<variable name="time" public_interface="in" units="second"/>
<variable name="N_Ki" public_interface="in" units="millimolar_micrometre"/>
<variable name="N_Ko" public_interface="in" units="millimolar_micrometre"/>
<variable name="N_Nai" public_interface="in" units="millimolar_micrometre"/>
<variable name="N_Nao" public_interface="in" units="millimolar_micrometre"/>
<variable name="N_Cli" public_interface="in" units="millimolar_micrometre"/>
<variable name="N_Clo" public_interface="in" units="millimolar_micrometre"/>
<variable name="N_HCO3i" public_interface="in" units="millimolar_micrometre"/>
<variable name="N_HCO3o" public_interface="in" units="millimolar_micrometre"/>
<variable name="wi" public_interface="in" units="micrometre"/>
<variable name="wo" public_interface="in" units="micrometre"/>
<variable initial_value="10" name="t0" units="second"/>
<variable initial_value="20" name="t1" units="second"/>
<variable initial_value="30" name="t2" units="second"/>
<variable initial_value="2" name="alpha" units="dimensionless"/>
<variable initial_value="14" name="beta" units="dimensionless"/>
<variable name="deltaT" units="second"/>
<variable name="gamma_alpha_beta" units="dimensionless"/>
<variable name="gamma_alpha" units="dimensionless"/>
<variable name="gamma_beta" units="dimensionless"/>
<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 xmlns:cellml="http://www.cellml.org/cellml/1.0#" 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 xmlns:cellml="http://www.cellml.org/cellml/1.0#" 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 xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
</apply>
</apply>
</apply>
<apply>
<and/>
<apply>
<geq/>
<ci>time</ci>
<ci>t0</ci>
</apply>
<apply>
<leq/>
<ci>time</ci>
<ci>t1</ci>
</apply>
</apply>
</piece>
<piece>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">-1</cn>
<apply>
<and/>
<apply>
<gt/>
<ci>time</ci>
<ci>t1</ci>
</apply>
<apply>
<lt/>
<ci>time</ci>
<ci>t2</ci>
</apply>
</apply>
</piece>
<otherwise>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0</cn>
</otherwise>
</piecewise>
</apply>
<apply>
<eq/>
<ci>deltaT</ci>
<apply>
<minus/>
<ci>t1</ci>
<ci>t0</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>gamma_alpha_beta</ci>
<apply>
<factorial/>
<apply>
<minus/>
<apply>
<plus/>
<ci>alpha</ci>
<ci>beta</ci>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>gamma_alpha</ci>
<apply>
<factorial/>
<apply>
<minus/>
<ci>alpha</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>gamma_beta</ci>
<apply>
<factorial/>
<apply>
<minus/>
<ci>beta</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Ki</ci>
<piecewise>
<piece>
<apply>
<divide/>
<ci>N_Ki</ci>
<ci>wi</ci>
</apply>
<apply>
<gt/>
<apply>
<divide/>
<ci>N_Ki</ci>
<ci>wi</ci>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millimolar">0</cn>
</apply>
</piece>
<otherwise>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millimolar">1e-180</cn>
</otherwise>
</piecewise>
</apply>
<apply>
<eq/>
<ci>Ko</ci>
<piecewise>
<piece>
<apply>
<divide/>
<ci>N_Ko</ci>
<ci>wo</ci>
</apply>
<apply>
<gt/>
<apply>
<divide/>
<ci>N_Ko</ci>
<ci>wo</ci>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millimolar">0</cn>
</apply>
</piece>
<otherwise>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millimolar">1e-180</cn>
</otherwise>
</piecewise>
</apply>
<apply>
<eq/>
<ci>Nai</ci>
<piecewise>
<piece>
<apply>
<divide/>
<ci>N_Nai</ci>
<ci>wi</ci>
</apply>
<apply>
<gt/>
<apply>
<divide/>
<ci>N_Nai</ci>
<ci>wi</ci>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millimolar">0</cn>
</apply>
</piece>
<otherwise>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millimolar">1e-180</cn>
</otherwise>
</piecewise>
</apply>
<apply>
<eq/>
<ci>Nao</ci>
<piecewise>
<piece>
<apply>
<divide/>
<ci>N_Nao</ci>
<ci>wo</ci>
</apply>
<apply>
<gt/>
<apply>
<divide/>
<ci>N_Nao</ci>
<ci>wo</ci>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millimolar">0</cn>
</apply>
</piece>
<otherwise>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millimolar">1e-180</cn>
</otherwise>
</piecewise>
</apply>
<apply>
<eq/>
<ci>Cli</ci>
<piecewise>
<piece>
<apply>
<divide/>
<ci>N_Cli</ci>
<ci>wi</ci>
</apply>
<apply>
<gt/>
<apply>
<divide/>
<ci>N_Cli</ci>
<ci>wi</ci>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millimolar">0</cn>
</apply>
</piece>
<otherwise>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millimolar">1e-180</cn>
</otherwise>
</piecewise>
</apply>
<apply>
<eq/>
<ci>Clo</ci>
<piecewise>
<piece>
<apply>
<divide/>
<ci>N_Clo</ci>
<ci>wo</ci>
</apply>
<apply>
<gt/>
<apply>
<divide/>
<ci>N_Clo</ci>
<ci>wo</ci>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millimolar">0</cn>
</apply>
</piece>
<otherwise>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millimolar">1e-180</cn>
</otherwise>
</piecewise>
</apply>
<apply>
<eq/>
<ci>HCO3i</ci>
<piecewise>
<piece>
<apply>
<divide/>
<ci>N_HCO3i</ci>
<ci>wi</ci>
</apply>
<apply>
<gt/>
<apply>
<divide/>
<ci>N_HCO3i</ci>
<ci>wi</ci>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millimolar">0</cn>
</apply>
</piece>
<otherwise>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millimolar">1e-180</cn>
</otherwise>
</piecewise>
</apply>
<apply>
<eq/>
<ci>HCO3o</ci>
<piecewise>
<piece>
<apply>
<divide/>
<ci>N_HCO3o</ci>
<ci>wo</ci>
</apply>
<apply>
<gt/>
<apply>
<divide/>
<ci>N_HCO3o</ci>
<ci>wo</ci>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millimolar">0</cn>
</apply>
</piece>
<otherwise>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millimolar">1e-180</cn>
</otherwise>
</piecewise>
</apply>
</math>
</component>
<connection>
<map_components component_1="membrane" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="wi" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="N_Nai" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="N_Ki" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="N_HCO3i" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="N_Cli" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="N_Nao" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="N_Ko" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="N_HCO3o" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="model_parameters" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="J_KCC1" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="J_NKCC1" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="wi" component_2="model_parameters"/>
<map_variables variable_1="Nai" variable_2="Nai"/>
<map_variables variable_1="Nao" variable_2="Nao"/>
<map_variables variable_1="Ki" variable_2="Ki"/>
<map_variables variable_1="Ko" variable_2="Ko"/>
<map_variables variable_1="Cli" variable_2="Cli"/>
<map_variables variable_1="Clo" variable_2="Clo"/>
<map_variables variable_1="HCO3i" variable_2="HCO3i"/>
<map_variables variable_1="HCO3o" variable_2="HCO3o"/>
<map_variables variable_1="Xi" variable_2="Xi"/>
<map_variables variable_1="wi" variable_2="wi"/>
<map_variables variable_1="Lp" variable_2="Lp"/>
</connection>
<connection>
<map_components component_1="wi" component_2="wo"/>
<map_variables variable_1="wi" variable_2="wi"/>
</connection>
<connection>
<map_components component_1="wo" component_2="model_parameters"/>
<map_variables variable_1="wo" variable_2="wo"/>
</connection>
<connection>
<map_components component_1="N_Nai" component_2="Nernst_potentials"/>
<map_variables variable_1="ENa" variable_2="ENa"/>
</connection>
<connection>
<map_components component_1="N_Nai" component_2="J_NaKATPase"/>
<map_variables variable_1="J_NaKATPase" variable_2="J_NaKATPase"/>
</connection>
<connection>
<map_components component_1="N_Nai" component_2="model_parameters"/>
<map_variables variable_1="N_Nai" variable_2="N_Nai"/>
<map_variables variable_1="F" variable_2="F"/>
<map_variables variable_1="gNa" variable_2="gNa"/>
<map_variables variable_1="theta_NKCC1" variable_2="theta_NKCC1"/>
<map_variables variable_1="theta_NBC" variable_2="theta_NBC"/>
</connection>
<connection>
<map_components component_1="N_Nai" component_2="membrane"/>
<map_variables variable_1="Vm" variable_2="Vm"/>
</connection>
<connection>
<map_components component_1="N_Nai" component_2="J_NKCC1"/>
<map_variables variable_1="J_NKCC1" variable_2="J_NKCC1"/>
</connection>
<connection>
<map_components component_1="N_Nai" component_2="J_NBC"/>
<map_variables variable_1="J_NBC" variable_2="J_NBC"/>
</connection>
<connection>
<map_components component_1="N_Nao" component_2="Nernst_potentials"/>
<map_variables variable_1="ENa" variable_2="ENa"/>
</connection>
<connection>
<map_components component_1="N_Nao" component_2="J_NaKATPase"/>
<map_variables variable_1="J_NaKATPase" variable_2="J_NaKATPase"/>
</connection>
<connection>
<map_components component_1="N_Nao" component_2="model_parameters"/>
<map_variables variable_1="N_Nao" variable_2="N_Nao"/>
<map_variables variable_1="kc" variable_2="kc"/>
<map_variables variable_1="y" variable_2="y"/>
<map_variables variable_1="F" variable_2="F"/>
<map_variables variable_1="gNa" variable_2="gNa"/>
<map_variables variable_1="theta_NKCC1" variable_2="theta_NKCC1"/>
<map_variables variable_1="theta_NBC" variable_2="theta_NBC"/>
</connection>
<connection>
<map_components component_1="N_Nao" component_2="membrane"/>
<map_variables variable_1="Vm" variable_2="Vm"/>
</connection>
<connection>
<map_components component_1="N_Nao" component_2="J_NKCC1"/>
<map_variables variable_1="J_NKCC1" variable_2="J_NKCC1"/>
</connection>
<connection>
<map_components component_1="N_Nao" component_2="J_NBC"/>
<map_variables variable_1="J_NBC" variable_2="J_NBC"/>
</connection>
<connection>
<map_components component_1="N_Ki" component_2="Nernst_potentials"/>
<map_variables variable_1="EK" variable_2="EK"/>
</connection>
<connection>
<map_components component_1="N_Ki" component_2="J_NaKATPase"/>
<map_variables variable_1="J_NaKATPase" variable_2="J_NaKATPase"/>
</connection>
<connection>
<map_components component_1="N_Ki" component_2="model_parameters"/>
<map_variables variable_1="N_Ki" variable_2="N_Ki"/>
<map_variables variable_1="F" variable_2="F"/>
<map_variables variable_1="gK" variable_2="gK"/>
<map_variables variable_1="theta_NKCC1" variable_2="theta_NKCC1"/>
<map_variables variable_1="theta_KCC1" variable_2="theta_KCC1"/>
</connection>
<connection>
<map_components component_1="N_Ki" component_2="membrane"/>
<map_variables variable_1="Vm" variable_2="Vm"/>
</connection>
<connection>
<map_components component_1="N_Ki" component_2="J_NKCC1"/>
<map_variables variable_1="J_NKCC1" variable_2="J_NKCC1"/>
</connection>
<connection>
<map_components component_1="N_Ki" component_2="J_KCC1"/>
<map_variables variable_1="J_KCC1" variable_2="J_KCC1"/>
</connection>
<connection>
<map_components component_1="N_Ko" component_2="Nernst_potentials"/>
<map_variables variable_1="EK" variable_2="EK"/>
</connection>
<connection>
<map_components component_1="N_Ko" component_2="J_NaKATPase"/>
<map_variables variable_1="J_NaKATPase" variable_2="J_NaKATPase"/>
</connection>
<connection>
<map_components component_1="N_Ko" component_2="model_parameters"/>
<map_variables variable_1="N_Ko" variable_2="N_Ko"/>
<map_variables variable_1="kc" variable_2="kc"/>
<map_variables variable_1="y" variable_2="y"/>
<map_variables variable_1="F" variable_2="F"/>
<map_variables variable_1="gK" variable_2="gK"/>
<map_variables variable_1="theta_NKCC1" variable_2="theta_NKCC1"/>
<map_variables variable_1="theta_KCC1" variable_2="theta_KCC1"/>
</connection>
<connection>
<map_components component_1="N_Ko" component_2="membrane"/>
<map_variables variable_1="Vm" variable_2="Vm"/>
</connection>
<connection>
<map_components component_1="N_Ko" component_2="J_NKCC1"/>
<map_variables variable_1="J_NKCC1" variable_2="J_NKCC1"/>
</connection>
<connection>
<map_components component_1="N_Ko" component_2="J_KCC1"/>
<map_variables variable_1="J_KCC1" variable_2="J_KCC1"/>
</connection>
<connection>
<map_components component_1="N_HCO3i" component_2="J_NBC"/>
<map_variables variable_1="J_NBC" variable_2="J_NBC"/>
</connection>
<connection>
<map_components component_1="N_HCO3i" component_2="model_parameters"/>
<map_variables variable_1="N_HCO3i" variable_2="N_HCO3i"/>
<map_variables variable_1="theta_NBC" variable_2="theta_NBC"/>
</connection>
<connection>
<map_components component_1="N_HCO3o" component_2="J_NBC"/>
<map_variables variable_1="J_NBC" variable_2="J_NBC"/>
</connection>
<connection>
<map_components component_1="N_HCO3o" component_2="model_parameters"/>
<map_variables variable_1="N_HCO3o" variable_2="N_HCO3o"/>
<map_variables variable_1="theta_NBC" variable_2="theta_NBC"/>
</connection>
<connection>
<map_components component_1="N_Cli" component_2="N_Nai"/>
<map_variables variable_1="dN_Nai_dt" variable_2="dN_Nai_dt"/>
</connection>
<connection>
<map_components component_1="N_Cli" component_2="N_Ki"/>
<map_variables variable_1="dN_Ki_dt" variable_2="dN_Ki_dt"/>
</connection>
<connection>
<map_components component_1="N_Cli" component_2="N_HCO3i"/>
<map_variables variable_1="dN_HCO3i_dt" variable_2="dN_HCO3i_dt"/>
</connection>
<connection>
<map_components component_1="N_Cli" component_2="model_parameters"/>
<map_variables variable_1="N_Cli" variable_2="N_Cli"/>
</connection>
<connection>
<map_components component_1="N_Clo" component_2="model_parameters"/>
<map_variables variable_1="N_Clo" variable_2="N_Clo"/>
</connection>
<connection>
<map_components component_1="N_Clo" component_2="N_Nao"/>
<map_variables variable_1="N_Nao" variable_2="N_Nao"/>
</connection>
<connection>
<map_components component_1="N_Clo" component_2="N_Ko"/>
<map_variables variable_1="N_Ko" variable_2="N_Ko"/>
</connection>
<connection>
<map_components component_1="N_Clo" component_2="N_HCO3o"/>
<map_variables variable_1="N_HCO3o" variable_2="N_HCO3o"/>
</connection>
<connection>
<map_components component_1="Nernst_potentials" component_2="model_parameters"/>
<map_variables variable_1="R" variable_2="R"/>
<map_variables variable_1="F" variable_2="F"/>
<map_variables variable_1="T" variable_2="T"/>
<map_variables variable_1="Nai" variable_2="Nai"/>
<map_variables variable_1="Nao" variable_2="Nao"/>
<map_variables variable_1="Ki" variable_2="Ki"/>
<map_variables variable_1="Ko" variable_2="Ko"/>
<map_variables variable_1="Cli" variable_2="Cli"/>
<map_variables variable_1="Clo" variable_2="Clo"/>
</connection>
<connection>
<map_components component_1="J_KCC1" component_2="model_parameters"/>
<map_variables variable_1="R" variable_2="R"/>
<map_variables variable_1="F" variable_2="F"/>
<map_variables variable_1="T" variable_2="T"/>
<map_variables variable_1="Ki" variable_2="Ki"/>
<map_variables variable_1="Ko" variable_2="Ko"/>
<map_variables variable_1="Cli" variable_2="Cli"/>
<map_variables variable_1="Clo" variable_2="Clo"/>
</connection>
<connection>
<map_components component_1="J_NBC" component_2="ENBC"/>
<map_variables variable_1="ENBC" variable_2="ENBC"/>
</connection>
<connection>
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