- Author:
- Anand Rampadarath <a.rampadarath@auckland.ac.nz>
- Date:
- 2018-11-14 14:40:18+13:00
- Desc:
- Merge branch 'Semgen_Annotation'
- Permanent Source URI:
- https://models.physiomeproject.org/workspace/547/rawfile/2ba5f9a429b532f05bcd8dda98f15363d9c2d0d1/ostby_oyehaug_einevoll_nagelhus_plahte_zeuthen_voipio_lloyd_ottersen_omholt_2008.cellml
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<title>Astrocytic processes explaining neural activity-induced shrinkage of extraneuronal space</title>
<author>
<firstname>Catherine</firstname>
<surname>Lloyd</surname>
<affiliation>
<shortaffil>Auckland Bioengineering Institute, The University of Auckland</shortaffil>
</affiliation>
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<section id="sec_status">
<title>Model Status</title>
<para>This cellML model is known to run in OpenCell and COR to recreate the published results. The units have been checked and they are consistent.</para>
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<sect1 id="sec_structure">
<title>Model Structure</title>
<para>ABSTRACT: Neuronal stimulation causes approximately 30% shrinkage of the extracellular space (ECS) between neurons and surrounding astrocytes in grey and white matter under experimental conditions. Despite its possible implications for a proper understanding of basic aspects of potassium clearance and astrocyte function, the phenomenon remains unexplained. Here we present a dynamic model that accounts for current experimental data related to the shrinkage phenomenon in wild-type as well as in gene knockout individuals. We find that neuronal release of potassium and uptake of sodium during stimulation, astrocyte uptake of potassium, sodium, and chloride in passive channels, action of the Na/K/ATPase pump, and osmotically driven transport of water through the astrocyte membrane together seem sufficient for generating ECS shrinkage as such. However, when taking into account ECS and astrocyte ion concentrations observed in connection with neuronal stimulation, the actions of the Na(+)/K(+)/Cl(-) (NKCC1) and the Na(+)/HCO(3) (-) (NBC) cotransporters appear to be critical determinants for achieving observed quantitative levels of ECS shrinkage. Considering the current state of knowledge, the model framework appears sufficiently detailed and constrained to guide future key experiments and pave the way for more comprehensive astroglia-neuron interaction models for normal as well as pathophysiological situations.</para>
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<title>model diagram</title>
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<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>
<para>The original paper reference is cited below:</para>
<para>
Astrocytic mechanisms explaining neural-activity-induced shrinkage of extraneuronal space, Ostby I, Oyehaug L, Einevoll GT, Nagelhus EA, Plahte E, Zeuthen T, Lloyd CM, Ottersen OP, and Omholt SW, 2009, PLoS Computational Biology, 5, 1, e1000272.
<ulink url="http://www.ncbi.nlm.nih.gov/pubmed/19165313">PubMed ID: 19165313</ulink>
</para>
</sect1>
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<apply>
<minus />
<apply>
<plus />
<apply>
<times />
<apply>
<divide />
<apply>
<times />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" type="e-notation" cellml:units="cm2_millimolar_micrometre_per_mol">
1
<sep />
10
</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#" type="e-notation" cellml:units="cm2_millimolar_micrometre_per_mol">
1
<sep />
10
</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 cmeta:id="N_HCO3o.N_HCO3o" initial_value="0.432552" name="N_HCO3o" public_interface="out" units="millimolar_micrometre" />
<variable cmeta:id="N_HCO3o.theta_NBC" name="theta_NBC" public_interface="in" units="dimensionless" />
<variable cmeta:id="N_HCO3o.J_NBC" name="J_NBC" public_interface="in" units="millimolar_micrometre_per_second" />
<variable cmeta:id="N_HCO3o.time" 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 cmeta:id="N_Clo.N_Clo" name="N_Clo" public_interface="out" units="millimolar_micrometre" />
<variable cmeta:id="N_Clo.N_Ko" name="N_Ko" public_interface="in" units="millimolar_micrometre" />
<variable cmeta:id="N_Clo.N_Nao" name="N_Nao" public_interface="in" units="millimolar_micrometre" />
<variable cmeta:id="N_Clo.N_HCO3o" 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 cmeta:id="Nernst_potentials.ENa" name="ENa" public_interface="out" units="volt" />
<variable cmeta:id="Nernst_potentials.EK" name="EK" public_interface="out" units="volt" />
<variable cmeta:id="Nernst_potentials.ECl" name="ECl" public_interface="out" units="volt" />
<variable cmeta:id="Nernst_potentials.T" name="T" public_interface="in" units="kelvin" />
<variable cmeta:id="Nernst_potentials.R" name="R" public_interface="in" units="J_per_mol_K" />
<variable cmeta:id="Nernst_potentials.F" name="F" public_interface="in" units="C_per_mol" />
<variable cmeta:id="Nernst_potentials.Nao" name="Nao" public_interface="in" units="millimolar" />
<variable cmeta:id="Nernst_potentials.Ko" name="Ko" public_interface="in" units="millimolar" />
<variable cmeta:id="Nernst_potentials.Clo" name="Clo" public_interface="in" units="millimolar" />
<variable cmeta:id="Nernst_potentials.Nai" name="Nai" public_interface="in" units="millimolar" />
<variable cmeta:id="Nernst_potentials.Ki" name="Ki" public_interface="in" units="millimolar" />
<variable cmeta:id="Nernst_potentials.Cli" 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 cmeta:id="J_KCC1.gKCC1" initial_value="1e-6" name="gKCC1" units="per_ohm_cm2" />
<variable cmeta:id="J_KCC1.ft" name="ft" units="dimensionless" />
<variable cmeta:id="J_KCC1.T" name="T" public_interface="in" units="kelvin" />
<variable cmeta:id="J_KCC1.R" name="R" public_interface="in" units="J_per_mol_K" />
<variable cmeta:id="J_KCC1.F" name="F" public_interface="in" units="C_per_mol" />
<variable cmeta:id="J_KCC1.Ko" name="Ko" public_interface="in" units="millimolar" />
<variable cmeta:id="J_KCC1.Ki" name="Ki" public_interface="in" units="millimolar" />
<variable cmeta:id="J_KCC1.Clo" name="Clo" public_interface="in" units="millimolar" />
<variable cmeta:id="J_KCC1.Cli" name="Cli" public_interface="in" units="millimolar" />
<variable cmeta:id="J_KCC1.time" 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#" type="e-notation" cellml:units="cm2_millimolar_micrometre_per_mol">
1
<sep />
10
</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 cmeta:id="J_NBC.gNBC" initial_value="9.03e-5" name="gNBC" public_interface="out" units="per_ohm_cm2" />
<variable cmeta:id="J_NBC.Vm" name="Vm" public_interface="in" units="volt" />
<variable cmeta:id="J_NBC.ENBC" name="ENBC" public_interface="in" units="volt" />
<variable cmeta:id="J_NBC.F" 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#" type="e-notation" cellml:units="cm2_millimolar_micrometre_per_mol">
1
<sep />
10
</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 cmeta:id="J_NKCC1.gNKCC1" initial_value="5.54e-6" name="gNKCC1" units="per_ohm_cm2" />
<variable cmeta:id="J_NKCC1.ft" name="ft" units="dimensionless" />
<variable cmeta:id="J_NKCC1.T" name="T" public_interface="in" units="kelvin" />
<variable cmeta:id="J_NKCC1.R" name="R" public_interface="in" units="J_per_mol_K" />
<variable cmeta:id="J_NKCC1.F" name="F" public_interface="in" units="C_per_mol" />
<variable cmeta:id="J_NKCC1.Ko" name="Ko" public_interface="in" units="millimolar" />
<variable cmeta:id="J_NKCC1.Nai" name="Nai" public_interface="in" units="millimolar" />
<variable cmeta:id="J_NKCC1.Nao" name="Nao" public_interface="in" units="millimolar" />
<variable cmeta:id="J_NKCC1.Ki" name="Ki" public_interface="in" units="millimolar" />
<variable cmeta:id="J_NKCC1.Clo" name="Clo" public_interface="in" units="millimolar" />
<variable cmeta:id="J_NKCC1.Cli" name="Cli" public_interface="in" units="millimolar" />
<variable cmeta:id="J_NKCC1.time" 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#" type="e-notation" cellml:units="cm2_millimolar_micrometre_per_mol">
1
<sep />
10
</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 cmeta:id="ENBC.ENBC" name="ENBC" public_interface="out" units="volt" />
<variable cmeta:id="ENBC.zNBC" initial_value="-1" name="zNBC" units="dimensionless" />
<variable cmeta:id="ENBC.T" name="T" public_interface="in" units="kelvin" />
<variable cmeta:id="ENBC.R" name="R" public_interface="in" units="J_per_mol_K" />
<variable cmeta:id="ENBC.F" name="F" public_interface="in" units="C_per_mol" />
<variable cmeta:id="ENBC.HCO3o" name="HCO3o" public_interface="in" units="millimolar" />
<variable cmeta:id="ENBC.Nai" name="Nai" public_interface="in" units="millimolar" />
<variable cmeta:id="ENBC.Nao" name="Nao" public_interface="in" units="millimolar" />
<variable cmeta:id="ENBC.HCO3i" 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 cmeta:id="membrane.F" name="F" public_interface="in" units="C_per_mol" />
<variable cmeta:id="membrane.J_NaKATPase" name="J_NaKATPase" public_interface="in" units="mole_per_cm2_second" />
<variable cmeta:id="membrane.ENa" name="ENa" public_interface="in" units="volt" />
<variable cmeta:id="membrane.EK" name="EK" public_interface="in" units="volt" />
<variable cmeta:id="membrane.ECl" name="ECl" public_interface="in" units="volt" />
<variable cmeta:id="membrane.ENBC" name="ENBC" public_interface="in" units="volt" />
<variable cmeta:id="membrane.gNa" name="gNa" public_interface="in" units="per_ohm_cm2" />
<variable cmeta:id="membrane.gK" name="gK" public_interface="in" units="per_ohm_cm2" />
<variable cmeta:id="membrane.gCl" name="gCl" public_interface="in" units="per_ohm_cm2" />
<variable cmeta:id="membrane.gNBC" name="gNBC" public_interface="in" units="per_ohm_cm2" />
<variable cmeta:id="membrane.theta_NBC" name="theta_NBC" public_interface="in" units="dimensionless" />
<variable cmeta:id="membrane.time" 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 cmeta:id="J_NaKATPase.Pmax" initial_value="1.4207e-10" name="Pmax" units="mole_per_cm2_second" />
<variable cmeta:id="J_NaKATPase.K_Nai" initial_value="10" name="K_Nai" units="millimolar" />
<variable cmeta:id="J_NaKATPase.K_Ko" initial_value="1.5" name="K_Ko" units="millimolar" />
<variable cmeta:id="J_NaKATPase.Nai" name="Nai" public_interface="in" units="millimolar" />
<variable cmeta:id="J_NaKATPase.Ko" 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 cmeta:id="I_K.gK" name="gK" public_interface="in" units="per_ohm_cm2" />
<variable cmeta:id="I_K.EK" name="EK" public_interface="in" units="volt" />
<variable cmeta:id="I_K.Vm" name="Vm" public_interface="in" units="volt" />
<variable cmeta:id="I_K.F" name="F" public_interface="in" units="C_per_mol" />
<variable cmeta:id="I_K.nA" name="nA" public_interface="in" units="per_mole" />
<variable cmeta:id="I_K.elementary_charge" name="elementary_charge" public_interface="in" units="C" />
<variable cmeta:id="I_K.J_NaKATPase" 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#" type="e-notation" cellml:units="cm2_millimolar_micrometre_per_mol">
1
<sep />
10
</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#" type="e-notation" cellml:units="cm2_millimolar_micrometre_per_mol">
1
<sep />
10
</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 cmeta:id="I_Cl.gCl" name="gCl" public_interface="in" units="per_ohm_cm2" />
<variable cmeta:id="I_Cl.ECl" name="ECl" public_interface="in" units="volt" />
<variable cmeta:id="I_Cl.Vm" name="Vm" public_interface="in" units="volt" />
<variable cmeta:id="I_Cl.nA" name="nA" public_interface="in" units="per_mole" />
<variable cmeta:id="I_Cl.elementary_charge" 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#" type="e-notation" cellml:units="cm2_millimolar_micrometre_per_mol">
1
<sep />
10
</cn>
<ci>gCl</ci>
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<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 cmeta:id="I_Na.gNa" name="gNa" public_interface="in" units="per_ohm_cm2" />
<variable cmeta:id="I_Na.ENa" name="ENa" public_interface="in" units="volt" />
<variable cmeta:id="I_Na.Vm" name="Vm" public_interface="in" units="volt" />
<variable cmeta:id="I_Na.F" name="F" public_interface="in" units="C_per_mol" />
<variable cmeta:id="I_Na.nA" name="nA" public_interface="in" units="per_mole" />
<variable cmeta:id="I_Na.elementary_charge" name="elementary_charge" public_interface="in" units="C" />
<variable cmeta:id="I_Na.J_NaKATPase" name="J_NaKATPase" public_interface="in" units="mole_per_cm2_second" />
<variable cmeta:id="I_Na.J_NBC" name="J_NBC" public_interface="in" units="millimolar_micrometre_per_second" />
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<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#" type="e-notation" cellml:units="cm2_millimolar_micrometre_per_mol">
1
<sep />
10
</cn>
<ci>gNa</ci>
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<apply>
<times />
<ci>elementary_charge</ci>
<ci>nA</ci>
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<apply>
<minus />
<ci>Vm</ci>
<ci>ENa</ci>
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</apply>
<apply>
<divide />
<apply>
<times />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" type="e-notation" cellml:units="cm2_millimolar_micrometre_per_mol">
1
<sep />
10
</cn>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">3</cn>
<ci>J_NaKATPase</ci>
<ci>F</ci>
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<apply>
<times />
<ci>elementary_charge</ci>
<ci>nA</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="model_parameters">
<variable cmeta:id="model_parameters.Nai" name="Nai" public_interface="out" units="millimolar" />
<variable cmeta:id="model_parameters.Ki" name="Ki" public_interface="out" units="millimolar" />
<variable cmeta:id="model_parameters.Cli" name="Cli" public_interface="out" units="millimolar" />
<variable cmeta:id="model_parameters.HCO3i" name="HCO3i" public_interface="out" units="millimolar" />
<variable cmeta:id="model_parameters.Nao" name="Nao" public_interface="out" units="millimolar" />
<variable cmeta:id="model_parameters.Ko" name="Ko" public_interface="out" units="millimolar" />
<variable cmeta:id="model_parameters.Clo" name="Clo" public_interface="out" units="millimolar" />
<variable cmeta:id="model_parameters.HCO3o" name="HCO3o" public_interface="out" units="millimolar" />
<variable cmeta:id="model_parameters.R" initial_value="8.315" name="R" public_interface="out" units="J_per_mol_K" />
<variable cmeta:id="model_parameters.F" initial_value="9.649e4" name="F" public_interface="out" units="C_per_mol" />
<variable cmeta:id="model_parameters.T" initial_value="300" name="T" public_interface="out" units="kelvin" />
<variable cmeta:id="model_parameters.gNa" initial_value="1.314e-4" name="gNa" public_interface="out" units="per_ohm_cm2" />
<variable cmeta:id="model_parameters.gK" initial_value="0.004" name="gK" public_interface="out" units="per_ohm_cm2" />
<variable cmeta:id="model_parameters.gCl" initial_value="8.797e-5" name="gCl" public_interface="out" units="per_ohm_cm2" />
<variable cmeta:id="model_parameters.elementary_charge" initial_value="1.6e-19" name="elementary_charge" public_interface="out" units="C" />
<variable cmeta:id="model_parameters.nA" initial_value="6.0221415e23" name="nA" public_interface="out" units="per_mole" />
<variable cmeta:id="model_parameters.Xi" initial_value="12.41" name="Xi" public_interface="out" units="millimolar_micrometre" />
<variable cmeta:id="model_parameters.kc" initial_value="7.35e-2" name="kc" public_interface="out" units="micrometre_millimolar_per_second" />
<variable cmeta:id="model_parameters.theta_NBC" initial_value="1" name="theta_NBC" public_interface="out" units="dimensionless" />
<variable cmeta:id="model_parameters.theta_NKCC1" initial_value="1" name="theta_NKCC1" public_interface="out" units="dimensionless" />
<variable cmeta:id="model_parameters.theta_KCC1" initial_value="1" name="theta_KCC1" public_interface="out" units="dimensionless" />
<variable cmeta:id="model_parameters.Lp" initial_value="2.1e-4" name="Lp" public_interface="out" units="cm_per_millimolar_second" />
<variable cmeta:id="model_parameters.y" name="y" public_interface="out" units="dimensionless" />
<variable cmeta:id="model_parameters.time" name="time" public_interface="in" units="second" />
<variable cmeta:id="model_parameters.N_Ki" name="N_Ki" public_interface="in" units="millimolar_micrometre" />
<variable cmeta:id="model_parameters.N_Ko" name="N_Ko" public_interface="in" units="millimolar_micrometre" />
<variable cmeta:id="model_parameters.N_Nai" name="N_Nai" public_interface="in" units="millimolar_micrometre" />
<variable cmeta:id="model_parameters.N_Nao" name="N_Nao" public_interface="in" units="millimolar_micrometre" />
<variable cmeta:id="model_parameters.N_Cli" name="N_Cli" public_interface="in" units="millimolar_micrometre" />
<variable cmeta:id="model_parameters.N_Clo" name="N_Clo" public_interface="in" units="millimolar_micrometre" />
<variable cmeta:id="model_parameters.N_HCO3i" name="N_HCO3i" public_interface="in" units="millimolar_micrometre" />
<variable cmeta:id="model_parameters.N_HCO3o" name="N_HCO3o" public_interface="in" units="millimolar_micrometre" />
<variable cmeta:id="model_parameters.wi" name="wi" public_interface="in" units="micrometre" />
<variable cmeta:id="model_parameters.wo" name="wo" public_interface="in" units="micrometre" />
<variable cmeta:id="model_parameters.t0" initial_value="10" name="t0" units="second" />
<variable cmeta:id="model_parameters.t1" initial_value="20" name="t1" units="second" />
<variable cmeta:id="model_parameters.t2" initial_value="30" name="t2" units="second" />
<variable cmeta:id="model_parameters.alpha" initial_value="2" name="alpha" units="dimensionless" />
<variable cmeta:id="model_parameters.beta" initial_value="14" name="beta" units="dimensionless" />
<variable cmeta:id="model_parameters.deltaT" name="deltaT" units="second" />
<variable cmeta:id="model_parameters.gamma_alpha_beta" name="gamma_alpha_beta" units="dimensionless" />
<variable cmeta:id="model_parameters.gamma_alpha" name="gamma_alpha" units="dimensionless" />
<variable cmeta:id="model_parameters.gamma_beta" name="gamma_beta" units="dimensionless" />
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<eq />
<ci>y</ci>
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<piece>
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<times />
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<divide />
<ci>gamma_alpha_beta</ci>
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<times />
<ci>gamma_alpha</ci>
<ci>gamma_beta</ci>
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<power />
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<minus />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
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<divide />
<apply>
<minus />
<ci>time</ci>
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<ci>deltaT</ci>
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<apply>
<minus />
<ci>beta</ci>
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<apply>
<power />
<apply>
<divide />
<apply>
<minus />
<ci>time</ci>
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<ci>deltaT</ci>
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<minus />
<ci>alpha</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
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<and />
<apply>
<geq />
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<leq />
<ci>time</ci>
<ci>t1</ci>
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</apply>
</piece>
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<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">-1</cn>
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<and />
<apply>
<gt />
<ci>time</ci>
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<lt />
<ci>time</ci>
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<minus />
<ci>t1</ci>
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<apply>
<eq />
<ci>gamma_alpha_beta</ci>
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<factorial />
<apply>
<minus />
<apply>
<plus />
<ci>alpha</ci>
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<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
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<apply>
<eq />
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<factorial />
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<minus />
<ci>alpha</ci>
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<eq />
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<factorial />
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<minus />
<ci>beta</ci>
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<eq />
<ci>Ki</ci>
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<piece>
<apply>
<divide />
<ci>N_Ki</ci>
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<gt />
<apply>
<divide />
<ci>N_Ki</ci>
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<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millimolar">0</cn>
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1
<sep />
-180
</cn>
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<apply>
<eq />
<ci>Ko</ci>
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<piece>
<apply>
<divide />
<ci>N_Ko</ci>
<ci>wo</ci>
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<apply>
<gt />
<apply>
<divide />
<ci>N_Ko</ci>
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<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millimolar">0</cn>
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1
<sep />
-180
</cn>
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<apply>
<eq />
<ci>Nai</ci>
<piecewise>
<piece>
<apply>
<divide />
<ci>N_Nai</ci>
<ci>wi</ci>
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<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>
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<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" type="e-notation" cellml:units="millimolar">
1
<sep />
-180
</cn>
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<apply>
<eq />
<ci>Nao</ci>
<piecewise>
<piece>
<apply>
<divide />
<ci>N_Nao</ci>
<ci>wo</ci>
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<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>
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<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" type="e-notation" cellml:units="millimolar">
1
<sep />
-180
</cn>
</otherwise>
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</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>
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</piece>
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<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" type="e-notation" cellml:units="millimolar">
1
<sep />
-180
</cn>
</otherwise>
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</apply>
<apply>
<eq />
<ci>Clo</ci>
<piecewise>
<piece>
<apply>
<divide />
<ci>N_Clo</ci>
<ci>wo</ci>
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<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>
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<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" type="e-notation" cellml:units="millimolar">
1
<sep />
-180
</cn>
</otherwise>
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</apply>
<apply>
<eq />
<ci>HCO3i</ci>
<piecewise>
<piece>
<apply>
<divide />
<ci>N_HCO3i</ci>
<ci>wi</ci>
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<apply>
<gt />
<apply>
<divide />
<ci>N_HCO3i</ci>
<ci>wi</ci>
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<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millimolar">0</cn>
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<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" type="e-notation" cellml:units="millimolar">
1
<sep />
-180
</cn>
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<apply>
<eq />
<ci>HCO3o</ci>
<piecewise>
<piece>
<apply>
<divide />
<ci>N_HCO3o</ci>
<ci>wo</ci>
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<apply>
<gt />
<apply>
<divide />
<ci>N_HCO3o</ci>
<ci>wo</ci>
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<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millimolar">0</cn>
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<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" type="e-notation" cellml:units="millimolar">
1
<sep />
-180
</cn>
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</math>
</component>
<connection>
<map_components component_1="Nernst_potentials" component_2="I_K" />
<map_variables variable_1="EK" variable_2="EK" />
</connection>
<connection>
<map_components component_1="environment" component_2="N_Ko" />
<map_variables variable_1="time" variable_2="time" />
</connection>
<connection>
<map_components component_1="model_parameters" component_2="N_HCO3i" />
<map_variables variable_1="theta_NBC" variable_2="theta_NBC" />
</connection>
<connection>
<map_components component_1="J_KCC1" component_2="N_Ko" />
<map_variables variable_1="J_KCC1" variable_2="J_KCC1" />
</connection>
<connection>
<map_components component_1="membrane" component_2="N_Ko" />
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</connection>
<connection>
<map_components component_1="model_parameters" component_2="I_Na" />
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<map_variables variable_1="nA" variable_2="nA" />
<map_variables variable_1="elementary_charge" variable_2="elementary_charge" />
<map_variables variable_1="F" variable_2="F" />
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<connection>
<map_components component_1="model_parameters" component_2="J_NBC" />
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</connection>
<connection>
<map_components component_1="N_Ki" component_2="N_Cli" />
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</connection>
<connection>
<map_components component_1="Nernst_potentials" component_2="N_Ki" />
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<connection>
<map_components component_1="J_NKCC1" component_2="N_Ko" />
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<connection>
<map_components component_1="membrane" component_2="I_Cl" />
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</connection>
<connection>
<map_components component_1="J_NaKATPase" component_2="N_Ko" />
<map_variables variable_1="J_NaKATPase" variable_2="J_NaKATPase" />
</connection>
<connection>
<map_components component_1="environment" component_2="J_NKCC1" />
<map_variables variable_1="time" variable_2="time" />
</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="model_parameters" component_2="N_HCO3o" />
<map_variables variable_1="theta_NBC" variable_2="theta_NBC" />
</connection>
<connection>
<map_components component_1="Nernst_potentials" component_2="N_Nao" />
<map_variables variable_1="ENa" variable_2="ENa" />
</connection>
<connection>
<map_components component_1="model_parameters" component_2="Nernst_potentials" />
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<map_variables variable_1="Ko" variable_2="Ko" />
<map_variables variable_1="Clo" variable_2="Clo" />
<map_variables variable_1="Cli" variable_2="Cli" />
<map_variables variable_1="F" variable_2="F" />
<map_variables variable_1="R" variable_2="R" />
<map_variables variable_1="Nao" variable_2="Nao" />
<map_variables variable_1="T" variable_2="T" />
<map_variables variable_1="Ki" variable_2="Ki" />
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<connection>
<map_components component_1="J_NKCC1" component_2="N_Ki" />
<map_variables variable_1="J_NKCC1" variable_2="J_NKCC1" />
</connection>
<connection>
<map_components component_1="ENBC" component_2="membrane" />
<map_variables variable_1="ENBC" variable_2="ENBC" />
</connection>
<connection>
<map_components component_1="J_KCC1" component_2="N_Ki" />
<map_variables variable_1="J_KCC1" variable_2="J_KCC1" />
</connection>
<connection>
<map_components component_1="J_NBC" component_2="membrane" />
<map_variables variable_1="gNBC" variable_2="gNBC" />
</connection>
<connection>
<map_components component_1="membrane" component_2="N_Nai" />
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</connection>
<connection>
<map_components component_1="J_NKCC1" component_2="N_Nao" />
<map_variables variable_1="J_NKCC1" variable_2="J_NKCC1" />
</connection>
<connection>
<map_components component_1="J_NBC" component_2="N_HCO3o" />
<map_variables variable_1="J_NBC" variable_2="J_NBC" />
</connection>
<connection>
<map_components component_1="model_parameters" component_2="N_Nai" />
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<map_variables variable_1="theta_NBC" variable_2="theta_NBC" />
<map_variables variable_1="theta_NKCC1" variable_2="theta_NKCC1" />
<map_variables variable_1="F" variable_2="F" />
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<connection>
<map_components component_1="environment" component_2="membrane" />
<map_variables variable_1="time" variable_2="time" />
</connection>
<connection>
<map_components component_1="membrane" component_2="N_Nao" />
<map_variables variable_1="Vm" variable_2="Vm" />
</connection>
<connection>
<map_components component_1="J_NaKATPase" component_2="I_K" />
<map_variables variable_1="J_NaKATPase" variable_2="J_NaKATPase" />
</connection>
<connection>
<map_components component_1="Nernst_potentials" component_2="I_Cl" />
<map_variables variable_1="ECl" variable_2="ECl" />
</connection>
<connection>
<map_components component_1="J_NaKATPase" component_2="I_Na" />
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</connection>
<connection>
<map_components component_1="environment" component_2="N_HCO3i" />
<map_variables variable_1="time" variable_2="time" />
</connection>
<connection>
<map_components component_1="N_Ki" component_2="model_parameters" />
<map_variables variable_1="N_Ki" variable_2="N_Ki" />
</connection>
<connection>
<map_components component_1="model_parameters" component_2="J_NKCC1" />
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<map_variables variable_1="Ko" variable_2="Ko" />
<map_variables variable_1="Clo" variable_2="Clo" />
<map_variables variable_1="Cli" variable_2="Cli" />
<map_variables variable_1="F" variable_2="F" />
<map_variables variable_1="R" variable_2="R" />
<map_variables variable_1="Nao" variable_2="Nao" />
<map_variables variable_1="T" variable_2="T" />
<map_variables variable_1="Ki" variable_2="Ki" />
</connection>
<connection>
<map_components component_1="environment" component_2="wi" />
<map_variables variable_1="time" variable_2="time" />
</connection>
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<semsim:isComputationalComponentFor>
<rdf:Description rdf:about="#property_14">
<semsim:physicalPropertyOf rdf:resource="#entity_0" />
<semsim:hasPhysicalDefinition rdf:resource="http://identifiers.org/opb/OPB_01581" />
</rdf:Description>
</semsim:isComputationalComponentFor>
<dcterms:description>Nernst potential of sodium for the astrocytic membrane.</dcterms:description>
</rdf:Description>
<rdf:Description rdf:about="#model_parameters.N_Ko">
<semsim:isComputationalComponentFor>
<rdf:Description rdf:about="#property_53">
<semsim:physicalPropertyOf rdf:resource="#entity_4" />
<semsim:hasPhysicalDefinition rdf:resource="http://identifiers.org/opb/OPB_01001" />
</rdf:Description>
</semsim:isComputationalComponentFor>
<dcterms:description>Rate of change in the number of potassium ions in the extracellular space.</dcterms:description>
</rdf:Description>
</rdf:RDF>
</model>
