<?xml version="1.0"?>
<!--
This CellML file was generated on 9/26/2011 at 10:02:50 at AM using:
COR (0.9.31.1409)
Copyright 2002-2011 Dr Alan Garny
http://cor.physiol.ox.ac.uk/ - cor@physiol.ox.ac.uk
CellML 1.0 was used to generate this model
http://www.cellml.org/
--><model xmlns="http://www.cellml.org/cellml/1.0#" xmlns:cmeta="http://www.cellml.org/metadata/1.0#" cmeta:id="grubelnik_2001_4b" name="grubelnik_2001_4b">
<units name="micromole">
<unit prefix="micro" units="mole"/>
</units>
<units name="micromolar">
<unit units="micromole"/>
<unit exponent="-1" units="litre"/>
</units>
<units name="micromolar_per_minute">
<unit units="micromolar"/>
<unit exponent="-1" units="second"/>
</units>
<units name="per_micromolar_per_second">
<unit exponent="-1" units="micromolar"/>
<unit exponent="-1" units="second"/>
</units>
<units name="minute">
<unit multiplier="60" units="second"/>
</units>
<units name="per_minute">
<unit exponent="-1" units="minute"/>
</units>
<units name="per_second">
<unit exponent="-1" units="second"/>
</units>
<component name="environment">
<variable cmeta:id="environment_time" name="time" public_interface="out" units="second"/>
</component>
<component name="Ca_m">
<variable cmeta:id="Ca_m_Ca_m" initial_value="0.1" name="Ca_m" public_interface="out" units="micromolar"/>
<variable name="J_min" public_interface="in" units="micromolar"/>
<variable name="J_mout" public_interface="in" units="micromolar"/>
<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>Ca_m</ci>
</apply>
<apply>
<minus/>
<ci>J_min</ci>
<ci>J_mout</ci>
</apply>
</apply>
</math>
</component>
<component name="J_min">
<variable cmeta:id="J_min_J_min" name="J_min" public_interface="out" units="micromolar"/>
<variable initial_value="330" name="k_min" units="micromolar"/>
<variable name="Ca_cyt" public_interface="in" units="micromolar"/>
<variable initial_value="1.6" name="K_m" units="micromolar"/>
<variable initial_value="8" name="n" units="micromolar"/>
<variable name="time" public_interface="in" units="second"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>J_min</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>k_min</ci>
<apply>
<power/>
<ci>Ca_cyt</ci>
<ci>n</ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci>K_m</ci>
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</apply>
<apply>
<power/>
<ci>Ca_cyt</ci>
<ci>n</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="J_mout">
<variable cmeta:id="J_mout_J_mout" name="J_mout" public_interface="out" units="micromolar"/>
<variable initial_value="0.5" name="k_mout" units="micromolar"/>
<variable name="Ca_m" public_interface="in" units="micromolar"/>
<variable name="time" public_interface="in" units="second"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>J_mout</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>k_mout</ci>
<ci>Ca_m</ci>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="micromolar">1</cn>
</apply>
</apply>
</math>
</component>
<component name="Ca_cyt">
<variable cmeta:id="Ca_cyt_Ca_cyt" initial_value="0.01" name="Ca_cyt" public_interface="out" units="micromolar"/>
<variable name="J_ERch" public_interface="in" units="micromolar"/>
<variable name="J_ERpump" public_interface="in" units="micromolar"/>
<variable name="J_ERleak" public_interface="in" units="micromolar"/>
<variable name="J_CaPr" public_interface="in" units="micromolar"/>
<variable name="J_Pr" public_interface="in" units="micromolar"/>
<variable initial_value="0.01" name="rho_m" public_interface="out" units="dimensionless"/>
<variable initial_value="0.025" name="beta_m" public_interface="out" units="dimensionless"/>
<variable name="J_mout" public_interface="in" units="micromolar"/>
<variable name="J_min" public_interface="in" units="micromolar"/>
<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>Ca_cyt</ci>
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<apply>
<times/>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<minus/>
<ci>J_ERch</ci>
<ci>J_ERpump</ci>
</apply>
<ci>J_ERleak</ci>
<ci>J_CaPr</ci>
</apply>
<ci>J_Pr</ci>
</apply>
<apply>
<times/>
<apply>
<divide/>
<ci>rho_m</ci>
<ci>beta_m</ci>
</apply>
<apply>
<minus/>
<ci>J_mout</ci>
<ci>J_min</ci>
</apply>
</apply>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_minute">1</cn>
</apply>
</apply>
</math>
</component>
<component name="Ca_tot">
<variable cmeta:id="Ca_tot_Ca_tot" initial_value="0.01" name="Ca_tot" public_interface="out" units="micromolar"/>
<variable name="Ca_cyt" public_interface="in" units="micromolar"/>
<variable name="Ca_ER" public_interface="in" units="micromolar"/>
<variable name="rho_m" public_interface="in" units="dimensionless"/>
<variable name="beta_m" public_interface="in" units="dimensionless"/>
<variable name="rho_ER" public_interface="in" units="dimensionless"/>
<variable name="beta_ER" public_interface="in" units="dimensionless"/>
<variable name="Ca_m" public_interface="in" units="micromolar"/>
<variable name="CaPr" public_interface="in" units="micromolar"/>
<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>Ca_tot</ci>
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<apply>
<plus/>
<ci>Ca_cyt</ci>
<apply>
<times/>
<apply>
<divide/>
<ci>rho_ER</ci>
<ci>beta_ER</ci>
</apply>
<ci>Ca_ER</ci>
</apply>
<apply>
<times/>
<apply>
<divide/>
<ci>rho_m</ci>
<ci>beta_m</ci>
</apply>
<ci>Ca_m</ci>
</apply>
<ci>CaPr</ci>
</apply>
</apply>
</math>
</component>
<component name="Ca_ER">
<variable cmeta:id="Ca_ER_Ca_ER" initial_value="20" name="Ca_ER" public_interface="out" units="micromolar"/>
<variable initial_value="0.0025" name="beta_ER" public_interface="out" units="dimensionless"/>
<variable initial_value="0.01" name="rho_ER" public_interface="out" units="dimensionless"/>
<variable name="J_ERpump" public_interface="in" units="micromolar"/>
<variable name="J_ERleak" public_interface="in" units="micromolar"/>
<variable name="J_ERch" public_interface="in" units="micromolar"/>
<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>
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<apply>
<times/>
<apply>
<divide/>
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<ci>rho_ER</ci>
</apply>
<apply>
<minus/>
<apply>
<minus/>
<ci>J_ERpump</ci>
<ci>J_ERleak</ci>
</apply>
<ci>J_ERch</ci>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_minute">1</cn>
</apply>
</apply>
</math>
</component>
<component name="J_ERch">
<variable cmeta:id="J_ERch_J_ERch" name="J_ERch" public_interface="out" units="micromolar"/>
<variable initial_value="0.001" name="k_ERch" units="micromolar"/>
<variable initial_value="5" name="K_ch" units="micromolar"/>
<variable name="Ca_cyt" public_interface="in" units="micromolar"/>
<variable name="Ca_ER" public_interface="in" units="micromolar"/>
<variable name="time" public_interface="in" units="second"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>J_ERch</ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci>k_ERch</ci>
<apply>
<power/>
<ci>Ca_cyt</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci>K_ch</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
</apply>
<apply>
<power/>
<ci>Ca_cyt</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
<apply>
<minus/>
<ci>Ca_ER</ci>
<ci>Ca_cyt</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="J_ERpump">
<variable cmeta:id="J_ERpump_J_ERpump" name="J_ERpump" public_interface="out" units="micromolar"/>
<variable name="Ca_cyt" public_interface="in" units="micromolar"/>
<variable initial_value="20" name="k_ERpump" units="per_second"/>
<variable name="time" public_interface="in" units="second"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>J_ERpump</ci>
<apply>
<times/>
<ci>k_ERpump</ci>
<ci>Ca_cyt</ci>
</apply>
</apply>
</math>
</component>
<component name="J_ERleak">
<variable cmeta:id="J_ERleak_J_ERleak" name="J_ERleak" public_interface="out" units="micromolar"/>
<variable initial_value="0.05" name="k_ERleak" units="per_second"/>
<variable name="Ca_ER" public_interface="in" units="micromolar"/>
<variable name="Ca_cyt" public_interface="in" units="micromolar"/>
<variable name="time" public_interface="in" units="second"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>J_ERleak</ci>
<apply>
<times/>
<ci>k_ERleak</ci>
<apply>
<minus/>
<ci>Ca_ER</ci>
<ci>Ca_cyt</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="J_CaPr">
<variable cmeta:id="J_CaPr_J_CaPr" name="J_CaPr" public_interface="out" units="micromolar"/>
<variable initial_value="0.01" name="k_min" units="per_second"/>
<variable name="CaPr" public_interface="in" units="micromolar"/>
<variable name="time" public_interface="in" units="second"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>J_CaPr</ci>
<apply>
<times/>
<ci>k_min</ci>
<ci>CaPr</ci>
</apply>
</apply>
</math>
</component>
<component name="J_Pr">
<variable cmeta:id="J_Pr_J_Pr" name="J_Pr" public_interface="out" units="micromolar"/>
<variable initial_value="0.1" name="k_plus" units="per_micromolar_per_second"/>
<variable name="Ca_cyt" public_interface="in" units="micromolar"/>
<variable name="Pr" public_interface="in" units="micromolar"/>
<variable name="time" public_interface="in" units="second"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>J_Pr</ci>
<apply>
<times/>
<ci>k_plus</ci>
<ci>Ca_cyt</ci>
<ci>Pr</ci>
</apply>
</apply>
</math>
</component>
<component name="CaPr">
<variable cmeta:id="CaPr_CaPr" name="CaPr" public_interface="out" units="micromolar"/>
<variable name="Ca_cyt" public_interface="in" units="micromolar"/>
<variable name="rho_ER" public_interface="in" units="dimensionless"/>
<variable name="beta_ER" public_interface="in" units="dimensionless"/>
<variable name="Ca_ER" public_interface="in" units="micromolar"/>
<variable initial_value="90" name="Ca_tot" units="micromolar"/>
<variable name="time" public_interface="in" units="second"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>CaPr</ci>
<apply>
<minus/>
<ci>Ca_tot</ci>
<apply>
<plus/>
<ci>Ca_cyt</ci>
<apply>
<times/>
<apply>
<divide/>
<ci>rho_ER</ci>
<ci>beta_ER</ci>
</apply>
<ci>Ca_ER</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="Pr">
<variable cmeta:id="Pr_Pr" name="Pr" public_interface="out" units="micromolar"/>
<variable initial_value="120" name="Pr_tot" units="micromolar"/>
<variable name="CaPr" public_interface="in" units="micromolar"/>
<variable name="time" public_interface="in" units="second"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>Pr</ci>
<apply>
<minus/>
<ci>Pr_tot</ci>
<ci>CaPr</ci>
</apply>
</apply>
</math>
</component>
<connection>
<map_components component_1="environment" component_2="Ca_tot"/>
<map_variables variable_1="time" variable_2="time"/>
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<connection>
<map_components component_1="environment" component_2="Ca_m"/>
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<connection>
<map_components component_1="environment" component_2="J_min"/>
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<connection>
<map_components component_1="environment" component_2="J_mout"/>
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<connection>
<map_components component_1="environment" component_2="Ca_cyt"/>
<map_variables variable_1="time" variable_2="time"/>
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<connection>
<map_components component_1="environment" component_2="Ca_ER"/>
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<connection>
<map_components component_1="environment" component_2="J_ERch"/>
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<connection>
<map_components component_1="environment" component_2="J_ERpump"/>
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<connection>
<map_components component_1="environment" component_2="J_ERleak"/>
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<connection>
<map_components component_1="environment" component_2="J_CaPr"/>
<map_variables variable_1="time" variable_2="time"/>
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<connection>
<map_components component_1="environment" component_2="J_Pr"/>
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<connection>
<map_components component_1="environment" component_2="CaPr"/>
<map_variables variable_1="time" variable_2="time"/>
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<connection>
<map_components component_1="environment" component_2="Pr"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="Ca_cyt" component_2="J_ERch"/>
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<map_variables variable_1="Ca_cyt" variable_2="Ca_cyt"/>
</connection>
<connection>
<map_components component_1="Ca_cyt" component_2="J_ERpump"/>
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<map_variables variable_1="Ca_cyt" variable_2="Ca_cyt"/>
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<connection>
<map_components component_1="Ca_cyt" component_2="J_ERleak"/>
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<map_variables variable_1="Ca_cyt" variable_2="Ca_cyt"/>
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<connection>
<map_components component_1="Ca_cyt" component_2="J_CaPr"/>
<map_variables variable_1="J_CaPr" variable_2="J_CaPr"/>
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<connection>
<map_components component_1="Ca_cyt" component_2="J_Pr"/>
<map_variables variable_1="Ca_cyt" variable_2="Ca_cyt"/>
<map_variables variable_1="J_Pr" variable_2="J_Pr"/>
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<connection>
<map_components component_1="Ca_cyt" component_2="CaPr"/>
<map_variables variable_1="Ca_cyt" variable_2="Ca_cyt"/>
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<connection>
<map_components component_1="Ca_cyt" component_2="Ca_tot"/>
<map_variables variable_1="rho_m" variable_2="rho_m"/>
<map_variables variable_1="beta_m" variable_2="beta_m"/>
<map_variables variable_1="Ca_cyt" variable_2="Ca_cyt"/>
</connection>
<connection>
<map_components component_1="Ca_cyt" component_2="J_min"/>
<map_variables variable_1="J_min" variable_2="J_min"/>
<map_variables variable_1="Ca_cyt" variable_2="Ca_cyt"/>
</connection>
<connection>
<map_components component_1="Ca_cyt" component_2="J_mout"/>
<map_variables variable_1="J_mout" variable_2="J_mout"/>
</connection>
<connection>
<map_components component_1="CaPr" component_2="Pr"/>
<map_variables variable_1="CaPr" variable_2="CaPr"/>
</connection>
<connection>
<map_components component_1="Ca_ER" component_2="J_ERpump"/>
<map_variables variable_1="J_ERpump" variable_2="J_ERpump"/>
</connection>
<connection>
<map_components component_1="Ca_ER" component_2="CaPr"/>
<map_variables variable_1="Ca_ER" variable_2="Ca_ER"/>
<map_variables variable_1="rho_ER" variable_2="rho_ER"/>
<map_variables variable_1="beta_ER" variable_2="beta_ER"/>
</connection>
<connection>
<map_components component_1="Ca_ER" component_2="J_ERch"/>
<map_variables variable_1="J_ERch" variable_2="J_ERch"/>
<map_variables variable_1="Ca_ER" variable_2="Ca_ER"/>
</connection>
<connection>
<map_components component_1="Pr" component_2="J_Pr"/>
<map_variables variable_1="Pr" variable_2="Pr"/>
</connection>
<connection>
<map_components component_1="CaPr" component_2="J_CaPr"/>
<map_variables variable_1="CaPr" variable_2="CaPr"/>
</connection>
<connection>
<map_components component_1="CaPr" component_2="Ca_tot"/>
<map_variables variable_1="CaPr" variable_2="CaPr"/>
</connection>
<connection>
<map_components component_1="Ca_m" component_2="Ca_tot"/>
<map_variables variable_1="Ca_m" variable_2="Ca_m"/>
</connection>
<connection>
<map_components component_1="Ca_m" component_2="J_mout"/>
<map_variables variable_1="Ca_m" variable_2="Ca_m"/>
<map_variables variable_1="J_mout" variable_2="J_mout"/>
</connection>
<connection>
<map_components component_1="Ca_m" component_2="J_min"/>
<map_variables variable_1="J_min" variable_2="J_min"/>
</connection>
<connection>
<map_components component_1="Ca_ER" component_2="Ca_tot"/>
<map_variables variable_1="rho_ER" variable_2="rho_ER"/>
<map_variables variable_1="beta_ER" variable_2="beta_ER"/>
<map_variables variable_1="Ca_ER" variable_2="Ca_ER"/>
</connection>
<connection>
<map_components component_1="J_ERleak" component_2="Ca_ER"/>
<map_variables variable_1="Ca_ER" variable_2="Ca_ER"/>
<map_variables variable_1="J_ERleak" variable_2="J_ERleak"/>
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