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full2-voltage-clamp-ikr-linleak.cellml
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full2-voltage-clamp-ikr-linleak.cellml
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<?xml version='1.0' encoding='UTF-8'?>
<model xmlns="http://www.cellml.org/cellml/1.0#" xmlns:cellml="http://www.cellml.org/cellml/1.0#" xmlns:cmeta="http://www.cellml.org/metadata/1.0#" xmlns:bqbiol="http://biomodels.net/biology-qualifiers/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" name="compensated_voltage_clamp_ikr">
<units name="A_per_F">
<unit units="gram" multiplier="1000"/>
<unit units="metre" exponent="2.0"/>
<unit units="second" exponent="-4.0"/>
<unit units="ampere" exponent="-1.0"/>
</units>
<units name="C_per_mol">
<unit units="second"/>
<unit units="ampere"/>
<unit units="mole" exponent="-1.0"/>
</units>
<units name="J_per_mol_per_K">
<unit units="gram" multiplier="1000"/>
<unit units="metre" exponent="2.0"/>
<unit units="second" exponent="-2.0"/>
<unit units="kelvin" exponent="-1.0"/>
<unit units="mole" exponent="-1.0"/>
</units>
<units name="Ohm_times_1e12">
<unit units="gram" multiplier="1000000000000"/>
<unit units="metre" exponent="2.0"/>
<unit units="second" exponent="-3.0"/>
<unit units="ampere" exponent="-2.0"/>
</units>
<units name="mM">
<unit units="metre" exponent="-3.0"/>
<unit units="mole"/>
</units>
<units name="mS_per_uF">
<unit units="second" exponent="-1.0" multiplier="1000"/>
</units>
<units name="mV">
<unit units="gram"/>
<unit units="metre" exponent="2.0"/>
<unit units="second" exponent="-3.0"/>
<unit units="ampere" exponent="-1.0"/>
</units>
<units name="ms">
<unit units="second" multiplier="0.001"/>
</units>
<units name="nS">
<unit units="gram" exponent="-1.0" multiplier="1e-12"/>
<unit units="metre" exponent="-2.0"/>
<unit units="second" exponent="3.0"/>
<unit units="ampere" exponent="2.0"/>
</units>
<units name="pA">
<unit units="ampere" multiplier="1e-12"/>
</units>
<units name="pF">
<unit units="gram" exponent="-1.0" multiplier="1e-15"/>
<unit units="metre" exponent="-2.0"/>
<unit units="second" exponent="4.0"/>
<unit units="ampere" exponent="2.0"/>
</units>
<units name="per_mV">
<unit units="gram" exponent="-1.0"/>
<unit units="metre" exponent="-2.0"/>
<unit units="second" exponent="3.0"/>
<unit units="ampere"/>
</units>
<component name="engine">
<variable name="pace" units="dimensionless" public_interface="out" initial_value="0.0"/>
<variable name="time" units="ms" public_interface="out"/>
</component>
<component name="ikr">
<variable name="EK" units="mV" public_interface="in"/>
<variable name="IKr" units="pA" public_interface="out"/>
<variable name="V" units="mV" public_interface="in"/>
<variable name="active" units="dimensionless" initial_value="1.0"/>
<variable name="g" units="nS"/>
<variable name="ikr_active_inf" units="dimensionless"/>
<variable name="ikr_active_tau" units="dimensionless"/>
<variable name="ikr_open_inf" units="dimensionless"/>
<variable name="ikr_open_tau" units="dimensionless"/>
<variable name="k1" units="dimensionless"/>
<variable name="k2" units="dimensionless"/>
<variable name="k3" units="dimensionless"/>
<variable name="k4" units="dimensionless"/>
<variable name="open" units="dimensionless" initial_value="0.0"/>
<variable name="p1" units="mS_per_uF" initial_value="0.000226"/>
<variable name="p2" units="per_mV" initial_value="0.0699"/>
<variable name="p3" units="mS_per_uF" initial_value="3.45e-05"/>
<variable name="p4" units="per_mV" initial_value="0.05462"/>
<variable name="p5" units="mS_per_uF" initial_value="0.0873"/>
<variable name="p6" units="per_mV" initial_value="0.00891"/>
<variable name="p7" units="mS_per_uF" initial_value="0.00515"/>
<variable name="p8" units="per_mV" initial_value="0.03158"/>
<variable name="time" units="ms" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>IKr</ci>
<apply>
<times/>
<apply>
<times/>
<apply>
<times/>
<ci>g</ci>
<ci>open</ci>
</apply>
<ci>active</ci>
</apply>
<apply>
<minus/>
<ci>V</ci>
<ci>EK</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>active</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>ikr_active_inf</ci>
<ci>active</ci>
</apply>
<ci>ikr_active_tau</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>g</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">0.1524</cn>
<cn cellml:units="nS">1000.0</cn>
</apply>
</apply>
<apply>
<eq/>
<ci>ikr_active_inf</ci>
<apply>
<times/>
<ci>k4</ci>
<ci>ikr_active_tau</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>ikr_active_tau</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1.0</cn>
<apply>
<plus/>
<ci>k3</ci>
<ci>k4</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>ikr_open_inf</ci>
<apply>
<times/>
<ci>k1</ci>
<ci>ikr_open_tau</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>ikr_open_tau</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1.0</cn>
<apply>
<plus/>
<ci>k1</ci>
<ci>k2</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>k1</ci>
<apply>
<times/>
<ci>p1</ci>
<apply>
<exp/>
<apply>
<times/>
<ci>p2</ci>
<ci>V</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>k2</ci>
<apply>
<times/>
<ci>p3</ci>
<apply>
<exp/>
<apply>
<times/>
<apply>
<minus/>
<ci>p4</ci>
</apply>
<ci>V</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>k3</ci>
<apply>
<times/>
<ci>p5</ci>
<apply>
<exp/>
<apply>
<times/>
<ci>p6</ci>
<ci>V</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>k4</ci>
<apply>
<times/>
<ci>p7</ci>
<apply>
<exp/>
<apply>
<times/>
<apply>
<minus/>
<ci>p8</ci>
</apply>
<ci>V</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>open</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>ikr_open_inf</ci>
<ci>open</ci>
</apply>
<ci>ikr_open_tau</ci>
</apply>
</apply>
</math>
</component>
<component name="membrane">
<variable name="IKr" units="pA" public_interface="in"/>
<variable name="ILeak" units="pA" public_interface="in"/>
<variable name="Iion" units="pA"/>
<variable name="V" units="mV" public_interface="out" initial_value="-80.0"/>
<variable name="Vp" units="mV" public_interface="in"/>
<variable name="cm" units="pF" initial_value="100.0"/>
<variable name="membrane_V_tau" units="ms"/>
<variable name="rseries" units="Ohm_times_1e12" public_interface="in"/>
<variable name="time" units="ms" public_interface="in"/>
<variable name="voffset_eff" units="mV" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>Iion</ci>
<apply>
<plus/>
<ci>IKr</ci>
<ci>ILeak</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>V</ci>
</apply>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<plus/>
<apply>
<minus/>
<ci>Vp</ci>
<ci>V</ci>
</apply>
<ci>voffset_eff</ci>
</apply>
<ci>membrane_V_tau</ci>
</apply>
<apply>
<divide/>
<ci>Iion</ci>
<ci>cm</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>membrane_V_tau</ci>
<apply>
<times/>
<ci>cm</ci>
<ci>rseries</ci>
</apply>
</apply>
</math>
</component>
<component name="phys">
<variable name="F" units="C_per_mol" initial_value="9.64853414999999950e+04"/>
<variable name="R" units="J_per_mol_per_K" initial_value="8.314472"/>
<variable name="RTF" units="mV" public_interface="out"/>
<variable name="T" units="kelvin" initial_value="310.0"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>RTF</ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
<ci>F</ci>
</apply>
<cn cellml:units="dimensionless">1000.0</cn>
</apply>
</apply>
</math>
</component>
<component name="potassium">
<variable name="Ki" units="mM" public_interface="out" initial_value="110.0"/>
<variable name="Ko" units="mM" public_interface="out" initial_value="4.0"/>
</component>
<component name="rev">
<variable name="EK" units="mV" public_interface="out"/>
<variable name="Ki" units="mM" public_interface="in"/>
<variable name="Ko" units="mM" public_interface="in"/>
<variable name="RTF" units="mV" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>EK</ci>
<apply>
<times/>
<ci>RTF</ci>
<apply>
<ln/>
<apply>
<divide/>
<ci>Ko</ci>
<ci>Ki</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="voltageclamp">
<variable name="ELeak" units="mV"/>
<variable name="ILeak" units="pA" public_interface="out"/>
<variable name="Iin" units="pA"/>
<variable name="Iout" units="pA" initial_value="0.0"/>
<variable name="V" units="mV" public_interface="in"/>
<variable name="Vc" units="mV"/>
<variable name="Vclamp" units="mV" initial_value="-80.0"/>
<variable name="Vest" units="mV" initial_value="-80.0"/>
<variable name="Vp" units="mV" public_interface="out" initial_value="-80.0"/>
<variable name="alpha" units="dimensionless" initial_value="0.8"/>
<variable name="cm_est" units="pF"/>
<variable name="cprs" units="pF" initial_value="4.0"/>
<variable name="cprs_est" units="pF"/>
<variable name="dVclampdt" units="A_per_F"/>
<variable name="dVestdt" units="A_per_F"/>
<variable name="dVpdt" units="A_per_F"/>
<variable name="gLeak" units="nS" initial_value="2.0"/>
<variable name="pace" units="dimensionless" public_interface="in"/>
<variable name="rseries" units="Ohm_times_1e12" public_interface="out"/>
<variable name="rseries_est" units="Ohm_times_1e12"/>
<variable name="tau_clamp" units="ms"/>
<variable name="tau_sum" units="ms" initial_value="0.04"/>
<variable name="time" units="ms" public_interface="in"/>
<variable name="voffset_eff" units="mV" public_interface="out" initial_value="5.0"/>
<variable name="voltageclamp_Iout_tau" units="ms"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>ELeak</ci>
<apply>
<minus/>
<cn cellml:units="mV">80.0</cn>
</apply>
</apply>
<apply>
<eq/>
<ci>ILeak</ci>
<apply>
<times/>
<ci>gLeak</ci>
<apply>
<minus/>
<ci>V</ci>
<ci>ELeak</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Iin</ci>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<plus/>
<apply>
<minus/>
<ci>Vp</ci>
<ci>V</ci>
</apply>
<ci>voffset_eff</ci>
</apply>
<ci>rseries</ci>
</apply>
<apply>
<times/>
<ci>cprs</ci>
<ci>dVpdt</ci>
</apply>
</apply>
<apply>
<times/>
<ci>cprs_est</ci>
<ci>dVclampdt</ci>
</apply>
</apply>
<apply>
<times/>
<ci>cm_est</ci>
<piecewise>
<piece>
<ci>dVclampdt</ci>
<apply>
<lt/>
<ci>rseries_est</ci>
<cn cellml:units="dimensionless">1e-06</cn>
</apply>
</piece>
<otherwise>
<ci>dVestdt</ci>
</otherwise>
</piecewise>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Iout</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>Iin</ci>
<ci>Iout</ci>
</apply>
<ci>voltageclamp_Iout_tau</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>Vc</ci>
<ci>pace</ci>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Vclamp</ci>
</apply>
<ci>dVclampdt</ci>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Vest</ci>
</apply>
<ci>dVestdt</ci>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Vp</ci>
</apply>
<ci>dVpdt</ci>
</apply>
<apply>
<eq/>
<ci>cm_est</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">0.9</cn>
<cn cellml:units="pF">100.0</cn>
</apply>
</apply>
<apply>
<eq/>
<ci>cprs_est</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">4.0</cn>
<cn cellml:units="pF">0.9</cn>
</apply>
</apply>
<apply>
<eq/>
<ci>dVclampdt</ci>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci>Vc</ci>
<apply>
<times/>
<apply>
<plus/>
<ci>Iout</ci>
<apply>
<times/>
<ci>cm_est</ci>
<ci>dVestdt</ci>
</apply>
</apply>
<ci>rseries_est</ci>
</apply>
</apply>
<ci>Vclamp</ci>
</apply>
<ci>tau_sum</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>dVestdt</ci>
<piecewise>
<piece>
<cn cellml:units="dimensionless">0.0</cn>
<apply>
<lt/>
<ci>cm_est</ci>
<cn cellml:units="dimensionless">1e-06</cn>
</apply>
</piece>
<piece>
<cn cellml:units="dimensionless">0.0</cn>
<apply>
<lt/>
<ci>rseries_est</ci>
<cn cellml:units="dimensionless">1e-06</cn>
</apply>
</piece>
<otherwise>
<apply>
<divide/>
<apply>
<minus/>
<ci>Vc</ci>
<ci>Vest</ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">1.0</cn>
<ci>alpha</ci>
</apply>
<ci>cm_est</ci>
</apply>
<ci>rseries_est</ci>
</apply>
<ci>alpha</ci>
</apply>
</apply>
</otherwise>
</piecewise>
</apply>
<apply>
<eq/>
<ci>dVpdt</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>Vclamp</ci>
<ci>Vp</ci>
</apply>
<ci>tau_clamp</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>rseries</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">10.0</cn>
<cn cellml:units="Ohm_times_1e12">0.001</cn>
</apply>
</apply>
<apply>
<eq/>
<ci>rseries_est</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">0.9</cn>
<cn cellml:units="Ohm_times_1e12">0.01</cn>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_clamp</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">0.8</cn>
<cn cellml:units="dimensionless">0.001</cn>
</apply>
</apply>
<apply>
<eq/>
<ci>voltageclamp_Iout_tau</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">7.5</cn>
<cn cellml:units="dimensionless">0.001</cn>
</apply>
</apply>
</math>
</component>
<connection>
<map_components component_1="engine" component_2="ikr"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="engine" component_2="membrane"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="engine" component_2="voltageclamp"/>
<map_variables variable_1="pace" variable_2="pace"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="ikr" component_2="membrane"/>
<map_variables variable_1="IKr" variable_2="IKr"/>
<map_variables variable_1="V" variable_2="V"/>
</connection>
<connection>
<map_components component_1="ikr" component_2="rev"/>
<map_variables variable_1="EK" variable_2="EK"/>
</connection>
<connection>
<map_components component_1="membrane" component_2="voltageclamp"/>
<map_variables variable_1="ILeak" variable_2="ILeak"/>
<map_variables variable_1="V" variable_2="V"/>
<map_variables variable_1="Vp" variable_2="Vp"/>
<map_variables variable_1="rseries" variable_2="rseries"/>
<map_variables variable_1="voffset_eff" variable_2="voffset_eff"/>
</connection>
<connection>
<map_components component_1="phys" component_2="rev"/>
<map_variables variable_1="RTF" variable_2="RTF"/>
</connection>
<connection>
<map_components component_1="potassium" component_2="rev"/>
<map_variables variable_1="Ki" variable_2="Ki"/>
<map_variables variable_1="Ko" variable_2="Ko"/>
</connection>
</model>