Location: BG_K @ 0727b987dfa9 / K_channel.cellml
- Author:
- Shelley Fong <s.fong@auckland.ac.nz>
- Date:
- 2022-02-17 10:17:09+13:00
- Desc:
- Init
- Permanent Source URI:
- https://models.physiomeproject.org/workspace/823/rawfile/0727b987dfa95cb1811ff8905ad0cfa3880b023e/K_channel.cellml
<?xml version='1.0' encoding='UTF-8'?>
<model name="cardiac_AP_K_only" xmlns="http://www.cellml.org/cellml/1.0#" xmlns:cellml="http://www.cellml.org/cellml/1.0#">
<units name="J_per_K_per_mol">
<unit units="joule"/>
<unit exponent="-1" units="kelvin"/>
<unit exponent="-1" units="mole"/>
</units>
<units name="C_per_mol">
<unit units="coulomb"/>
<unit exponent="-1" units="mole"/>
</units>
<units name="fF">
<unit prefix="femto" units="farad"/>
</units>
<units name="fmol">
<unit prefix="femto" units="mole"/>
</units>
<units name="per_fmol">
<unit exponent="-1" units="fmol"/>
</units>
<units name="fmol_per_sec">
<unit units="fmol"/>
<unit exponent="-1" units="second"/>
</units>
<units name="fC">
<unit prefix="femto" units="coulomb"/>
</units>
<units name="fA">
<unit prefix="femto" units="ampere"/>
</units>
<units name="J_per_mol">
<unit units="joule"/>
<unit exponent="-1" units="mole"/>
</units>
<component name="environment">
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<variable initial_value="310" name="T" public_interface="out" units="kelvin"/>
<variable initial_value="96485" name="F" public_interface="out" units="C_per_mol"/>
<variable initial_value="153400" name="C_m" public_interface="out" units="fF"/>
<variable initial_value="27.9828" name="x_Ke_init" units="fmol"/>
<variable initial_value="5510" name="x_Ki_init" units="fmol"/>
<variable initial_value="4.5648e-06" name="x_S00_K_init" units="fmol"/>
<variable initial_value="1.1412e-06" name="x_S01_K_init" units="fmol"/>
<variable initial_value="2.2824e-06" name="x_S10_K_init" units="fmol"/>
<variable initial_value="5.706e-07" name="x_S11_K_init" units="fmol"/>
<variable initial_value="2.853e-07" name="x_S20_K_init" units="fmol"/>
<variable initial_value="7.1325e-08" name="x_S21_K_init" units="fmol"/>
<variable name="x_Ki_mK" public_interface="in" units="fmol"/>
<variable name="x_Ki" public_interface="out" units="fmol"/>
<variable name="x_Ke_mK" public_interface="in" units="fmol"/>
<variable name="x_Ke" public_interface="out" units="fmol"/>
<variable name="x_S00_K_mK" public_interface="in" units="fmol"/>
<variable name="x_S00_K" public_interface="out" units="fmol"/>
<variable name="x_S01_K_mK" public_interface="in" units="fmol"/>
<variable name="x_S01_K" public_interface="out" units="fmol"/>
<variable name="x_S10_K_mK" public_interface="in" units="fmol"/>
<variable name="x_S10_K" public_interface="out" units="fmol"/>
<variable name="x_S11_K_mK" public_interface="in" units="fmol"/>
<variable name="x_S11_K" public_interface="out" units="fmol"/>
<variable name="x_S20_K_mK" public_interface="in" units="fmol"/>
<variable name="x_S20_K" public_interface="out" units="fmol"/>
<variable name="x_S21_K_mK" public_interface="in" units="fmol"/>
<variable name="x_S21_K" public_interface="out" units="fmol"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
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<eq/>
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<plus/>
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<plus/>
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</math>
</component>
<component name="K_parameters">
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<variable initial_value="22.3033" name="K_01_K" public_interface="out" units="per_fmol"/>
<variable initial_value="16.5777" name="K_10_K" public_interface="out" units="per_fmol"/>
<variable initial_value="2.8732" name="K_11_K" public_interface="out" units="per_fmol"/>
<variable initial_value="8.5423" name="K_20_K" public_interface="out" units="per_fmol"/>
<variable initial_value="1.4805" name="K_21_K" public_interface="out" units="per_fmol"/>
<variable initial_value="0.059344" name="K_Ke" public_interface="out" units="per_fmol"/>
<variable initial_value="0.0080926" name="K_Ki" public_interface="out" units="per_fmol"/>
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<variable name="R" public_interface="in" units="J_per_K_per_mol"/>
<variable name="T" public_interface="in" units="kelvin"/>
<variable name="F" public_interface="in" units="C_per_mol"/>
<variable name="C_m" public_interface="in" units="fF"/>
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<variable name="K_01_K" public_interface="in" units="per_fmol"/>
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<variable name="K_11_K" public_interface="in" units="per_fmol"/>
<variable name="K_20_K" public_interface="in" units="per_fmol"/>
<variable name="K_21_K" public_interface="in" units="per_fmol"/>
<variable name="K_Ke" public_interface="in" units="per_fmol"/>
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<variable name="kappa_i10" public_interface="in" units="fmol_per_sec"/>
<variable name="kappa_i20" public_interface="in" units="fmol_per_sec"/>
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<apply>
<exp/>
<apply>
<divide/>
<ci>Ar_i20</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Af_K</ci>
<apply>
<plus/>
<ci>mu_Ki</ci>
<apply>
<times/>
<ci>zK</ci>
<ci>F</ci>
<ci>V_mem</ci>
</apply>
<ci>mu_S21_K</ci>
<apply>
<times/>
<ci>nK</ci>
<ci>mu_Ke</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Af_X00</ci>
<apply>
<plus/>
<ci>mu_S00_K</ci>
<apply>
<times/>
<ci>z_fX</ci>
<ci>F</ci>
<ci>V_mem</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Af_X01</ci>
<apply>
<plus/>
<ci>mu_S01_K</ci>
<apply>
<times/>
<ci>z_fX</ci>
<ci>F</ci>
<ci>V_mem</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Af_X10</ci>
<apply>
<plus/>
<ci>mu_S10_K</ci>
<apply>
<times/>
<ci>z_fX</ci>
<ci>F</ci>
<ci>V_mem</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Af_X11</ci>
<apply>
<plus/>
<ci>mu_S11_K</ci>
<apply>
<times/>
<ci>z_fX</ci>
<ci>F</ci>
<ci>V_mem</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Af_i00</ci>
<apply>
<plus/>
<ci>mu_S00_K</ci>
<apply>
<times/>
<ci>z_fXi</ci>
<ci>F</ci>
<ci>V_mem</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Af_i10</ci>
<apply>
<plus/>
<ci>mu_S10_K</ci>
<apply>
<times/>
<ci>z_fXi</ci>
<ci>F</ci>
<ci>V_mem</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Af_i20</ci>
<apply>
<plus/>
<ci>mu_S20_K</ci>
<apply>
<times/>
<ci>z_fXi</ci>
<ci>F</ci>
<ci>V_mem</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Am_K</ci>
<apply>
<times/>
<ci>zK</ci>
<ci>F</ci>
<ci>V_mem</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>Ar_K</ci>
<apply>
<plus/>
<ci>mu_Ke</ci>
<ci>mu_S21_K</ci>
<apply>
<times/>
<ci>nK</ci>
<ci>mu_Ke</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Ar_X00</ci>
<apply>
<plus/>
<ci>mu_S10_K</ci>
<apply>
<times/>
<ci>z_rX</ci>
<ci>F</ci>
<ci>V_mem</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Ar_X01</ci>
<apply>
<plus/>
<ci>mu_S11_K</ci>
<apply>
<times/>
<ci>z_rX</ci>
<ci>F</ci>
<ci>V_mem</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Ar_X10</ci>
<apply>
<plus/>
<ci>mu_S20_K</ci>
<apply>
<times/>
<ci>z_rX</ci>
<ci>F</ci>
<ci>V_mem</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Ar_X11</ci>
<apply>
<plus/>
<ci>mu_S21_K</ci>
<apply>
<times/>
<ci>z_rX</ci>
<ci>F</ci>
<ci>V_mem</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Ar_i00</ci>
<apply>
<plus/>
<ci>mu_S01_K</ci>
<apply>
<times/>
<ci>z_rXi</ci>
<ci>F</ci>
<ci>V_mem</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Ar_i10</ci>
<apply>
<plus/>
<ci>mu_S11_K</ci>
<apply>
<times/>
<ci>z_rXi</ci>
<ci>F</ci>
<ci>V_mem</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Ar_i20</ci>
<apply>
<plus/>
<ci>mu_S21_K</ci>
<apply>
<times/>
<ci>z_rXi</ci>
<ci>F</ci>
<ci>V_mem</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v_Ke</ci>
<apply>
<minus/>
<ci>v_K</ci>
<apply>
<times/>
<ci>nK</ci>
<apply>
<minus/>
<ci>v_K</ci>
<ci>v_K</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v_Ki</ci>
<apply>
<minus/>
<ci>v_K</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_S00_K</ci>
<apply>
<minus/>
<apply>
<minus/>
<ci>v_X00</ci>
</apply>
<ci>v_i00</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_S01_K</ci>
<apply>
<plus/>
<apply>
<minus/>
<ci>v_X01</ci>
</apply>
<ci>v_i00</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_S10_K</ci>
<apply>
<minus/>
<apply>
<minus/>
<ci>v_X00</ci>
<ci>v_X10</ci>
</apply>
<ci>v_i10</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_S11_K</ci>
<apply>
<plus/>
<apply>
<minus/>
<ci>v_X01</ci>
<ci>v_X11</ci>
</apply>
<ci>v_i10</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_S20_K</ci>
<apply>
<minus/>
<ci>v_X10</ci>
<ci>v_i20</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_S21_K</ci>
<apply>
<minus/>
<apply>
<plus/>
<ci>v_X11</ci>
<ci>v_i20</ci>
</apply>
<apply>
<minus/>
<ci>v_K</ci>
<ci>v_K</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>x_Ke</ci>
</apply>
<ci>v_Ke</ci>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>x_Ki</ci>
</apply>
<ci>v_Ki</ci>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>x_S00_K</ci>
</apply>
<ci>v_S00_K</ci>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>x_S01_K</ci>
</apply>
<ci>v_S01_K</ci>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>x_S10_K</ci>
</apply>
<ci>v_S10_K</ci>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>x_S11_K</ci>
</apply>
<ci>v_S11_K</ci>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>x_S20_K</ci>
</apply>
<ci>v_S20_K</ci>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>x_S21_K</ci>
</apply>
<ci>v_S21_K</ci>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_mem</ci>
</apply>
<ci>I_mem</ci>
</apply>
<apply>
<eq/>
<ci>v_K</ci>
<piecewise>
<piece>
<apply>
<times/>
<ci>kappa_K</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>Af_K</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>Ar_K</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Am_K</ci>
<cn cellml:units="J_per_mol">0</cn>
</apply>
</piece>
<otherwise>
<apply>
<times/>
<apply>
<divide/>
<apply>
<divide/>
<apply>
<times/>
<ci>kappa_K</ci>
<ci>Am_K</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>Am_K</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless">1</cn>
</apply>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>Af_K</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>Ar_K</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</otherwise>
</piecewise>
</apply>
</math>
</component>
<connection>
<map_components component_1="K_channel" component_2="K_parameters"/>
<map_variables variable_1="K_00_K" variable_2="K_00_K"/>
<map_variables variable_1="K_01_K" variable_2="K_01_K"/>
<map_variables variable_1="K_10_K" variable_2="K_10_K"/>
<map_variables variable_1="K_11_K" variable_2="K_11_K"/>
<map_variables variable_1="K_20_K" variable_2="K_20_K"/>
<map_variables variable_1="K_21_K" variable_2="K_21_K"/>
<map_variables variable_1="K_Ke" variable_2="K_Ke"/>
<map_variables variable_1="K_Ki" variable_2="K_Ki"/>
<map_variables variable_1="kappa_K" variable_2="kappa_K"/>
<map_variables variable_1="kappa_X00" variable_2="kappa_X00"/>
<map_variables variable_1="kappa_X01" variable_2="kappa_X01"/>
<map_variables variable_1="kappa_X10" variable_2="kappa_X10"/>
<map_variables variable_1="kappa_X11" variable_2="kappa_X11"/>
<map_variables variable_1="kappa_i00" variable_2="kappa_i00"/>
<map_variables variable_1="kappa_i10" variable_2="kappa_i10"/>
<map_variables variable_1="kappa_i20" variable_2="kappa_i20"/>
<map_variables variable_1="nK" variable_2="nK"/>
<map_variables variable_1="zK" variable_2="zK"/>
<map_variables variable_1="z_fX" variable_2="z_fX"/>
<map_variables variable_1="z_fXi" variable_2="z_fXi"/>
<map_variables variable_1="z_rX" variable_2="z_rX"/>
<map_variables variable_1="z_rXi" variable_2="z_rXi"/>
</connection>
<connection>
<map_components component_1="K_channel" component_2="environment"/>
<map_variables variable_1="t" variable_2="t"/>
<map_variables variable_1="R" variable_2="R"/>
<map_variables variable_1="T" variable_2="T"/>
<map_variables variable_1="F" variable_2="F"/>
<map_variables variable_1="C_m" variable_2="C_m"/>
<map_variables variable_1="x_Ke_global" variable_2="x_Ke"/>
<map_variables variable_1="x_Ke" variable_2="x_Ke_mK"/>
<map_variables variable_1="x_Ki_global" variable_2="x_Ki"/>
<map_variables variable_1="x_Ki" variable_2="x_Ki_mK"/>
<map_variables variable_1="x_S00_K_global" variable_2="x_S00_K"/>
<map_variables variable_1="x_S00_K" variable_2="x_S00_K_mK"/>
<map_variables variable_1="x_S01_K_global" variable_2="x_S01_K"/>
<map_variables variable_1="x_S01_K" variable_2="x_S01_K_mK"/>
<map_variables variable_1="x_S10_K_global" variable_2="x_S10_K"/>
<map_variables variable_1="x_S10_K" variable_2="x_S10_K_mK"/>
<map_variables variable_1="x_S11_K_global" variable_2="x_S11_K"/>
<map_variables variable_1="x_S11_K" variable_2="x_S11_K_mK"/>
<map_variables variable_1="x_S20_K_global" variable_2="x_S20_K"/>
<map_variables variable_1="x_S20_K" variable_2="x_S20_K_mK"/>
<map_variables variable_1="x_S21_K_global" variable_2="x_S21_K"/>
<map_variables variable_1="x_S21_K" variable_2="x_S21_K_mK"/>
<map_variables variable_1="q_mem_global" variable_2="q_mem"/>
<map_variables variable_1="q_mem" variable_2="q_mem_mK"/>
</connection>
</model>