- Author:
- Shelley Fong <s.fong@auckland.ac.nz>
- Date:
- 2022-02-11 11:57:37+13:00
- Desc:
- Adding stimulus current (potassium)
- Permanent Source URI:
- https://models.physiomeproject.org/workspace/81b/rawfile/c0a0e649241aaf29c407852f96f4e607533122e5/K1_channel.cellml
<?xml version='1.0' encoding='UTF-8'?>
<model name="cardiac_AP_K1_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">
<variable initial_value="0" name="t" public_interface="out" units="second"/>
<variable initial_value="8.314" name="R" public_interface="out" units="J_per_K_per_mol"/>
<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="5.6606e-06" name="x_C_K1_init" units="fmol"/>
<variable initial_value="1.4151e-06" name="x_O_K1_init" units="fmol"/>
<variable name="x_Ke_mK1" public_interface="in" units="fmol"/>
<variable name="x_Ke" public_interface="out" units="fmol"/>
<variable name="x_Ki_mK1" public_interface="in" units="fmol"/>
<variable name="x_Ki" public_interface="out" units="fmol"/>
<variable name="x_C_K1_mK1" public_interface="in" units="fmol"/>
<variable name="x_C_K1" public_interface="out" units="fmol"/>
<variable name="x_O_K1_mK1" public_interface="in" units="fmol"/>
<variable name="x_O_K1" public_interface="out" units="fmol"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>x_Ke</ci>
<apply>
<plus/>
<ci>x_Ke_init</ci>
<ci>x_Ke_mK1</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>x_Ki</ci>
<apply>
<plus/>
<ci>x_Ki_init</ci>
<ci>x_Ki_mK1</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>x_C_K1</ci>
<apply>
<plus/>
<ci>x_C_K1_init</ci>
<ci>x_C_K1_mK1</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>x_O_K1</ci>
<apply>
<plus/>
<ci>x_O_K1_init</ci>
<ci>x_O_K1_mK1</ci>
</apply>
</apply>
</math>
<variable initial_value="-13039" name="q_mem_init" units="fC"/>
<variable name="q_mem_mK1" public_interface="in" units="fC"/>
<variable name="q_mem" public_interface="out" units="fC"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>q_mem</ci>
<apply>
<plus/>
<ci>q_mem_init</ci>
<ci>q_mem_mK1</ci>
</apply>
</apply>
</math>
</component>
<component name="K1_parameters">
<variable initial_value="1.329" name="K_C_K1" 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"/>
<variable initial_value="15967.3543" name="K_O_K1" public_interface="out" units="per_fmol"/>
<variable initial_value="25.0154" name="kappa_K1" public_interface="out" units="fmol_per_sec"/>
<variable initial_value="848.2812" name="kappa_gK1" public_interface="out" units="fmol_per_sec"/>
<variable initial_value="0.5" name="nK" public_interface="out" units="dimensionless"/>
<variable initial_value="1" name="zK" public_interface="out" units="dimensionless"/>
<variable initial_value="0.033569" name="z_fK1" public_interface="out" units="dimensionless"/>
<variable initial_value="3.1153" name="z_rK1" public_interface="out" units="dimensionless"/>
</component>
<component name="K1_channel">
<variable name="t" public_interface="in" units="second"/>
<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"/>
<variable name="K_C_K1" public_interface="in" units="per_fmol"/>
<variable name="K_Ke" public_interface="in" units="per_fmol"/>
<variable name="K_Ki" public_interface="in" units="per_fmol"/>
<variable name="K_O_K1" public_interface="in" units="per_fmol"/>
<variable name="kappa_K1" public_interface="in" units="fmol_per_sec"/>
<variable name="kappa_gK1" public_interface="in" units="fmol_per_sec"/>
<variable name="nK" public_interface="in" units="dimensionless"/>
<variable name="zK" public_interface="in" units="dimensionless"/>
<variable name="z_fK1" public_interface="in" units="dimensionless"/>
<variable name="z_rK1" public_interface="in" units="dimensionless"/>
<variable name="x_Ke_global" public_interface="in" units="fmol"/>
<variable name="x_Ki_global" public_interface="in" units="fmol"/>
<variable name="x_C_K1_global" public_interface="in" units="fmol"/>
<variable name="x_O_K1_global" public_interface="in" units="fmol"/>
<variable name="q_mem_global" public_interface="in" units="fC"/>
<variable initial_value="0" name="x_Ke" public_interface="out" units="fmol"/>
<variable initial_value="0" name="x_Ki" public_interface="out" units="fmol"/>
<variable initial_value="0" name="q_mem" public_interface="out" units="fC"/>
<variable initial_value="0" name="x_C_K1" public_interface="out" units="fmol"/>
<variable initial_value="0" name="x_O_K1" public_interface="out" units="fmol"/>
<variable name="mu_Ke" units="J_per_mol"/>
<variable name="mu_Ki" units="J_per_mol"/>
<variable name="mu_C_K1" units="J_per_mol"/>
<variable name="mu_O_K1" units="J_per_mol"/>
<variable name="v_Ke" units="fmol_per_sec"/>
<variable name="v_Ki" units="fmol_per_sec"/>
<variable name="v_C_K1" units="fmol_per_sec"/>
<variable name="v_O_K1" units="fmol_per_sec"/>
<variable name="Am_K1" units="J_per_mol"/>
<variable name="Af_K1" units="J_per_mol"/>
<variable name="Ar_K1" units="J_per_mol"/>
<variable name="v_K1" units="fmol_per_sec"/>
<variable name="Af_gK1" units="J_per_mol"/>
<variable name="Ar_gK1" units="J_per_mol"/>
<variable name="v_gK1" units="fmol_per_sec"/>
<variable name="V_mem" units="volt"/>
<variable name="I_mem" units="fA"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>V_mem</ci>
<apply>
<divide/>
<ci>q_mem_global</ci>
<ci>C_m</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>I_mem</ci>
<apply>
<times/>
<ci>F</ci>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<ci>zK</ci>
</apply>
<ci>v_K1</ci>
</apply>
<apply>
<times/>
<ci>z_rK1</ci>
<ci>v_gK1</ci>
</apply>
</apply>
<apply>
<times/>
<ci>z_fK1</ci>
<ci>v_gK1</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_Ke</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_Ke</ci>
<ci>x_Ke_global</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_Ki</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_Ki</ci>
<ci>x_Ki_global</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_C_K1</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_C_K1</ci>
<ci>x_C_K1_global</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_O_K1</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_O_K1</ci>
<ci>x_O_K1_global</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Af_K1</ci>
<apply>
<plus/>
<ci>mu_Ki</ci>
<apply>
<times/>
<ci>zK</ci>
<ci>F</ci>
<ci>V_mem</ci>
</apply>
<ci>mu_O_K1</ci>
<apply>
<times/>
<ci>nK</ci>
<ci>mu_Ke</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Ar_K1</ci>
<apply>
<plus/>
<ci>mu_Ke</ci>
<ci>mu_O_K1</ci>
<apply>
<times/>
<ci>nK</ci>
<ci>mu_Ke</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Am_K1</ci>
<apply>
<times/>
<ci>zK</ci>
<ci>F</ci>
<ci>V_mem</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_gK1</ci>
<apply>
<times/>
<ci>kappa_gK1</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>Af_gK1</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>Ar_gK1</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Af_gK1</ci>
<apply>
<plus/>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_C_K1</ci>
<ci>x_C_K1_global</ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci>z_fK1</ci>
<ci>F</ci>
<ci>V_mem</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Ar_gK1</ci>
<apply>
<plus/>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_O_K1</ci>
<ci>x_O_K1_global</ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci>z_rK1</ci>
<ci>F</ci>
<ci>V_mem</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v_C_K1</ci>
<apply>
<minus/>
<ci>v_gK1</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_Ke</ci>
<apply>
<minus/>
<ci>v_K1</ci>
<apply>
<times/>
<ci>nK</ci>
<apply>
<minus/>
<ci>v_K1</ci>
<ci>v_K1</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v_Ki</ci>
<apply>
<minus/>
<ci>v_K1</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_O_K1</ci>
<apply>
<minus/>
<apply>
<minus/>
<ci>v_gK1</ci>
<ci>v_K1</ci>
</apply>
<ci>v_K1</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_K1</ci>
<piecewise>
<piece>
<apply>
<times/>
<ci>kappa_K1</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>Af_K1</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>Ar_K1</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Am_K1</ci>
<cn cellml:units="J_per_mol">0</cn>
</apply>
</piece>
<otherwise>
<apply>
<times/>
<apply>
<divide/>
<apply>
<divide/>
<apply>
<times/>
<ci>kappa_K1</ci>
<ci>Am_K1</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>Am_K1</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_K1</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>Ar_K1</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</otherwise>
</piecewise>
</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_C_K1</ci>
</apply>
<ci>v_C_K1</ci>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>x_O_K1</ci>
</apply>
<ci>v_O_K1</ci>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_mem</ci>
</apply>
<ci>I_mem</ci>
</apply>
</math>
</component>
<connection>
<map_components component_1="K1_channel" component_2="K1_parameters"/>
<map_variables variable_1="K_C_K1" variable_2="K_C_K1"/>
<map_variables variable_1="K_Ke" variable_2="K_Ke"/>
<map_variables variable_1="K_Ki" variable_2="K_Ki"/>
<map_variables variable_1="K_O_K1" variable_2="K_O_K1"/>
<map_variables variable_1="kappa_K1" variable_2="kappa_K1"/>
<map_variables variable_1="kappa_gK1" variable_2="kappa_gK1"/>
<map_variables variable_1="nK" variable_2="nK"/>
<map_variables variable_1="zK" variable_2="zK"/>
<map_variables variable_1="z_fK1" variable_2="z_fK1"/>
<map_variables variable_1="z_rK1" variable_2="z_rK1"/>
</connection>
<connection>
<map_components component_1="K1_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_mK1"/>
<map_variables variable_1="x_Ki_global" variable_2="x_Ki"/>
<map_variables variable_1="x_Ki" variable_2="x_Ki_mK1"/>
<map_variables variable_1="x_C_K1_global" variable_2="x_C_K1"/>
<map_variables variable_1="x_C_K1" variable_2="x_C_K1_mK1"/>
<map_variables variable_1="x_O_K1_global" variable_2="x_O_K1"/>
<map_variables variable_1="x_O_K1" variable_2="x_O_K1_mK1"/>
<map_variables variable_1="q_mem_global" variable_2="q_mem"/>
<map_variables variable_1="q_mem" variable_2="q_mem_mK1"/>
</connection>
</model>
