- Author:
- Shelley Fong <s.fong@auckland.ac.nz>
- Date:
- 2022-03-17 09:03:17+13:00
- Desc:
- Fix comment
- Permanent Source URI:
- https://models.physiomeproject.org/workspace/83a/rawfile/fb45139f62b80c97f07d7174391252672309376e/BG_K_ATP.cellml
<?xml version='1.0' encoding='UTF-8'?>
<!-- NOTE: ATP was used in G_GHK fitting, but it is not treated as an input species to the bond graph of this model.-->
<model name="cardiac_AP_K_ATP_only" xmlns="http://www.cellml.org/cellml/1.1#" xmlns:cellml="http://www.cellml.org/cellml/1.1#" xmlns:xlink="http://www.w3.org/1999/xlink">
<import xlink:href="units_and_constants/units_BG.cellml">
<units name="mM" units_ref="mM"/>
<units name="fmol" units_ref="fmol"/>
<units name="per_fmol" units_ref="per_fmol"/>
<units name="J_per_mol" units_ref="J_per_mol"/>
<units name="fmol_per_sec" units_ref="fmol_per_sec"/>
<units name="C_per_mol" units_ref="C_per_mol"/>
<units name="J_per_C" units_ref="J_per_C"/>
<units name="J_per_K_per_mol" units_ref="J_per_K_per_mol"/>
<units name="fF" units_ref="fF"/>
<units name="fC" units_ref="fC"/>
<units name="fA" units_ref="fA"/>
</import>
<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="q_K_o" public_interface="out" units="fmol"/>
<variable initial_value="5510" name="q_K_i" public_interface="out" units="fmol"/>
<variable name="v_K_ATP" public_interface="in" units="fmol_per_sec"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_K_o</ci>
</apply>
<ci>v_K_ATP</ci>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_K_i</ci>
</apply>
<apply>
<minus/>
<ci>v_K_ATP</ci>
</apply>
</apply>
</math>
<variable initial_value="-13039" name="q_mem" public_interface="out" units="fC"/>
<variable name="I_mem_K_ATP" public_interface="in" units="fA"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_mem</ci>
</apply>
<ci>I_mem_K_ATP</ci>
</apply>
</math>
</component>
<component name="K_ATP_parameters">
<variable initial_value="0.0231623" name="kappa_K_ATP" public_interface="out" units="fmol_per_sec"/>
<variable initial_value="0.00442418" name="K_K_i" public_interface="out" units="per_fmol"/>
<variable initial_value="0.0293693" name="K_K_o" public_interface="out" units="per_fmol"/>
<variable initial_value="1" name="zK" public_interface="out" units="dimensionless"/>
</component>
<component name="K_ATP">
<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_K_o" public_interface="in" units="per_fmol"/>
<variable name="K_K_i" public_interface="in" units="per_fmol"/>
<variable name="kappa_K_ATP" public_interface="in" units="fmol_per_sec"/>
<variable name="zK" public_interface="in" units="dimensionless"/>
<variable name="q_K_o" public_interface="in" units="fmol"/>
<variable name="q_K_i" public_interface="in" units="fmol"/>
<variable name="q_mem" public_interface="in" units="fC"/>
<variable name="mu_K_o" units="J_per_mol"/>
<variable name="mu_K_i" units="J_per_mol"/>
<variable name="Am_K_ATP" units="J_per_mol"/>
<variable name="Af_K_ATP" units="J_per_mol"/>
<variable name="Ar_K_ATP" units="J_per_mol"/>
<variable name="v_K_ATP" public_interface="out" units="fmol_per_sec"/>
<variable name="V_mem" units="volt"/>
<variable name="I_mem_K_ATP" public_interface="out" units="fA"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>V_mem</ci>
<apply>
<divide/>
<ci>q_mem</ci>
<ci>C_m</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_K_o</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_K_o</ci>
<ci>q_K_o</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_K_i</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_K_i</ci>
<ci>q_K_i</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Af_K_ATP</ci>
<apply>
<plus/>
<ci>mu_K_i</ci>
<apply>
<times/>
<ci>zK</ci>
<ci>F</ci>
<ci>V_mem</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Am_K_ATP</ci>
<apply>
<times/>
<ci>zK</ci>
<ci>F</ci>
<ci>V_mem</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>Ar_K_ATP</ci>
<ci>mu_K_o</ci>
</apply>
<apply>
<eq/>
<ci>I_mem_K_ATP</ci>
<apply>
<times/>
<ci>F</ci>
<apply>
<times/>
<apply>
<minus/>
<ci>zK</ci>
</apply>
<ci>v_K_ATP</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v_K_ATP</ci>
<piecewise>
<piece>
<apply>
<times/>
<ci>kappa_K_ATP</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>Af_K_ATP</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>Ar_K_ATP</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Am_K_ATP</ci>
<cn cellml:units="J_per_mol">0</cn>
</apply>
</piece>
<otherwise>
<apply>
<times/>
<apply>
<divide/>
<apply>
<divide/>
<apply>
<times/>
<ci>kappa_K_ATP</ci>
<ci>Am_K_ATP</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>Am_K_ATP</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_ATP</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>Ar_K_ATP</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_ATP" component_2="K_ATP_parameters"/>
<map_variables variable_1="K_K_o" variable_2="K_K_o"/>
<map_variables variable_1="K_K_i" variable_2="K_K_i"/>
<map_variables variable_1="kappa_K_ATP" variable_2="kappa_K_ATP"/>
<map_variables variable_1="zK" variable_2="zK"/>
</connection>
<connection>
<map_components component_1="K_ATP" 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="q_K_o" variable_2="q_K_o"/>
<map_variables variable_1="q_K_i" variable_2="q_K_i"/>
<map_variables variable_1="v_K_ATP" variable_2="v_K_ATP"/>
<map_variables variable_1="q_mem" variable_2="q_mem"/>
<map_variables variable_1="I_mem_K_ATP" variable_2="I_mem_K_ATP"/>
</connection>
</model>
