- Author:
- Shelley Fong <s.fong@auckland.ac.nz>
- Date:
- 2022-03-17 11:11:36+13:00
- Desc:
- Updated parameter finding and cellml script
- Permanent Source URI:
- https://models.physiomeproject.org/workspace/83b/rawfile/6da40f865c787757867dbc173c29f385f7a3bf29/BG_ns_Ca.cellml
<?xml version='1.0' encoding='UTF-8'?>
<!-- NOTE: Nao, Nai, Ko, Ki were used in G_GHK fitting, but it is not treated as input species to the bond graph of this model.-->
<model name="cardiac_AP_ns_Ca_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_Ca_o" public_interface="out" units="fmol"/>
<variable initial_value="5510" name="q_Ca_i" public_interface="out" units="fmol"/>
<variable name="v_ns_Ca" 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_Ca_o</ci>
</apply>
<ci>v_ns_Ca</ci>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_Ca_i</ci>
</apply>
<apply>
<minus/>
<ci>v_ns_Ca</ci>
</apply>
</apply>
</math>
<variable initial_value="-13039" name="q_mem" public_interface="out" units="fC"/>
<variable name="I_mem_ns_Ca" 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_ns_Ca</ci>
</apply>
</math>
</component>
<component name="ns_Ca_parameters">
<variable initial_value="0.013843" name="kappa_ns_Ca" public_interface="out" units="fmol_per_sec"/>
<variable initial_value="0.00342024" name="K_Ca_i" public_interface="out" units="per_fmol"/>
<variable initial_value="0.0227048" name="K_Ca_o" public_interface="out" units="per_fmol"/>
<variable initial_value="2" name="zCa" public_interface="out" units="dimensionless"/>
</component>
<component name="ns_Ca">
<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_Ca_o" public_interface="in" units="per_fmol"/>
<variable name="K_Ca_i" public_interface="in" units="per_fmol"/>
<variable name="kappa_ns_Ca" public_interface="in" units="fmol_per_sec"/>
<variable name="zCa" public_interface="in" units="dimensionless"/>
<variable name="q_Ca_o" public_interface="in" units="fmol"/>
<variable name="q_Ca_i" public_interface="in" units="fmol"/>
<variable name="q_mem" public_interface="in" units="fC"/>
<variable name="mu_Ca_o" units="J_per_mol"/>
<variable name="mu_Ca_i" units="J_per_mol"/>
<variable name="Am_ns_Ca" units="J_per_mol"/>
<variable name="Af_ns_Ca" units="J_per_mol"/>
<variable name="Ar_ns_Ca" units="J_per_mol"/>
<variable name="v_ns_Ca" public_interface="out" units="fmol_per_sec"/>
<variable name="V_mem" units="volt"/>
<variable name="I_mem_ns_Ca" 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_Ca_o</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_Ca_o</ci>
<ci>q_Ca_o</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_Ca_i</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_Ca_i</ci>
<ci>q_Ca_i</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Af_ns_Ca</ci>
<apply>
<plus/>
<ci>mu_Ca_i</ci>
<apply>
<times/>
<ci>zCa</ci>
<ci>F</ci>
<ci>V_mem</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Am_ns_Ca</ci>
<apply>
<times/>
<ci>zCa</ci>
<ci>F</ci>
<ci>V_mem</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>Ar_ns_Ca</ci>
<ci>mu_Ca_o</ci>
</apply>
<apply>
<eq/>
<ci>I_mem_ns_Ca</ci>
<apply>
<times/>
<ci>F</ci>
<apply>
<minus/>
<ci>zCa</ci>
</apply>
<ci>v_ns_Ca</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_ns_Ca</ci>
<piecewise>
<piece>
<apply>
<times/>
<ci>kappa_ns_Ca</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>Af_ns_Ca</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>Ar_ns_Ca</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Am_ns_Ca</ci>
<cn cellml:units="J_per_mol">0</cn>
</apply>
</piece>
<otherwise>
<apply>
<times/>
<apply>
<divide/>
<apply>
<divide/>
<apply>
<times/>
<ci>kappa_ns_Ca</ci>
<ci>Am_ns_Ca</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>Am_ns_Ca</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_ns_Ca</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>Ar_ns_Ca</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</otherwise>
</piecewise>
</apply>
</math>
</component>
<connection>
<map_components component_1="ns_Ca" component_2="ns_Ca_parameters"/>
<map_variables variable_1="K_Ca_o" variable_2="K_Ca_o"/>
<map_variables variable_1="K_Ca_i" variable_2="K_Ca_i"/>
<map_variables variable_1="kappa_ns_Ca" variable_2="kappa_ns_Ca"/>
<map_variables variable_1="zCa" variable_2="zCa"/>
</connection>
<connection>
<map_components component_1="ns_Ca" 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_Ca_o" variable_2="q_Ca_o"/>
<map_variables variable_1="q_Ca_i" variable_2="q_Ca_i"/>
<map_variables variable_1="v_ns_Ca" variable_2="v_ns_Ca"/>
<map_variables variable_1="q_mem" variable_2="q_mem"/>
<map_variables variable_1="I_mem_ns_Ca" variable_2="I_mem_ns_Ca"/>
</connection>
</model>
