- Author:
- Shelley Fong <sfon036@UoA.auckland.ac.nz>
- Date:
- 2025-07-18 14:36:42+12:00
- Desc:
- Adding Vm arg
- Permanent Source URI:
- https://staging.physiomeproject.org/workspace/d47/rawfile/bc7052a7b1304d5cdbc223b018f269cd19737289/BG_BK.cellml
<?xml version='1.0' encoding='UTF-8'?>
<model name="individual_BK" 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.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_s"/>
<units name="C_per_mol" units_ref="C_per_mol"/>
<units name="J_per_C" units_ref="J_per_C"/>
<units name="microm3" units_ref="microm3"/>
<units name="fF" units_ref="fF"/>
<units name="fC" units_ref="fC"/>
<units name="fA" units_ref="fA"/>
<units name="per_second" units_ref="per_second"/>
<units name="millivolt" units_ref="millivolt"/>
<units name="per_sec" units_ref="per_sec"/>
<units name="J_per_K_per_mol" units_ref="J_per_K_mol"/>
<units name="fmol_per_L" units_ref="fmol_per_L"/>
<units name="fmol_per_L_per_sec" units_ref="fmol_per_L_per_sec"/>
<units name="per_sec_per_fmol_per_L" units_ref="per_sec_per_fmol_per_L"/>
<units name="uM" units_ref="uM"/>
<units name="mM_per_sec" units_ref="mM_per_sec"/>
<units name="uM_per_sec" units_ref="uM_per_sec"/>
<units name="pL" units_ref="pL"/>
<units name="m_to_u" units_ref="m_to_u"/>
</import>
<import xlink:href="units_and_constants/constants.cellml">
<component component_ref="constants" name="constants"/>
</import>
<component name="environment">
<variable name="time" public_interface="out" units="second"/>
<variable initial_value="-13039" name="q_mem" public_interface="out" units="fC"/>
<variable initial_value="153400" name="C_m" public_interface="out" units="fF"/>
<!-- initial values-->
<variable initial_value="98" name="q_K_i" public_interface="out" units="fmol"/>
<variable initial_value="0.753197674" name="q_K_o" public_interface="out" units="fmol"/>
<!-- From submodule-->
<variable name="v_rBK" public_interface="in" units="fmol_per_sec"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>q_K_i</ci>
</apply>
<apply>
<minus/>
<ci>v_rBK</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>q_K_o</ci>
</apply>
<ci>v_rBK</ci>
</apply>
</math>
</component>
<component name="BK_parameters">
<variable initial_value="0.161965" name="kappa_rBK" public_interface="out" units="fmol_per_sec"/>
<variable initial_value="0.574926" name="K_K_i" public_interface="out" units="per_fmol"/>
<variable initial_value="2.6716" name="K_K_o" public_interface="out" units="per_fmol"/>
</component>
<component name="BK">
<variable name="time" 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" private_interface="out" public_interface="in" units="C_per_mol"/>
<variable name="V_mem" units="J_per_C"/>
<variable name="C_m" public_interface="in" units="fF"/>
<!-- parameters-->
<variable name="kappa_rBK" public_interface="in" units="fmol_per_sec"/>
<variable name="K_K_i" public_interface="in" units="per_fmol"/>
<variable name="K_K_o" public_interface="in" units="per_fmol"/>
<!-- Input from global environment-->
<variable name="q_K_i" public_interface="in" units="fmol"/>
<variable name="q_K_o" public_interface="in" units="fmol"/>
<variable name="q_mem" public_interface="in" units="fC"/>
<!-- Constitutive parameters-->
<variable name="mu_K_i" units="J_per_mol"/>
<variable name="mu_K_o" units="J_per_mol"/>
<variable name="v_rBK" public_interface="out" units="fmol_per_sec"/>
<variable name="Am_rBK" units="J_per_mol"/>
<variable name="Af_rBK" units="J_per_mol"/>
<variable name="Ar_rBK" units="J_per_mol"/>
<variable initial_value="1" name="zK" units="dimensionless"/>
<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>
<!-- Constitutive relations - Convention: positive flow from inside to outside-->
<apply>
<eq/>
<ci>Am_rBK</ci>
<apply>
<times/>
<ci>zK</ci>
<ci>F</ci>
<ci>V_mem</ci>
</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>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>Af_rBK</ci>
<apply>
<plus/>
<ci>mu_K_i</ci>
<ci>Am_rBK</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>Ar_rBK</ci>
<ci>mu_K_o</ci>
</apply>
<!-- v_rBK = kappa_rBK*exp((mu_K_i-mu_K_o)/(R*T));-->
<apply>
<eq/>
<ci>v_rBK</ci>
<piecewise>
<piece>
<apply>
<times/>
<cn cellml:units="dimensionless">1</cn>
<ci>kappa_rBK</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>Af_rBK</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>Ar_rBK</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Am_rBK</ci>
<cn cellml:units="J_per_mol">0</cn>
</apply>
</piece>
<otherwise>
<apply>
<times/>
<apply>
<divide/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">1</cn>
<ci>kappa_rBK</ci>
<ci>Am_rBK</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>Am_rBK</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_rBK</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>Ar_rBK</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</otherwise>
</piecewise>
</apply>
</math>
</component>
<connection>
<map_components component_1="environment" component_2="BK"/>
<map_variables variable_1="time" variable_2="time"/>
<map_variables variable_1="q_mem" variable_2="q_mem"/>
<map_variables variable_1="C_m" variable_2="C_m"/>
<map_variables variable_1="q_K_i" variable_2="q_K_i"/>
<map_variables variable_1="q_K_o" variable_2="q_K_o"/>
<map_variables variable_1="v_rBK" variable_2="v_rBK"/>
</connection>
<connection>
<map_components component_1="BK" component_2="BK_parameters"/>
<map_variables variable_1="kappa_rBK" variable_2="kappa_rBK"/>
<map_variables variable_1="K_K_i" variable_2="K_K_i"/>
<map_variables variable_1="K_K_o" variable_2="K_K_o"/>
</connection>
<connection>
<map_components component_1="constants" component_2="BK"/>
<map_variables variable_1="R" variable_2="R"/>
<map_variables variable_1="T" variable_2="T"/>
<map_variables variable_1="F" variable_2="F"/>
</connection>
</model>
