- Author:
- Shelley Fong <s.fong@auckland.ac.nz>
- Date:
- 2022-03-07 09:03:44+13:00
- Desc:
- Updating equations to find kp and km
- Permanent Source URI:
- https://models.physiomeproject.org/workspace/833/rawfile/4e60d0dad2475491d216fde2fcea66e75d08fd71/BG_pCa.cellml
<?xml version='1.0' encoding='UTF-8'?>
<model name="pCa_model" 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="per_mol" units_ref="per_mol"/>
<units name="J_per_mol" units_ref="J_per_mol"/>
<units name="J_per_C" units_ref="J_per_C"/>
<units name="mol_per_s" units_ref="mol_per_s"/>
<units name="C_per_mol" units_ref="C_per_mol"/>
<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="fmol" units_ref="fmol"/>
<units name="fmol_per_sec" units_ref="fmol_per_sec"/>
<units name="per_fmol" units_ref="per_fmol"/>
<units name="pL" units_ref="pL"/>
<units name="mA_per_mM" units_ref="mA_per_mM"/>
</import>
<component name="environment">
<variable name="t" public_interface="out" units="second"/>
<variable initial_value="1e6" name="C_m" public_interface="out" units="fF"/>
<variable initial_value="25.8" name="w_i" public_interface="out" units="pL"/>
<variable initial_value="3.52" name="w_o" public_interface="out" units="pL"/>
<variable initial_value="-8.5e4" name="q_mem" public_interface="out" units="fC"/>
<variable initial_value="2494.34" name="RT" public_interface="out" units="J_per_mol"/>
<variable initial_value="96500" name="F" public_interface="out" units="C_per_mol"/>
<variable name="v_pCa_R1" public_interface="in" units="fmol_per_sec"/>
<variable name="v_pCa_R2" public_interface="in" units="fmol_per_sec"/>
<variable initial_value="9.3276" name="q_Ca_o" public_interface="out" units="fmol"/>
<variable initial_value="0.00456" name="q_Ca_i" public_interface="out" units="fmol"/>
<!-- find [pCa] using [E0] = Vmax/kcat (see MATLAB solver)-->
<variable initial_value="0.0032" name="q_pCa" public_interface="out" units="fmol"/>
<variable initial_value="1e-9" name="q_pCa_Ca" public_interface="out" units="fmol"/>
<variable name="V_mem" units="J_per_C"/>
<variable name="I_mem" 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_Ca_i</ci>
</apply>
<apply>
<minus/>
<ci>v_pCa_R1</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_Ca_o</ci>
</apply>
<ci>v_pCa_R2</ci>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_pCa</ci>
</apply>
<apply>
<plus/>
<apply>
<minus/>
<ci>v_pCa_R1</ci>
</apply>
<ci>v_pCa_R2</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_pCa_Ca</ci>
</apply>
<apply>
<minus/>
<ci>v_pCa_R1</ci>
<ci>v_pCa_R2</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_mem</ci>
</apply>
<ci>I_mem</ci>
</apply>
<apply>
<eq/>
<ci>V_mem</ci>
<apply>
<divide/>
<ci>q_mem</ci>
<ci>C_m</ci>
</apply>
</apply>
</math>
<!-- check conservations-->
<variable name="Ca_T" units="fmol"/>
<variable name="channel_T" units="fmol"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>Ca_T</ci>
<apply>
<plus/>
<ci>q_Ca_i</ci>
<ci>q_Ca_o</ci>
<ci>q_pCa_Ca</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>channel_T</ci>
<apply>
<plus/>
<ci>q_pCa</ci>
<ci>q_pCa_Ca</ci>
</apply>
</apply>
</math>
</component>
<component name="pCa_parameters">
<variable initial_value="80260.3" name="kappa_pCa_R1" public_interface="out" units="fmol_per_sec"/>
<variable initial_value="4.17158e-07" name="kappa_pCa_R2" public_interface="out" units="fmol_per_sec"/>
<variable initial_value="0.0673919" name="K_Ca_i" public_interface="out" units="per_fmol"/>
<variable initial_value="0.447372" name="K_Ca_o" public_interface="out" units="per_fmol"/>
<variable initial_value="0.156234" name="K_pCa" public_interface="out" units="per_fmol"/>
<variable initial_value="0.000181097" name="K_pCa_Ca" public_interface="out" units="per_fmol"/>
<variable initial_value="2" name="zCa" public_interface="out" units="dimensionless"/>
</component>
<component name="pCa">
<variable name="t" public_interface="in" units="second"/>
<variable name="RT" public_interface="in" units="J_per_mol"/>
<variable name="zCa" public_interface="in" units="dimensionless"/>
<variable name="F" public_interface="in" units="C_per_mol"/>
<variable name="K_Ca_i" public_interface="in" units="per_fmol"/>
<variable name="K_Ca_o" public_interface="in" units="per_fmol"/>
<variable name="K_pCa" public_interface="in" units="per_fmol"/>
<variable name="K_pCa_Ca" public_interface="in" units="per_fmol"/>
<variable name="kappa_pCa_R1" public_interface="in" units="fmol_per_sec"/>
<variable name="kappa_pCa_R2" public_interface="in" units="fmol_per_sec"/>
<variable name="q_Ca_i" public_interface="in" units="fmol"/>
<variable name="q_Ca_o" public_interface="in" units="fmol"/>
<variable name="q_pCa" public_interface="in" units="fmol"/>
<variable name="q_pCa_Ca" public_interface="in" units="fmol"/>
<variable name="mu_Ca_i" units="J_per_mol"/>
<variable name="mu_Ca_o" units="J_per_mol"/>
<variable name="mu_pCa" units="J_per_mol"/>
<variable name="mu_pCa_Ca" units="J_per_mol"/>
<variable name="v_pCa_R1" public_interface="out" units="fmol_per_sec"/>
<variable name="v_pCa_R2" public_interface="out" units="fmol_per_sec"/>
<variable name="I_mem" public_interface="out" units="fA"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>mu_Ca_i</ci>
<apply>
<times/>
<ci>RT</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_Ca_i</ci>
<ci>q_Ca_i</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_Ca_o</ci>
<apply>
<times/>
<ci>RT</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_Ca_o</ci>
<ci>q_Ca_o</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_pCa</ci>
<apply>
<times/>
<ci>RT</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_pCa</ci>
<ci>q_pCa</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_pCa_Ca</ci>
<apply>
<times/>
<ci>RT</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_pCa_Ca</ci>
<ci>q_pCa_Ca</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v_pCa_R1</ci>
<apply>
<times/>
<ci>kappa_pCa_R1</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>mu_Ca_i</ci>
<ci>mu_pCa</ci>
</apply>
<ci>RT</ci>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>mu_pCa_Ca</ci>
<ci>RT</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v_pCa_R2</ci>
<apply>
<times/>
<ci>kappa_pCa_R2</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>mu_pCa_Ca</ci>
<ci>RT</ci>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>mu_Ca_o</ci>
<ci>mu_pCa</ci>
</apply>
<ci>RT</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>I_mem</ci>
<apply>
<times/>
<ci>zCa</ci>
<ci>F</ci>
<ci>v_pCa_R2</ci>
</apply>
</apply>
</math>
</component>
<connection>
<map_components component_1="environment" component_2="pCa"/>
<map_variables variable_1="t" variable_2="t"/>
<map_variables variable_1="RT" variable_2="RT"/>
<map_variables variable_1="F" variable_2="F"/>
<map_variables variable_1="v_pCa_R1" variable_2="v_pCa_R1"/>
<map_variables variable_1="v_pCa_R2" variable_2="v_pCa_R2"/>
<map_variables variable_1="I_mem" variable_2="I_mem"/>
<map_variables variable_1="q_Ca_i" variable_2="q_Ca_i"/>
<map_variables variable_1="q_Ca_o" variable_2="q_Ca_o"/>
<map_variables variable_1="q_pCa" variable_2="q_pCa"/>
<map_variables variable_1="q_pCa_Ca" variable_2="q_pCa_Ca"/>
</connection>
<connection>
<map_components component_1="pCa" component_2="pCa_parameters"/>
<map_variables variable_1="K_Ca_i" variable_2="K_Ca_i"/>
<map_variables variable_1="K_Ca_o" variable_2="K_Ca_o"/>
<map_variables variable_1="K_pCa" variable_2="K_pCa"/>
<map_variables variable_1="K_pCa_Ca" variable_2="K_pCa_Ca"/>
<map_variables variable_1="kappa_pCa_R1" variable_2="kappa_pCa_R1"/>
<map_variables variable_1="kappa_pCa_R2" variable_2="kappa_pCa_R2"/>
<map_variables variable_1="zCa" variable_2="zCa"/>
</connection>
</model>
