Location: BG_TCC @ ecb0b1376135 / BG_TCC.cellml
- Author:
- Shelley Fong <s.fong@auckland.ac.nz>
- Date:
- 2022-04-08 16:56:48+12:00
- Desc:
- Reformulate gate to be same as Kernik
- Permanent Source URI:
- https://models.physiomeproject.org/workspace/831/rawfile/ecb0b13761350d73cb4539f699c6ad662070a1a8/BG_TCC.cellml
<?xml version='1.0' encoding='UTF-8'?>
<!-- T-type calcium channel-->
<model name="BG_TCC_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="fmol" units_ref="fmol"/>
<units name="per_fmol" units_ref="per_fmol"/>
<units name="J_per_mol" units_ref="J_per_mol"/>
<units name="J_per_K_per_mol" units_ref="J_per_K_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="microm3" units_ref="microm3"/>
<units name="fF" units_ref="fF"/>
<units name="fC" units_ref="fC"/>
<units name="fA" units_ref="fA"/>
</import>
<component name="environment">
<variable name="time" public_interface="out" units="second"/>
<variable initial_value="153400" name="C_m" public_interface="out" units="fF"/>
<variable initial_value="0.04653" name="q_Ca_o" public_interface="out" units="fmol"/>
<variable initial_value="0.000001551" name="q_Ca_i" public_interface="out" units="fmol"/>
<variable initial_value="-8.5e4" name="q_mem" public_interface="out" units="fC"/>
<variable name="V_mem" units="volt"/>
<variable initial_value="8.31" 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="96500" name="F" public_interface="out" units="C_per_mol"/>
<variable name="v_TCC" public_interface="in" units="fmol_per_sec"/>
<variable name="I_mem_TCC" public_interface="in" units="fA"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>q_Ca_i</ci>
</apply>
<apply>
<minus/>
<ci>v_TCC</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>q_Ca_o</ci>
</apply>
<ci>v_TCC</ci>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>q_mem</ci>
</apply>
<ci>I_mem_TCC</ci>
</apply>
<apply>
<eq/>
<ci>V_mem</ci>
<apply>
<divide/>
<ci>q_mem</ci>
<ci>C_m</ci>
</apply>
</apply>
</math>
</component>
<component name="TCC_parameters">
<variable initial_value="1076.14" name="kappa_TCC" public_interface="out" units="fmol_per_sec"/>
<variable initial_value="40.0387" name="kappa_R1_TCC" public_interface="out" units="fmol_per_sec"/>
<variable initial_value="0.137081" name="kappa_R2_TCC" public_interface="out" units="fmol_per_sec"/>
<variable initial_value="0.0426788" name="kappa_R3_TCC" public_interface="out" units="fmol_per_sec"/>
<variable initial_value="0.235519" name="kappa_R4_TCC" public_interface="out" units="fmol_per_sec"/>
<variable initial_value="0.953619" name="K_Ca_i" public_interface="out" units="per_fmol"/>
<variable initial_value="6.33047" name="K_Ca_o" public_interface="out" units="per_fmol"/>
<variable initial_value="0.0666161" name="K_S00_TCC" public_interface="out" units="per_fmol"/>
<variable initial_value="0.0120716" name="K_S10_TCC" public_interface="out" units="per_fmol"/>
<variable initial_value="19.4573" name="K_S01_TCC" public_interface="out" units="per_fmol"/>
<variable initial_value="3.52589" name="K_S11_TCC" public_interface="out" units="per_fmol"/>
<variable initial_value="2" name="zCa" public_interface="out" units="dimensionless"/>
<variable initial_value="0.876568910405296" name="z_df" public_interface="out" units="dimensionless"/>
<variable initial_value="-0.576510778245838" name="z_ff" public_interface="out" units="dimensionless"/>
<variable initial_value="-0.872117216889333" name="z_dr" public_interface="out" units="dimensionless"/>
<variable initial_value="1.73582739545622" name="z_fr" public_interface="out" units="dimensionless"/>
</component>
<component name="TCC">
<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="zCa" public_interface="in" units="dimensionless"/>
<variable name="F" public_interface="in" units="C_per_mol"/>
<variable name="C_m" public_interface="in" units="fF"/>
<variable name="kappa_TCC" public_interface="in" units="fmol_per_sec"/>
<variable name="K_Ca_i" public_interface="in" units="per_fmol"/>
<variable name="K_Ca_o" public_interface="in" units="per_fmol"/>
<!-- state variables-->
<variable name="q_Ca_i" public_interface="in" units="fmol"/>
<variable name="q_Ca_o" public_interface="in" units="fmol"/>
<variable name="q_mem" public_interface="in" units="fC"/>
<variable name="v_TCC" public_interface="out" units="fmol_per_sec"/>
<variable name="I_mem_TCC" public_interface="out" units="fA"/>
<variable name="u_Ca_i" units="J_per_mol"/>
<variable name="u_Ca_o" units="J_per_mol"/>
<variable name="V_mem" units="J_per_C"/>
<variable name="Am_TCC" units="J_per_mol"/>
<variable name="Af_Ca" units="J_per_mol"/>
<variable name="Ar_Ca" units="J_per_mol"/>
<!-- Constitutive relations - Convention: positive flow from inside to outside-->
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>Am_TCC</ci>
<apply>
<times/>
<ci>F</ci>
<ci>V_mem</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_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>u_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>Af_Ca</ci>
<apply>
<plus/>
<ci>mu_s11_TCC</ci>
<ci>u_Ca_i</ci>
<ci>Am_TCC</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>Ar_Ca</ci>
<apply>
<plus/>
<ci>mu_s11_TCC</ci>
<ci>u_Ca_o</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_TCC</ci>
<piecewise>
<piece>
<apply>
<times/>
<ci>kappa_TCC</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>Af_Ca</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>Ar_Ca</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Am_TCC</ci>
<cn cellml:units="J_per_mol">0</cn>
</apply>
</piece>
<otherwise>
<apply>
<times/>
<apply>
<divide/>
<apply>
<divide/>
<apply>
<times/>
<ci>kappa_TCC</ci>
<ci>Am_TCC</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>Am_TCC</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_Ca</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>Ar_Ca</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</otherwise>
</piecewise>
</apply>
<apply>
<eq/>
<ci>V_mem</ci>
<apply>
<divide/>
<ci>q_mem</ci>
<ci>C_m</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>I_mem_TCC</ci>
<apply>
<times/>
<ci>F</ci>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<ci>zCa</ci>
</apply>
<ci>v_TCC</ci>
</apply>
<apply>
<times/>
<ci>v_R1_TCC</ci>
<apply>
<minus/>
<ci>z_dr</ci>
<ci>z_df</ci>
</apply>
</apply>
<apply>
<times/>
<ci>v_R2_TCC</ci>
<apply>
<minus/>
<ci>z_dr</ci>
<ci>z_df</ci>
</apply>
</apply>
<apply>
<times/>
<ci>v_R3_TCC</ci>
<apply>
<minus/>
<ci>z_fr</ci>
<ci>z_ff</ci>
</apply>
</apply>
<apply>
<times/>
<ci>v_R4_TCC</ci>
<apply>
<minus/>
<ci>z_fr</ci>
<ci>z_ff</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
<!-- GATE-->
<variable name="v_s00_TCC" units="fmol_per_sec"/>
<variable name="v_s10_TCC" units="fmol_per_sec"/>
<variable name="v_s01_TCC" units="fmol_per_sec"/>
<variable name="v_s11_TCC" units="fmol_per_sec"/>
<variable name="v_R1_TCC" units="fmol_per_sec"/>
<variable name="v_R2_TCC" units="fmol_per_sec"/>
<variable name="v_R3_TCC" units="fmol_per_sec"/>
<variable name="v_R4_TCC" units="fmol_per_sec"/>
<variable name="mu_s00_TCC" units="J_per_mol"/>
<variable name="mu_s10_TCC" units="J_per_mol"/>
<variable name="mu_s01_TCC" units="J_per_mol"/>
<variable name="mu_s11_TCC" units="J_per_mol"/>
<variable name="Af_R1_TCC" units="J_per_mol"/>
<variable name="Ar_R1_TCC" units="J_per_mol"/>
<variable name="Af_R2_TCC" units="J_per_mol"/>
<variable name="Ar_R2_TCC" units="J_per_mol"/>
<variable name="Af_R3_TCC" units="J_per_mol"/>
<variable name="Ar_R3_TCC" units="J_per_mol"/>
<variable name="Af_R4_TCC" units="J_per_mol"/>
<variable name="Ar_R4_TCC" units="J_per_mol"/>
<variable name="kappa_R1_TCC" public_interface="in" units="fmol_per_sec"/>
<variable name="kappa_R2_TCC" public_interface="in" units="fmol_per_sec"/>
<variable name="kappa_R3_TCC" public_interface="in" units="fmol_per_sec"/>
<variable name="kappa_R4_TCC" public_interface="in" units="fmol_per_sec"/>
<variable name="K_S00_TCC" public_interface="in" units="per_fmol"/>
<variable name="K_S10_TCC" public_interface="in" units="per_fmol"/>
<variable name="K_S01_TCC" public_interface="in" units="per_fmol"/>
<variable name="K_S11_TCC" public_interface="in" units="per_fmol"/>
<variable name="z_df" public_interface="in" units="dimensionless"/>
<variable name="z_ff" public_interface="in" units="dimensionless"/>
<variable name="z_dr" public_interface="in" units="dimensionless"/>
<variable name="z_fr" public_interface="in" units="dimensionless"/>
<variable initial_value="0.999995" name="q_s00_TCC" units="fmol"/>
<variable initial_value="1e-6" name="q_s10_TCC" units="fmol"/>
<variable initial_value="1e-6" name="q_s01_TCC" units="fmol"/>
<variable initial_value="1e-6" name="q_s11_TCC" units="fmol"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>Af_R1_TCC</ci>
<apply>
<plus/>
<ci>mu_s00_TCC</ci>
<apply>
<times/>
<ci>z_df</ci>
<ci>F</ci>
<ci>V_mem</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Ar_R1_TCC</ci>
<apply>
<plus/>
<ci>mu_s10_TCC</ci>
<apply>
<times/>
<ci>z_dr</ci>
<ci>F</ci>
<ci>V_mem</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Af_R2_TCC</ci>
<apply>
<plus/>
<ci>mu_s01_TCC</ci>
<apply>
<times/>
<ci>z_df</ci>
<ci>F</ci>
<ci>V_mem</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Ar_R2_TCC</ci>
<apply>
<plus/>
<ci>mu_s11_TCC</ci>
<apply>
<times/>
<ci>z_dr</ci>
<ci>F</ci>
<ci>V_mem</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Af_R3_TCC</ci>
<apply>
<plus/>
<ci>mu_s00_TCC</ci>
<apply>
<times/>
<ci>z_ff</ci>
<ci>F</ci>
<ci>V_mem</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Ar_R3_TCC</ci>
<apply>
<plus/>
<ci>mu_s01_TCC</ci>
<apply>
<times/>
<ci>z_fr</ci>
<ci>F</ci>
<ci>V_mem</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Af_R4_TCC</ci>
<apply>
<plus/>
<ci>mu_s10_TCC</ci>
<apply>
<times/>
<ci>z_ff</ci>
<ci>F</ci>
<ci>V_mem</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Ar_R4_TCC</ci>
<apply>
<plus/>
<ci>mu_s11_TCC</ci>
<apply>
<times/>
<ci>z_fr</ci>
<ci>F</ci>
<ci>V_mem</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v_R1_TCC</ci>
<apply>
<times/>
<ci>kappa_R1_TCC</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>Af_R1_TCC</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>Ar_R1_TCC</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v_R2_TCC</ci>
<apply>
<times/>
<ci>kappa_R2_TCC</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>Af_R2_TCC</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>Ar_R2_TCC</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v_R3_TCC</ci>
<apply>
<times/>
<ci>kappa_R3_TCC</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>Af_R3_TCC</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>Ar_R3_TCC</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v_R4_TCC</ci>
<apply>
<times/>
<ci>kappa_R4_TCC</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>Af_R4_TCC</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>Ar_R4_TCC</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v_s00_TCC</ci>
<apply>
<minus/>
<apply>
<minus/>
<ci>v_R1_TCC</ci>
</apply>
<ci>v_R3_TCC</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_s10_TCC</ci>
<apply>
<minus/>
<ci>v_R1_TCC</ci>
<ci>v_R4_TCC</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_s01_TCC</ci>
<apply>
<minus/>
<ci>v_R3_TCC</ci>
<ci>v_R2_TCC</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_s11_TCC</ci>
<apply>
<plus/>
<ci>v_R2_TCC</ci>
<ci>v_R4_TCC</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_s00_TCC</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_S00_TCC</ci>
<ci>q_s00_TCC</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_s10_TCC</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_S10_TCC</ci>
<ci>q_s10_TCC</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_s01_TCC</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_S01_TCC</ci>
<ci>q_s01_TCC</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_s11_TCC</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_S11_TCC</ci>
<ci>q_s11_TCC</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_s00_TCC</ci>
</apply>
<ci>v_s00_TCC</ci>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_s10_TCC</ci>
</apply>
<ci>v_s10_TCC</ci>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_s01_TCC</ci>
</apply>
<ci>v_s01_TCC</ci>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_s11_TCC</ci>
</apply>
<ci>v_s11_TCC</ci>
</apply>
</math>
</component>
<connection>
<map_components component_1="environment" component_2="TCC"/>
<map_variables variable_1="time" 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="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_mem" variable_2="q_mem"/>
<map_variables variable_1="C_m" variable_2="C_m"/>
<map_variables variable_1="v_TCC" variable_2="v_TCC"/>
<map_variables variable_1="I_mem_TCC" variable_2="I_mem_TCC"/>
</connection>
<connection>
<map_components component_1="TCC_parameters" component_2="TCC"/>
<map_variables variable_1="kappa_TCC" variable_2="kappa_TCC"/>
<map_variables variable_1="kappa_R1_TCC" variable_2="kappa_R1_TCC"/>
<map_variables variable_1="kappa_R2_TCC" variable_2="kappa_R2_TCC"/>
<map_variables variable_1="kappa_R3_TCC" variable_2="kappa_R3_TCC"/>
<map_variables variable_1="kappa_R4_TCC" variable_2="kappa_R4_TCC"/>
<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_S00_TCC" variable_2="K_S00_TCC"/>
<map_variables variable_1="K_S10_TCC" variable_2="K_S10_TCC"/>
<map_variables variable_1="K_S01_TCC" variable_2="K_S01_TCC"/>
<map_variables variable_1="K_S11_TCC" variable_2="K_S11_TCC"/>
<map_variables variable_1="z_df" variable_2="z_df"/>
<map_variables variable_1="z_ff" variable_2="z_ff"/>
<map_variables variable_1="z_dr" variable_2="z_dr"/>
<map_variables variable_1="z_fr" variable_2="z_fr"/>
<map_variables variable_1="zCa" variable_2="zCa"/>
</connection>
</model>