- Author:
- Shelley Fong <s.fong@auckland.ac.nz>
- Date:
- 2021-11-08 10:39:28+13:00
- Desc:
- Adding Ca gate complexes
- Permanent Source URI:
- https://models.physiomeproject.org/workspace/6e3/rawfile/26bc79b31ca6ae66485191b89c073ef7c2eff394/BG_RyR.cellml
<?xml version='1.0' encoding='UTF-8'?>
<model name="individual_RyR" 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="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_per_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_BG.cellml">
<component component_ref="constants" name="constants"/>
</import>
<import xlink:href="units_and_constants/ion_valency.cellml">
<component component_ref="ion_valences" name="ion_valences"/>
</import>
<component name="environment">
<variable name="time" public_interface="out" units="second"/>
<variable name="V_m" public_interface="out" units="volt"/>
<variable initial_value="1.381e5" name="C_m" units="fF"/>
<variable name="v_RyR" public_interface="in" units="fmol_per_sec"/>
<variable name="F" public_interface="in" units="C_per_mol"/>
<variable name="zCa" public_interface="in" units="dimensionless"/>
<!-- initial values-->
<variable initial_value="6.41e-1" name="q_Ca_SR_init" units="fmol"/>
<variable initial_value="3.09e-6" name="q_Ca_di_init" units="fmol"/>
<variable initial_value="6.82e-3" name="q_Cai_init" units="fmol"/>
<!-- Global value-->
<variable name="q_Ca_SR" public_interface="out" units="fmol"/>
<variable name="q_Cai" public_interface="out" units="fmol"/>
<!-- From submodule-->
<variable name="q_Ca_SR_mRyR" public_interface="in" units="fmol"/>
<variable name="q_Cai_mRyR" public_interface="in" units="fmol"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>q_Ca_SR</ci>
<apply>
<plus/>
<ci>q_Ca_SR_mRyR</ci>
<ci>q_Ca_SR_init</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>q_Cai</ci>
<apply>
<plus/>
<ci>q_Cai_mRyR</ci>
<ci>q_Cai_init</ci>
</apply>
</apply>
</math>
<!-- membrane potential change-->
<variable initial_value="-13039" name="q_membrane" public_interface="out" units="fC"/>
<variable name="v_E_RyR" units="fA"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v_E_RyR</ci>
<apply>
<times/>
<ci>zCa</ci>
<ci>v_RyR</ci>
<ci>F</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>q_membrane</ci>
</apply>
<apply>
<minus/>
<ci>v_E_RyR</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>V_m</ci>
<apply>
<divide/>
<ci>q_membrane</ci>
<ci>C_m</ci>
</apply>
</apply>
</math>
</component>
<component name="RyR_parameters">
<variable initial_value="34574.2" name="kappa_RyR" public_interface="out" units="fmol_per_sec"/>
<variable initial_value="8.83262" name="kappa_OC" public_interface="out" units="fmol_per_sec"/>
<variable initial_value="0.12618" name="kappa_CCI" public_interface="out" units="fmol_per_sec"/>
<variable initial_value="883.262" name="kappa_CII" public_interface="out" units="fmol_per_sec"/>
<variable initial_value="73.6052" name="kappa_IO" public_interface="out" units="fmol_per_sec"/>
<variable initial_value="154.436" name="K_Ca_SR" public_interface="out" units="per_fmol"/>
<variable initial_value="100.283" name="K_Cai" public_interface="out" units="per_fmol"/>
<variable initial_value="3962.58" name="K_C_RyR" public_interface="out" units="per_fmol"/>
<variable initial_value="39.6258" name="K_CI_RyR" public_interface="out" units="per_fmol"/>
<variable initial_value="0.06793" name="K_I_RyR" public_interface="out" units="per_fmol"/>
<variable initial_value="6.793" name="K_O_RyR" public_interface="out" units="per_fmol"/>
<!-- var kappa_RyR: fmol_per_sec {init: 1.8838e+06, pub: out};
var kappa_OC: fmol_per_sec {init: 8.83262, pub: out};
var kappa_CCI: fmol_per_sec {init: 0.12618, pub: out};
var kappa_CII: fmol_per_sec {init: 883.262, pub: out};
var kappa_IO: fmol_per_sec {init: 73.6052, pub: out};
var K_Cai: per_fmol {init: 0.0464875, pub: out};
var K_Ca_SR: per_fmol {init: 0.0992057, pub: out};
var K_Cai: per_fmol {init: 0.0992057, pub: out};
var K_C_RyR: per_fmol {init: 115.191, pub: out};
var K_CI_RyR: per_fmol {init: 1.15191, pub: out};
var K_I_RyR: per_fmol {init: 0.00197471, pub: out};
var K_O_RyR: per_fmol {init: 0.197471, pub: out};-->
</component>
<component name="RyR">
<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" public_interface="in" units="C_per_mol"/>
<variable name="zCa" public_interface="in" units="dimensionless"/>
<variable name="V_m" public_interface="in" units="volt"/>
<variable initial_value="1" name="nCa_1" public_interface="out" units="dimensionless"/>
<variable initial_value="2" name="nCa_2" public_interface="out" units="dimensionless"/>
<!-- parameters-->
<variable name="kappa_RyR" public_interface="in" units="fmol_per_sec"/>
<variable name="K_Ca_SR" public_interface="in" units="per_fmol"/>
<variable name="K_Cai" public_interface="in" units="per_fmol"/>
<!-- Input from global environment-->
<variable name="q_Ca_SR_global" public_interface="in" units="fmol"/>
<variable name="q_Cai_global" public_interface="in" units="fmol"/>
<!-- Output to global environment-->
<variable initial_value="1e-16" name="q_Ca_SR" public_interface="out" units="fmol"/>
<variable initial_value="1e-16" name="q_Cai" public_interface="out" units="fmol"/>
<!-- determine gate particle amounts within the gate component
var q_C_RyR: fmol {init: 1e-16, pub: out};
var q_CI_RyR: fmol {init: 1e-16, pub: out};
var q_I_RyR: fmol {init: 1e-16, pub: out};
var q_O_RyR: fmol {init: 1e-16, pub: out};-->
<!-- Constitutive parameters-->
<variable name="mu_Ca_SR" units="J_per_mol"/>
<variable name="mu_Cai" public_interface="out" units="J_per_mol"/>
<variable name="v_RyR" public_interface="out" units="fmol_per_sec"/>
<variable name="v_gate_Cai" public_interface="out" units="fmol_per_sec"/>
<variable name="mu_O_RyR" public_interface="in" units="J_per_mol"/>
<variable name="v_OC" public_interface="in" units="fmol_per_sec"/>
<variable name="v_CCI" public_interface="in" units="fmol_per_sec"/>
<variable name="v_CII" public_interface="in" units="fmol_per_sec"/>
<variable name="v_IO" public_interface="in" units="fmol_per_sec"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>mu_Ca_SR</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_Ca_SR</ci>
<ci>q_Ca_SR_global</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_Cai</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_Cai</ci>
<ci>q_Cai_global</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v_RyR</ci>
<apply>
<times/>
<ci>kappa_RyR</ci>
<apply>
<exp/>
<apply>
<divide/>
<ci>mu_O_RyR</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>mu_Ca_SR</ci>
<apply>
<times/>
<ci>zCa</ci>
<ci>F</ci>
<ci>V_m</ci>
</apply>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>mu_Cai</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v_gate_Cai</ci>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<times/>
<ci>nCa_2</ci>
<ci>v_OC</ci>
</apply>
<apply>
<times/>
<ci>nCa_1</ci>
<ci>v_CCI</ci>
</apply>
</apply>
<apply>
<times/>
<ci>nCa_2</ci>
<ci>v_CII</ci>
</apply>
</apply>
<apply>
<times/>
<ci>nCa_1</ci>
<ci>v_IO</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>q_Ca_SR</ci>
</apply>
<apply>
<minus/>
<ci>v_RyR</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>q_Cai</ci>
</apply>
<apply>
<plus/>
<ci>v_RyR</ci>
<ci>v_gate_Cai</ci>
</apply>
</apply>
</math>
</component>
<component name="RyR_gate">
<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="kappa_OC" public_interface="in" units="fmol_per_sec"/>
<variable name="kappa_CCI" public_interface="in" units="fmol_per_sec"/>
<variable name="kappa_CII" public_interface="in" units="fmol_per_sec"/>
<variable name="kappa_IO" public_interface="in" units="fmol_per_sec"/>
<variable name="K_C_RyR" public_interface="in" units="per_fmol"/>
<variable name="K_CI_RyR" public_interface="in" units="per_fmol"/>
<variable name="K_I_RyR" public_interface="in" units="per_fmol"/>
<variable name="K_O_RyR" public_interface="in" units="per_fmol"/>
<variable name="nCa_1" public_interface="in" units="dimensionless"/>
<variable name="nCa_2" public_interface="in" units="dimensionless"/>
<!-- Output to global environment-->
<variable initial_value="0.25e-3" name="q_C_RyR" public_interface="out" units="fmol"/>
<variable initial_value="0.25e-3" name="q_CI_RyR" public_interface="out" units="fmol"/>
<variable initial_value="0.25e-3" name="q_I_RyR" public_interface="out" units="fmol"/>
<variable initial_value="0.25e-3" name="q_O_RyR" public_interface="out" units="fmol"/>
<variable name="q_Ca_gate_complexes" public_interface="out" units="fmol"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>q_Ca_gate_complexes</ci>
<apply>
<plus/>
<apply>
<times/>
<ci>nCa_2</ci>
<ci>q_O_RyR</ci>
</apply>
<apply>
<times/>
<ci>nCa_1</ci>
<ci>q_CI_RyR</ci>
</apply>
<apply>
<times/>
<apply>
<plus/>
<ci>nCa_1</ci>
<ci>nCa_2</ci>
</apply>
<ci>q_I_RyR</ci>
</apply>
</apply>
</apply>
</math>
<!-- Constitutive parameters-->
<variable name="mu_Cai" public_interface="in" units="J_per_mol"/>
<variable name="mu_C_RyR" units="J_per_mol"/>
<variable name="mu_CI_RyR" units="J_per_mol"/>
<variable name="mu_I_RyR" units="J_per_mol"/>
<variable name="mu_O_RyR" public_interface="out" units="J_per_mol"/>
<variable name="v_OC" public_interface="out" units="fmol_per_sec"/>
<variable name="v_CCI" public_interface="out" units="fmol_per_sec"/>
<variable name="v_CII" public_interface="out" units="fmol_per_sec"/>
<variable name="v_IO" public_interface="out" units="fmol_per_sec"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>mu_C_RyR</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_C_RyR</ci>
<ci>q_C_RyR</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_CI_RyR</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_CI_RyR</ci>
<ci>q_CI_RyR</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_I_RyR</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_I_RyR</ci>
<ci>q_I_RyR</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_O_RyR</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_O_RyR</ci>
<ci>q_O_RyR</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v_OC</ci>
<apply>
<times/>
<ci>kappa_OC</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>mu_O_RyR</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>mu_C_RyR</ci>
<apply>
<times/>
<ci>nCa_2</ci>
<ci>mu_Cai</ci>
</apply>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v_CCI</ci>
<apply>
<times/>
<ci>kappa_CCI</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>mu_C_RyR</ci>
<apply>
<times/>
<ci>nCa_1</ci>
<ci>mu_Cai</ci>
</apply>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>mu_CI_RyR</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v_CII</ci>
<apply>
<times/>
<ci>kappa_CII</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>mu_CI_RyR</ci>
<apply>
<times/>
<ci>nCa_2</ci>
<ci>mu_Cai</ci>
</apply>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>mu_I_RyR</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v_IO</ci>
<apply>
<times/>
<ci>kappa_IO</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>mu_I_RyR</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>mu_O_RyR</ci>
<apply>
<times/>
<ci>nCa_1</ci>
<ci>mu_Cai</ci>
</apply>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>q_O_RyR</ci>
</apply>
<apply>
<minus/>
<ci>v_IO</ci>
<ci>v_OC</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>q_C_RyR</ci>
</apply>
<apply>
<minus/>
<ci>v_OC</ci>
<ci>v_CCI</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>q_CI_RyR</ci>
</apply>
<apply>
<minus/>
<ci>v_CCI</ci>
<ci>v_CII</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>q_I_RyR</ci>
</apply>
<apply>
<minus/>
<ci>v_CII</ci>
<ci>v_IO</ci>
</apply>
</apply>
</math>
</component>
<connection>
<map_components component_1="environment" component_2="RyR"/>
<map_variables variable_1="time" variable_2="time"/>
<map_variables variable_1="V_m" variable_2="V_m"/>
<map_variables variable_1="v_RyR" variable_2="v_RyR"/>
<map_variables variable_1="q_Ca_SR_mRyR" variable_2="q_Ca_SR"/>
<map_variables variable_1="q_Ca_SR" variable_2="q_Ca_SR_global"/>
<map_variables variable_1="q_Cai_mRyR" variable_2="q_Cai"/>
<map_variables variable_1="q_Cai" variable_2="q_Cai_global"/>
</connection>
<connection>
<map_components component_1="environment" component_2="RyR_gate"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="RyR" component_2="RyR_parameters"/>
<map_variables variable_1="kappa_RyR" variable_2="kappa_RyR"/>
<map_variables variable_1="K_Ca_SR" variable_2="K_Ca_SR"/>
<map_variables variable_1="K_Cai" variable_2="K_Cai"/>
</connection>
<connection>
<map_components component_1="RyR" component_2="RyR_gate"/>
<map_variables variable_1="mu_Cai" variable_2="mu_Cai"/>
<map_variables variable_1="mu_O_RyR" variable_2="mu_O_RyR"/>
<map_variables variable_1="v_OC" variable_2="v_OC"/>
<map_variables variable_1="v_CCI" variable_2="v_CCI"/>
<map_variables variable_1="v_CII" variable_2="v_CII"/>
<map_variables variable_1="v_IO" variable_2="v_IO"/>
<map_variables variable_1="nCa_1" variable_2="nCa_1"/>
<map_variables variable_1="nCa_2" variable_2="nCa_2"/>
</connection>
<connection>
<map_components component_1="RyR_gate" component_2="RyR_parameters"/>
<map_variables variable_1="kappa_OC" variable_2="kappa_OC"/>
<map_variables variable_1="kappa_CCI" variable_2="kappa_CCI"/>
<map_variables variable_1="kappa_CII" variable_2="kappa_CII"/>
<map_variables variable_1="kappa_IO" variable_2="kappa_IO"/>
<map_variables variable_1="K_C_RyR" variable_2="K_C_RyR"/>
<map_variables variable_1="K_CI_RyR" variable_2="K_CI_RyR"/>
<map_variables variable_1="K_I_RyR" variable_2="K_I_RyR"/>
<map_variables variable_1="K_O_RyR" variable_2="K_O_RyR"/>
</connection>
<connection>
<map_components component_1="constants" component_2="environment"/>
<map_variables variable_1="F" variable_2="F"/>
</connection>
<connection>
<map_components component_1="constants" component_2="RyR"/>
<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>
<connection>
<map_components component_1="constants" component_2="RyR_gate"/>
<map_variables variable_1="R" variable_2="R"/>
<map_variables variable_1="T" variable_2="T"/>
</connection>
<connection>
<map_components component_1="ion_valences" component_2="RyR"/>
<map_variables variable_1="zCa" variable_2="zCa"/>
</connection>
<connection>
<map_components component_1="ion_valences" component_2="environment"/>
<map_variables variable_1="zCa" variable_2="zCa"/>
</connection>
</model>
