<?xml version='1.0' encoding='UTF-8'?>
<!-- Ryanodine receptor: controls release of Ca from SR into cytosol of myocyte (AKA J_rel).
It does not sit on the sarcolemma. I am unsure of charge on the SR membrane, so neglecting this.-->
<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="t" public_interface="out" units="second"/>
<variable initial_value="153400" 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"/>
<!-- initial values-->
<!-- estimating [Ca]_SR is 1mM and vol_SR is 10% of the myocyte (34.4 pL)-->
<variable initial_value="3.44" name="q_Ca_SR" public_interface="out" units="fmol"/>
<variable initial_value="2.69E-03" name="q_Ca_D" public_interface="out" units="fmol"/>
<variable initial_value="2.9682830E-06" name="q_C_RyR" public_interface="out" units="fmol"/>
<variable initial_value="2.9682830E-06" name="q_CI_RyR" public_interface="out" units="fmol"/>
<variable initial_value="2.9682830E-06" name="q_I_RyR" public_interface="out" units="fmol"/>
<variable initial_value="2.9682830E-06" name="q_O_RyR" public_interface="out" units="fmol"/>
<!-- From submodule-->
<variable name="v_RyRgate_Ca_D" 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_SR</ci>
</apply>
<apply>
<minus/>
<ci>v_RyR</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_Ca_D</ci>
</apply>
<apply>
<plus/>
<ci>v_RyR</ci>
<ci>v_RyRgate_Ca_D</ci>
</apply>
</apply>
</math>
</component>
<component name="RyR_parameters">
<variable initial_value="498020" name="kappa_RyR" public_interface="out" units="fmol_per_sec"/>
<variable initial_value="5.01701" name="kappa_OC" public_interface="out" units="fmol_per_sec"/>
<variable initial_value="6.61466" name="kappa_CCI" public_interface="out" units="fmol_per_sec"/>
<variable initial_value="5.43605" name="kappa_CII" public_interface="out" units="fmol_per_sec"/>
<variable initial_value="0.453004" name="kappa_IO" public_interface="out" units="fmol_per_sec"/>
<variable initial_value="102.047" name="K_Ca_SR" public_interface="out" units="per_fmol"/>
<variable initial_value="66.2643" name="K_Ca_D" public_interface="out" units="per_fmol"/>
<variable initial_value="0.819033" name="K_C_RyR" public_interface="out" units="per_fmol"/>
<variable initial_value="0.755897" name="K_CI_RyR" public_interface="out" units="per_fmol"/>
<variable initial_value="11.0374" name="K_I_RyR" public_interface="out" units="per_fmol"/>
<variable initial_value="11.9593" name="K_O_RyR" public_interface="out" units="per_fmol"/>
</component>
<component name="RyR">
<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 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_Ca_D" public_interface="in" units="per_fmol"/>
<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"/>
<!-- Input from global environment-->
<variable name="q_Ca_SR" public_interface="in" units="fmol"/>
<variable name="q_Ca_D" public_interface="in" units="fmol"/>
<!-- Constitutive parameters-->
<variable name="mu_Ca_SR" units="J_per_mol"/>
<variable name="mu_Ca_D" public_interface="out" units="J_per_mol"/>
<variable name="v_RyR" public_interface="out" units="fmol_per_sec"/>
<variable name="v_RyRgate_Ca_D" public_interface="out" 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</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_Ca_D</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_Ca_D</ci>
<ci>q_Ca_D</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/>
<ci>mu_Ca_SR</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>mu_Ca_D</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v_RyRgate_Ca_D</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>
</math>
<!-- gate-->
<variable name="q_C_RyR" public_interface="in" units="fmol"/>
<variable name="q_CI_RyR" public_interface="in" units="fmol"/>
<variable name="q_I_RyR" public_interface="in" units="fmol"/>
<variable name="q_O_RyR" public_interface="in" 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>
<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" units="J_per_mol"/>
<variable name="v_OC" units="fmol_per_sec"/>
<variable name="v_CCI" units="fmol_per_sec"/>
<variable name="v_CII" units="fmol_per_sec"/>
<variable name="v_IO" 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_Ca_D</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_Ca_D</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_Ca_D</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_Ca_D</ci>
</apply>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</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>t</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>t</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>t</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="t" variable_2="t"/>
<map_variables variable_1="v_RyR" variable_2="v_RyR"/>
<map_variables variable_1="v_RyRgate_Ca_D" variable_2="v_RyRgate_Ca_D"/>
<map_variables variable_1="q_Ca_SR" variable_2="q_Ca_SR"/>
<map_variables variable_1="q_Ca_D" variable_2="q_Ca_D"/>
<map_variables variable_1="q_C_RyR" variable_2="q_C_RyR"/>
<map_variables variable_1="q_O_RyR" variable_2="q_O_RyR"/>
<map_variables variable_1="q_CI_RyR" variable_2="q_CI_RyR"/>
<map_variables variable_1="q_I_RyR" variable_2="q_I_RyR"/>
</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_Ca_D" variable_2="K_Ca_D"/>
<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>
</model>
