- Author:
- Shelley Fong <s.fong@auckland.ac.nz>
- Date:
- 2021-11-16 16:23:09+13:00
- Desc:
- Finding rational nullspace
- Permanent Source URI:
- https://models.cellml.org/workspace/6ba/rawfile/915ab06a088cfd92a95bafcadf0a8c0774778698/BG_LRGbinding.cellml
<?xml version='1.0' encoding='UTF-8'?>
<!-- BG model of ligand binding receptor, based on substep within beta1 adrenergic receptor activation (saucerman2003)
Species: L(igand), R(eceptor), LR, RG, LRG
1sep21 initialising file -->
<model name="BG_LRGbinding" 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="per_sec" units_ref="per_sec"/>
<units name="J_per_K_per_mol" units_ref="J_per_K_per_mol"/>
<units name="C_per_mol" units_ref="C_per_mol"/>
<units name="fmol" units_ref="fmol"/>
<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="per_fmol" units_ref="per_fmol"/>
<units name="fmol_per_sec" units_ref="fmol_per_sec"/>
<units name="J_per_mol" units_ref="J_per_mol"/>
<units name="mM" units_ref="mM"/>
<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>
<component name="environment">
<variable name="time" public_interface="out" units="second"/>
<variable initial_value="0.0000508778" name="q_R" public_interface="out" units="fmol"/>
<variable initial_value="0.0290876489" name="q_G" public_interface="out" units="fmol"/>
<variable initial_value="0.0000508778" name="q_RG" public_interface="out" units="fmol"/>
<variable initial_value="0.0000508778" name="q_LRG" public_interface="out" units="fmol"/>
<variable initial_value="0" name="q_L" public_interface="out" units="fmol"/>
<variable initial_value="0" name="q_LR" public_interface="out" units="fmol"/>
<variable name="vsig1" public_interface="in" units="fmol_per_sec"/>
<variable name="vsig2" public_interface="in" units="fmol_per_sec"/>
<variable name="vsig3" public_interface="in" units="fmol_per_sec"/>
<variable name="vsig4" public_interface="in" units="fmol_per_sec"/>
<!-- placeholder ODEs-->
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>q_L</ci>
</apply>
<apply>
<minus/>
<apply>
<minus/>
<ci>vsig2</ci>
</apply>
<ci>vsig4</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>q_R</ci>
</apply>
<apply>
<minus/>
<apply>
<minus/>
<ci>vsig1</ci>
</apply>
<ci>vsig4</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>q_G</ci>
</apply>
<apply>
<minus/>
<apply>
<minus/>
<ci>vsig1</ci>
</apply>
<ci>vsig3</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>q_LR</ci>
</apply>
<apply>
<plus/>
<apply>
<minus/>
<ci>vsig3</ci>
</apply>
<ci>vsig4</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>q_RG</ci>
</apply>
<apply>
<minus/>
<ci>vsig1</ci>
<ci>vsig2</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>q_LRG</ci>
</apply>
<apply>
<plus/>
<ci>vsig2</ci>
<ci>vsig3</ci>
</apply>
</apply>
</math>
</component>
<component name="LRGbinding_parameters">
<variable initial_value="23956.9" name="kappa_sig1" public_interface="out" units="fmol_per_sec"/>
<variable initial_value="18.7535" name="kappa_sig2" public_interface="out" units="fmol_per_sec"/>
<variable initial_value="65.8018" name="kappa_sig3" public_interface="out" units="fmol_per_sec"/>
<variable initial_value="65.8018" name="kappa_sig4" public_interface="out" units="fmol_per_sec"/>
<variable initial_value="1.12532" name="K_L" public_interface="out" units="per_fmol"/>
<variable initial_value="19.5713" name="K_R" public_interface="out" units="per_fmol"/>
<variable initial_value="0.00180233" name="K_G" public_interface="out" units="per_fmol"/>
<variable initial_value="441.777" name="K_LR" public_interface="out" units="per_fmol"/>
<variable initial_value="40.0429" name="K_RG" public_interface="out" units="per_fmol"/>
<variable initial_value="441.777" name="K_LRG" public_interface="out" units="per_fmol"/>
</component>
<component name="LRGbinding">
<variable name="time" public_interface="in" units="second"/>
<!-- Physical parameters-->
<variable name="R" public_interface="in" units="J_per_K_per_mol"/>
<variable name="T" public_interface="in" units="kelvin"/>
<!-- Bond graph parameters, found using pinv of kinetic parameters-->
<variable name="kappa_sig1" public_interface="in" units="fmol_per_sec"/>
<variable name="kappa_sig2" public_interface="in" units="fmol_per_sec"/>
<variable name="kappa_sig3" public_interface="in" units="fmol_per_sec"/>
<variable name="kappa_sig4" public_interface="in" units="fmol_per_sec"/>
<variable name="K_L" public_interface="in" units="per_fmol"/>
<variable name="K_R" public_interface="in" units="per_fmol"/>
<variable name="K_G" public_interface="in" units="per_fmol"/>
<variable name="K_LR" public_interface="in" units="per_fmol"/>
<variable name="K_RG" public_interface="in" units="per_fmol"/>
<variable name="K_LRG" public_interface="in" units="per_fmol"/>
<!-- States (and initial conditions)-->
<variable name="q_R" public_interface="in" units="fmol"/>
<!--{init: 0.0000508778};-->
<variable name="q_G" public_interface="in" units="fmol"/>
<!--{init: 0.0290876489};-->
<variable name="q_RG" public_interface="in" units="fmol"/>
<!--{init: 0.0000508778};-->
<variable name="q_LRG" public_interface="in" units="fmol"/>
<!--{init: 0.0000508778};-->
<variable name="q_L" public_interface="in" units="fmol"/>
<!--{init: 0};-->
<variable name="q_LR" public_interface="in" units="fmol"/>
<!--{init: 0};-->
<!-- Bond variables-->
<variable name="mu_L" units="J_per_mol"/>
<variable name="mu_R" units="J_per_mol"/>
<variable name="mu_G" units="J_per_mol"/>
<variable name="mu_LR" units="J_per_mol"/>
<variable name="mu_RG" units="J_per_mol"/>
<variable name="mu_LRG" units="J_per_mol"/>
<variable name="vsig1" public_interface="out" units="fmol_per_sec"/>
<variable name="vsig2" public_interface="out" units="fmol_per_sec"/>
<variable name="vsig3" public_interface="out" units="fmol_per_sec"/>
<variable name="vsig4" public_interface="out" units="fmol_per_sec"/>
<!-- Concentrations - for plotting-->
<variable name="c_L" public_interface="out" units="uM"/>
<variable name="c_R" public_interface="out" units="uM"/>
<variable name="c_G" public_interface="out" units="uM"/>
<variable name="c_LR" public_interface="out" units="uM"/>
<variable name="c_RG" public_interface="out" units="uM"/>
<variable name="c_LRG" public_interface="out" units="uM"/>
<variable initial_value="34.4" name="vol" units="pL"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>c_L</ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="m_to_u" type="e-notation">1<sep/>3</cn>
<ci>q_L</ci>
</apply>
<ci>vol</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>c_R</ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="m_to_u" type="e-notation">1<sep/>3</cn>
<ci>q_R</ci>
</apply>
<ci>vol</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>c_G</ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="m_to_u" type="e-notation">1<sep/>3</cn>
<ci>q_G</ci>
</apply>
<ci>vol</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>c_LR</ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="m_to_u" type="e-notation">1<sep/>3</cn>
<ci>q_LR</ci>
</apply>
<ci>vol</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>c_RG</ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="m_to_u" type="e-notation">1<sep/>3</cn>
<ci>q_RG</ci>
</apply>
<ci>vol</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>c_LRG</ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="m_to_u" type="e-notation">1<sep/>3</cn>
<ci>q_LRG</ci>
</apply>
<ci>vol</ci>
</apply>
</apply>
<!-- Constitutive equations-->
<apply>
<eq/>
<ci>mu_L</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_L</ci>
<ci>q_L</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_R</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_R</ci>
<ci>q_R</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_G</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_G</ci>
<ci>q_G</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_LR</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_LR</ci>
<ci>q_LR</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_RG</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_RG</ci>
<ci>q_RG</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_LRG</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_LRG</ci>
<ci>q_LRG</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>vsig1</ci>
<apply>
<minus/>
<apply>
<times/>
<ci>kappa_sig1</ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>mu_R</ci>
<ci>mu_G</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>mu_RG</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>vsig2</ci>
<apply>
<minus/>
<apply>
<times/>
<ci>kappa_sig2</ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>mu_RG</ci>
<ci>mu_L</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>mu_LRG</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>vsig3</ci>
<apply>
<minus/>
<apply>
<times/>
<ci>kappa_sig3</ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>mu_LR</ci>
<ci>mu_G</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>mu_LRG</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>vsig4</ci>
<apply>
<minus/>
<apply>
<times/>
<ci>kappa_sig4</ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>mu_R</ci>
<ci>mu_L</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>mu_LR</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<connection>
<map_components component_1="environment" component_2="LRGbinding"/>
<map_variables variable_1="time" variable_2="time"/>
<map_variables variable_1="q_L" variable_2="q_L"/>
<map_variables variable_1="q_LR" variable_2="q_LR"/>
<map_variables variable_1="q_LRG" variable_2="q_LRG"/>
<map_variables variable_1="q_R" variable_2="q_R"/>
<map_variables variable_1="q_RG" variable_2="q_RG"/>
<map_variables variable_1="q_G" variable_2="q_G"/>
<map_variables variable_1="vsig1" variable_2="vsig1"/>
<map_variables variable_1="vsig2" variable_2="vsig2"/>
<map_variables variable_1="vsig3" variable_2="vsig3"/>
<map_variables variable_1="vsig4" variable_2="vsig4"/>
</connection>
<connection>
<map_components component_1="LRGbinding_parameters" component_2="LRGbinding"/>
<map_variables variable_1="kappa_sig1" variable_2="kappa_sig1"/>
<map_variables variable_1="kappa_sig2" variable_2="kappa_sig2"/>
<map_variables variable_1="kappa_sig3" variable_2="kappa_sig3"/>
<map_variables variable_1="kappa_sig4" variable_2="kappa_sig4"/>
<map_variables variable_1="K_L" variable_2="K_L"/>
<map_variables variable_1="K_R" variable_2="K_R"/>
<map_variables variable_1="K_G" variable_2="K_G"/>
<map_variables variable_1="K_LR" variable_2="K_LR"/>
<map_variables variable_1="K_RG" variable_2="K_RG"/>
<map_variables variable_1="K_LRG" variable_2="K_LRG"/>
</connection>
<connection>
<map_components component_1="constants" component_2="LRGbinding"/>
<map_variables variable_1="R" variable_2="R"/>
<map_variables variable_1="T" variable_2="T"/>
</connection>
</model>
