- Author:
- Shelley Fong <s.fong@auckland.ac.nz>
- Date:
- 2021-10-11 14:05:43+13:00
- Desc:
- Adding conservation of chemostat mass check in environment. Fixing ICs to have negligible enzyme complexes
- Permanent Source URI:
- https://models.physiomeproject.org/workspace/707/rawfile/7bf820308163969768c077f0cb093512a1bbe045/BG_LRGbinding_M2.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
6sept21 with parameters from saucerman2003 for beta1adrenergic receptor or iancu2007 for muscarinic receptor-->
<model name="BG_LRGbinding_M2" 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 name="q_L_M2_init" units="fmol"/>
<variable initial_value="0.00072162" name="q_R_M2_init" units="fmol"/>
<variable initial_value="0.00836" name="q_Gi_init" units="fmol"/>
<variable initial_value="1e-18" name="q_LR_M2_init" units="fmol"/>
<variable initial_value="1e-18" name="q_R_M2Gi_init" units="fmol"/>
<variable initial_value="1e-18" name="q_LR_M2Gi_init" units="fmol"/>
<variable name="L_T" public_interface="in" units="fmol"/>
<variable name="R_T" public_interface="in" units="fmol"/>
<variable name="Gi_T" public_interface="in" units="fmol"/>
<!-- Global value-->
<variable name="q_L_M2" public_interface="out" units="fmol"/>
<variable name="q_R_M2" public_interface="out" units="fmol"/>
<variable name="q_Gi" public_interface="out" units="fmol"/>
<variable name="q_LR_M2" public_interface="out" units="fmol"/>
<variable name="q_R_M2Gi" public_interface="out" units="fmol"/>
<variable name="q_LR_M2Gi" public_interface="out" units="fmol"/>
<!-- From submodule-->
<variable name="q_L_M2_mLRGbinding_M2" public_interface="in" units="fmol"/>
<variable name="q_R_M2_mLRGbinding_M2" public_interface="in" units="fmol"/>
<variable name="q_Gi_mLRGbinding_M2" public_interface="in" units="fmol"/>
<variable name="q_LR_M2_mLRGbinding_M2" public_interface="in" units="fmol"/>
<variable name="q_R_M2Gi_mLRGbinding_M2" public_interface="in" units="fmol"/>
<variable name="q_LR_M2Gi_mLRGbinding_M2" public_interface="in" units="fmol"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>q_L_M2</ci>
<apply>
<plus/>
<ci>q_L_M2_mLRGbinding_M2</ci>
<ci>q_L_M2_init</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>q_R_M2</ci>
<apply>
<plus/>
<ci>q_R_M2_mLRGbinding_M2</ci>
<ci>q_R_M2_init</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>q_Gi</ci>
<apply>
<plus/>
<ci>q_Gi_mLRGbinding_M2</ci>
<ci>q_Gi_init</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>q_LR_M2</ci>
<apply>
<plus/>
<ci>q_LR_M2_mLRGbinding_M2</ci>
<ci>q_LR_M2_init</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>q_R_M2Gi</ci>
<apply>
<plus/>
<ci>q_R_M2Gi_mLRGbinding_M2</ci>
<ci>q_R_M2Gi_init</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>q_LR_M2Gi</ci>
<apply>
<plus/>
<ci>q_LR_M2Gi_mLRGbinding_M2</ci>
<ci>q_LR_M2Gi_init</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>q_L_M2_init</ci>
<piecewise>
<piece>
<cn cellml:units="fmol" type="e-notation">1<sep/>-4</cn>
<apply>
<and/>
<apply>
<lt/>
<ci>time</ci>
<cn cellml:units="second" type="e-notation">5<sep/>-1</cn>
</apply>
<apply>
<gt/>
<ci>time</ci>
<cn cellml:units="second" type="e-notation">4<sep/>-1</cn>
</apply>
</apply>
</piece>
<otherwise>
<cn cellml:units="fmol" type="e-notation">1<sep/>-4</cn>
</otherwise>
</piecewise>
</apply>
</math>
</component>
<component name="LRGbinding_parameters">
<variable initial_value="9542.66" name="kappa_sig1_M2" units="fmol_per_sec"/>
<variable initial_value="45.8005" name="kappa_sig2_M2" units="fmol_per_sec"/>
<variable initial_value="124.91" name="kappa_sig3_M2" units="fmol_per_sec"/>
<variable initial_value="6830.09" name="kappa_sig4_M2" units="fmol_per_sec"/>
<variable initial_value="0.201892" name="K_L_M2" units="per_fmol"/>
<variable initial_value="0.612826" name="K_R_M2" units="per_fmol"/>
<variable initial_value="0.144503" name="K_Gi" units="per_fmol"/>
<variable initial_value="46.8175" name="K_LR_M2" units="per_fmol"/>
<variable initial_value="91.3889" name="K_R_M2Gi" units="per_fmol"/>
<variable initial_value="101.553" name="K_LR_M2Gi" units="per_fmol"/>
</component>
<component name="LRGbinding_M2">
<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_M2" public_interface="in" units="fmol_per_sec"/>
<variable name="kappa_sig2_M2" public_interface="in" units="fmol_per_sec"/>
<variable name="kappa_sig3_M2" public_interface="in" units="fmol_per_sec"/>
<variable name="kappa_sig4_M2" public_interface="in" units="fmol_per_sec"/>
<variable name="K_L_M2" public_interface="in" units="per_fmol"/>
<variable name="K_R_M2" public_interface="in" units="per_fmol"/>
<variable name="K_Gi" public_interface="in" units="per_fmol"/>
<variable name="K_LR_M2" public_interface="in" units="per_fmol"/>
<variable name="K_R_M2Gi" public_interface="in" units="per_fmol"/>
<variable name="K_LR_M2Gi" public_interface="in" units="per_fmol"/>
<!-- Input from global environment-->
<variable name="q_L_M2_global" public_interface="in" units="fmol"/>
<variable name="q_R_M2_global" public_interface="in" units="fmol"/>
<variable name="q_Gi_global" public_interface="in" units="fmol"/>
<variable name="q_LR_M2_global" public_interface="in" units="fmol"/>
<variable name="q_R_M2Gi_global" public_interface="in" units="fmol"/>
<variable name="q_LR_M2Gi_global" public_interface="in" units="fmol"/>
<!-- Output to global environment-->
<variable initial_value="1e-16" name="q_L_M2" public_interface="out" units="fmol"/>
<variable initial_value="1e-16" name="q_R_M2" public_interface="out" units="fmol"/>
<variable initial_value="1e-16" name="q_Gi" public_interface="out" units="fmol"/>
<variable initial_value="1e-16" name="q_LR_M2" public_interface="out" units="fmol"/>
<variable initial_value="1e-16" name="q_R_M2Gi" public_interface="out" units="fmol"/>
<variable initial_value="1e-16" name="q_LR_M2Gi" public_interface="out" units="fmol"/>
<!-- Bond variables-->
<variable name="mu_L_M2" units="J_per_mol"/>
<variable name="mu_R_M2" units="J_per_mol"/>
<variable name="mu_Gi" units="J_per_mol"/>
<variable name="mu_LR_M2" units="J_per_mol"/>
<variable name="mu_R_M2Gi" units="J_per_mol"/>
<variable name="mu_LR_M2Gi" units="J_per_mol"/>
<variable name="vsig1_M2" units="fmol_per_sec"/>
<variable name="vsig2_M2" units="fmol_per_sec"/>
<variable name="vsig3_M2" units="fmol_per_sec"/>
<variable name="vsig4_M2" units="fmol_per_sec"/>
<!-- -->
<variable initial_value="34.4" name="vol" units="pL"/>
<!-- Constitutive equations-->
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>mu_L_M2</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_L_M2</ci>
<ci>q_L_M2_global</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_R_M2</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_R_M2</ci>
<ci>q_R_M2_global</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_Gi</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_Gi</ci>
<ci>q_Gi_global</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_LR_M2</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_LR_M2</ci>
<ci>q_LR_M2_global</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_R_M2Gi</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_R_M2Gi</ci>
<ci>q_R_M2Gi_global</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_LR_M2Gi</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_LR_M2Gi</ci>
<ci>q_LR_M2Gi_global</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>vsig1_M2</ci>
<apply>
<minus/>
<apply>
<times/>
<ci>kappa_sig1_M2</ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>mu_R_M2</ci>
<ci>mu_Gi</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>mu_R_M2Gi</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>vsig2_M2</ci>
<apply>
<minus/>
<apply>
<times/>
<ci>kappa_sig2_M2</ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>mu_R_M2Gi</ci>
<ci>mu_L_M2</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>mu_LR_M2Gi</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>vsig3_M2</ci>
<apply>
<minus/>
<apply>
<times/>
<ci>kappa_sig3_M2</ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>mu_LR_M2</ci>
<ci>mu_Gi</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>mu_LR_M2Gi</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>vsig4_M2</ci>
<apply>
<minus/>
<apply>
<times/>
<ci>kappa_sig4_M2</ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>mu_R_M2</ci>
<ci>mu_L_M2</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>mu_LR_M2</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>q_L_M2</ci>
</apply>
<apply>
<minus/>
<apply>
<minus/>
<ci>vsig2_M2</ci>
</apply>
<ci>vsig4_M2</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>q_R_M2</ci>
</apply>
<apply>
<minus/>
<apply>
<minus/>
<ci>vsig1_M2</ci>
</apply>
<ci>vsig4_M2</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>q_Gi</ci>
</apply>
<apply>
<minus/>
<apply>
<minus/>
<ci>vsig1_M2</ci>
</apply>
<ci>vsig3_M2</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>q_LR_M2</ci>
</apply>
<apply>
<plus/>
<apply>
<minus/>
<ci>vsig3_M2</ci>
</apply>
<ci>vsig4_M2</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>q_R_M2Gi</ci>
</apply>
<apply>
<minus/>
<ci>vsig1_M2</ci>
<ci>vsig2_M2</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>q_LR_M2Gi</ci>
</apply>
<apply>
<plus/>
<ci>vsig2_M2</ci>
<ci>vsig3_M2</ci>
</apply>
</apply>
</math>
<!-- mass conservation checks -->
<variable name="L_T" public_interface="out" units="fmol"/>
<variable name="R_T" public_interface="out" units="fmol"/>
<variable name="Gi_T" public_interface="out" units="fmol"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>L_T</ci>
<apply>
<plus/>
<ci>q_L_M2_global</ci>
<ci>q_LR_M2_global</ci>
<ci>q_LR_M2Gi_global</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>R_T</ci>
<apply>
<plus/>
<ci>q_R_M2_global</ci>
<ci>q_LR_M2_global</ci>
<ci>q_R_M2Gi_global</ci>
<ci>q_LR_M2Gi_global</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>Gi_T</ci>
<apply>
<plus/>
<ci>q_Gi_global</ci>
<ci>q_R_M2Gi_global</ci>
<ci>q_LR_M2Gi_global</ci>
</apply>
</apply>
</math>
</component>
<connection>
<map_components component_1="environment" component_2="LRGbinding_M2"/>
<map_variables variable_1="time" variable_2="time"/>
<map_variables variable_1="q_L_M2_mLRGbinding_M2" variable_2="q_L_M2"/>
<map_variables variable_1="q_L_M2" variable_2="q_L_M2_global"/>
<map_variables variable_1="q_R_M2_mLRGbinding_M2" variable_2="q_R_M2"/>
<map_variables variable_1="q_R_M2" variable_2="q_R_M2_global"/>
<map_variables variable_1="q_Gi_mLRGbinding_M2" variable_2="q_Gi"/>
<map_variables variable_1="q_Gi" variable_2="q_Gi_global"/>
<map_variables variable_1="q_LR_M2_mLRGbinding_M2" variable_2="q_LR_M2"/>
<map_variables variable_1="q_LR_M2" variable_2="q_LR_M2_global"/>
<map_variables variable_1="q_R_M2Gi_mLRGbinding_M2" variable_2="q_R_M2Gi"/>
<map_variables variable_1="q_R_M2Gi" variable_2="q_R_M2Gi_global"/>
<map_variables variable_1="q_LR_M2Gi_mLRGbinding_M2" variable_2="q_LR_M2Gi"/>
<map_variables variable_1="q_LR_M2Gi" variable_2="q_LR_M2Gi_global"/>
<map_variables variable_1="L_T" variable_2="L_T"/>
<map_variables variable_1="R_T" variable_2="R_T"/>
<map_variables variable_1="Gi_T" variable_2="Gi_T"/>
</connection>
<connection>
<map_components component_1="LRGbinding_parameters" component_2="LRGbinding_M2"/>
<map_variables variable_1="kappa_sig1_M2" variable_2="kappa_sig1_M2"/>
<map_variables variable_1="kappa_sig2_M2" variable_2="kappa_sig2_M2"/>
<map_variables variable_1="kappa_sig3_M2" variable_2="kappa_sig3_M2"/>
<map_variables variable_1="kappa_sig4_M2" variable_2="kappa_sig4_M2"/>
<map_variables variable_1="K_L_M2" variable_2="K_L_M2"/>
<map_variables variable_1="K_R_M2" variable_2="K_R_M2"/>
<map_variables variable_1="K_Gi" variable_2="K_Gi"/>
<map_variables variable_1="K_LR_M2" variable_2="K_LR_M2"/>
<map_variables variable_1="K_R_M2Gi" variable_2="K_R_M2Gi"/>
<map_variables variable_1="K_LR_M2Gi" variable_2="K_LR_M2Gi"/>
</connection>
<connection>
<map_components component_1="constants" component_2="LRGbinding_M2"/>
<map_variables variable_1="R" variable_2="R"/>
<map_variables variable_1="T" variable_2="T"/>
</connection>
</model>
