- Author:
- Shelley Fong <s.fong@auckland.ac.nz>
- Date:
- 2021-11-17 10:24:18+13:00
- Desc:
- Using sympy for rational nullspace
- Permanent Source URI:
- https://models.cellml.org/workspace/6f9/rawfile/df183a1b55c67436e9a30db3a32568f3dd8d850a/BG_GiProtein.cellml
<?xml version='1.0' encoding='UTF-8'?>
<!-- Gi protein metabolism, with reActions:
Activation (Act1 and Act2), Hydration (Hyd), Reassociation (Reassoc)
14Oct21 with separated Phosphate binding from Activation of RG and LRG
26Oct21 with an intermediate compound formed after GDP ejection from G protein, and before GTP enters alpha binding site-->
<model name="GiProtein" 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"/>
<!--Initial conditions-->
<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_R_M2Gi_init" units="fmol"/>
<variable initial_value="1e-1" name="q_LR_M2_init" units="fmol"/>
<variable initial_value="1e-18" name="q_LR_M2Gi_init" units="fmol"/>
<variable initial_value="1e-18" name="q_a_Gi_GTP_init" units="fmol"/>
<variable initial_value="1e-18" name="q_beta_gamma_Gi_init" units="fmol"/>
<variable initial_value="1e-18" name="q_a_Gi_GDP_init" units="fmol"/>
<variable initial_value="570" name="q_Pi_init" units="fmol"/>
<variable initial_value="1e-18" name="q_R_M2_aby_init" units="fmol"/>
<variable initial_value="1e-18" name="q_R_M2_aby_T_init" units="fmol"/>
<variable initial_value="1e-18" name="q_LR_M2_aby_init" units="fmol"/>
<variable initial_value="1e-18" name="q_LR_M2_aby_T_init" units="fmol"/>
<variable initial_value="2.2" name="q_GTP_init" public_interface="out" units="fmol"/>
<variable initial_value="1.1" name="q_GDP_init" public_interface="out" units="fmol"/>
<!-- mass conservation checks-->
<variable name="R_T" public_interface="in" units="fmol"/>
<variable name="Gi_T" public_interface="in" units="fmol"/>
<!-- Global value-->
<variable name="q_R_M2" public_interface="out" units="fmol"/>
<variable name="q_Gi" public_interface="out" units="fmol"/>
<variable name="q_R_M2Gi" public_interface="out" units="fmol"/>
<variable name="q_LR_M2" public_interface="out" units="fmol"/>
<variable name="q_LR_M2Gi" public_interface="out" units="fmol"/>
<variable name="q_a_Gi_GTP" public_interface="out" units="fmol"/>
<variable name="q_beta_gamma_Gi" public_interface="out" units="fmol"/>
<variable name="q_a_Gi_GDP" public_interface="out" units="fmol"/>
<variable name="q_Pi" public_interface="out" units="fmol"/>
<variable name="q_R_M2_aby" public_interface="out" units="fmol"/>
<variable name="q_R_M2_aby_T" public_interface="out" units="fmol"/>
<variable name="q_LR_M2_aby" public_interface="out" units="fmol"/>
<variable name="q_LR_M2_aby_T" public_interface="out" units="fmol"/>
<variable name="q_GTP" public_interface="out" units="fmol"/>
<variable name="q_GDP" public_interface="out" units="fmol"/>
<!-- From submodule-->
<variable name="q_R_M2_mGiProtein" public_interface="in" units="fmol"/>
<variable name="q_Gi_mGiProtein" public_interface="in" units="fmol"/>
<variable name="q_R_M2Gi_mGiProtein" public_interface="in" units="fmol"/>
<variable name="q_LR_M2_mGiProtein" public_interface="in" units="fmol"/>
<variable name="q_LR_M2Gi_mGiProtein" public_interface="in" units="fmol"/>
<variable name="q_a_Gi_GTP_mGiProtein" public_interface="in" units="fmol"/>
<variable name="q_beta_gamma_Gi_mGiProtein" public_interface="in" units="fmol"/>
<variable name="q_a_Gi_GDP_mGiProtein" public_interface="in" units="fmol"/>
<variable name="q_Pi_mGiProtein" public_interface="in" units="fmol"/>
<variable name="q_R_M2_aby_mGiProtein" public_interface="in" units="fmol"/>
<variable name="q_R_M2_aby_T_mGiProtein" public_interface="in" units="fmol"/>
<variable name="q_LR_M2_aby_mGiProtein" public_interface="in" units="fmol"/>
<variable name="q_LR_M2_aby_T_mGiProtein" public_interface="in" units="fmol"/>
<variable name="q_GTP_mGiProtein" public_interface="in" units="fmol"/>
<variable name="q_GDP_mGiProtein" public_interface="in" units="fmol"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>q_R_M2</ci>
<apply>
<plus/>
<ci>q_R_M2_mGiProtein</ci>
<ci>q_R_M2_init</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>q_Gi</ci>
<apply>
<plus/>
<ci>q_Gi_mGiProtein</ci>
<ci>q_Gi_init</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>q_R_M2Gi</ci>
<apply>
<plus/>
<ci>q_R_M2Gi_mGiProtein</ci>
<ci>q_R_M2Gi_init</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>q_LR_M2</ci>
<apply>
<plus/>
<ci>q_LR_M2_mGiProtein</ci>
<ci>q_LR_M2_init</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>q_LR_M2Gi</ci>
<apply>
<plus/>
<ci>q_LR_M2Gi_mGiProtein</ci>
<ci>q_LR_M2Gi_init</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>q_a_Gi_GTP</ci>
<apply>
<plus/>
<ci>q_a_Gi_GTP_mGiProtein</ci>
<ci>q_a_Gi_GTP_init</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>q_beta_gamma_Gi</ci>
<apply>
<plus/>
<ci>q_beta_gamma_Gi_mGiProtein</ci>
<ci>q_beta_gamma_Gi_init</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>q_a_Gi_GDP</ci>
<apply>
<plus/>
<ci>q_a_Gi_GDP_mGiProtein</ci>
<ci>q_a_Gi_GDP_init</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>q_Pi</ci>
<apply>
<plus/>
<ci>q_Pi_mGiProtein</ci>
<ci>q_Pi_init</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>q_R_M2_aby</ci>
<apply>
<plus/>
<ci>q_R_M2_aby_mGiProtein</ci>
<ci>q_R_M2_aby_init</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>q_R_M2_aby_T</ci>
<apply>
<plus/>
<ci>q_R_M2_aby_T_mGiProtein</ci>
<ci>q_R_M2_aby_T_init</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>q_LR_M2_aby</ci>
<apply>
<plus/>
<ci>q_LR_M2_aby_mGiProtein</ci>
<ci>q_LR_M2_aby_init</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>q_LR_M2_aby_T</ci>
<apply>
<plus/>
<ci>q_LR_M2_aby_T_mGiProtein</ci>
<ci>q_LR_M2_aby_T_init</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>q_GTP</ci>
<apply>
<plus/>
<ci>q_GTP_mGiProtein</ci>
<ci>q_GTP_init</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>q_GDP</ci>
<apply>
<plus/>
<ci>q_GDP_mGiProtein</ci>
<ci>q_GDP_init</ci>
</apply>
</apply>
</math>
</component>
<component name="GiProtein_parameters">
<variable initial_value="2.60723" name="kappa_Doff1_Gi" public_interface="out" units="fmol_per_sec"/>
<variable initial_value="0.0123541" name="kappa_Ton1_Gi" public_interface="out" units="fmol_per_sec"/>
<variable initial_value="30.8853" name="kappa_Act1_Gi" public_interface="out" units="fmol_per_sec"/>
<variable initial_value="4.55922" name="kappa_Doff2_Gi" public_interface="out" units="fmol_per_sec"/>
<variable initial_value="0.0216034" name="kappa_Ton2_Gi" public_interface="out" units="fmol_per_sec"/>
<variable initial_value="1.08017" name="kappa_Act2_Gi" public_interface="out" units="fmol_per_sec"/>
<variable initial_value="5.27319" name="kappa_hyd_Gi" public_interface="out" units="fmol_per_sec"/>
<variable initial_value="561629" name="kappa_reassoc_Gi" public_interface="out" units="fmol_per_sec"/>
<variable initial_value="0.00034316" name="K_R_M2" public_interface="out" units="per_fmol"/>
<variable initial_value="125.259" name="K_Gi" public_interface="out" units="per_fmol"/>
<variable initial_value="11.1497" name="K_R_M2Gi" public_interface="out" units="per_fmol"/>
<variable initial_value="0.00019624" name="K_LR_M2" public_interface="out" units="per_fmol"/>
<variable initial_value="6.37605" name="K_LR_M2Gi" public_interface="out" units="per_fmol"/>
<variable initial_value="0.0044102" name="K_a_Gi_GTP" public_interface="out" units="per_fmol"/>
<variable initial_value="0.000525554" name="K_beta_gamma_Gi" public_interface="out" units="per_fmol"/>
<variable initial_value="0.00346419" name="K_a_Gi_GDP" public_interface="out" units="per_fmol"/>
<variable initial_value="4.62603e-05" name="K_Pi" public_interface="out" units="per_fmol"/>
<variable initial_value="0.078908" name="K_R_M2_aby" public_interface="out" units="per_fmol"/>
<variable initial_value="0.00235304" name="K_R_M2_aby_T" public_interface="out" units="per_fmol"/>
<variable initial_value="0.0451244" name="K_LR_M2_aby" public_interface="out" units="per_fmol"/>
<variable initial_value="0.00134561" name="K_LR_M2_aby_T" public_interface="out" units="per_fmol"/>
<variable initial_value="866.863" name="K_GTP" public_interface="out" units="per_fmol"/>
<variable initial_value="4.10754e-06" name="K_GDP" public_interface="out" units="per_fmol"/>
</component>
<component name="GiProtein">
<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"/>
<!-- BG parameters-->
<variable name="kappa_Doff1_Gi" public_interface="in" units="fmol_per_sec"/>
<variable name="kappa_Ton1_Gi" public_interface="in" units="fmol_per_sec"/>
<variable name="kappa_Act1_Gi" public_interface="in" units="fmol_per_sec"/>
<variable name="kappa_Doff2_Gi" public_interface="in" units="fmol_per_sec"/>
<variable name="kappa_Ton2_Gi" public_interface="in" units="fmol_per_sec"/>
<variable name="kappa_Act2_Gi" public_interface="in" units="fmol_per_sec"/>
<variable name="kappa_hyd_Gi" public_interface="in" units="fmol_per_sec"/>
<variable name="kappa_reassoc_Gi" public_interface="in" units="fmol_per_sec"/>
<variable name="K_R_M2" public_interface="in" units="per_fmol"/>
<variable name="K_Gi" public_interface="in" units="per_fmol"/>
<variable name="K_R_M2Gi" public_interface="in" units="per_fmol"/>
<variable name="K_LR_M2" public_interface="in" units="per_fmol"/>
<variable name="K_LR_M2Gi" public_interface="in" units="per_fmol"/>
<variable name="K_a_Gi_GTP" public_interface="in" units="per_fmol"/>
<variable name="K_beta_gamma_Gi" public_interface="in" units="per_fmol"/>
<variable name="K_a_Gi_GDP" public_interface="in" units="per_fmol"/>
<variable name="K_Pi" public_interface="in" units="per_fmol"/>
<variable name="K_R_M2_aby" public_interface="in" units="per_fmol"/>
<variable name="K_R_M2_aby_T" public_interface="in" units="per_fmol"/>
<variable name="K_LR_M2_aby" public_interface="in" units="per_fmol"/>
<variable name="K_LR_M2_aby_T" public_interface="in" units="per_fmol"/>
<variable name="K_GTP" public_interface="in" units="per_fmol"/>
<variable name="K_GDP" public_interface="in" units="per_fmol"/>
<!-- Input from global environment-->
<variable name="q_R_M2_global" public_interface="in" units="fmol"/>
<variable name="q_Gi_global" public_interface="in" units="fmol"/>
<variable name="q_R_M2Gi_global" public_interface="in" units="fmol"/>
<variable name="q_LR_M2_global" public_interface="in" units="fmol"/>
<variable name="q_LR_M2Gi_global" public_interface="in" units="fmol"/>
<variable name="q_a_Gi_GTP_global" public_interface="in" units="fmol"/>
<variable name="q_beta_gamma_Gi_global" public_interface="in" units="fmol"/>
<variable name="q_a_Gi_GDP_global" public_interface="in" units="fmol"/>
<variable name="q_Pi_global" public_interface="in" units="fmol"/>
<variable name="q_R_M2_aby_global" public_interface="in" units="fmol"/>
<variable name="q_R_M2_aby_T_global" public_interface="in" units="fmol"/>
<variable name="q_LR_M2_aby_global" public_interface="in" units="fmol"/>
<variable name="q_LR_M2_aby_T_global" public_interface="in" units="fmol"/>
<variable name="q_GTP_global" public_interface="in" units="fmol"/>
<variable name="q_GDP_global" public_interface="in" units="fmol"/>
<!-- Output to global environment-->
<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_R_M2Gi" 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_LR_M2Gi" public_interface="out" units="fmol"/>
<variable initial_value="1e-16" name="q_a_Gi_GTP" public_interface="out" units="fmol"/>
<variable initial_value="1e-16" name="q_beta_gamma_Gi" public_interface="out" units="fmol"/>
<variable initial_value="1e-16" name="q_a_Gi_GDP" public_interface="out" units="fmol"/>
<variable initial_value="1e-16" name="q_Pi" public_interface="out" units="fmol"/>
<variable initial_value="1e-16" name="q_R_M2_aby" public_interface="out" units="fmol"/>
<variable initial_value="1e-16" name="q_R_M2_aby_T" public_interface="out" units="fmol"/>
<variable initial_value="1e-16" name="q_LR_M2_aby" public_interface="out" units="fmol"/>
<variable initial_value="1e-16" name="q_LR_M2_aby_T" public_interface="out" units="fmol"/>
<variable initial_value="1e-16" name="q_GTP" public_interface="out" units="fmol"/>
<variable initial_value="1e-16" name="q_GDP" public_interface="out" units="fmol"/>
<!-- Bond variables-->
<variable name="vDoff1_Gi" units="fmol_per_sec"/>
<variable name="vTon1_Gi" units="fmol_per_sec"/>
<variable name="vAct1_Gi" units="fmol_per_sec"/>
<variable name="vDoff2_Gi" units="fmol_per_sec"/>
<variable name="vTon2_Gi" units="fmol_per_sec"/>
<variable name="vAct2_Gi" units="fmol_per_sec"/>
<variable name="vhyd_Gi" units="fmol_per_sec"/>
<variable name="vreassoc_Gi" units="fmol_per_sec"/>
<variable name="mu_R_M2" units="J_per_mol"/>
<variable name="mu_Gi" units="J_per_mol"/>
<variable name="mu_R_M2Gi" units="J_per_mol"/>
<variable name="mu_LR_M2" units="J_per_mol"/>
<variable name="mu_LR_M2Gi" units="J_per_mol"/>
<variable name="mu_a_Gi_GTP" units="J_per_mol"/>
<variable name="mu_beta_gamma_Gi" units="J_per_mol"/>
<variable name="mu_a_Gi_GDP" units="J_per_mol"/>
<variable name="mu_Pi" units="J_per_mol"/>
<variable name="mu_R_M2_aby" units="J_per_mol"/>
<variable name="mu_R_M2_aby_T" units="J_per_mol"/>
<variable name="mu_LR_M2_aby" units="J_per_mol"/>
<variable name="mu_LR_M2_aby_T" units="J_per_mol"/>
<variable name="mu_GTP" units="J_per_mol"/>
<variable name="mu_GDP" units="J_per_mol"/>
<!-- Constitutive equations-->
<math xmlns="http://www.w3.org/1998/Math/MathML">
<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_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_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_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>mu_a_Gi_GTP</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_a_Gi_GTP</ci>
<ci>q_a_Gi_GTP_global</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_beta_gamma_Gi</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_beta_gamma_Gi</ci>
<ci>q_beta_gamma_Gi_global</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_a_Gi_GDP</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_a_Gi_GDP</ci>
<ci>q_a_Gi_GDP_global</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_Pi</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_Pi</ci>
<ci>q_Pi_global</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_R_M2_aby</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_R_M2_aby</ci>
<ci>q_R_M2_aby_global</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_R_M2_aby_T</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_R_M2_aby_T</ci>
<ci>q_R_M2_aby_T_global</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_LR_M2_aby</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_LR_M2_aby</ci>
<ci>q_LR_M2_aby_global</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_LR_M2_aby_T</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_LR_M2_aby_T</ci>
<ci>q_LR_M2_aby_T_global</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_GTP</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_GTP</ci>
<ci>q_GTP_global</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_GDP</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_GDP</ci>
<ci>q_GDP_global</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>vDoff1_Gi</ci>
<apply>
<times/>
<ci>kappa_Doff1_Gi</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>mu_R_M2Gi</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>mu_R_M2_aby</ci>
<ci>mu_GDP</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>vTon1_Gi</ci>
<apply>
<times/>
<ci>kappa_Ton1_Gi</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>mu_R_M2_aby</ci>
<ci>mu_GTP</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>mu_R_M2_aby_T</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>vAct1_Gi</ci>
<apply>
<times/>
<ci>kappa_Act1_Gi</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>mu_R_M2_aby_T</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>mu_a_Gi_GTP</ci>
<ci>mu_beta_gamma_Gi</ci>
<ci>mu_R_M2</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>vDoff2_Gi</ci>
<apply>
<times/>
<ci>kappa_Doff2_Gi</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>mu_LR_M2Gi</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>mu_LR_M2_aby</ci>
<ci>mu_GDP</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>vTon2_Gi</ci>
<apply>
<times/>
<ci>kappa_Ton2_Gi</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>mu_LR_M2_aby</ci>
<ci>mu_GTP</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>mu_LR_M2_aby_T</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>vAct2_Gi</ci>
<apply>
<times/>
<ci>kappa_Act2_Gi</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>mu_LR_M2_aby_T</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>mu_a_Gi_GTP</ci>
<ci>mu_beta_gamma_Gi</ci>
<ci>mu_LR_M2</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>vhyd_Gi</ci>
<apply>
<times/>
<ci>kappa_hyd_Gi</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>mu_a_Gi_GTP</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>mu_a_Gi_GDP</ci>
<ci>mu_Pi</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>vreassoc_Gi</ci>
<apply>
<times/>
<ci>kappa_reassoc_Gi</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>mu_a_Gi_GDP</ci>
<ci>mu_beta_gamma_Gi</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>mu_Gi</ci>
<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_R_M2</ci>
</apply>
<ci>vAct1_Gi</ci>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>q_R_M2Gi</ci>
</apply>
<apply>
<minus/>
<ci>vDoff1_Gi</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>q_Gi</ci>
</apply>
<ci>vreassoc_Gi</ci>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>q_LR_M2</ci>
</apply>
<ci>vAct2_Gi</ci>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>q_LR_M2Gi</ci>
</apply>
<apply>
<minus/>
<ci>vDoff2_Gi</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>q_a_Gi_GTP</ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<ci>vAct1_Gi</ci>
<ci>vAct2_Gi</ci>
</apply>
<ci>vhyd_Gi</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>q_beta_gamma_Gi</ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<ci>vAct1_Gi</ci>
<ci>vAct2_Gi</ci>
</apply>
<ci>vreassoc_Gi</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>q_a_Gi_GDP</ci>
</apply>
<apply>
<minus/>
<ci>vhyd_Gi</ci>
<ci>vreassoc_Gi</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>q_Pi</ci>
</apply>
<ci>vhyd_Gi</ci>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>q_R_M2_aby</ci>
</apply>
<apply>
<minus/>
<ci>vDoff1_Gi</ci>
<ci>vTon1_Gi</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>q_R_M2_aby_T</ci>
</apply>
<apply>
<minus/>
<ci>vTon1_Gi</ci>
<ci>vAct1_Gi</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>q_LR_M2_aby</ci>
</apply>
<apply>
<minus/>
<ci>vDoff2_Gi</ci>
<ci>vTon2_Gi</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>q_LR_M2_aby_T</ci>
</apply>
<apply>
<minus/>
<ci>vTon2_Gi</ci>
<ci>vAct2_Gi</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>q_GTP</ci>
</apply>
<apply>
<minus/>
<apply>
<minus/>
<ci>vTon1_Gi</ci>
</apply>
<ci>vTon2_Gi</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>q_GDP</ci>
</apply>
<apply>
<plus/>
<ci>vDoff1_Gi</ci>
<ci>vDoff2_Gi</ci>
</apply>
</apply>
</math>
<!-- mass conservation checks -->
<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>R_T</ci>
<apply>
<plus/>
<ci>q_R_M2_global</ci>
<ci>q_R_M2Gi_global</ci>
<ci>q_LR_M2_global</ci>
<ci>q_LR_M2Gi_global</ci>
<ci>q_R_M2_aby_global</ci>
<ci>q_R_M2_aby_T_global</ci>
<ci>q_LR_M2_aby_global</ci>
<ci>q_LR_M2_aby_T_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>
<ci>q_a_Gi_GTP_global</ci>
<ci>q_a_Gi_GDP_global</ci>
<ci>q_R_M2_aby_global</ci>
<ci>q_R_M2_aby_T_global</ci>
<ci>q_LR_M2_aby_global</ci>
<ci>q_LR_M2_aby_T_global</ci>
</apply>
</apply>
</math>
</component>
<connection>
<map_components component_1="environment" component_2="GiProtein"/>
<map_variables variable_1="time" variable_2="time"/>
<map_variables variable_1="q_R_M2_mGiProtein" variable_2="q_R_M2"/>
<map_variables variable_1="q_R_M2" variable_2="q_R_M2_global"/>
<map_variables variable_1="q_Gi_mGiProtein" variable_2="q_Gi"/>
<map_variables variable_1="q_Gi" variable_2="q_Gi_global"/>
<map_variables variable_1="q_R_M2Gi_mGiProtein" variable_2="q_R_M2Gi"/>
<map_variables variable_1="q_R_M2Gi" variable_2="q_R_M2Gi_global"/>
<map_variables variable_1="q_LR_M2_mGiProtein" variable_2="q_LR_M2"/>
<map_variables variable_1="q_LR_M2" variable_2="q_LR_M2_global"/>
<map_variables variable_1="q_LR_M2Gi_mGiProtein" variable_2="q_LR_M2Gi"/>
<map_variables variable_1="q_LR_M2Gi" variable_2="q_LR_M2Gi_global"/>
<map_variables variable_1="q_a_Gi_GTP_mGiProtein" variable_2="q_a_Gi_GTP"/>
<map_variables variable_1="q_a_Gi_GTP" variable_2="q_a_Gi_GTP_global"/>
<map_variables variable_1="q_beta_gamma_Gi_mGiProtein" variable_2="q_beta_gamma_Gi"/>
<map_variables variable_1="q_beta_gamma_Gi" variable_2="q_beta_gamma_Gi_global"/>
<map_variables variable_1="q_a_Gi_GDP_mGiProtein" variable_2="q_a_Gi_GDP"/>
<map_variables variable_1="q_a_Gi_GDP" variable_2="q_a_Gi_GDP_global"/>
<map_variables variable_1="q_Pi_mGiProtein" variable_2="q_Pi"/>
<map_variables variable_1="q_Pi" variable_2="q_Pi_global"/>
<map_variables variable_1="q_R_M2_aby_mGiProtein" variable_2="q_R_M2_aby"/>
<map_variables variable_1="q_R_M2_aby" variable_2="q_R_M2_aby_global"/>
<map_variables variable_1="q_R_M2_aby_T_mGiProtein" variable_2="q_R_M2_aby_T"/>
<map_variables variable_1="q_R_M2_aby_T" variable_2="q_R_M2_aby_T_global"/>
<map_variables variable_1="q_LR_M2_aby_mGiProtein" variable_2="q_LR_M2_aby"/>
<map_variables variable_1="q_LR_M2_aby" variable_2="q_LR_M2_aby_global"/>
<map_variables variable_1="q_LR_M2_aby_T_mGiProtein" variable_2="q_LR_M2_aby_T"/>
<map_variables variable_1="q_LR_M2_aby_T" variable_2="q_LR_M2_aby_T_global"/>
<map_variables variable_1="q_GTP_mGiProtein" variable_2="q_GTP"/>
<map_variables variable_1="q_GTP" variable_2="q_GTP_global"/>
<map_variables variable_1="q_GDP_mGiProtein" variable_2="q_GDP"/>
<map_variables variable_1="q_GDP" variable_2="q_GDP_global"/>
<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="GiProtein_parameters" component_2="GiProtein"/>
<map_variables variable_1="kappa_Doff1_Gi" variable_2="kappa_Doff1_Gi"/>
<map_variables variable_1="kappa_Ton1_Gi" variable_2="kappa_Ton1_Gi"/>
<map_variables variable_1="kappa_Act1_Gi" variable_2="kappa_Act1_Gi"/>
<map_variables variable_1="kappa_Doff2_Gi" variable_2="kappa_Doff2_Gi"/>
<map_variables variable_1="kappa_Ton2_Gi" variable_2="kappa_Ton2_Gi"/>
<map_variables variable_1="kappa_Act2_Gi" variable_2="kappa_Act2_Gi"/>
<map_variables variable_1="kappa_hyd_Gi" variable_2="kappa_hyd_Gi"/>
<map_variables variable_1="kappa_reassoc_Gi" variable_2="kappa_reassoc_Gi"/>
<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_R_M2Gi" variable_2="K_R_M2Gi"/>
<map_variables variable_1="K_LR_M2" variable_2="K_LR_M2"/>
<map_variables variable_1="K_LR_M2Gi" variable_2="K_LR_M2Gi"/>
<map_variables variable_1="K_a_Gi_GTP" variable_2="K_a_Gi_GTP"/>
<map_variables variable_1="K_beta_gamma_Gi" variable_2="K_beta_gamma_Gi"/>
<map_variables variable_1="K_a_Gi_GDP" variable_2="K_a_Gi_GDP"/>
<map_variables variable_1="K_Pi" variable_2="K_Pi"/>
<map_variables variable_1="K_R_M2_aby" variable_2="K_R_M2_aby"/>
<map_variables variable_1="K_R_M2_aby_T" variable_2="K_R_M2_aby_T"/>
<map_variables variable_1="K_LR_M2_aby" variable_2="K_LR_M2_aby"/>
<map_variables variable_1="K_LR_M2_aby_T" variable_2="K_LR_M2_aby_T"/>
<map_variables variable_1="K_GTP" variable_2="K_GTP"/>
<map_variables variable_1="K_GDP" variable_2="K_GDP"/>
</connection>
<connection>
<map_components component_1="constants" component_2="GiProtein"/>
<map_variables variable_1="R" variable_2="R"/>
<map_variables variable_1="T" variable_2="T"/>
</connection>
</model>
