Location: BG_B1AR @ d4ede2c913ae / BG_beta1AR.cellml
- Author:
- Shelley Fong <s.fong@auckland.ac.nz>
- Date:
- 2021-07-21 13:20:16+12:00
- Desc:
- Adding constraint of Gibbs free energy for R+L binding
- Permanent Source URI:
- https://models.cellml.org/workspace/6ba/rawfile/d4ede2c913ae89ecfd962290fc5c536c82836840/BG_beta1AR.cellml
<?xml version='1.0' encoding='UTF-8'?>
<!-- BG model of beta1 adrenergic receptor activation + Gs ctivation, based on saucerman2003, v1
1jul21 initialising file
19 Jul beta1AR only: no Gactivation (see GPCR_sneyd)-->
<model name="BG_beta1AR" xmlns="http://www.cellml.org/cellml/1.0#" xmlns:cellml="http://www.cellml.org/cellml/1.0#">
<!-- def unit per_sec as
unit second {expo: -1};
enddef;-->
<!-- def unit J_per_K_per_mol as
unit joule;
unit kelvin {expo: -1};
unit mole {expo: -1};
enddef;-->
<!-- def unit C_per_mol as
unit coulomb;
unit mole {expo: -1};
enddef;-->
<!-- def unit fmol as
unit mole {pref: femto};
enddef;-->
<!-- def unit fmol_per_L as
unit mole {pref: femto};
unit litre {expo: -1};
enddef;-->
<!-- def unit fmol_per_L_per_sec as
unit fmol_per_L;
unit second {expo: -1};
enddef;-->
<!-- def unit per_sec_per_fmol_per_L as
unit second {expo: -1};
unit fmol_per_L {expo: -1};
enddef;-->
<!-- def unit per_fmol as
unit fmol {expo: -1};
enddef;-->
<!-- def unit fmol_per_sec as
unit fmol;
unit second {expo: -1};
enddef;-->
<!-- def unit J_per_mol as
unit joule;
unit mole {expo: -1};
enddef;-->
<!-- def unit mM as
unit mole {pref: milli};
unit litre {expo: -1};
enddef;-->
<!-- def unit uM as
unit mole {pref: micro};
unit litre {expo: -1};
enddef;-->
<!-- def unit mM_per_sec as
unit mM;
unit second {expo: -1.0};
enddef;-->
<!-- def unit uM_per_sec as
unit uM;
unit second {expo: -1.0};
enddef;-->
<!-- def unit pL as
unit litre {pref: pico};
enddef;-->
<!-- def unit m_to_u as
unit second {pref: micro};
unit second {pref: milli};
enddef;-->
<component name="B1AR">
<variable name="t" public_interface="in" units="second"/>
<!-- Physical parameters-->
<variable initial_value="8.31" name="R" units="J_per_K_per_mol"/>
<variable initial_value="310" name="T" units="kelvin"/>
<variable initial_value="96485" name="F" units="C_per_mol"/>
<!-- Bond graph parameters, found using pinv of kinetic parameters-->
<variable initial_value="1.7183e-05" name="kappa_B11" units="fmol_per_sec"/>
<variable initial_value="7810.45" name="kappa_B12" units="fmol_per_sec"/>
<variable initial_value="1.7183e-05" name="kappa_B21" units="fmol_per_sec"/>
<variable initial_value="7810.45" name="kappa_B22" units="fmol_per_sec"/>
<variable initial_value="0.000556101" name="kappa_P1" units="fmol_per_sec"/>
<variable initial_value="5.34978e-05" name="kappa_P2" units="fmol_per_sec"/>
<variable initial_value="0.0971047" name="K_LR" units="per_fmol"/>
<variable initial_value="0.0971047" name="K_LRG" units="per_fmol"/>
<variable initial_value="0.000116526" name="K_B1d" units="per_fmol"/>
<variable initial_value="1.09876e-06" name="K_BARK" units="per_fmol"/>
<variable initial_value="128.034" name="K_LR_BARK" units="per_fmol"/>
<variable initial_value="128.034" name="K_LRG_BARK" units="per_fmol"/>
<variable initial_value="0.00406745" name="K_B1p" units="per_fmol"/>
<variable initial_value="0.00406745" name="K_B1tot" units="per_fmol"/>
<variable initial_value="1.65441e-05" name="K_PKACI" units="per_fmol"/>
<variable initial_value="0.00179823" name="K_PKACI_B1p" units="per_fmol"/>
<!-- States (and initial conditions)-->
<!-- 8jul21 original kinetic concs + equal division of enzyme states-->
<variable initial_value="1.697e-06" name="q_LR" units="fmol"/>
<variable initial_value="0.00010466" name="q_LRG" units="fmol"/>
<variable initial_value="1.697e-06" name="q_LR_BARK" units="fmol"/>
<variable initial_value="0.00010466" name="q_LRG_BARK" units="fmol"/>
<variable initial_value="0" name="q_B1d" units="fmol"/>
<variable initial_value="2.1926e-05" name="q_B1p" units="fmol"/>
<variable initial_value="2.1926e-05" name="q_PKACI_B1p" units="fmol"/>
<variable initial_value="0.0004579" name="q_B1tot" units="fmol"/>
<variable initial_value="0.00221209" name="q_PKACI" units="fmol"/>
<variable initial_value="0.0228" name="q_BARK" units="fmol"/>
<variable name="q_LR_global" public_interface="in" units="fmol"/>
<!-- Bond variables-->
<variable name="vB11" units="fmol_per_sec"/>
<variable name="vB12" units="fmol_per_sec"/>
<variable name="vB21" units="fmol_per_sec"/>
<variable name="vB22" units="fmol_per_sec"/>
<variable name="vP1" units="fmol_per_sec"/>
<variable name="vP2" units="fmol_per_sec"/>
<variable name="mu_LR" units="J_per_mol"/>
<variable name="mu_LRG" units="J_per_mol"/>
<variable name="mu_B1d" units="J_per_mol"/>
<variable name="mu_BARK" units="J_per_mol"/>
<variable name="mu_LR_BARK" units="J_per_mol"/>
<variable name="mu_LRG_BARK" units="J_per_mol"/>
<variable name="mu_B1p" units="J_per_mol"/>
<variable name="mu_B1tot" units="J_per_mol"/>
<variable name="mu_PKACI" units="J_per_mol"/>
<variable name="mu_PKACI_B1p" units="J_per_mol"/>
<!-- Concentrations - for plotting-->
<variable name="c_LR" public_interface="out" units="uM"/>
<variable name="c_B1d" public_interface="out" units="uM"/>
<variable name="c_BARK" public_interface="out" units="uM"/>
<variable name="c_LR_BARK" public_interface="out" units="uM"/>
<variable name="c_LRG" public_interface="out" units="uM"/>
<variable name="c_LRG_BARK" public_interface="out" units="uM"/>
<variable name="c_B1p" public_interface="out" units="uM"/>
<variable name="c_B1tot" public_interface="out" units="uM"/>
<variable name="c_PKACI" public_interface="out" units="uM"/>
<variable name="c_PKACI_B1p" public_interface="out" units="uM"/>
<variable initial_value="38.0" name="vol" units="pL"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<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_global</ci>
</apply>
<ci>vol</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>c_B1d</ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="m_to_u" type="e-notation">1<sep/>3</cn>
<ci>q_B1d</ci>
</apply>
<ci>vol</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>c_BARK</ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="m_to_u" type="e-notation">1<sep/>3</cn>
<ci>q_BARK</ci>
</apply>
<ci>vol</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>c_LR_BARK</ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="m_to_u" type="e-notation">1<sep/>3</cn>
<ci>q_LR_BARK</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>
<apply>
<eq/>
<ci>c_LRG_BARK</ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="m_to_u" type="e-notation">1<sep/>3</cn>
<ci>q_LRG_BARK</ci>
</apply>
<ci>vol</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>c_B1p</ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="m_to_u" type="e-notation">1<sep/>3</cn>
<ci>q_B1p</ci>
</apply>
<ci>vol</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>c_B1tot</ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="m_to_u" type="e-notation">1<sep/>3</cn>
<ci>q_B1tot</ci>
</apply>
<ci>vol</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>c_PKACI</ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="m_to_u" type="e-notation">1<sep/>3</cn>
<ci>q_PKACI</ci>
</apply>
<ci>vol</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>c_PKACI_B1p</ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="m_to_u" type="e-notation">1<sep/>3</cn>
<ci>q_PKACI_B1p</ci>
</apply>
<ci>vol</ci>
</apply>
</apply>
<!-- Constitutive equations-->
<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_global</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>mu_B1d</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_B1d</ci>
<ci>q_B1d</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_BARK</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_BARK</ci>
<ci>q_BARK</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_LR_BARK</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_LR_BARK</ci>
<ci>q_LR_BARK</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_LRG_BARK</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_LRG_BARK</ci>
<ci>q_LRG_BARK</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_B1p</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_B1p</ci>
<ci>q_B1p</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_B1tot</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_B1tot</ci>
<ci>q_B1tot</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_PKACI</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_PKACI</ci>
<ci>q_PKACI</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_PKACI_B1p</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_PKACI_B1p</ci>
<ci>q_PKACI_B1p</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>vB11</ci>
<apply>
<times/>
<ci>kappa_B11</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>mu_LR</ci>
<ci>mu_BARK</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>mu_LR_BARK</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>vB12</ci>
<apply>
<times/>
<ci>kappa_B12</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>mu_LR_BARK</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>mu_BARK</ci>
<ci>mu_B1d</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>vB21</ci>
<apply>
<times/>
<ci>kappa_B21</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>mu_LRG</ci>
<ci>mu_BARK</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>mu_LRG_BARK</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>vB22</ci>
<apply>
<times/>
<ci>kappa_B22</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>mu_LRG_BARK</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>mu_BARK</ci>
<ci>mu_B1d</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>vP1</ci>
<apply>
<times/>
<ci>kappa_P1</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>mu_B1p</ci>
<ci>mu_PKACI</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>mu_PKACI_B1p</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>vP2</ci>
<apply>
<times/>
<ci>kappa_P2</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>mu_PKACI_B1p</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>mu_PKACI</ci>
<ci>mu_B1tot</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
<!-- velocity in uM_per_sec-->
<variable name="v1b_kinetic" units="uM_per_sec"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v1b_kinetic</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>vB12</ci>
<cn cellml:units="m_to_u" type="e-notation">1<sep/>3</cn>
</apply>
<ci>vol</ci>
</apply>
</apply>
<!-- saucerman: not all reactions are accounted for.-->
<!-- BG model-->
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_LR</ci>
</apply>
<apply>
<minus/>
<ci>vB11</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_B1d</ci>
</apply>
<apply>
<plus/>
<ci>vB12</ci>
<ci>vB22</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_BARK</ci>
</apply>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<plus/>
<ci>vB12</ci>
<ci>vB22</ci>
</apply>
<ci>vB11</ci>
</apply>
<ci>vB21</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_LR_BARK</ci>
</apply>
<apply>
<minus/>
<ci>vB11</ci>
<ci>vB12</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_LRG</ci>
</apply>
<apply>
<minus/>
<ci>vB21</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_LRG_BARK</ci>
</apply>
<apply>
<minus/>
<ci>vB21</ci>
<ci>vB22</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_B1p</ci>
</apply>
<apply>
<minus/>
<ci>vP1</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_B1tot</ci>
</apply>
<ci>vP2</ci>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_PKACI</ci>
</apply>
<apply>
<minus/>
<ci>vP2</ci>
<ci>vP1</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_PKACI_B1p</ci>
</apply>
<apply>
<minus/>
<ci>vP1</ci>
<ci>vP2</ci>
</apply>
</apply>
</math>
</component>
</model>