Location: BG_GsProtein_sneyd @ a49a5c3db559 / BG_GPCR.cellml

Author:
Shelley Fong <s.fong@auckland.ac.nz>
Date:
2021-08-25 11:08:53+12:00
Desc:
Adding volume arguments and changing dimensions of input kinetic parameters to uM (source literature)
Permanent Source URI:
https://models.cellml.org/workspace/6cb/rawfile/a49a5c3db55972ea84a81b002f53b21f4739e28e/BG_GPCR.cellml

<?xml version='1.0' encoding='UTF-8'?>
<model name="BG_GPCR" 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" name="q_LR_global" units="fmol"/>
        <variable name="c_L" public_interface="in" units="uM"/>
        <variable name="c_R" public_interface="in" units="uM"/>
        <variable name="c_G" public_interface="in" units="uM"/>
        <variable name="c_LR" public_interface="in" units="uM"/>
        <variable name="c_a_GTP" public_interface="in" units="uM"/>
        <variable name="c_beta_gamma" public_interface="in" units="uM"/>
        <variable name="c_a_GDP" public_interface="in" units="uM"/>
    </component>
    <component name="GPCR">
        <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"/>
        <!-- 21july FKC with all 3 constraints, and detailed bal for ksig4m and for scheme2 kP2p. Merged GsabyGDP into G. R and LR in scheme 4. new constraint of R + L to LR using Gibbs free energy -->
        <variable initial_value="2.99219e-07" name="kappa_bind" units="fmol_per_sec"/>
        <variable initial_value="3.05365e-06" name="kappa_act" units="fmol_per_sec"/>
        <variable initial_value="0.0125026" name="kappa_hyd" units="fmol_per_sec"/>
        <variable initial_value="2955.93" name="kappa_reassoc" units="fmol_per_sec"/>
        <variable initial_value="9.71522e+07" name="K_L" units="per_fmol"/>
        <variable initial_value="0.101999" name="K_R" units="per_fmol"/>
        <variable initial_value="1.18996e-05" name="K_G" units="per_fmol"/>
        <variable initial_value="9.71522e+07" name="K_LR" units="per_fmol"/>
        <variable initial_value="1.86008" name="K_a_GTP" units="per_fmol"/>
        <variable initial_value="0.148776" name="K_beta_gamma" units="per_fmol"/>
        <variable initial_value="0.0023251" name="K_a_GDP" units="per_fmol"/>
        <!-- States (and initial conditions)
 8jul21 original kinetic concs + equal division of enzyme states-->
        <variable initial_value="0.000167285" name="q_L" public_interface="out" units="fmol"/>
        <variable initial_value="1.697e-06" name="q_LR" public_interface="out" units="fmol"/>
        <variable initial_value="0.000219725" name="q_R" public_interface="out" units="fmol"/>
        <variable initial_value="0.145305" name="q_G" public_interface="out" units="fmol"/>
        <variable initial_value="0.0009519" name="q_a_GTP" public_interface="out" units="fmol"/>
        <variable initial_value="0.00097622" name="q_beta_gamma" public_interface="out" units="fmol"/>
        <variable initial_value="2.44948e-05" name="q_a_GDP" public_interface="out" units="fmol"/>
        <variable name="q_LR_global" public_interface="in" units="fmol"/>
        <!-- Bond variables-->
        <variable name="vBind" units="fmol_per_sec"/>
        <variable name="vAct" units="fmol_per_sec"/>
        <variable name="vHyd" units="fmol_per_sec"/>
        <variable name="vReassoc" units="fmol_per_sec"/>
        <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_a_GTP" units="J_per_mol"/>
        <variable name="mu_beta_gamma" units="J_per_mol"/>
        <variable name="mu_a_GDP" units="J_per_mol"/>
        <!-- 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_a_GTP" public_interface="out" units="uM"/>
        <variable name="c_beta_gamma" public_interface="out" units="uM"/>
        <variable name="c_a_GDP" 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_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_global</ci>
                    </apply>
                    <ci>vol</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>c_a_GTP</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <cn cellml:units="m_to_u" type="e-notation">1<sep/>3</cn>
                        <ci>q_a_GTP</ci>
                    </apply>
                    <ci>vol</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>c_beta_gamma</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <cn cellml:units="m_to_u" type="e-notation">1<sep/>3</cn>
                        <ci>q_beta_gamma</ci>
                    </apply>
                    <ci>vol</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>c_a_GDP</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <cn cellml:units="m_to_u" type="e-notation">1<sep/>3</cn>
                        <ci>q_a_GDP</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_global</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>mu_a_GTP</ci>
                <apply>
                    <times/>
                    <ci>R</ci>
                    <ci>T</ci>
                    <apply>
                        <ln/>
                        <apply>
                            <times/>
                            <ci>K_a_GTP</ci>
                            <ci>q_a_GTP</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>mu_beta_gamma</ci>
                <apply>
                    <times/>
                    <ci>R</ci>
                    <ci>T</ci>
                    <apply>
                        <ln/>
                        <apply>
                            <times/>
                            <ci>K_beta_gamma</ci>
                            <ci>q_beta_gamma</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>mu_a_GDP</ci>
                <apply>
                    <times/>
                    <ci>R</ci>
                    <ci>T</ci>
                    <apply>
                        <ln/>
                        <apply>
                            <times/>
                            <ci>K_a_GDP</ci>
                            <ci>q_a_GDP</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>vBind</ci>
                <apply>
                    <times/>
                    <ci>kappa_bind</ci>
                    <apply>
                        <minus/>
                        <apply>
                            <exp/>
                            <apply>
                                <divide/>
                                <apply>
                                    <plus/>
                                    <ci>mu_L</ci>
                                    <ci>mu_R</ci>
                                </apply>
                                <apply>
                                    <times/>
                                    <ci>R</ci>
                                    <ci>T</ci>
                                </apply>
                            </apply>
                        </apply>
                        <apply>
                            <exp/>
                            <apply>
                                <divide/>
                                <ci>mu_LR</ci>
                                <apply>
                                    <times/>
                                    <ci>R</ci>
                                    <ci>T</ci>
                                </apply>
                            </apply>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>vAct</ci>
                <apply>
                    <times/>
                    <ci>kappa_act</ci>
                    <apply>
                        <minus/>
                        <apply>
                            <exp/>
                            <apply>
                                <divide/>
                                <ci>mu_LR</ci>
                                <apply>
                                    <times/>
                                    <ci>R</ci>
                                    <ci>T</ci>
                                </apply>
                            </apply>
                        </apply>
                        <apply>
                            <exp/>
                            <apply>
                                <divide/>
                                <apply>
                                    <plus/>
                                    <ci>mu_a_GTP</ci>
                                    <ci>mu_beta_gamma</ci>
                                </apply>
                                <apply>
                                    <times/>
                                    <ci>R</ci>
                                    <ci>T</ci>
                                </apply>
                            </apply>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>vHyd</ci>
                <apply>
                    <times/>
                    <ci>kappa_hyd</ci>
                    <apply>
                        <minus/>
                        <apply>
                            <exp/>
                            <apply>
                                <divide/>
                                <ci>mu_a_GTP</ci>
                                <apply>
                                    <times/>
                                    <ci>R</ci>
                                    <ci>T</ci>
                                </apply>
                            </apply>
                        </apply>
                        <apply>
                            <exp/>
                            <apply>
                                <divide/>
                                <ci>mu_a_GDP</ci>
                                <apply>
                                    <times/>
                                    <ci>R</ci>
                                    <ci>T</ci>
                                </apply>
                            </apply>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>vReassoc</ci>
                <apply>
                    <times/>
                    <ci>kappa_reassoc</ci>
                    <apply>
                        <minus/>
                        <apply>
                            <exp/>
                            <apply>
                                <divide/>
                                <apply>
                                    <plus/>
                                    <ci>mu_a_GDP</ci>
                                    <ci>mu_beta_gamma</ci>
                                </apply>
                                <apply>
                                    <times/>
                                    <ci>R</ci>
                                    <ci>T</ci>
                                </apply>
                            </apply>
                        </apply>
                        <apply>
                            <exp/>
                            <apply>
                                <divide/>
                                <ci>mu_G</ci>
                                <apply>
                                    <times/>
                                    <ci>R</ci>
                                    <ci>T</ci>
                                </apply>
                            </apply>
                        </apply>
                    </apply>
                </apply>
            </apply>
        </math>
        <!-- velocity in uM_per_sec-->
        <variable name="vAct_kinetic" units="uM_per_sec"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>vAct_kinetic</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <ci>vAct</ci>
                        <cn cellml:units="m_to_u" type="e-notation">1<sep/>3</cn>
                    </apply>
                    <ci>vol</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>time</ci>
                    </bvar>
                    <ci>q_L</ci>
                </apply>
                <apply>
                    <minus/>
                    <ci>vBind</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>time</ci>
                    </bvar>
                    <ci>q_R</ci>
                </apply>
                <apply>
                    <minus/>
                    <ci>vBind</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>time</ci>
                    </bvar>
                    <ci>q_G</ci>
                </apply>
                <apply>
                    <minus/>
                    <ci>vReassoc</ci>
                    <ci>vAct</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>time</ci>
                    </bvar>
                    <ci>q_LR</ci>
                </apply>
                <apply>
                    <minus/>
                    <ci>vBind</ci>
                    <ci>vAct</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>time</ci>
                    </bvar>
                    <ci>q_a_GTP</ci>
                </apply>
                <apply>
                    <minus/>
                    <ci>vAct</ci>
                    <ci>vHyd</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>time</ci>
                    </bvar>
                    <ci>q_beta_gamma</ci>
                </apply>
                <apply>
                    <minus/>
                    <ci>vAct</ci>
                    <ci>vReassoc</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>time</ci>
                    </bvar>
                    <ci>q_a_GDP</ci>
                </apply>
                <apply>
                    <minus/>
                    <ci>vHyd</ci>
                    <ci>vReassoc</ci>
                </apply>
            </apply>
        </math>
    </component>
    <connection>
        <map_components component_1="environment" component_2="GPCR"/>
        <map_variables variable_1="time" variable_2="time"/>
        <map_variables variable_1="q_LR_global" variable_2="q_LR_global"/>
        <map_variables variable_1="c_L" variable_2="c_L"/>
        <map_variables variable_1="c_R" variable_2="c_R"/>
        <map_variables variable_1="c_G" variable_2="c_G"/>
        <map_variables variable_1="c_LR" variable_2="c_LR"/>
        <map_variables variable_1="c_a_GTP" variable_2="c_a_GTP"/>
        <map_variables variable_1="c_beta_gamma" variable_2="c_beta_gamma"/>
        <map_variables variable_1="c_a_GDP" variable_2="c_a_GDP"/>
    </connection>
    <connection>
        <map_components component_1="constants" component_2="GPCR"/>
        <map_variables variable_1="R" variable_2="R"/>
        <map_variables variable_1="T" variable_2="T"/>
    </connection>
</model>