Location: BG_B1AR @ 915ab06a088c / BG_LRGbinding.cellml

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>