Location: SLC transporters @ 9eddc7900fe3 / Facilitated transporter / GLUT1_ss_io_no_constraint.cellml

Author:
Weiwei Ai <wai484@aucklanduni.ac.nz>
Date:
2024-03-27 10:41:53+13:00
Desc:
modify the ss to reflect the new change in Peter's lecture note
Permanent Source URI:
https://models.physiomeproject.org/workspace/b65/rawfile/9eddc7900fe34b917753e86040fca04544414e88/Facilitated transporter/GLUT1_ss_io_no_constraint.cellml
Compare... Download Source 

<?xml version='1.0' encoding='UTF-8'?>
<model name="GLUT1_BG" 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.cellml">
        <units name="fmol" units_ref="fmol"/>
        <units name="J_per_K_mol" units_ref="J_per_K_mol"/>
        <units name="fmol_per_s" units_ref="fmol_per_s"/>
        <units name="J_per_mol" units_ref="J_per_mol"/>
        <units name="per_fmol" units_ref="per_fmol"/>
        <units name="mM" units_ref="mM"/>
        <units name="mM_per_s" units_ref="mM_per_s"/>
        <units name="pL" units_ref="pL"/>
    </import>
    <import xlink:href="params_BG_fit_ss_io.cellml">
        <component component_ref="params_BG" name="params_BG"/>
    </import>
    <component name="GLUT1_BG">
        <variable name="t" public_interface="in" units="second"/>
        <variable name="K_Ai" public_interface="in" units="per_fmol"/>
        <variable name="K_Ao" public_interface="in" units="per_fmol"/>
        <variable name="K_1" public_interface="in" units="per_fmol"/>
        <variable name="K_2" public_interface="in" units="per_fmol"/>
        <variable name="K_3" public_interface="in" units="per_fmol"/>
        <variable name="K_4" public_interface="in" units="per_fmol"/>
        <variable name="kappa_r1" public_interface="in" units="fmol_per_s"/>
        <variable name="kappa_r2" public_interface="in" units="fmol_per_s"/>
        <variable name="kappa_r3" public_interface="in" units="fmol_per_s"/>
        <variable name="kappa_r4" public_interface="in" units="fmol_per_s"/>
        <variable name="q_Ai" public_interface="in" units="fmol"/>
        <variable name="q_Ao" public_interface="in" units="fmol"/>
        <variable name="lambda" units="dimensionless"/>
        <variable name="q_tot" public_interface="in" units="fmol"/>
        <variable name="v_max" units="fmol_per_s"/>
        <variable name="k_m_1" units="dimensionless"/>
        <variable name="k_m_2" units="dimensionless"/>
        <variable name="k_m_3" units="dimensionless"/>
        <variable name="v" units="fmol_per_s"/>
        <variable name="v_max_free" units="fmol_per_s"/>
        <variable name="v_free" units="fmol_per_s"/>
        <variable name="k_m_1_free" units="dimensionless"/>
        <variable name="k_m_2_free" units="dimensionless"/>
        <variable initial_value="218.96" name="k_m_3_free" units="dimensionless"/>
        <variable initial_value="0.1094" name="k_oi_math" units="mM"/>
        <variable initial_value="1.609" name="k_io_math" units="mM"/>
        <variable initial_value="0.004839" name="v_oi_max" units="mM_per_s"/>
        <variable initial_value="0.07117" name="v_io_max" units="mM_per_s"/>
        <variable initial_value="90" name="V_i" units="pL"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>v_max_free</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <ci>v_oi_max</ci>
                        <ci>V_i</ci>
                    </apply>
                    <ci>k_m_1_free</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>k_m_1_free</ci>
                <apply>
                    <times/>
                    <ci>k_oi_math</ci>
                    <ci>V_i</ci>
                    <ci>K_Ai</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>k_m_2_free</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <ci>v_io_max</ci>
                        <ci>V_i</ci>
                    </apply>
                    <ci>v_max_free</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>lambda</ci>
                <apply>
                    <divide/>
                    <ci>kappa_r2</ci>
                    <ci>kappa_r1</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>v_max</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <ci>q_tot</ci>
                        <ci>kappa_r2</ci>
                        <ci>K_3</ci>
                    </apply>
                    <apply>
                        <plus/>
                        <apply>
                            <divide/>
                            <ci>K_3</ci>
                            <ci>K_1</ci>
                        </apply>
                        <apply>
                            <divide/>
                            <ci>K_3</ci>
                            <ci>K_4</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>k_m_1</ci>
                <apply>
                    <divide/>
                    <apply>
                        <plus/>
                        <apply>
                            <divide/>
                            <ci>K_3</ci>
                            <ci>K_1</ci>
                        </apply>
                        <apply>
                            <divide/>
                            <ci>K_3</ci>
                            <ci>K_4</ci>
                        </apply>
                    </apply>
                    <apply>
                        <plus/>
                        <apply>
                            <divide/>
                            <ci>K_3</ci>
                            <ci>K_2</ci>
                        </apply>
                        <apply>
                            <divide/>
                            <apply>
                                <times/>
                                <ci>lambda</ci>
                                <ci>K_3</ci>
                            </apply>
                            <ci>K_4</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>k_m_2</ci>
                <apply>
                    <divide/>
                    <apply>
                        <plus/>
                        <apply>
                            <divide/>
                            <ci>K_3</ci>
                            <ci>K_1</ci>
                        </apply>
                        <apply>
                            <divide/>
                            <ci>K_3</ci>
                            <ci>K_4</ci>
                        </apply>
                    </apply>
                    <apply>
                        <plus/>
                        <cn cellml:units="dimensionless">1</cn>
                        <apply>
                            <divide/>
                            <apply>
                                <times/>
                                <ci>lambda</ci>
                                <ci>K_3</ci>
                            </apply>
                            <ci>K_1</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>k_m_3</ci>
                <apply>
                    <divide/>
                    <apply>
                        <plus/>
                        <apply>
                            <divide/>
                            <ci>K_3</ci>
                            <ci>K_1</ci>
                        </apply>
                        <apply>
                            <divide/>
                            <ci>K_3</ci>
                            <ci>K_4</ci>
                        </apply>
                    </apply>
                    <apply>
                        <times/>
                        <ci>lambda</ci>
                        <apply>
                            <plus/>
                            <cn cellml:units="dimensionless">1</cn>
                            <apply>
                                <divide/>
                                <ci>K_3</ci>
                                <ci>K_2</ci>
                            </apply>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>v</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <ci>v_max</ci>
                        <apply>
                            <minus/>
                            <apply>
                                <times/>
                                <ci>K_Ao</ci>
                                <ci>q_Ao</ci>
                            </apply>
                            <apply>
                                <times/>
                                <ci>K_Ai</ci>
                                <ci>q_Ai</ci>
                            </apply>
                        </apply>
                    </apply>
                    <apply>
                        <plus/>
                        <cn cellml:units="dimensionless">1</cn>
                        <apply>
                            <divide/>
                            <apply>
                                <times/>
                                <ci>K_Ao</ci>
                                <ci>q_Ao</ci>
                            </apply>
                            <ci>k_m_1</ci>
                        </apply>
                        <apply>
                            <divide/>
                            <apply>
                                <times/>
                                <ci>K_Ai</ci>
                                <ci>q_Ai</ci>
                            </apply>
                            <ci>k_m_2</ci>
                        </apply>
                        <apply>
                            <divide/>
                            <apply>
                                <times/>
                                <ci>K_Ao</ci>
                                <ci>q_Ao</ci>
                                <ci>K_Ai</ci>
                                <ci>q_Ai</ci>
                            </apply>
                            <ci>k_m_3</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>v_free</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <ci>v_max_free</ci>
                        <apply>
                            <minus/>
                            <apply>
                                <times/>
                                <ci>K_Ao</ci>
                                <ci>q_Ao</ci>
                            </apply>
                            <apply>
                                <times/>
                                <ci>K_Ai</ci>
                                <ci>q_Ai</ci>
                            </apply>
                        </apply>
                    </apply>
                    <apply>
                        <plus/>
                        <cn cellml:units="dimensionless">1</cn>
                        <apply>
                            <divide/>
                            <apply>
                                <times/>
                                <ci>K_Ao</ci>
                                <ci>q_Ao</ci>
                            </apply>
                            <ci>k_m_1_free</ci>
                        </apply>
                        <apply>
                            <divide/>
                            <apply>
                                <times/>
                                <ci>K_Ai</ci>
                                <ci>q_Ai</ci>
                            </apply>
                            <ci>k_m_2_free</ci>
                        </apply>
                        <apply>
                            <divide/>
                            <apply>
                                <times/>
                                <ci>K_Ao</ci>
                                <ci>q_Ao</ci>
                                <ci>K_Ai</ci>
                                <ci>q_Ai</ci>
                            </apply>
                            <ci>k_m_3_free</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
        </math>
    </component>
    <connection>
        <map_components component_1="params_BG" component_2="GLUT1_BG"/>
        <map_variables variable_1="t" variable_2="t"/>
        <map_variables variable_1="K_Ai" variable_2="K_Ai"/>
        <map_variables variable_1="K_Ao" variable_2="K_Ao"/>
        <map_variables variable_1="K_1" variable_2="K_1"/>
        <map_variables variable_1="K_2" variable_2="K_2"/>
        <map_variables variable_1="K_3" variable_2="K_3"/>
        <map_variables variable_1="q_init_Ai" variable_2="q_Ai"/>
        <map_variables variable_1="q_init_Ao" variable_2="q_Ao"/>
        <map_variables variable_1="K_4" variable_2="K_4"/>
        <map_variables variable_1="E" variable_2="q_tot"/>
        <map_variables variable_1="kappa_r1" variable_2="kappa_r1"/>
        <map_variables variable_1="kappa_r2" variable_2="kappa_r2"/>
        <map_variables variable_1="kappa_r3" variable_2="kappa_r3"/>
        <map_variables variable_1="kappa_r4" variable_2="kappa_r4"/>
    </connection>
</model>