Location: FAIR DOs example 4.2 @ 4beb9a11d550 / FAIRDO BG example 4.2.cellml

Author:

David Nickerson <david.nickerson@gmail.com>

Date:

2024-01-15 23:23:39+13:00

Desc:

Initial documentation to create exposure

Permanent Source URI:

https://models.cellml.org/workspace/b58/rawfile/4beb9a11d550b3a8425b57b40b9c06088468d9e5/FAIRDO BG example 4.2.cellml

<?xml version='1.0' encoding='UTF-8'?>
<model name="BG42" xmlns="http://www.cellml.org/cellml/1.1#" xmlns:cellml="http://www.cellml.org/cellml/1.1#">
    <!-- Facilitated diffusion with SS flux and rapid binding and unbinding-->
    <units name="dim">
        <unit units="dimensionless"/>
    </units>
    <units name="per_s">
        <unit exponent="-1" units="second"/>
    </units>
    <units name="per_mol">
        <unit exponent="-1" units="mole"/>
    </units>
    <units name="mol_per_s">
        <unit units="mole"/>
        <unit exponent="-1" units="second"/>
    </units>
    <units name="mM">
        <unit units="mole"/>
        <unit exponent="-3" units="meter"/>
    </units>
    <units name="mM_per_s">
        <unit units="mM"/>
        <unit exponent="-1" units="second"/>
    </units>
    <component name="main">
        <variable initial_value="0" name="t" units="second"/>
        <variable initial_value="10" name="q_1" units="mole"/>
        <variable initial_value="0" name="q_2" units="mole"/>
        <variable initial_value="0" name="q" units="mole"/>
        <variable initial_value="10" name="E_tot" units="mole"/>
        <variable name="v" units="mol_per_s"/>
        <variable initial_value="1" name="kappa_3" units="mol_per_s"/>
        <variable initial_value="0.1" name="kappa_4" units="mol_per_s"/>
        <variable initial_value="0.1" name="K_s" units="per_mol"/>
        <variable initial_value="1" name="K_m" units="per_mol"/>
        <variable name="k_m" units="mole"/>
        <variable name="v_max" units="mol_per_s"/>
        <variable name="v_MM" units="mol_per_s"/>
        <variable initial_value="0" name="q20" units="mole"/>
        <variable name="v_0" units="mol_per_s"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>k_m</ci>
                <apply>
                    <divide/>
                    <cn cellml:units="dim">2</cn>
                    <apply>
                        <times/>
                        <ci>K_s</ci>
                        <apply>
                            <plus/>
                            <cn cellml:units="dim">1</cn>
                            <apply>
                                <divide/>
                                <ci>kappa_3</ci>
                                <ci>kappa_4</ci>
                            </apply>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>v_max</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <ci>E_tot</ci>
                        <ci>kappa_3</ci>
                        <ci>K_m</ci>
                    </apply>
                    <apply>
                        <plus/>
                        <cn cellml:units="dim">1</cn>
                        <apply>
                            <divide/>
                            <ci>kappa_3</ci>
                            <ci>kappa_4</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>q_1</ci>
                </apply>
                <apply>
                    <minus/>
                    <ci>v</ci>
                </apply>
            </apply>
            <!--        ode(q_2, t) =  v;-->
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>q_2</ci>
                </apply>
                <apply>
                    <minus/>
                    <ci>v</ci>
                    <apply>
                        <times/>
                        <cn cellml:units="dim">0.1</cn>
                        <ci>q_2</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>v</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <ci>E_tot</ci>
                        <ci>kappa_3</ci>
                        <ci>kappa_4</ci>
                        <ci>K_m</ci>
                        <ci>K_s</ci>
                        <apply>
                            <minus/>
                            <ci>q_1</ci>
                            <ci>q_2</ci>
                        </apply>
                    </apply>
                    <apply>
                        <plus/>
                        <apply>
                            <times/>
                            <cn cellml:units="dim">2</cn>
                            <ci>kappa_4</ci>
                        </apply>
                        <apply>
                            <times/>
                            <apply>
                                <plus/>
                                <ci>kappa_3</ci>
                                <ci>kappa_4</ci>
                            </apply>
                            <ci>K_s</ci>
                            <apply>
                                <plus/>
                                <ci>q_1</ci>
                                <ci>q_2</ci>
                            </apply>
                        </apply>
                        <apply>
                            <times/>
                            <cn cellml:units="dim">2</cn>
                            <ci>kappa_3</ci>
                            <ci>K_s</ci>
                            <ci>K_s</ci>
                            <ci>q_1</ci>
                            <ci>q_2</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>v_0</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <ci>E_tot</ci>
                        <ci>kappa_3</ci>
                        <ci>kappa_4</ci>
                        <ci>K_m</ci>
                        <ci>K_s</ci>
                        <apply>
                            <minus/>
                            <ci>q_1</ci>
                            <ci>q20</ci>
                        </apply>
                    </apply>
                    <apply>
                        <plus/>
                        <apply>
                            <times/>
                            <cn cellml:units="dim">2</cn>
                            <ci>kappa_4</ci>
                        </apply>
                        <apply>
                            <times/>
                            <apply>
                                <plus/>
                                <ci>kappa_3</ci>
                                <ci>kappa_4</ci>
                            </apply>
                            <ci>K_s</ci>
                            <apply>
                                <plus/>
                                <ci>q_1</ci>
                                <ci>q20</ci>
                            </apply>
                        </apply>
                        <apply>
                            <times/>
                            <cn cellml:units="dim">2</cn>
                            <ci>kappa_3</ci>
                            <ci>K_s</ci>
                            <ci>K_s</ci>
                            <ci>q_1</ci>
                            <ci>q20</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>v_MM</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <ci>v_max</ci>
                        <ci>q_1</ci>
                    </apply>
                    <apply>
                        <plus/>
                        <ci>k_m</ci>
                        <ci>q_1</ci>
                    </apply>
                </apply>
            </apply>
        </math>
    </component>
</model>