Location: The Physics of Physiology - Example 6: An enzyme-catalyzed reaction and Michaelis-Menten kinetics @ b70c68cac481 / FAIRDO BG example 3.6.cellml

Author:

David Nickerson <david.nickerson@gmail.com>

Date:

2024-01-16 17:34:48+13:00

Desc:

updates to the model and SED-ML, separate out example 3.7

Permanent Source URI:

https://models.physiomeproject.org/workspace/af2/rawfile/b70c68cac4814ff329fa16813fb4b6b93850ae28/FAIRDO BG example 3.6.cellml

<?xml version='1.0' encoding='UTF-8'?>
<model name="BG6" xmlns="http://www.cellml.org/cellml/1.1#" xmlns:cellml="http://www.cellml.org/cellml/1.1#">
    <!-- Enzyme catalyzed reaction (kinetic, SS reduced & MM)-->
    <units name="mol_per_s">
        <unit units="mole"/>
        <unit exponent="-1" units="second"/>
    </units>
    <units name="per_mol">
        <unit exponent="-1" units="mole"/>
    </units>
    <component name="main">
        <variable initial_value="0" name="t" units="second"/>
        <!-- State variables & flux variables-->
        <variable initial_value="30" name="q_1" units="mole"/>
        <variable initial_value="0" name="q_2" units="mole"/>
        <variable initial_value="10" name="q_3" units="mole"/>
        <variable initial_value="0" name="q_4" units="mole"/>
        <variable name="v_1" units="mol_per_s"/>
        <variable name="v_2" units="mol_per_s"/>
        <variable name="v_SS" units="mol_per_s"/>
        <variable name="v_MM" units="mol_per_s"/>
        <!-- Constitutive parameters-->
        <variable initial_value="0.1" name="K_1" units="per_mol"/>
        <variable initial_value="0.1" name="K_2" units="per_mol"/>
        <variable initial_value="0.1" name="K_3" units="per_mol"/>
        <variable initial_value="0.1" name="K_4" units="per_mol"/>
        <variable initial_value="10" name="kappa_1" units="mol_per_s"/>
        <variable initial_value="10" name="kappa_2" units="mol_per_s"/>
        <variable name="E_0" units="mole"/>
        <variable name="k_m" units="mole"/>
        <variable name="v_max" units="mol_per_s"/>
        <!-- Conservation laws-->
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>E_0</ci>
                <apply>
                    <plus/>
                    <ci>q_3</ci>
                    <ci>q_4</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>q_1</ci>
                </apply>
                <apply>
                    <minus/>
                    <ci>v_1</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>q_2</ci>
                </apply>
                <ci>v_2</ci>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>q_3</ci>
                </apply>
                <apply>
                    <minus/>
                    <ci>v_2</ci>
                    <ci>v_1</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>q_4</ci>
                </apply>
                <apply>
                    <minus/>
                    <ci>v_1</ci>
                    <ci>v_2</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>v_1</ci>
                <apply>
                    <times/>
                    <ci>kappa_1</ci>
                    <apply>
                        <minus/>
                        <apply>
                            <times/>
                            <ci>K_1</ci>
                            <ci>q_1</ci>
                            <ci>K_3</ci>
                            <ci>q_3</ci>
                        </apply>
                        <apply>
                            <times/>
                            <ci>K_4</ci>
                            <ci>q_4</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>v_2</ci>
                <apply>
                    <times/>
                    <ci>kappa_2</ci>
                    <apply>
                        <minus/>
                        <apply>
                            <times/>
                            <ci>K_4</ci>
                            <ci>q_4</ci>
                        </apply>
                        <apply>
                            <times/>
                            <ci>K_2</ci>
                            <ci>q_2</ci>
                            <ci>K_3</ci>
                            <ci>q_3</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <!-- Reduced models (SS & MM)        -->
            <apply>
                <eq/>
                <ci>v_SS</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <ci>E_0</ci>
                        <ci>kappa_1</ci>
                        <ci>kappa_2</ci>
                        <ci>K_3</ci>
                        <ci>K_4</ci>
                        <apply>
                            <minus/>
                            <apply>
                                <times/>
                                <ci>K_1</ci>
                                <ci>q_1</ci>
                            </apply>
                            <apply>
                                <times/>
                                <ci>K_2</ci>
                                <ci>q_2</ci>
                            </apply>
                        </apply>
                    </apply>
                    <apply>
                        <plus/>
                        <apply>
                            <times/>
                            <ci>K_4</ci>
                            <apply>
                                <plus/>
                                <ci>kappa_1</ci>
                                <ci>kappa_2</ci>
                            </apply>
                        </apply>
                        <apply>
                            <times/>
                            <ci>kappa_1</ci>
                            <ci>K_1</ci>
                            <ci>K_3</ci>
                            <ci>q_1</ci>
                        </apply>
                        <apply>
                            <times/>
                            <ci>kappa_2</ci>
                            <ci>K_2</ci>
                            <ci>K_3</ci>
                            <ci>q_2</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>v_max</ci>
                <apply>
                    <times/>
                    <ci>E_0</ci>
                    <ci>kappa_2</ci>
                    <ci>K_4</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>k_m</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <apply>
                            <plus/>
                            <ci>kappa_1</ci>
                            <ci>kappa_2</ci>
                        </apply>
                        <ci>K_4</ci>
                    </apply>
                    <apply>
                        <times/>
                        <ci>kappa_1</ci>
                        <ci>K_1</ci>
                        <ci>K_3</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>v_MM</ci>
                <apply>
                    <times/>
                    <ci>v_max</ci>
                    <apply>
                        <divide/>
                        <ci>q_1</ci>
                        <apply>
                            <plus/>
                            <ci>k_m</ci>
                            <ci>q_1</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
        </math>
    </component>
</model>