Location: Kobro-Flatmoen & Omholt 2024 @ 81ddf848bab3 / fig1.cellml

Author:

David Nickerson <david.nickerson@gmail.com>

Date:

2024-09-30 15:07:25+13:00

Desc:

Adding variant for Re+alECLII neurons in Figure 2

Permanent Source URI:

https://staging.physiomeproject.org/workspace/be4/rawfile/81ddf848bab39d0a740b3c121561d7788dfc3a7f/fig1.cellml

<?xml version='1.0' encoding='UTF-8'?>
<model name="my_model" xmlns="http://www.cellml.org/cellml/1.1#" xmlns:cellml="http://www.cellml.org/cellml/1.1#">
    <!-- (4 eqn model for Alzheimer calculation) -->
    <units name="molecules">
        <unit units="dimensionless"/>
    </units>
    <units name="hour">
        <unit multiplier="3600" units="second"/>
    </units>
    <units name="per_hour">
        <unit exponent="-1" units="hour"/>
    </units>
    <units name="molecules_per_hour">
        <unit units="molecules"/>
        <unit units="per_hour"/>
    </units>
    <units name="per_molecules_per_hour">
        <unit exponent="-1" units="molecules"/>
        <unit units="per_hour"/>
    </units>
    <units name="per_hour2">
        <unit exponent="-2" units="hour"/>
    </units>
    <units name="per_hour4">
        <unit exponent="-4" units="hour"/>
    </units>
    <units name="micrometer">
        <unit prefix="micro" units="meter"/>
    </units>
    <units name="micrometer_cubed">
        <unit exponent="3" units="micrometer"/>
    </units>
    <units name="nM">
        <unit exponent="-1" units="micrometer_cubed"/>
    </units>
    <component name="main">
        <variable initial_value="0" name="t" units="hour"/>
        <variable initial_value="0.1" name="beta" units="per_hour"/>
        <variable initial_value="0.005" name="gamma" units="per_molecules_per_hour"/>
        <variable initial_value="14500" name="tau" units="molecules_per_hour"/>
        <variable initial_value="0.05" name="rho" units="per_hour"/>
        <variable initial_value="0.02" name="delta" units="per_hour"/>
        <variable initial_value="12" name="eta" units="per_hour"/>
        <variable initial_value="0.65" name="kappa" units="per_hour"/>
        <variable initial_value="50000" name="G_tot" units="molecules"/>
        <variable name="Q" units="per_hour2"/>
        <variable name="QQ" units="per_hour4"/>
        <variable initial_value="AB_SS" name="AB" units="molecules"/>
        <variable name="AB_SS" units="molecules"/>
        <variable initial_value="Reelin_SS" name="Reelin" units="molecules"/>
        <variable name="Reelin_SS" units="molecules"/>
        <variable initial_value="ABR_SS" name="ABR" units="molecules"/>
        <variable name="ABR_SS" units="molecules"/>
        <variable initial_value="GSK3Bp_SS" name="GSK3Bp" units="molecules"/>
        <variable name="GSK3Bp_SS" units="molecules"/>
        <variable initial_value="50" name="period_1" units="hour"/>
        <variable initial_value="170" name="period_2" units="hour"/>
        <variable name="alpha" units="molecules_per_hour"/>
        <variable initial_value="44000" name="alpha_infection" units="molecules_per_hour"/>
        <variable initial_value="1560" name="alpha_initial" units="molecules_per_hour"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>alpha</ci>
                <piecewise>
                    <piece>
                        <ci>alpha_initial</ci>
                        <apply>
                            <lt/>
                            <ci>t</ci>
                            <ci>period_1</ci>
                        </apply>
                    </piece>
                    <piece>
                        <ci>alpha_infection</ci>
                        <apply>
                            <lt/>
                            <ci>t</ci>
                            <ci>period_2</ci>
                        </apply>
                    </piece>
                    <otherwise>
                        <ci>alpha_initial</ci>
                    </otherwise>
                </piecewise>
            </apply>
            <!--Steady state-->
            <apply>
                <eq/>
                <ci>Q</ci>
                <apply>
                    <root/>
                    <apply>
                        <plus/>
                        <apply>
                            <power/>
                            <apply>
                                <times/>
                                <ci>alpha_initial</ci>
                                <ci>gamma</ci>
                            </apply>
                            <cn cellml:units="dimensionless">2</cn>
                        </apply>
                        <apply>
                            <power/>
                            <apply>
                                <times/>
                                <ci>beta</ci>
                                <ci>rho</ci>
                            </apply>
                            <cn cellml:units="dimensionless">2</cn>
                        </apply>
                        <apply>
                            <power/>
                            <apply>
                                <times/>
                                <ci>gamma</ci>
                                <ci>tau</ci>
                            </apply>
                            <cn cellml:units="dimensionless">2</cn>
                        </apply>
                        <apply>
                            <times/>
                            <cn cellml:units="dimensionless">2</cn>
                            <apply>
                                <plus/>
                                <apply>
                                    <minus/>
                                    <apply>
                                        <times/>
                                        <ci>alpha_initial</ci>
                                        <ci>beta</ci>
                                        <ci>gamma</ci>
                                        <ci>rho</ci>
                                    </apply>
                                    <apply>
                                        <times/>
                                        <ci>alpha_initial</ci>
                                        <apply>
                                            <power/>
                                            <ci>gamma</ci>
                                            <cn cellml:units="dimensionless">2</cn>
                                        </apply>
                                        <ci>tau</ci>
                                    </apply>
                                </apply>
                                <apply>
                                    <times/>
                                    <ci>beta</ci>
                                    <ci>gamma</ci>
                                    <ci>rho</ci>
                                    <ci>tau</ci>
                                </apply>
                            </apply>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>QQ</ci>
                <apply>
                    <times/>
                    <cn cellml:units="dimensionless">2</cn>
                    <apply>
                        <minus/>
                        <apply>
                            <minus/>
                            <apply>
                                <times/>
                                <apply>
                                    <power/>
                                    <ci>G_tot</ci>
                                    <cn cellml:units="dimensionless">2</cn>
                                </apply>
                                <ci>gamma</ci>
                                <apply>
                                    <power/>
                                    <ci>kappa</ci>
                                    <cn cellml:units="dimensionless">2</cn>
                                </apply>
                                <ci>rho</ci>
                            </apply>
                            <apply>
                                <times/>
                                <ci>G_tot</ci>
                                <apply>
                                    <minus/>
                                    <apply>
                                        <plus/>
                                        <apply>
                                            <times/>
                                            <ci>alpha_initial</ci>
                                            <ci>eta</ci>
                                            <ci>gamma</ci>
                                            <ci>kappa</ci>
                                        </apply>
                                        <apply>
                                            <times/>
                                            <ci>beta</ci>
                                            <ci>eta</ci>
                                            <ci>kappa</ci>
                                            <ci>rho</ci>
                                        </apply>
                                    </apply>
                                    <apply>
                                        <times/>
                                        <ci>eta</ci>
                                        <ci>gamma</ci>
                                        <ci>kappa</ci>
                                        <ci>tau</ci>
                                    </apply>
                                </apply>
                            </apply>
                        </apply>
                        <apply>
                            <times/>
                            <ci>beta</ci>
                            <apply>
                                <power/>
                                <ci>eta</ci>
                                <cn cellml:units="dimensionless">2</cn>
                            </apply>
                            <ci>tau</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>AB_SS</ci>
                <apply>
                    <divide/>
                    <apply>
                        <plus/>
                        <apply>
                            <minus/>
                            <apply>
                                <minus/>
                                <apply>
                                    <times/>
                                    <ci>alpha_initial</ci>
                                    <ci>gamma</ci>
                                </apply>
                                <apply>
                                    <times/>
                                    <ci>beta</ci>
                                    <ci>rho</ci>
                                </apply>
                            </apply>
                            <apply>
                                <times/>
                                <ci>gamma</ci>
                                <ci>tau</ci>
                            </apply>
                        </apply>
                        <ci>Q</ci>
                    </apply>
                    <apply>
                        <times/>
                        <cn cellml:units="dimensionless">2</cn>
                        <ci>beta</ci>
                        <ci>gamma</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>Reelin_SS</ci>
                <apply>
                    <divide/>
                    <apply>
                        <plus/>
                        <apply>
                            <minus/>
                            <apply>
                                <times/>
                                <apply>
                                    <minus/>
                                    <ci>alpha_initial</ci>
                                </apply>
                                <ci>gamma</ci>
                            </apply>
                            <apply>
                                <times/>
                                <ci>beta</ci>
                                <ci>rho</ci>
                            </apply>
                        </apply>
                        <apply>
                            <times/>
                            <ci>gamma</ci>
                            <ci>tau</ci>
                        </apply>
                        <ci>Q</ci>
                    </apply>
                    <apply>
                        <times/>
                        <cn cellml:units="dimensionless">2</cn>
                        <ci>gamma</ci>
                        <ci>rho</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>ABR_SS</ci>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <apply>
                            <plus/>
                            <apply>
                                <times/>
                                <ci>alpha_initial</ci>
                                <ci>gamma</ci>
                            </apply>
                            <apply>
                                <times/>
                                <ci>beta</ci>
                                <ci>rho</ci>
                            </apply>
                            <apply>
                                <times/>
                                <ci>gamma</ci>
                                <ci>tau</ci>
                            </apply>
                        </apply>
                        <ci>Q</ci>
                    </apply>
                    <apply>
                        <times/>
                        <cn cellml:units="dimensionless">2</cn>
                        <ci>delta</ci>
                        <ci>gamma</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>GSK3Bp_SS</ci>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <apply>
                            <times/>
                            <apply>
                                <power/>
                                <ci>G_tot</ci>
                                <cn cellml:units="dimensionless">2</cn>
                            </apply>
                            <ci>eta</ci>
                            <ci>kappa</ci>
                            <ci>Q</ci>
                        </apply>
                        <apply>
                            <times/>
                            <ci>G_tot</ci>
                            <ci>eta</ci>
                            <apply>
                                <plus/>
                                <apply>
                                    <times/>
                                    <ci>G_tot</ci>
                                    <apply>
                                        <minus/>
                                        <apply>
                                            <plus/>
                                            <apply>
                                                <times/>
                                                <ci>alpha_initial</ci>
                                                <ci>gamma</ci>
                                                <ci>kappa</ci>
                                            </apply>
                                            <apply>
                                                <times/>
                                                <ci>beta</ci>
                                                <ci>kappa</ci>
                                                <ci>rho</ci>
                                            </apply>
                                        </apply>
                                        <apply>
                                            <times/>
                                            <ci>gamma</ci>
                                            <ci>kappa</ci>
                                            <ci>tau</ci>
                                        </apply>
                                    </apply>
                                </apply>
                                <apply>
                                    <times/>
                                    <cn cellml:units="dimensionless">2</cn>
                                    <ci>beta</ci>
                                    <ci>eta</ci>
                                    <ci>tau</ci>
                                </apply>
                            </apply>
                        </apply>
                    </apply>
                    <ci>QQ</ci>
                </apply>
            </apply>
            <!--Transients-->
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>AB</ci>
                </apply>
                <apply>
                    <minus/>
                    <apply>
                        <minus/>
                        <ci>alpha</ci>
                        <apply>
                            <times/>
                            <ci>beta</ci>
                            <ci>AB</ci>
                        </apply>
                    </apply>
                    <apply>
                        <times/>
                        <ci>gamma</ci>
                        <ci>AB</ci>
                        <ci>Reelin</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>Reelin</ci>
                </apply>
                <apply>
                    <minus/>
                    <apply>
                        <minus/>
                        <ci>tau</ci>
                        <apply>
                            <times/>
                            <ci>rho</ci>
                            <ci>Reelin</ci>
                        </apply>
                    </apply>
                    <apply>
                        <times/>
                        <ci>gamma</ci>
                        <ci>AB</ci>
                        <ci>Reelin</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>ABR</ci>
                </apply>
                <apply>
                    <minus/>
                    <apply>
                        <times/>
                        <ci>gamma</ci>
                        <ci>AB</ci>
                        <ci>Reelin</ci>
                    </apply>
                    <apply>
                        <times/>
                        <ci>delta</ci>
                        <ci>ABR</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>GSK3Bp</ci>
                </apply>
                <apply>
                    <minus/>
                    <apply>
                        <times/>
                        <ci>eta</ci>
                        <ci>Reelin</ci>
                        <apply>
                            <minus/>
                            <cn cellml:units="dimensionless">1</cn>
                            <apply>
                                <divide/>
                                <ci>GSK3Bp</ci>
                                <ci>G_tot</ci>
                            </apply>
                        </apply>
                    </apply>
                    <apply>
                        <times/>
                        <ci>kappa</ci>
                        <ci>GSK3Bp</ci>
                    </apply>
                </apply>
            </apply>
        </math>
        <!--Putting eqns 2 & 3 to equilibrium-->
        <variable name="Reelin_equil" units="molecules_per_hour"/>
        <variable name="ABR_equil" units="molecules_per_hour"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>Reelin_equil</ci>
                <apply>
                    <divide/>
                    <ci>tau</ci>
                    <apply>
                        <plus/>
                        <ci>rho</ci>
                        <apply>
                            <times/>
                            <ci>gamma</ci>
                            <ci>AB</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>ABR_equil</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <apply>
                            <divide/>
                            <ci>tau</ci>
                            <ci>delta</ci>
                        </apply>
                        <ci>AB</ci>
                    </apply>
                    <apply>
                        <plus/>
                        <apply>
                            <divide/>
                            <ci>rho</ci>
                            <ci>gamma</ci>
                        </apply>
                        <ci>AB</ci>
                    </apply>
                </apply>
            </apply>
        </math>
        <!--Express AB, Reelin & ABR as concentrations and normalise GSK3Bp-->
        <variable initial_value="4846" name="volume" units="micrometer_cubed"/>
        <variable name="AB_conc" units="nM"/>
        <variable name="Reelin_conc" units="nM"/>
        <variable name="ABR_conc" units="nM"/>
        <variable name="GSK3Bp_norm" units="molecules"/>
        <variable initial_value="0.6023" name="A_N" units="dimensionless"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>AB_conc</ci>
                <apply>
                    <divide/>
                    <ci>AB</ci>
                    <apply>
                        <times/>
                        <ci>volume</ci>
                        <ci>A_N</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>Reelin_conc</ci>
                <apply>
                    <divide/>
                    <ci>Reelin</ci>
                    <apply>
                        <times/>
                        <ci>volume</ci>
                        <ci>A_N</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>ABR_conc</ci>
                <apply>
                    <divide/>
                    <ci>ABR</ci>
                    <apply>
                        <times/>
                        <ci>volume</ci>
                        <ci>A_N</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>GSK3Bp_norm</ci>
                <apply>
                    <divide/>
                    <ci>GSK3Bp</ci>
                    <ci>G_tot</ci>
                </apply>
            </apply>
        </math>
    </component>
</model>