Location: Model of Human Jejunal Smooth Muscle Cell Electrophysiology @ d5a44a9d9492 / Components / Ionic_concentrations.cellml

Author:
WeiweiAi <wai484@aucklanduni.ac.nz>
Date:
2021-06-02 14:40:15+12:00
Desc:
Add E_Nernst to instantiate Nernst potential for Ca, Na and K and modify relevant models to accommodate the change. Add experiment of Periodic_stimulation, which can run.
Permanent Source URI:
https://models.cellml.org/workspace/692/rawfile/d5a44a9d949275dfd1b2e46aeaa827571356cd68/Components/Ionic_concentrations.cellml
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<?xml version='1.0' encoding='UTF-8'?>
<model name="Ionic_concentrations" 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="pA" units_ref="pA"/>
        <units name="C_per_mmol" units_ref="C_per_mmol"/>
        <units name="mM" units_ref="mM"/>
        <units name="ms" units_ref="ms"/>
        <units name="mM_per_ms" units_ref="mM_per_ms"/>
        <units name="fM_per_s2mM_per_ms" units_ref="fM_per_s2mM_per_ms"/>
    </import>
    <component name="Cai">
        <variable name="F" public_interface="in" units="C_per_mmol"/>
        <variable name="n_CRT" public_interface="in" units="dimensionless"/>
        <variable name="n_CaM" public_interface="in" units="dimensionless"/>
        <variable name="CRT_total" public_interface="in" units="mM"/>
        <variable name="CaM_total" public_interface="in" units="mM"/>
        <variable name="K_D_CRT" public_interface="in" units="mM"/>
        <variable name="K_D_CaM" public_interface="in" units="mM4"/>
        <variable name="I_CaL" public_interface="in" units="pA"/>
        <variable name="I_CaT" public_interface="in" units="pA"/>
        <variable name="I_NCX" public_interface="in" units="pA"/>
        <variable name="V_cell" public_interface="in" units="litre"/>
        <variable name="time" public_interface="in" units="ms"/>
        <variable name="Cai_total_init" public_interface="in" units="mM"/>
        <variable name="Cai_init" public_interface="in" units="mM"/>
        <variable initial_value="Cai_total_init" name="Cai_total" public_interface="out" units="mM"/>
        <variable initial_value="Cai_init" name="Cai" public_interface="out" units="mM"/>
        <variable name="Cai_total_rate" units="mM_per_ms"/>
        <variable initial_value="1e-15" name="Cvt" units="fM_per_s2mM_per_ms"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>Cai_total_rate</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <apply>
                            <minus/>
                            <apply>
                                <minus/>
                                <apply>
                                    <plus/>
                                    <ci>I_CaL</ci>
                                    <ci>I_CaT</ci>
                                </apply>
                                <apply>
                                    <times/>
                                    <cn cellml:units="dimensionless">2</cn>
                                    <ci>I_NCX</ci>
                                </apply>
                            </apply>
                        </apply>
                        <ci>Cvt</ci>
                    </apply>
                    <apply>
                        <times/>
                        <cn cellml:units="dimensionless">2</cn>
                        <ci>F</ci>
                        <ci>V_cell</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>time</ci>
                    </bvar>
                    <ci>Cai_total</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <apply>
                            <minus/>
                            <apply>
                                <minus/>
                                <apply>
                                    <plus/>
                                    <ci>I_CaL</ci>
                                    <ci>I_CaT</ci>
                                </apply>
                                <apply>
                                    <times/>
                                    <cn cellml:units="dimensionless">2</cn>
                                    <ci>I_NCX</ci>
                                </apply>
                            </apply>
                        </apply>
                        <ci>Cvt</ci>
                    </apply>
                    <apply>
                        <times/>
                        <cn cellml:units="dimensionless">2</cn>
                        <ci>F</ci>
                        <ci>V_cell</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>time</ci>
                    </bvar>
                    <ci>Cai</ci>
                </apply>
                <apply>
                    <divide/>
                    <ci>Cai_total_rate</ci>
                    <apply>
                        <plus/>
                        <cn cellml:units="dimensionless">1</cn>
                        <apply>
                            <divide/>
                            <apply>
                                <times/>
                                <ci>n_CRT</ci>
                                <ci>CRT_total</ci>
                                <ci>K_D_CRT</ci>
                                <apply>
                                    <power/>
                                    <ci>Cai</ci>
                                    <apply>
                                        <minus/>
                                        <ci>n_CRT</ci>
                                        <cn cellml:units="dimensionless">1</cn>
                                    </apply>
                                </apply>
                            </apply>
                            <apply>
                                <power/>
                                <apply>
                                    <plus/>
                                    <apply>
                                        <power/>
                                        <ci>Cai</ci>
                                        <ci>n_CRT</ci>
                                    </apply>
                                    <ci>K_D_CRT</ci>
                                </apply>
                                <cn cellml:units="dimensionless">2</cn>
                            </apply>
                        </apply>
                        <apply>
                            <divide/>
                            <apply>
                                <times/>
                                <ci>n_CaM</ci>
                                <ci>CaM_total</ci>
                                <ci>K_D_CaM</ci>
                                <apply>
                                    <power/>
                                    <ci>Cai</ci>
                                    <apply>
                                        <minus/>
                                        <ci>n_CaM</ci>
                                        <cn cellml:units="dimensionless">1</cn>
                                    </apply>
                                </apply>
                            </apply>
                            <apply>
                                <power/>
                                <apply>
                                    <plus/>
                                    <apply>
                                        <power/>
                                        <ci>Cai</ci>
                                        <ci>n_CaM</ci>
                                    </apply>
                                    <ci>K_D_CaM</ci>
                                </apply>
                                <cn cellml:units="dimensionless">2</cn>
                            </apply>
                        </apply>
                    </apply>
                </apply>
            </apply>
        </math>
    </component>
    <component name="Nai">
        <variable name="F" public_interface="in" units="C_per_mmol"/>
        <variable name="I_Na" public_interface="in" units="pA"/>
        <variable name="I_NaK" public_interface="in" units="pA"/>
        <variable name="I_NCX" public_interface="in" units="pA"/>
        <variable name="I_NsNa" public_interface="in" units="pA"/>
        <variable name="V_cell" public_interface="in" units="litre"/>
        <variable name="time" public_interface="in" units="ms"/>
        <variable name="Nai_init" public_interface="in" units="mM"/>
        <variable initial_value="Nai_init" name="Nai" public_interface="out" units="mM"/>
        <variable initial_value="1e-15" name="Cvt" units="fM_per_s2mM_per_ms"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>time</ci>
                    </bvar>
                    <ci>Nai</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <apply>
                            <minus/>
                            <apply>
                                <plus/>
                                <ci>I_Na</ci>
                                <apply>
                                    <times/>
                                    <cn cellml:units="dimensionless">3</cn>
                                    <ci>I_NaK</ci>
                                </apply>
                                <apply>
                                    <times/>
                                    <cn cellml:units="dimensionless">3</cn>
                                    <ci>I_NCX</ci>
                                </apply>
                                <ci>I_NsNa</ci>
                            </apply>
                        </apply>
                        <ci>Cvt</ci>
                    </apply>
                    <apply>
                        <times/>
                        <ci>F</ci>
                        <ci>V_cell</ci>
                    </apply>
                </apply>
            </apply>
        </math>
    </component>
    <component name="Ki">
        <variable name="F" public_interface="in" units="C_per_mmol"/>
        <variable name="I_Kv" public_interface="in" units="pA"/>
        <variable name="I_BK" public_interface="in" units="pA"/>
        <variable name="I_stim" public_interface="in" units="pA"/>
        <variable name="I_NaK" public_interface="in" units="pA"/>
        <variable name="I_NsK" public_interface="in" units="pA"/>
        <variable name="V_cell" public_interface="in" units="litre"/>
        <variable name="time" public_interface="in" units="ms"/>
        <variable name="Ki_init" public_interface="in" units="mM"/>
        <variable initial_value="Ki_init" name="Ki" public_interface="out" units="mM"/>
        <variable initial_value="1e-15" name="Cvt" units="fM_per_s2mM_per_ms"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>time</ci>
                    </bvar>
                    <ci>Ki</ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <apply>
                            <minus/>
                            <apply>
                                <plus/>
                                <apply>
                                    <minus/>
                                    <apply>
                                        <plus/>
                                        <ci>I_Kv</ci>
                                        <ci>I_BK</ci>
                                        <ci>I_stim</ci>
                                    </apply>
                                    <apply>
                                        <times/>
                                        <cn cellml:units="dimensionless">2</cn>
                                        <ci>I_NaK</ci>
                                    </apply>
                                </apply>
                                <ci>I_NsK</ci>
                            </apply>
                        </apply>
                        <ci>Cvt</ci>
                    </apply>
                    <apply>
                        <times/>
                        <ci>F</ci>
                        <ci>V_cell</ci>
                    </apply>
                </apply>
            </apply>
        </math>
    </component>
</model>