Location: 12 L Platform 1 model codes @ 4c1ab73f48d7 / Airway_FTU / wang2010 / wang2010.cellml

Author:
aram148 <a.rampadarath@auckland.ac.nz>
Date:
2021-11-04 16:02:42+13:00
Desc:
Updated USMC-Bursztyn model
Permanent Source URI:
http://models.cellml.org/workspace/6b0/rawfile/4c1ab73f48d7150c2094cf8017425482a1594ccf/Airway_FTU/wang2010/wang2010.cellml

<?xml version='1.0'?>
<model name="wang_2010" 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="per_mM_per_sec" units_ref="per_mM_per_sec"/>
        <units name="mV" units_ref="mV"/>
        <units name="per_sec" units_ref="per_sec"/>
        <units name="mM" units_ref="mM"/>
        <units name="nS_per_mM" units_ref="nS_per_mM"/>
        <units name="C_per_mol" units_ref="C_per_mol"/>
        <units name="per_mM" units_ref="per_mM"/>
        <units name="mM_per_sec" units_ref="mM_per_sec"/>
        <units name="mJ_per_K_per_mol" units_ref="mJ_per_K_per_mol"/>
        <units name="uA_per_cmsq" units_ref="uA_per_cmsq"/>
    </import>
    <component name="environment">
        <variable name="time" public_interface="out" units="second"/>
    </component>
    <component name="ca_parameters">
        <variable initial_value="2000" name="k_1" public_interface="out" units="per_mM_per_sec"/>
        <variable initial_value="1.0" name="k_2" public_interface="out" units="per_mM_per_sec"/>
        <variable initial_value="2000" name="k_3" public_interface="out" units="per_mM_per_sec"/>
        <variable initial_value="1.0" name="k_4" public_interface="out" units="per_mM_per_sec"/>
        <variable initial_value="100" name="k_5" public_interface="out" units="per_mM_per_sec"/>
        <variable initial_value="260" name="k_m1" public_interface="out" units="per_sec"/>
        <variable initial_value="1.05" name="k_m2" public_interface="out" units="per_sec"/>
        <variable initial_value="1886" name="k_m3" public_interface="out" units="per_sec"/>
        <variable initial_value="0.145" name="k_m4" public_interface="out" units="per_sec"/>
        <variable initial_value="8.2" name="k_m5" public_interface="out" units="per_sec"/>
        <variable initial_value="0.0072" name="k_ryr0" public_interface="out" units="per_sec"/>
        <variable initial_value="0.334" name="k_ryr1" public_interface="out" units="per_sec"/>
        <variable initial_value="0.5" name="k_ryr2" public_interface="out" units="mM"/>
        <variable initial_value="38" name="k_ryr3" public_interface="out" units="mM"/>
        <variable initial_value="5.55" name="k_ipr" public_interface="out" units="per_sec"/>
        <variable initial_value="5.0" name="k_RyR" public_interface="out" units="per_sec"/>
        <variable initial_value="-50" name="Vm" public_interface="out" units="mV"/>
        <variable initial_value="12" name="km" public_interface="out" units="mV"/>
        <variable initial_value="9" name="gca" public_interface="out" units="nS_per_mM"/>
        <variable initial_value="96485" name="F" public_interface="out" units="C_per_mol"/>
        <variable initial_value="8345" name="R" public_interface="out" units="mJ_per_K_per_mol"/>
        <variable initial_value="310" name="T" public_interface="out" units="kelvin"/>
        <variable initial_value="0.05" name="alpha0" public_interface="out" units="mM_per_sec"/>
        <variable initial_value="0.25" name="alpha1" public_interface="out" units="dimensionless"/>
        <variable initial_value="1" name="alpha2" public_interface="out" units="per_sec"/>
        <variable initial_value="0.1" name="Jer" public_interface="out" units="per_sec"/>
        <variable initial_value="4.5" name="Ve" public_interface="out" units="mM_per_sec"/>
        <variable initial_value="0.1" name="Ke" public_interface="out" units="mM"/>
        <variable initial_value="4.5" name="Vp" public_interface="out" units="mM_per_sec"/>
        <variable initial_value="0.4" name="Kp" public_interface="out" units="mM"/>
        <variable initial_value="5.5" name="gamma" public_interface="out" units="dimensionless"/>
        <variable initial_value="0.05" name="delta" public_interface="out" units="dimensionless"/>
    </component>
    <component name="asm_ca">
        <variable name="time" public_interface="in" units="second"/>
        <variable initial_value="0.112" name="c" public_interface="out" units="mM"/>
        <variable name="J_release" units="mM_per_sec"/>
        <variable name="J_serca" units="mM_per_sec"/>
        <variable name="J_in" units="mM_per_sec"/>
        <variable name="J_pm" units="mM_per_sec"/>
        <variable name="k_ipr" public_interface="in" units="per_sec"/>
        <variable name="P_ipr" units="dimensionless"/>
        <variable name="k_RyR" public_interface="in" units="per_sec"/>
        <variable name="P_RyR" units="dimensionless"/>
        <variable name="Jer" public_interface="in" units="per_sec"/>
        <variable initial_value="24" name="cs" units="mM"/>
        <variable name="p" public_interface="out" units="mM"/>
        <variable name="k_ryr0" public_interface="in" units="per_sec"/>
        <variable name="k_ryr1" public_interface="in" units="per_sec"/>
        <variable name="k_ryr2" public_interface="in" units="mM"/>
        <variable name="k_ryr3" public_interface="in" units="mM"/>
        <variable name="Ve" public_interface="in" units="mM_per_sec"/>
        <variable name="Ke" public_interface="in" units="mM"/>
        <variable name="Vp" public_interface="in" units="mM_per_sec"/>
        <variable name="Kp" public_interface="in" units="mM"/>
        <variable name="alpha0" public_interface="in" units="mM_per_sec"/>
        <variable name="alpha1" public_interface="in" units="dimensionless"/>
        <variable name="alpha2" public_interface="in" units="per_sec"/>
        <variable name="F" public_interface="in" units="C_per_mol"/>
        <variable initial_value="0" name="y" units="dimensionless"/>
        <variable name="phi1" units="dimensionless"/>
        <variable name="phi2" units="dimensionless"/>
        <variable name="k_1" public_interface="in" units="per_mM_per_sec"/>
        <variable name="k_2" public_interface="in" units="per_mM_per_sec"/>
        <variable name="k_3" public_interface="in" units="per_mM_per_sec"/>
        <variable name="k_4" public_interface="in" units="per_mM_per_sec"/>
        <variable name="k_5" public_interface="in" units="per_mM_per_sec"/>
        <variable name="k_m1" public_interface="in" units="per_sec"/>
        <variable name="k_m2" public_interface="in" units="per_sec"/>
        <variable name="k_m3" public_interface="in" units="per_sec"/>
        <variable name="k_m4" public_interface="in" units="per_sec"/>
        <variable name="k_m5" public_interface="in" units="per_sec"/>
        <variable name="K1" units="dimensionless"/>
        <variable name="K2" units="dimensionless"/>
        <variable name="K3" units="dimensionless"/>
        <variable name="K4" units="dimensionless"/>
        <variable name="K5" units="dimensionless"/>
        <variable name="delta" public_interface="in" units="dimensionless"/>
        <variable name="V" units="mV"/>
        <variable name="gamma" public_interface="in" units="dimensionless"/>
        <variable name="R" public_interface="in" units="mJ_per_K_per_mol"/>
        <variable name="T" public_interface="in" units="kelvin"/>
        <variable name="I_ca" units="uA_per_cmsq"/>
        <variable name="gca" public_interface="in" units="nS_per_mM"/>
        <variable name="m" units="dimensionless"/>
        <variable name="V_ca" units="mV"/>
        <variable name="Vm" public_interface="in" units="mV"/>
        <variable name="km" public_interface="in" units="mV"/>
        <variable initial_value="0" name="ce" units="mM"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>V</ci>
                <apply>
                    <plus/>
                    <apply>
                        <times/>
                        <apply>
                            <minus/>
                            <cn cellml:units="mV">60</cn>
                        </apply>
                        <apply>
                            <lt/>
                            <ci>time</ci>
                            <cn cellml:units="second">50</cn>
                        </apply>
                    </apply>
                    <apply>
                        <times/>
                        <apply>
                            <minus/>
                            <cn cellml:units="mV">30</cn>
                        </apply>
                        <apply>
                            <and/>
                            <apply>
                                <geq/>
                                <ci>time</ci>
                                <cn cellml:units="second">50</cn>
                            </apply>
                            <apply>
                                <leq/>
                                <ci>time</ci>
                                <cn cellml:units="second">400</cn>
                            </apply>
                        </apply>
                    </apply>
                    <apply>
                        <times/>
                        <apply>
                            <minus/>
                            <cn cellml:units="mV">60</cn>
                        </apply>
                        <apply>
                            <gt/>
                            <ci>time</ci>
                            <cn cellml:units="second">400</cn>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>K1</ci>
                <apply>
                    <divide/>
                    <ci>k_m1</ci>
                    <ci>k_1</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>K2</ci>
                <apply>
                    <divide/>
                    <ci>k_m2</ci>
                    <ci>k_2</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>K3</ci>
                <apply>
                    <divide/>
                    <ci>k_m3</ci>
                    <ci>k_3</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>K4</ci>
                <apply>
                    <divide/>
                    <ci>k_m4</ci>
                    <ci>k_4</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>K5</ci>
                <apply>
                    <divide/>
                    <ci>k_m5</ci>
                    <ci>k_5</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>I_ca</ci>
                <apply>
                    <times/>
                    <ci>gca</ci>
                    <apply>
                        <power/>
                        <ci>m</ci>
                        <cn cellml:units="dimensionless">2</cn>
                    </apply>
                    <ci>V_ca</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>m</ci>
                <apply>
                    <divide/>
                    <cn cellml:units="dimensionless">1</cn>
                    <apply>
                        <plus/>
                        <cn cellml:units="dimensionless">1</cn>
                        <apply>
                            <exp/>
                            <apply>
                                <divide/>
                                <apply>
                                    <minus/>
                                    <apply>
                                        <minus/>
                                        <ci>V</ci>
                                        <ci>Vm</ci>
                                    </apply>
                                </apply>
                                <ci>km</ci>
                            </apply>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>V_ca</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <ci>V</ci>
                        <apply>
                            <minus/>
                            <ci>c</ci>
                            <apply>
                                <times/>
                                <ci>ce</ci>
                                <apply>
                                    <exp/>
                                    <apply>
                                        <divide/>
                                        <apply>
                                            <times/>
                                            <apply>
                                                <minus/>
                                                <cn cellml:units="dimensionless">2</cn>
                                            </apply>
                                            <ci>V</ci>
                                            <ci>F</ci>
                                        </apply>
                                        <apply>
                                            <times/>
                                            <ci>R</ci>
                                            <ci>T</ci>
                                        </apply>
                                    </apply>
                                </apply>
                            </apply>
                        </apply>
                    </apply>
                    <apply>
                        <minus/>
                        <cn cellml:units="dimensionless">1</cn>
                        <apply>
                            <exp/>
                            <apply>
                                <divide/>
                                <apply>
                                    <times/>
                                    <apply>
                                        <minus/>
                                        <cn cellml:units="dimensionless">2</cn>
                                    </apply>
                                    <ci>V</ci>
                                    <ci>F</ci>
                                </apply>
                                <apply>
                                    <times/>
                                    <ci>R</ci>
                                    <ci>T</ci>
                                </apply>
                            </apply>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>J_pm</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <ci>Vp</ci>
                        <apply>
                            <power/>
                            <ci>c</ci>
                            <cn cellml:units="dimensionless">4</cn>
                        </apply>
                    </apply>
                    <apply>
                        <plus/>
                        <apply>
                            <power/>
                            <ci>Kp</ci>
                            <cn cellml:units="dimensionless">4</cn>
                        </apply>
                        <apply>
                            <power/>
                            <ci>c</ci>
                            <cn cellml:units="dimensionless">4</cn>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>J_serca</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <ci>Ve</ci>
                        <apply>
                            <power/>
                            <ci>c</ci>
                            <cn cellml:units="dimensionless">2</cn>
                        </apply>
                    </apply>
                    <apply>
                        <plus/>
                        <apply>
                            <power/>
                            <ci>Ke</ci>
                            <cn cellml:units="dimensionless">2</cn>
                        </apply>
                        <apply>
                            <power/>
                            <ci>c</ci>
                            <cn cellml:units="dimensionless">2</cn>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>J_release</ci>
                <apply>
                    <times/>
                    <apply>
                        <plus/>
                        <apply>
                            <times/>
                            <ci>k_ipr</ci>
                            <ci>P_ipr</ci>
                        </apply>
                        <apply>
                            <times/>
                            <ci>k_RyR</ci>
                            <ci>P_RyR</ci>
                        </apply>
                        <ci>Jer</ci>
                    </apply>
                    <apply>
                        <minus/>
                        <ci>cs</ci>
                        <ci>c</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>J_in</ci>
                <apply>
                    <plus/>
                    <apply>
                        <times/>
                        <apply>
                            <plus/>
                            <apply>
                                <minus/>
                                <ci>alpha0</ci>
                                <apply>
                                    <divide/>
                                    <apply>
                                        <times/>
                                        <ci>alpha1</ci>
                                        <ci>I_ca</ci>
                                    </apply>
                                    <apply>
                                        <times/>
                                        <cn cellml:units="dimensionless">2</cn>
                                        <ci>F</ci>
                                    </apply>
                                </apply>
                            </apply>
                            <apply>
                                <times/>
                                <ci>alpha2</ci>
                                <ci>p</ci>
                            </apply>
                        </apply>
                        <apply>
                            <lt/>
                            <ci>time</ci>
                            <cn cellml:units="second">50</cn>
                        </apply>
                    </apply>
                    <apply>
                        <times/>
                        <cn cellml:units="dimensionless">0</cn>
                        <apply>
                            <geq/>
                            <ci>time</ci>
                            <cn cellml:units="second">50</cn>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>P_ipr</ci>
                <apply>
                    <power/>
                    <apply>
                        <divide/>
                        <apply>
                            <times/>
                            <ci>p</ci>
                            <ci>c</ci>
                            <apply>
                                <minus/>
                                <cn cellml:units="dimensionless">1</cn>
                                <ci>y</ci>
                            </apply>
                        </apply>
                        <apply>
                            <times/>
                            <apply>
                                <plus/>
                                <ci>p</ci>
                                <ci>K1</ci>
                            </apply>
                            <apply>
                                <plus/>
                                <ci>c</ci>
                                <ci>K5</ci>
                            </apply>
                        </apply>
                    </apply>
                    <cn cellml:units="dimensionless">3</cn>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>P_RyR</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <apply>
                            <plus/>
                            <ci>k_ryr0</ci>
                            <apply>
                                <divide/>
                                <apply>
                                    <times/>
                                    <ci>k_ryr1</ci>
                                    <apply>
                                        <power/>
                                        <ci>c</ci>
                                        <cn cellml:units="dimensionless">3</cn>
                                    </apply>
                                </apply>
                                <apply>
                                    <plus/>
                                    <apply>
                                        <power/>
                                        <ci>k_ryr2</ci>
                                        <cn cellml:units="dimensionless">3</cn>
                                    </apply>
                                    <apply>
                                        <power/>
                                        <ci>c</ci>
                                        <cn cellml:units="dimensionless">3</cn>
                                    </apply>
                                </apply>
                            </apply>
                        </apply>
                        <apply>
                            <power/>
                            <ci>cs</ci>
                            <cn cellml:units="dimensionless">4</cn>
                        </apply>
                    </apply>
                    <apply>
                        <plus/>
                        <apply>
                            <power/>
                            <ci>k_ryr3</ci>
                            <cn cellml:units="dimensionless">4</cn>
                        </apply>
                        <apply>
                            <power/>
                            <ci>c</ci>
                            <cn cellml:units="dimensionless">4</cn>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>phi1</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <apply>
                            <plus/>
                            <apply>
                                <times/>
                                <ci>k_m4</ci>
                                <ci>K2</ci>
                                <ci>K1</ci>
                            </apply>
                            <apply>
                                <times/>
                                <ci>k_m2</ci>
                                <ci>K4</ci>
                                <ci>p</ci>
                            </apply>
                        </apply>
                        <ci>c</ci>
                    </apply>
                    <apply>
                        <times/>
                        <ci>K4</ci>
                        <ci>K2</ci>
                        <apply>
                            <plus/>
                            <ci>K1</ci>
                            <ci>p</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>phi2</ci>
                <apply>
                    <divide/>
                    <apply>
                        <plus/>
                        <apply>
                            <times/>
                            <ci>k_m2</ci>
                            <ci>p</ci>
                        </apply>
                        <apply>
                            <times/>
                            <ci>k_m4</ci>
                            <ci>K3</ci>
                        </apply>
                    </apply>
                    <apply>
                        <plus/>
                        <ci>K3</ci>
                        <ci>p</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>time</ci>
                    </bvar>
                    <ci>y</ci>
                </apply>
                <apply>
                    <minus/>
                    <apply>
                        <times/>
                        <ci>phi1</ci>
                        <apply>
                            <minus/>
                            <cn cellml:units="dimensionless">1</cn>
                            <ci>y</ci>
                        </apply>
                    </apply>
                    <apply>
                        <times/>
                        <ci>phi2</ci>
                        <ci>y</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>time</ci>
                    </bvar>
                    <ci>c</ci>
                </apply>
                <apply>
                    <plus/>
                    <apply>
                        <minus/>
                        <ci>J_release</ci>
                        <ci>J_serca</ci>
                    </apply>
                    <apply>
                        <times/>
                        <ci>delta</ci>
                        <apply>
                            <minus/>
                            <ci>J_in</ci>
                            <ci>J_pm</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>time</ci>
                    </bvar>
                    <ci>cs</ci>
                </apply>
                <apply>
                    <times/>
                    <ci>gamma</ci>
                    <apply>
                        <minus/>
                        <ci>J_serca</ci>
                        <ci>J_release</ci>
                    </apply>
                </apply>
            </apply>
            <!--        p = 0{dimensionless};-->
            <apply>
                <eq/>
                <ci>p</ci>
                <apply>
                    <times/>
                    <apply>
                        <divide/>
                        <apply>
                            <times/>
                            <cn cellml:units="dimensionless">0.35</cn>
                            <cn cellml:units="dimensionless">1</cn>
                        </apply>
                        <apply>
                            <plus/>
                            <cn cellml:units="dimensionless">1</cn>
                            <apply>
                                <exp/>
                                <apply>
                                    <times/>
                                    <apply>
                                        <minus/>
                                        <cn cellml:units="dimensionless">0.0699</cn>
                                    </apply>
                                    <apply>
                                        <minus/>
                                        <ci>time</ci>
                                        <cn cellml:units="second">50</cn>
                                    </apply>
                                </apply>
                            </apply>
                        </apply>
                    </apply>
                    <apply>
                        <gt/>
                        <ci>time</ci>
                        <cn cellml:units="second">50</cn>
                    </apply>
                </apply>
            </apply>
        </math>
    </component>
    <connection>
        <map_components component_1="ca_parameters" component_2="asm_ca"/>
        <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="k_4" variable_2="k_4"/>
        <map_variables variable_1="k_5" variable_2="k_5"/>
        <map_variables variable_1="k_m1" variable_2="k_m1"/>
        <map_variables variable_1="k_m2" variable_2="k_m2"/>
        <map_variables variable_1="k_m3" variable_2="k_m3"/>
        <map_variables variable_1="k_m4" variable_2="k_m4"/>
        <map_variables variable_1="k_m5" variable_2="k_m5"/>
        <map_variables variable_1="gamma" variable_2="gamma"/>
        <map_variables variable_1="delta" variable_2="delta"/>
        <map_variables variable_1="F" variable_2="F"/>
        <map_variables variable_1="R" variable_2="R"/>
        <map_variables variable_1="T" variable_2="T"/>
        <map_variables variable_1="alpha0" variable_2="alpha0"/>
        <map_variables variable_1="alpha1" variable_2="alpha1"/>
        <map_variables variable_1="alpha2" variable_2="alpha2"/>
        <map_variables variable_1="k_ipr" variable_2="k_ipr"/>
        <map_variables variable_1="k_RyR" variable_2="k_RyR"/>
        <map_variables variable_1="Jer" variable_2="Jer"/>
        <map_variables variable_1="k_ryr0" variable_2="k_ryr0"/>
        <map_variables variable_1="k_ryr1" variable_2="k_ryr1"/>
        <map_variables variable_1="k_ryr2" variable_2="k_ryr2"/>
        <map_variables variable_1="k_ryr3" variable_2="k_ryr3"/>
        <map_variables variable_1="Ve" variable_2="Ve"/>
        <map_variables variable_1="Ke" variable_2="Ke"/>
        <map_variables variable_1="Vp" variable_2="Vp"/>
        <map_variables variable_1="Kp" variable_2="Kp"/>
        <map_variables variable_1="gca" variable_2="gca"/>
        <map_variables variable_1="Vm" variable_2="Vm"/>
        <map_variables variable_1="km" variable_2="km"/>
    </connection>
</model>