Location: BG_K_ATP @ f7866162901c / BG_K_ATP.cellml

Author:
Shelley Fong <s.fong@auckland.ac.nz>
Date:
2022-04-11 14:58:43+12:00
Desc:
Changing method of number of channels present. Guess density. Using SA of human iPSC for Kernik. Updating volumes
Permanent Source URI:
https://models.physiomeproject.org/workspace/83a/rawfile/f7866162901c791abc6610a6eb544540c298d618/BG_K_ATP.cellml

<?xml version='1.0' encoding='UTF-8'?>
<!-- NOTE: ATP was used in G_GHK fitting, but it is not treated as an input species to the bond graph of this model.-->
<model name="cardiac_AP_K_ATP_only" 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_and_constants/units_BG.cellml">
        <units name="mM" units_ref="mM"/>
        <units name="fmol" units_ref="fmol"/>
        <units name="per_fmol" units_ref="per_fmol"/>
        <units name="J_per_mol" units_ref="J_per_mol"/>
        <units name="fmol_per_sec" units_ref="fmol_per_sec"/>
        <units name="C_per_mol" units_ref="C_per_mol"/>
        <units name="J_per_C" units_ref="J_per_C"/>
        <units name="J_per_K_per_mol" units_ref="J_per_K_per_mol"/>
        <units name="fF" units_ref="fF"/>
        <units name="fC" units_ref="fC"/>
        <units name="fA" units_ref="fA"/>
    </import>
    <component name="environment">
        <variable initial_value="0" name="t" public_interface="out" units="second"/>
        <variable initial_value="8.314" name="R" public_interface="out" units="J_per_K_per_mol"/>
        <variable initial_value="310" name="T" public_interface="out" units="kelvin"/>
        <variable initial_value="96485" name="F" public_interface="out" units="C_per_mol"/>
        <variable initial_value="153400" name="C_m" public_interface="out" units="fF"/>
        <variable initial_value="27.9828" name="q_K_o" public_interface="out" units="fmol"/>
        <variable initial_value="5510" name="q_K_i" public_interface="out" units="fmol"/>
        <variable name="v_K_ATP" public_interface="in" units="fmol_per_sec"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>q_K_o</ci>
                </apply>
                <ci>v_K_ATP</ci>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>q_K_i</ci>
                </apply>
                <apply>
                    <minus/>
                    <ci>v_K_ATP</ci>
                </apply>
            </apply>
        </math>
        <variable initial_value="-13039" name="q_mem" public_interface="out" units="fC"/>
        <variable name="I_mem_K_ATP" public_interface="in" units="fA"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>q_mem</ci>
                </apply>
                <ci>I_mem_K_ATP</ci>
            </apply>
        </math>
    </component>
    <component name="K_ATP_parameters">
        <variable initial_value="1.1812e-05" name="kappa_K_ATP" public_interface="out" units="fmol_per_sec"/>
        <variable initial_value="9.99086e-05" name="K_K_i" public_interface="out" units="per_fmol"/>
        <variable initial_value="0.000663229" name="K_K_o" public_interface="out" units="per_fmol"/>
        <variable initial_value="1" name="zK" public_interface="out" units="dimensionless"/>
    </component>
    <component name="K_ATP">
        <variable name="t" public_interface="in" units="second"/>
        <variable name="R" public_interface="in" units="J_per_K_per_mol"/>
        <variable name="T" public_interface="in" units="kelvin"/>
        <variable name="F" public_interface="in" units="C_per_mol"/>
        <variable name="C_m" public_interface="in" units="fF"/>
        <variable name="K_K_o" public_interface="in" units="per_fmol"/>
        <variable name="K_K_i" public_interface="in" units="per_fmol"/>
        <variable name="kappa_K_ATP" public_interface="in" units="fmol_per_sec"/>
        <variable name="zK" public_interface="in" units="dimensionless"/>
        <variable name="q_K_o" public_interface="in" units="fmol"/>
        <variable name="q_K_i" public_interface="in" units="fmol"/>
        <variable name="q_mem" public_interface="in" units="fC"/>
        <variable name="mu_K_o" units="J_per_mol"/>
        <variable name="mu_K_i" units="J_per_mol"/>
        <variable name="Am_K_ATP" units="J_per_mol"/>
        <variable name="Af_K_ATP" units="J_per_mol"/>
        <variable name="Ar_K_ATP" units="J_per_mol"/>
        <variable name="v_K_ATP" public_interface="out" units="fmol_per_sec"/>
        <variable name="V_mem" units="volt"/>
        <variable name="I_mem_K_ATP" public_interface="out" units="fA"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>V_mem</ci>
                <apply>
                    <divide/>
                    <ci>q_mem</ci>
                    <ci>C_m</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>mu_K_o</ci>
                <apply>
                    <times/>
                    <ci>R</ci>
                    <ci>T</ci>
                    <apply>
                        <ln/>
                        <apply>
                            <times/>
                            <ci>K_K_o</ci>
                            <ci>q_K_o</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>mu_K_i</ci>
                <apply>
                    <times/>
                    <ci>R</ci>
                    <ci>T</ci>
                    <apply>
                        <ln/>
                        <apply>
                            <times/>
                            <ci>K_K_i</ci>
                            <ci>q_K_i</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>Af_K_ATP</ci>
                <apply>
                    <plus/>
                    <ci>mu_K_i</ci>
                    <apply>
                        <times/>
                        <ci>zK</ci>
                        <ci>F</ci>
                        <ci>V_mem</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>Am_K_ATP</ci>
                <apply>
                    <times/>
                    <ci>zK</ci>
                    <ci>F</ci>
                    <ci>V_mem</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>Ar_K_ATP</ci>
                <ci>mu_K_o</ci>
            </apply>
            <apply>
                <eq/>
                <ci>I_mem_K_ATP</ci>
                <apply>
                    <times/>
                    <ci>F</ci>
                    <apply>
                        <minus/>
                        <ci>zK</ci>
                    </apply>
                    <ci>v_K_ATP</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>v_K_ATP</ci>
                <piecewise>
                    <piece>
                        <apply>
                            <times/>
                            <ci>kappa_K_ATP</ci>
                            <apply>
                                <minus/>
                                <apply>
                                    <exp/>
                                    <apply>
                                        <divide/>
                                        <ci>Af_K_ATP</ci>
                                        <apply>
                                            <times/>
                                            <ci>R</ci>
                                            <ci>T</ci>
                                        </apply>
                                    </apply>
                                </apply>
                                <apply>
                                    <exp/>
                                    <apply>
                                        <divide/>
                                        <ci>Ar_K_ATP</ci>
                                        <apply>
                                            <times/>
                                            <ci>R</ci>
                                            <ci>T</ci>
                                        </apply>
                                    </apply>
                                </apply>
                            </apply>
                        </apply>
                        <apply>
                            <eq/>
                            <ci>Am_K_ATP</ci>
                            <cn cellml:units="J_per_mol">0</cn>
                        </apply>
                    </piece>
                    <otherwise>
                        <apply>
                            <times/>
                            <apply>
                                <divide/>
                                <apply>
                                    <divide/>
                                    <apply>
                                        <times/>
                                        <ci>kappa_K_ATP</ci>
                                        <ci>Am_K_ATP</ci>
                                    </apply>
                                    <apply>
                                        <times/>
                                        <ci>R</ci>
                                        <ci>T</ci>
                                    </apply>
                                </apply>
                                <apply>
                                    <minus/>
                                    <apply>
                                        <exp/>
                                        <apply>
                                            <divide/>
                                            <ci>Am_K_ATP</ci>
                                            <apply>
                                                <times/>
                                                <ci>R</ci>
                                                <ci>T</ci>
                                            </apply>
                                        </apply>
                                    </apply>
                                    <cn cellml:units="dimensionless">1</cn>
                                </apply>
                            </apply>
                            <apply>
                                <minus/>
                                <apply>
                                    <exp/>
                                    <apply>
                                        <divide/>
                                        <ci>Af_K_ATP</ci>
                                        <apply>
                                            <times/>
                                            <ci>R</ci>
                                            <ci>T</ci>
                                        </apply>
                                    </apply>
                                </apply>
                                <apply>
                                    <exp/>
                                    <apply>
                                        <divide/>
                                        <ci>Ar_K_ATP</ci>
                                        <apply>
                                            <times/>
                                            <ci>R</ci>
                                            <ci>T</ci>
                                        </apply>
                                    </apply>
                                </apply>
                            </apply>
                        </apply>
                    </otherwise>
                </piecewise>
            </apply>
        </math>
    </component>
    <connection>
        <map_components component_1="K_ATP" component_2="K_ATP_parameters"/>
        <map_variables variable_1="K_K_o" variable_2="K_K_o"/>
        <map_variables variable_1="K_K_i" variable_2="K_K_i"/>
        <map_variables variable_1="kappa_K_ATP" variable_2="kappa_K_ATP"/>
        <map_variables variable_1="zK" variable_2="zK"/>
    </connection>
    <connection>
        <map_components component_1="K_ATP" component_2="environment"/>
        <map_variables variable_1="t" variable_2="t"/>
        <map_variables variable_1="R" variable_2="R"/>
        <map_variables variable_1="T" variable_2="T"/>
        <map_variables variable_1="F" variable_2="F"/>
        <map_variables variable_1="C_m" variable_2="C_m"/>
        <map_variables variable_1="q_K_o" variable_2="q_K_o"/>
        <map_variables variable_1="q_K_i" variable_2="q_K_i"/>
        <map_variables variable_1="v_K_ATP" variable_2="v_K_ATP"/>
        <map_variables variable_1="q_mem" variable_2="q_mem"/>
        <map_variables variable_1="I_mem_K_ATP" variable_2="I_mem_K_ATP"/>
    </connection>
</model>