<?xml version='1.0' encoding='UTF-8'?>
<model name="NKE_BG_4_state_ATPNaZK" 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">
    <units name="dim">
        <unit units="dimensionless"/>
    </units>
    <component name="NKE_BG_4_state_ATPNaZK_ss">
        <variable name="K_1" public_interface="in" units="per_fmol"/>
        <variable name="K_2" public_interface="in" units="per_fmol"/>
        <variable name="K_3" public_interface="in" units="per_fmol"/>
        <variable name="K_4" public_interface="in" units="per_fmol"/>
        <variable name="K_Ki" public_interface="in" units="per_fmol"/>
        <variable name="R" public_interface="in" units="J_per_K_mol"/>
        <variable name="T" public_interface="in" units="kelvin"/>
        <variable name="q_0_Ki" public_interface="in" units="fmol"/>
        <variable name="K_Ko" public_interface="in" units="per_fmol"/>
        <variable name="q_0_Ko" public_interface="in" units="fmol"/>
        <variable name="K_Nai" public_interface="in" units="per_fmol"/>
        <variable name="q_0_Nai" public_interface="in" units="fmol"/>
        <variable name="K_Nao" public_interface="in" units="per_fmol"/>
        <variable name="q_0_Nao" public_interface="in" units="fmol"/>
        <variable name="K_ATP" public_interface="in" units="per_fmol"/>
        <variable name="q_0_ATP" public_interface="in" units="fmol"/>
        <variable name="K_ADP" public_interface="in" units="per_fmol"/>
        <variable name="q_0_ADP" public_interface="in" units="fmol"/>
        <variable name="K_Pi" public_interface="in" units="per_fmol"/>
        <variable name="q_0_Pi" public_interface="in" units="fmol"/>
        <variable name="K_H" public_interface="in" units="per_fmol"/>
        <variable name="q_0_H" public_interface="in" units="fmol"/>
        <variable name="u_0_Vm" public_interface="in" units="volt"/>
        <variable name="z_z1" public_interface="in" units="dimensionless"/>
        <variable name="F" public_interface="in" units="C_per_mol"/>
        <variable name="z_z2" public_interface="in" units="dimensionless"/>
        <variable name="kappa_r1" public_interface="in" units="fmol_per_s"/>
        <variable name="kappa_r2" public_interface="in" units="fmol_per_s"/>
        <variable name="kappa_r3" public_interface="in" units="fmol_per_s"/>
        <variable name="kappa_r4" public_interface="in" units="fmol_per_s"/>
        <variable name="q_1_init" public_interface="in" units="fmol"/>
        <variable initial_value="q_1_init" name="q_1" units="fmol"/>
        <variable name="q_2_init" public_interface="in" units="fmol"/>
        <variable initial_value="q_2_init" name="q_2" units="fmol"/>
        <variable name="q_3_init" public_interface="in" units="fmol"/>
        <variable initial_value="q_3_init" name="q_3" units="fmol"/>
        <variable name="q_4_init" public_interface="in" units="fmol"/>
        <variable initial_value="q_4_init" name="q_4" units="fmol"/>
        <variable name="u_Vm" units="volt"/>
        <variable name="e_0" units="dim"/>
        <variable name="e_1" units="dim"/>
        <variable name="e_2" units="dim"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>u_Vm</ci>
                <ci>u_0_Vm</ci>
            </apply>
            <apply>
                <eq/>
                <ci>e_0</ci>
                <apply>
                    <exp/>
                    <apply>
                        <divide/>
                        <apply>
                            <times/>
                            <apply>
                                <minus/>
                                <ci>F</ci>
                            </apply>
                            <ci>u_Vm</ci>
                        </apply>
                        <apply>
                            <times/>
                            <ci>R</ci>
                            <ci>T</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>e_1</ci>
                <apply>
                    <exp/>
                    <apply>
                        <divide/>
                        <apply>
                            <times/>
                            <apply>
                                <minus/>
                                <ci>z_z1</ci>
                            </apply>
                            <ci>F</ci>
                            <ci>u_Vm</ci>
                        </apply>
                        <apply>
                            <times/>
                            <ci>R</ci>
                            <ci>T</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>e_2</ci>
                <apply>
                    <exp/>
                    <apply>
                        <divide/>
                        <apply>
                            <times/>
                            <ci>z_z2</ci>
                            <ci>F</ci>
                            <ci>u_Vm</ci>
                        </apply>
                        <apply>
                            <times/>
                            <ci>R</ci>
                            <ci>T</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
        </math>
        <variable name="lambda_1" units="dim"/>
        <variable name="lambda_2" units="dim"/>
        <variable name="lambda_3" units="dim"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>lambda_1</ci>
                <apply>
                    <divide/>
                    <ci>kappa_r4</ci>
                    <ci>kappa_r1</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>lambda_2</ci>
                <apply>
                    <divide/>
                    <ci>kappa_r4</ci>
                    <ci>kappa_r2</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>lambda_3</ci>
                <apply>
                    <divide/>
                    <ci>kappa_r4</ci>
                    <ci>kappa_r3</ci>
                </apply>
            </apply>
        </math>
        <variable name="Q_Nao" units="dim"/>
        <variable name="Q_Nai" units="dim"/>
        <variable name="Q_Ko" units="dim"/>
        <variable name="Q_Ki" units="dim"/>
        <variable name="Q_ATP" units="dim"/>
        <variable name="Q_ADP" units="dim"/>
        <variable name="Q_Pi" units="dim"/>
        <variable name="Q_H" units="dim"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>Q_Nai</ci>
                <apply>
                    <times/>
                    <ci>K_Nai</ci>
                    <ci>q_0_Nai</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>Q_Nao</ci>
                <apply>
                    <times/>
                    <ci>K_Nao</ci>
                    <ci>q_0_Nao</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>Q_Ki</ci>
                <apply>
                    <times/>
                    <ci>K_Ki</ci>
                    <ci>q_0_Ki</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>Q_Ko</ci>
                <apply>
                    <times/>
                    <ci>K_Ko</ci>
                    <ci>q_0_Ko</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>Q_ATP</ci>
                <apply>
                    <times/>
                    <ci>K_ATP</ci>
                    <ci>q_0_ATP</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>Q_ADP</ci>
                <apply>
                    <times/>
                    <ci>K_ADP</ci>
                    <ci>q_0_ADP</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>Q_Pi</ci>
                <apply>
                    <times/>
                    <ci>K_Pi</ci>
                    <ci>q_0_Pi</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>Q_H</ci>
                <apply>
                    <times/>
                    <ci>K_H</ci>
                    <ci>q_0_H</ci>
                </apply>
            </apply>
        </math>
        <variable name="gamma_1" units="dim"/>
        <variable name="gamma_2" units="dim"/>
        <variable name="gamma_3" units="dim"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>gamma_1</ci>
                <apply>
                    <divide/>
                    <ci>K_4</ci>
                    <ci>K_1</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>gamma_2</ci>
                <apply>
                    <divide/>
                    <ci>K_4</ci>
                    <ci>K_2</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>gamma_3</ci>
                <apply>
                    <divide/>
                    <ci>K_4</ci>
                    <ci>K_3</ci>
                </apply>
            </apply>
        </math>
        <variable name="Q_NKE" units="dim"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>Q_NKE</ci>
                <apply>
                    <divide/>
                    <ci>Q_ATP</ci>
                    <apply>
                        <times/>
                        <ci>Q_ADP</ci>
                        <ci>Q_Pi</ci>
                        <ci>Q_H</ci>
                    </apply>
                </apply>
            </apply>
        </math>
        <variable name="A_NKE" units="dim"/>
        <variable name="B_NKE" units="dim"/>
        <variable name="B_NKE_1" units="dim"/>
        <variable name="B_NKE_2" units="dim"/>
        <variable name="B_NKE_3" units="dim"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>B_NKE_1</ci>
                <apply>
                    <plus/>
                    <apply>
                        <times/>
                        <apply>
                            <divide/>
                            <ci>gamma_1</ci>
                            <apply>
                                <times/>
                                <ci>Q_Pi</ci>
                                <ci>Q_H</ci>
                            </apply>
                        </apply>
                        <ci>e_1</ci>
                    </apply>
                    <apply>
                        <times/>
                        <ci>gamma_2</ci>
                        <apply>
                            <power/>
                            <ci>Q_Nai</ci>
                            <cn cellml:units="dim">3</cn>
                        </apply>
                        <ci>Q_NKE</ci>
                        <ci>e_1</ci>
                    </apply>
                    <apply>
                        <times/>
                        <ci>gamma_3</ci>
                        <apply>
                            <power/>
                            <apply>
                                <divide/>
                                <ci>Q_Nai</ci>
                                <ci>Q_Nao</ci>
                            </apply>
                            <cn cellml:units="dim">3</cn>
                        </apply>
                        <ci>Q_NKE</ci>
                    </apply>
                    <apply>
                        <times/>
                        <apply>
                            <divide/>
                            <apply>
                                <power/>
                                <ci>Q_Ki</ci>
                                <cn cellml:units="dimensionless">2</cn>
                            </apply>
                            <apply>
                                <times/>
                                <ci>Q_Pi</ci>
                                <ci>Q_H</ci>
                            </apply>
                        </apply>
                        <ci>e_0</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>B_NKE_2</ci>
                <apply>
                    <plus/>
                    <apply>
                        <divide/>
                        <apply>
                            <times/>
                            <ci>Q_Pi</ci>
                            <ci>Q_H</ci>
                        </apply>
                        <apply>
                            <power/>
                            <ci>Q_Ko</ci>
                            <cn cellml:units="dimensionless">2</cn>
                        </apply>
                    </apply>
                    <apply>
                        <divide/>
                        <apply>
                            <plus/>
                            <apply>
                                <times/>
                                <apply>
                                    <divide/>
                                    <ci>lambda_1</ci>
                                    <ci>Q_ADP</ci>
                                </apply>
                                <apply>
                                    <exp/>
                                    <apply>
                                        <divide/>
                                        <apply>
                                            <times/>
                                            <ci>z_z1</ci>
                                            <ci>F</ci>
                                            <ci>u_Vm</ci>
                                        </apply>
                                        <apply>
                                            <times/>
                                            <ci>R</ci>
                                            <ci>T</ci>
                                        </apply>
                                    </apply>
                                </apply>
                            </apply>
                            <ci>lambda_2</ci>
                        </apply>
                        <apply>
                            <power/>
                            <ci>Q_Nao</ci>
                            <cn cellml:units="dim">3</cn>
                        </apply>
                    </apply>
                    <apply>
                        <divide/>
                        <ci>lambda_3</ci>
                        <apply>
                            <power/>
                            <ci>Q_Ko</ci>
                            <cn cellml:units="dimensionless">2</cn>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>B_NKE_3</ci>
                <apply>
                    <times/>
                    <ci>A_NKE</ci>
                    <apply>
                        <minus/>
                        <apply>
                            <minus/>
                            <cn cellml:units="dim">1</cn>
                            <apply>
                                <divide/>
                                <apply>
                                    <times/>
                                    <ci>lambda_1</ci>
                                    <ci>gamma_2</ci>
                                </apply>
                                <ci>Q_ADP</ci>
                            </apply>
                        </apply>
                        <apply>
                            <times/>
                            <apply>
                                <plus/>
                                <apply>
                                    <times/>
                                    <apply>
                                        <divide/>
                                        <apply>
                                            <times/>
                                            <ci>lambda_1</ci>
                                            <ci>gamma_3</ci>
                                        </apply>
                                        <ci>Q_ADP</ci>
                                    </apply>
                                    <apply>
                                        <exp/>
                                        <apply>
                                            <divide/>
                                            <apply>
                                                <times/>
                                                <ci>z_z1</ci>
                                                <ci>F</ci>
                                                <ci>u_Vm</ci>
                                            </apply>
                                            <apply>
                                                <times/>
                                                <ci>R</ci>
                                                <ci>T</ci>
                                            </apply>
                                        </apply>
                                    </apply>
                                </apply>
                                <apply>
                                    <times/>
                                    <ci>lambda_2</ci>
                                    <ci>gamma_3</ci>
                                </apply>
                            </apply>
                            <apply>
                                <power/>
                                <ci>Q_Nao</ci>
                                <apply>
                                    <minus/>
                                    <cn cellml:units="dim">3</cn>
                                </apply>
                            </apply>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>A_NKE</ci>
                <apply>
                    <minus/>
                    <apply>
                        <times/>
                        <apply>
                            <power/>
                            <apply>
                                <divide/>
                                <ci>Q_Nai</ci>
                                <ci>Q_Nao</ci>
                            </apply>
                            <cn cellml:units="dim">3</cn>
                        </apply>
                        <ci>Q_NKE</ci>
                    </apply>
                    <apply>
                        <times/>
                        <apply>
                            <power/>
                            <apply>
                                <divide/>
                                <ci>Q_Ki</ci>
                                <ci>Q_Ko</ci>
                            </apply>
                            <cn cellml:units="dimensionless">2</cn>
                        </apply>
                        <apply>
                            <exp/>
                            <apply>
                                <divide/>
                                <apply>
                                    <times/>
                                    <apply>
                                        <minus/>
                                        <ci>F</ci>
                                    </apply>
                                    <ci>u_Vm</ci>
                                </apply>
                                <apply>
                                    <times/>
                                    <ci>R</ci>
                                    <ci>T</ci>
                                </apply>
                            </apply>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>B_NKE</ci>
                <apply>
                    <plus/>
                    <apply>
                        <times/>
                        <ci>B_NKE_1</ci>
                        <ci>B_NKE_2</ci>
                    </apply>
                    <ci>B_NKE_3</ci>
                </apply>
            </apply>
        </math>
        <variable initial_value="1" name="q_tot" units="fmol"/>
        <variable name="v_NKE" units="fmol_per_s"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>v_NKE</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <ci>K_4</ci>
                        <ci>kappa_r4</ci>
                        <ci>q_tot</ci>
                        <ci>A_NKE</ci>
                    </apply>
                    <ci>B_NKE</ci>
                </apply>
            </apply>
        </math>
    </component>
    <import xlink:href="units.cellml">
        <units name="fA" units_ref="fA"/>
        <units name="J_per_mol" units_ref="J_per_mol"/>
        <units name="J_per_K_mol" units_ref="J_per_K_mol"/>
        <units name="fmol" units_ref="fmol"/>
        <units name="per_fmol" units_ref="per_fmol"/>
        <units name="C_per_mol" units_ref="C_per_mol"/>
        <units name="fmol_per_s" units_ref="fmol_per_s"/>
    </import>
    <import xlink:href="NKE_BG_4_state_ATPNaZK_param.cellml">
        <component component_ref="NKE_BG_param" name="NKE_BG_param"/>
    </import>
    <import xlink:href="NKE_BG_Env_fixedV.cellml">
        <component component_ref="NKE_BG_Env" name="NKE_BG_Env"/>
    </import>
    <connection>
        <map_components component_1="NKE_BG_4_state_ATPNaZK_ss" component_2="NKE_BG_param"/>
        <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="z_z1" variable_2="z_z1"/>
        <map_variables variable_1="F" variable_2="F"/>
        <map_variables variable_1="z_z2" variable_2="z_z2"/>
        <map_variables variable_1="kappa_r1" variable_2="kappa_r1"/>
        <map_variables variable_1="kappa_r2" variable_2="kappa_r2"/>
        <map_variables variable_1="kappa_r3" variable_2="kappa_r3"/>
        <map_variables variable_1="kappa_r4" variable_2="kappa_r4"/>
        <map_variables variable_1="q_1_init" variable_2="q_1_init"/>
        <map_variables variable_1="q_2_init" variable_2="q_2_init"/>
        <map_variables variable_1="q_3_init" variable_2="q_3_init"/>
        <map_variables variable_1="q_4_init" variable_2="q_4_init"/>
    </connection>
    <connection>
        <map_components component_1="NKE_BG_4_state_ATPNaZK_ss" component_2="NKE_BG_Env"/>
        <map_variables variable_1="K_Ki" variable_2="K_Ki"/>
        <map_variables variable_1="R" variable_2="R"/>
        <map_variables variable_1="T" variable_2="T"/>
        <map_variables variable_1="q_0_Ki" variable_2="q_0_Ki"/>
        <map_variables variable_1="K_Ko" variable_2="K_Ko"/>
        <map_variables variable_1="q_0_Ko" variable_2="q_0_Ko"/>
        <map_variables variable_1="K_Nai" variable_2="K_Nai"/>
        <map_variables variable_1="q_0_Nai" variable_2="q_0_Nai"/>
        <map_variables variable_1="K_Nao" variable_2="K_Nao"/>
        <map_variables variable_1="q_0_Nao" variable_2="q_0_Nao"/>
        <map_variables variable_1="K_ATP" variable_2="K_ATP"/>
        <map_variables variable_1="q_0_ATP" variable_2="q_0_ATP"/>
        <map_variables variable_1="K_ADP" variable_2="K_ADP"/>
        <map_variables variable_1="q_0_ADP" variable_2="q_0_ADP"/>
        <map_variables variable_1="K_Pi" variable_2="K_Pi"/>
        <map_variables variable_1="q_0_Pi" variable_2="q_0_Pi"/>
        <map_variables variable_1="K_H" variable_2="K_H"/>
        <map_variables variable_1="q_0_H" variable_2="q_0_H"/>
        <map_variables variable_1="u_0_Vm" variable_2="u_0_Vm"/>
    </connection>
</model>
