Location: BG_Kr @ 78241c53362e / BG_Kr.cellml

Author:
Shelley Fong <s.fong@auckland.ac.nz>
Date:
2022-04-22 11:22:10+12:00
Desc:
Changing units to s for alpha and beta gate parameters
Permanent Source URI:
https://models.physiomeproject.org/workspace/82c/rawfile/78241c53362eaa4197ccb6597082fae1be26b9ee/BG_Kr.cellml

<?xml version='1.0' encoding='UTF-8'?>
<!-- rapid delayed rectifier (potassium) 1, based on Kernik 19
 gate variables
 Sa: xr_10 xr_20
 Sb: xr_11 xr_20
 Sc: xr_10 xr_21
 Sd: xr_11 xr_21
 gate variable transitions
 x10: a to b
 x11: c to d
 x20: a to c
 x21: b to d-->
<model name="BG_Kr_model" 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="J_per_K_per_mol" units_ref="J_per_K_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="fF" units_ref="fF"/>
        <units name="fC" units_ref="fC"/>
        <units name="fA" units_ref="fA"/>
    </import>
    <units name="uA_per_uF">
        <unit prefix="micro" units="ampere"/>
        <unit exponent="-1" prefix="micro" units="farad"/>
    </units>
    <component name="environment">
        <variable name="t" public_interface="out" units="second"/>
        <variable initial_value="60000" name="C_m" public_interface="out" units="fF"/>
        <variable initial_value="20.0448" name="q_K_o" public_interface="out" units="fmol"/>
        <variable initial_value="388.832" name="q_K_i" public_interface="out" units="fmol"/>
        <variable initial_value="1.598306E-07" name="q_Sa" public_interface="out" units="fmol"/>
        <variable initial_value="1.598306E-07" name="q_Sb" public_interface="out" units="fmol"/>
        <variable initial_value="1.598306E-07" name="q_Sc" public_interface="out" units="fmol"/>
        <variable initial_value="1.598306E-07" name="q_Sd" public_interface="out" units="fmol"/>
        <variable name="q_mem" public_interface="out" units="fC"/>
        <variable name="Vmem" units="volt"/>
        <variable initial_value="8.31" 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="96500" name="F" public_interface="out" units="C_per_mol"/>
        <variable name="v_Kr" public_interface="in" units="fmol_per_sec"/>
        <variable name="I_mem_Kr" public_interface="in" units="fA"/>
        <!--        ode(q_K_i, t) = -v_Kr;
        ode(q_K_o, t) = v_Kr;-->
        <!--        ode(q_mem, t) = I_mem_Kr+I_stim;
        Vmem = q_mem/C_m;-->
        <!--        var I_stim: fA;
        var stimPeriod: second {init: 1};
        var stimDuration: second {init: 0.0001};
        var tPeriod: second;-->
        <!--        tPeriod = t-floor(t/stimPeriod)*stimPeriod;-->
        <!--        I_stim = sel
            case (tPeriod >= 0.3{second}) and (tPeriod <= 0.3{second}+stimDuration):
                0.075{volt}*C_m/stimDuration;
            otherwise:
                0.0{fA};
        endsel;-->
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>Vmem</ci>
                <piecewise>
                    <piece>
                        <apply>
                            <minus/>
                            <cn cellml:units="volt">0.09</cn>
                        </apply>
                        <apply>
                            <and/>
                            <apply>
                                <geq/>
                                <ci>t</ci>
                                <cn cellml:units="second">0</cn>
                            </apply>
                            <apply>
                                <lt/>
                                <ci>t</ci>
                                <cn cellml:units="second">4</cn>
                            </apply>
                        </apply>
                    </piece>
                    <piece>
                        <apply>
                            <minus/>
                            <cn cellml:units="volt">0.06</cn>
                        </apply>
                        <apply>
                            <and/>
                            <apply>
                                <gt/>
                                <ci>t</ci>
                                <cn cellml:units="second">10.1</cn>
                            </apply>
                            <apply>
                                <lt/>
                                <ci>t</ci>
                                <cn cellml:units="second">13.1</cn>
                            </apply>
                        </apply>
                    </piece>
                    <piece>
                        <apply>
                            <minus/>
                            <cn cellml:units="volt">0.04</cn>
                        </apply>
                        <apply>
                            <and/>
                            <apply>
                                <gt/>
                                <ci>t</ci>
                                <cn cellml:units="second">14.1</cn>
                            </apply>
                            <apply>
                                <lt/>
                                <ci>t</ci>
                                <cn cellml:units="second">15.1</cn>
                            </apply>
                        </apply>
                    </piece>
                    <piece>
                        <cn cellml:units="volt">0.09</cn>
                        <apply>
                            <gt/>
                            <ci>t</ci>
                            <cn cellml:units="second">17.0</cn>
                        </apply>
                    </piece>
                    <otherwise>
                        <apply>
                            <minus/>
                            <cn cellml:units="volt">0.08</cn>
                        </apply>
                    </otherwise>
                </piecewise>
            </apply>
        </math>
        <variable name="i_Kr" units="uA_per_uF"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>i_Kr</ci>
                <apply>
                    <times/>
                    <apply>
                        <divide/>
                        <apply>
                            <times/>
                            <cn cellml:units="dimensionless" type="e-notation">1<sep/>-9</cn>
                            <ci>F</ci>
                        </apply>
                        <ci>C_m</ci>
                    </apply>
                    <ci>v_Kr</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>q_mem</ci>
                <apply>
                    <times/>
                    <ci>Vmem</ci>
                    <ci>C_m</ci>
                </apply>
            </apply>
        </math>
        <!--        cKi = 1.04748824394112106e+02 mM-->
    </component>
    <component name="Kr_parameters">
        <variable initial_value="175.029" name="kappa_Kr" public_interface="out" units="fmol_per_sec"/>
        <variable initial_value="0.0794844" name="kappa_xr10" public_interface="out" units="fmol_per_sec"/>
        <variable initial_value="0.00212813" name="kappa_xr11" public_interface="out" units="fmol_per_sec"/>
        <variable initial_value="0.267259" name="kappa_xr20" public_interface="out" units="fmol_per_sec"/>
        <variable initial_value="2.18134" name="kappa_xr21" public_interface="out" units="fmol_per_sec"/>
        <variable initial_value="12.9706" name="K_K_i" public_interface="out" units="per_fmol"/>
        <variable initial_value="95.1175" name="K_K_o" public_interface="out" units="per_fmol"/>
        <variable initial_value="0.0465841" name="K_Sa_Kr" public_interface="out" units="per_fmol"/>
        <variable initial_value="0.00570751" name="K_Sb_Kr" public_interface="out" units="per_fmol"/>
        <variable initial_value="1.73989" name="K_Sc_Kr" public_interface="out" units="per_fmol"/>
        <variable initial_value="0.213172" name="K_Sd_Kr" public_interface="out" units="per_fmol"/>
        <variable initial_value="1" name="zK" public_interface="out" units="dimensionless"/>
        <variable initial_value="1.6149028778859738" name="z_xr1_f" public_interface="out" units="dimensionless"/>
        <variable initial_value="-1.3218634652232777" name="z_xr1_r" public_interface="out" units="dimensionless"/>
        <variable initial_value="-1.0273976425216251" name="z_xr2_f" public_interface="out" units="dimensionless"/>
        <variable initial_value="-0.18153135376657775" name="z_xr2_r" public_interface="out" units="dimensionless"/>
    </component>
    <component name="Kr">
        <variable name="t" private_interface="out" 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" private_interface="out" public_interface="in" units="C_per_mol"/>
        <variable name="C_m" public_interface="in" units="fF"/>
        <!-- Parameters-->
        <!-- overall ion permeability (GHK) is kappa_{ion}-->
        <variable name="kappa_Kr" public_interface="in" units="fmol_per_sec"/>
        <variable name="K_K_o" public_interface="in" units="per_fmol"/>
        <variable name="K_K_i" public_interface="in" units="per_fmol"/>
        <!-- state variables-->
        <variable name="q_K_i" public_interface="in" units="fmol"/>
        <variable name="q_K_o" public_interface="in" units="fmol"/>
        <variable name="q_mem" public_interface="in" units="fC"/>
        <variable name="v_Kr" public_interface="out" units="fmol_per_sec"/>
        <variable name="I_mem_Kr" public_interface="out" units="fA"/>
        <variable name="u_K_i" units="J_per_mol"/>
        <variable name="u_K_o" units="J_per_mol"/>
        <variable name="V_mem" private_interface="out" units="J_per_C"/>
        <variable name="Am_Kr" units="J_per_mol"/>
        <variable name="Af_Kr" units="J_per_mol"/>
        <variable name="Ar_Kr" units="J_per_mol"/>
        <variable name="zK" public_interface="in" units="dimensionless"/>
        <!-- Conservation laws-->
        <!-- Constitutive relations - Convention: positive flow from inside to outside-->
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>Am_Kr</ci>
                <apply>
                    <times/>
                    <ci>zK</ci>
                    <ci>F</ci>
                    <ci>V_mem</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u_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>u_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>Af_Kr</ci>
                <apply>
                    <plus/>
                    <ci>mu_Sd</ci>
                    <ci>u_K_i</ci>
                    <ci>Am_Kr</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>Ar_Kr</ci>
                <apply>
                    <plus/>
                    <ci>mu_Sd</ci>
                    <ci>u_K_o</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>v_Kr</ci>
                <piecewise>
                    <piece>
                        <apply>
                            <times/>
                            <cn cellml:units="dimensionless">1</cn>
                            <ci>kappa_Kr</ci>
                            <apply>
                                <minus/>
                                <apply>
                                    <exp/>
                                    <apply>
                                        <divide/>
                                        <ci>Af_Kr</ci>
                                        <apply>
                                            <times/>
                                            <ci>R</ci>
                                            <ci>T</ci>
                                        </apply>
                                    </apply>
                                </apply>
                                <apply>
                                    <exp/>
                                    <apply>
                                        <divide/>
                                        <ci>Ar_Kr</ci>
                                        <apply>
                                            <times/>
                                            <ci>R</ci>
                                            <ci>T</ci>
                                        </apply>
                                    </apply>
                                </apply>
                            </apply>
                        </apply>
                        <apply>
                            <eq/>
                            <ci>Am_Kr</ci>
                            <cn cellml:units="J_per_mol">0</cn>
                        </apply>
                    </piece>
                    <otherwise>
                        <apply>
                            <times/>
                            <apply>
                                <divide/>
                                <apply>
                                    <divide/>
                                    <apply>
                                        <times/>
                                        <cn cellml:units="dimensionless">1</cn>
                                        <ci>kappa_Kr</ci>
                                        <ci>Am_Kr</ci>
                                    </apply>
                                    <apply>
                                        <times/>
                                        <ci>R</ci>
                                        <ci>T</ci>
                                    </apply>
                                </apply>
                                <apply>
                                    <minus/>
                                    <apply>
                                        <exp/>
                                        <apply>
                                            <divide/>
                                            <ci>Am_Kr</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_Kr</ci>
                                        <apply>
                                            <times/>
                                            <ci>R</ci>
                                            <ci>T</ci>
                                        </apply>
                                    </apply>
                                </apply>
                                <apply>
                                    <exp/>
                                    <apply>
                                        <divide/>
                                        <ci>Ar_Kr</ci>
                                        <apply>
                                            <times/>
                                            <ci>R</ci>
                                            <ci>T</ci>
                                        </apply>
                                    </apply>
                                </apply>
                            </apply>
                        </apply>
                    </otherwise>
                </piecewise>
            </apply>
            <apply>
                <eq/>
                <ci>V_mem</ci>
                <apply>
                    <divide/>
                    <ci>q_mem</ci>
                    <ci>C_m</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>I_mem_Kr</ci>
                <apply>
                    <times/>
                    <ci>F</ci>
                    <apply>
                        <plus/>
                        <apply>
                            <times/>
                            <apply>
                                <minus/>
                                <ci>zK</ci>
                            </apply>
                            <ci>v_Kr</ci>
                        </apply>
                        <apply>
                            <times/>
                            <ci>v_x10</ci>
                            <apply>
                                <minus/>
                                <ci>z_xr1_r</ci>
                                <ci>z_xr1_f</ci>
                            </apply>
                        </apply>
                        <apply>
                            <times/>
                            <ci>v_x11</ci>
                            <apply>
                                <minus/>
                                <ci>z_xr1_r</ci>
                                <ci>z_xr1_r</ci>
                            </apply>
                        </apply>
                        <apply>
                            <times/>
                            <ci>v_x20</ci>
                            <apply>
                                <minus/>
                                <ci>z_xr2_r</ci>
                                <ci>z_xr2_f</ci>
                            </apply>
                        </apply>
                        <apply>
                            <times/>
                            <ci>v_x21</ci>
                            <apply>
                                <minus/>
                                <ci>z_xr2_r</ci>
                                <ci>z_xr2_f</ci>
                            </apply>
                        </apply>
                    </apply>
                </apply>
            </apply>
        </math>
        <!-- GATE
 channel states variables
 Sa: xr_10 xr_20
 Sb: xr_11 xr_20
 Sc: xr_10 xr_21
 Sd: xr_11 xr_21-->
        <variable name="v_Sa" units="fmol_per_sec"/>
        <variable name="v_Sb" units="fmol_per_sec"/>
        <variable name="v_Sc" units="fmol_per_sec"/>
        <variable name="v_Sd" units="fmol_per_sec"/>
        <!-- gate variable transitions
 x10: a to b
 x11: c to d
 x20: a to c
 x21: b to d-->
        <variable name="v_x10" units="fmol_per_sec"/>
        <variable name="v_x11" units="fmol_per_sec"/>
        <variable name="v_x20" units="fmol_per_sec"/>
        <variable name="v_x21" units="fmol_per_sec"/>
        <variable name="mu_Sa" units="J_per_mol"/>
        <variable name="mu_Sb" units="J_per_mol"/>
        <variable name="mu_Sc" units="J_per_mol"/>
        <variable name="mu_Sd" units="J_per_mol"/>
        <!-- forward/reverse affinities at each reaction-->
        <variable name="Af_x10" units="J_per_mol"/>
        <variable name="Ar_x10" units="J_per_mol"/>
        <variable name="Af_x11" units="J_per_mol"/>
        <variable name="Ar_x11" units="J_per_mol"/>
        <variable name="Af_x20" units="J_per_mol"/>
        <variable name="Ar_x20" units="J_per_mol"/>
        <variable name="Af_x21" units="J_per_mol"/>
        <variable name="Ar_x21" units="J_per_mol"/>
        <!-- gating variables-->
        <variable name="kappa_xr10" public_interface="in" units="fmol_per_sec"/>
        <variable name="kappa_xr11" public_interface="in" units="fmol_per_sec"/>
        <variable name="kappa_xr20" public_interface="in" units="fmol_per_sec"/>
        <variable name="kappa_xr21" public_interface="in" units="fmol_per_sec"/>
        <variable name="K_Sa_Kr" public_interface="in" units="per_fmol"/>
        <variable name="K_Sb_Kr" public_interface="in" units="per_fmol"/>
        <variable name="K_Sc_Kr" public_interface="in" units="per_fmol"/>
        <variable name="K_Sd_Kr" public_interface="in" units="per_fmol"/>
        <variable name="z_xr1_f" public_interface="in" units="dimensionless"/>
        <variable name="z_xr1_r" public_interface="in" units="dimensionless"/>
        <variable name="z_xr2_f" public_interface="in" units="dimensionless"/>
        <variable name="z_xr2_r" public_interface="in" units="dimensionless"/>
        <variable name="q_Sa" public_interface="in" units="fmol"/>
        <variable name="q_Sb" public_interface="in" units="fmol"/>
        <variable name="q_Sc" public_interface="in" units="fmol"/>
        <variable name="q_Sd" public_interface="in" units="fmol"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>Af_x10</ci>
                <apply>
                    <plus/>
                    <ci>mu_Sa</ci>
                    <apply>
                        <times/>
                        <ci>z_xr1_f</ci>
                        <ci>F</ci>
                        <ci>V_mem</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>Ar_x10</ci>
                <apply>
                    <plus/>
                    <ci>mu_Sb</ci>
                    <apply>
                        <times/>
                        <ci>z_xr1_r</ci>
                        <ci>F</ci>
                        <ci>V_mem</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>Af_x11</ci>
                <apply>
                    <plus/>
                    <ci>mu_Sc</ci>
                    <apply>
                        <times/>
                        <ci>z_xr1_f</ci>
                        <ci>F</ci>
                        <ci>V_mem</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>Ar_x11</ci>
                <apply>
                    <plus/>
                    <ci>mu_Sd</ci>
                    <apply>
                        <times/>
                        <ci>z_xr1_r</ci>
                        <ci>F</ci>
                        <ci>V_mem</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>Af_x20</ci>
                <apply>
                    <plus/>
                    <ci>mu_Sa</ci>
                    <apply>
                        <times/>
                        <ci>z_xr2_f</ci>
                        <ci>F</ci>
                        <ci>V_mem</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>Ar_x20</ci>
                <apply>
                    <plus/>
                    <ci>mu_Sc</ci>
                    <apply>
                        <times/>
                        <ci>z_xr2_r</ci>
                        <ci>F</ci>
                        <ci>V_mem</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>Af_x21</ci>
                <apply>
                    <plus/>
                    <ci>mu_Sb</ci>
                    <apply>
                        <times/>
                        <ci>z_xr2_f</ci>
                        <ci>F</ci>
                        <ci>V_mem</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>Ar_x21</ci>
                <apply>
                    <plus/>
                    <ci>mu_Sd</ci>
                    <apply>
                        <times/>
                        <ci>z_xr2_r</ci>
                        <ci>F</ci>
                        <ci>V_mem</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>v_x10</ci>
                <apply>
                    <times/>
                    <ci>kappa_xr10</ci>
                    <apply>
                        <minus/>
                        <apply>
                            <exp/>
                            <apply>
                                <divide/>
                                <ci>Af_x10</ci>
                                <apply>
                                    <times/>
                                    <ci>R</ci>
                                    <ci>T</ci>
                                </apply>
                            </apply>
                        </apply>
                        <apply>
                            <exp/>
                            <apply>
                                <divide/>
                                <ci>Ar_x10</ci>
                                <apply>
                                    <times/>
                                    <ci>R</ci>
                                    <ci>T</ci>
                                </apply>
                            </apply>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>v_x11</ci>
                <apply>
                    <times/>
                    <ci>kappa_xr11</ci>
                    <apply>
                        <minus/>
                        <apply>
                            <exp/>
                            <apply>
                                <divide/>
                                <ci>Af_x11</ci>
                                <apply>
                                    <times/>
                                    <ci>R</ci>
                                    <ci>T</ci>
                                </apply>
                            </apply>
                        </apply>
                        <apply>
                            <exp/>
                            <apply>
                                <divide/>
                                <ci>Ar_x11</ci>
                                <apply>
                                    <times/>
                                    <ci>R</ci>
                                    <ci>T</ci>
                                </apply>
                            </apply>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>v_x20</ci>
                <apply>
                    <times/>
                    <ci>kappa_xr20</ci>
                    <apply>
                        <minus/>
                        <apply>
                            <exp/>
                            <apply>
                                <divide/>
                                <ci>Af_x20</ci>
                                <apply>
                                    <times/>
                                    <ci>R</ci>
                                    <ci>T</ci>
                                </apply>
                            </apply>
                        </apply>
                        <apply>
                            <exp/>
                            <apply>
                                <divide/>
                                <ci>Ar_x20</ci>
                                <apply>
                                    <times/>
                                    <ci>R</ci>
                                    <ci>T</ci>
                                </apply>
                            </apply>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>v_x21</ci>
                <apply>
                    <times/>
                    <ci>kappa_xr21</ci>
                    <apply>
                        <minus/>
                        <apply>
                            <exp/>
                            <apply>
                                <divide/>
                                <ci>Af_x21</ci>
                                <apply>
                                    <times/>
                                    <ci>R</ci>
                                    <ci>T</ci>
                                </apply>
                            </apply>
                        </apply>
                        <apply>
                            <exp/>
                            <apply>
                                <divide/>
                                <ci>Ar_x21</ci>
                                <apply>
                                    <times/>
                                    <ci>R</ci>
                                    <ci>T</ci>
                                </apply>
                            </apply>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>v_Sa</ci>
                <apply>
                    <minus/>
                    <apply>
                        <minus/>
                        <ci>v_x10</ci>
                    </apply>
                    <ci>v_x20</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>v_Sb</ci>
                <apply>
                    <minus/>
                    <ci>v_x10</ci>
                    <ci>v_x21</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>v_Sc</ci>
                <apply>
                    <minus/>
                    <ci>v_x20</ci>
                    <ci>v_x11</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>v_Sd</ci>
                <apply>
                    <plus/>
                    <ci>v_x11</ci>
                    <ci>v_x21</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>mu_Sa</ci>
                <apply>
                    <times/>
                    <ci>R</ci>
                    <ci>T</ci>
                    <apply>
                        <ln/>
                        <apply>
                            <times/>
                            <ci>K_Sa_Kr</ci>
                            <ci>q_Sa</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>mu_Sb</ci>
                <apply>
                    <times/>
                    <ci>R</ci>
                    <ci>T</ci>
                    <apply>
                        <ln/>
                        <apply>
                            <times/>
                            <ci>K_Sb_Kr</ci>
                            <ci>q_Sb</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>mu_Sc</ci>
                <apply>
                    <times/>
                    <ci>R</ci>
                    <ci>T</ci>
                    <apply>
                        <ln/>
                        <apply>
                            <times/>
                            <ci>K_Sc_Kr</ci>
                            <ci>q_Sc</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>mu_Sd</ci>
                <apply>
                    <times/>
                    <ci>R</ci>
                    <ci>T</ci>
                    <apply>
                        <ln/>
                        <apply>
                            <times/>
                            <ci>K_Sd_Kr</ci>
                            <ci>q_Sd</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>q_Sa</ci>
                </apply>
                <ci>v_Sa</ci>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>q_Sb</ci>
                </apply>
                <ci>v_Sb</ci>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>q_Sc</ci>
                </apply>
                <ci>v_Sc</ci>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>q_Sd</ci>
                </apply>
                <ci>v_Sd</ci>
            </apply>
        </math>
    </component>
    <connection>
        <map_components component_1="environment" component_2="Kr"/>
        <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="q_K_i" variable_2="q_K_i"/>
        <map_variables variable_1="q_K_o" variable_2="q_K_o"/>
        <map_variables variable_1="q_Sa" variable_2="q_Sa"/>
        <map_variables variable_1="q_Sb" variable_2="q_Sb"/>
        <map_variables variable_1="q_Sc" variable_2="q_Sc"/>
        <map_variables variable_1="q_Sd" variable_2="q_Sd"/>
        <map_variables variable_1="q_mem" variable_2="q_mem"/>
        <map_variables variable_1="C_m" variable_2="C_m"/>
        <map_variables variable_1="v_Kr" variable_2="v_Kr"/>
        <map_variables variable_1="I_mem_Kr" variable_2="I_mem_Kr"/>
    </connection>
    <connection>
        <map_components component_1="Kr" component_2="Kr_parameters"/>
        <map_variables variable_1="kappa_Kr" variable_2="kappa_Kr"/>
        <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_xr10" variable_2="kappa_xr10"/>
        <map_variables variable_1="kappa_xr11" variable_2="kappa_xr11"/>
        <map_variables variable_1="kappa_xr20" variable_2="kappa_xr20"/>
        <map_variables variable_1="kappa_xr21" variable_2="kappa_xr21"/>
        <map_variables variable_1="K_Sa_Kr" variable_2="K_Sa_Kr"/>
        <map_variables variable_1="K_Sb_Kr" variable_2="K_Sb_Kr"/>
        <map_variables variable_1="K_Sc_Kr" variable_2="K_Sc_Kr"/>
        <map_variables variable_1="K_Sd_Kr" variable_2="K_Sd_Kr"/>
        <map_variables variable_1="z_xr1_f" variable_2="z_xr1_f"/>
        <map_variables variable_1="z_xr1_r" variable_2="z_xr1_r"/>
        <map_variables variable_1="z_xr2_f" variable_2="z_xr2_f"/>
        <map_variables variable_1="z_xr2_r" variable_2="z_xr2_r"/>
        <map_variables variable_1="zK" variable_2="zK"/>
    </connection>
</model>