Location: BG_TCC @ e236e9ab05e6 / BG_TCC.cellml
- Author:
- Shelley Fong <s.fong@auckland.ac.nz>
- Date:
- 2022-02-28 14:45:16+13:00
- Desc:
- Fix equation finding K Kappa and update parameters
- Permanent Source URI:
- https://models.physiomeproject.org/workspace/831/rawfile/e236e9ab05e6d6c68759cde94bf4d795dea6c1ff/BG_TCC.cellml
<?xml version='1.0' encoding='UTF-8'?>
<!-- T-type calcium channel-->
<model name="BG_TCC_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="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="microm3" units_ref="microm3"/>
<units name="fF" units_ref="fF"/>
<units name="fC" units_ref="fC"/>
<units name="fA" units_ref="fA"/>
</import>
<units name="microm3">
<unit exponent="3" prefix="micro" units="metre"/>
</units>
<component name="environment">
<variable name="time" public_interface="out" units="second"/>
<variable initial_value="1.0e6" name="C_m" public_interface="out" units="fF"/>
<variable initial_value="0.04653" name="q_Cae" public_interface="out" units="fmol"/>
<variable initial_value="0.000001551" name="q_Cai" public_interface="out" units="fmol"/>
<variable initial_value="1e4" name="vol_o" public_interface="out" units="microm3"/>
<variable initial_value="-8.5e4" name="q_mem" public_interface="out" units="fC"/>
<variable name="V_mem" units="volt"/>
<variable initial_value="2494.34" name="RT" public_interface="out" units="J_per_mol"/>
<variable initial_value="2" name="z" public_interface="out" units="dimensionless"/>
<variable initial_value="96500" name="F" public_interface="out" units="C_per_mol"/>
<variable name="v_TCC" public_interface="in" units="fmol_per_sec"/>
<variable name="I_mem" public_interface="in" units="fA"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>q_Cai</ci>
</apply>
<apply>
<minus/>
<ci>v_TCC</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>q_Cae</ci>
</apply>
<ci>v_TCC</ci>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>q_mem</ci>
</apply>
<apply>
<minus/>
<ci>I_mem</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>V_mem</ci>
<apply>
<divide/>
<ci>q_mem</ci>
<ci>C_m</ci>
</apply>
</apply>
</math>
</component>
<component name="TCC_parameters">
<variable initial_value="5054.82" name="kappa_TCC" public_interface="out" units="fmol_per_sec"/>
<variable initial_value="54.3421" name="kappa_b00" public_interface="out" units="fmol_per_sec"/>
<variable initial_value="2.00823" name="kappa_b01" public_interface="out" units="fmol_per_sec"/>
<variable initial_value="147.348" name="kappa_b10" public_interface="out" units="fmol_per_sec"/>
<variable initial_value="5.44529" name="kappa_b11" public_interface="out" units="fmol_per_sec"/>
<variable initial_value="0.363554" name="kappa_g00" public_interface="out" units="fmol_per_sec"/>
<variable initial_value="1.97154" name="kappa_g10" public_interface="out" units="fmol_per_sec"/>
<variable initial_value="2.6729" name="kappa_g20" public_interface="out" units="fmol_per_sec"/>
<variable initial_value="1.87098" name="K_Cai" public_interface="out" units="per_fmol"/>
<variable initial_value="13.72" name="K_Cae" public_interface="out" units="per_fmol"/>
<variable initial_value="4.87717" name="K_S00" public_interface="out" units="per_fmol"/>
<variable initial_value="0.899355" name="K_S10" public_interface="out" units="per_fmol"/>
<variable initial_value="0.663368" name="K_S20" public_interface="out" units="per_fmol"/>
<variable initial_value="131.975" name="K_S01" public_interface="out" units="per_fmol"/>
<variable initial_value="24.3362" name="K_S11" public_interface="out" units="per_fmol"/>
<variable initial_value="17.9505" name="K_S21" public_interface="out" units="per_fmol"/>
<variable initial_value="0.342985" name="z_bf" public_interface="out" units="dimensionless"/>
<variable initial_value="-0.450091" name="z_gf" public_interface="out" units="dimensionless"/>
<variable initial_value="-0.27751" name="z_br" public_interface="out" units="dimensionless"/>
<variable initial_value="0.375201" name="z_gr" public_interface="out" units="dimensionless"/>
</component>
<component name="TCC_channel">
<variable name="t" public_interface="in" units="second"/>
<variable name="RT" public_interface="in" units="J_per_mol"/>
<variable name="z" public_interface="in" units="dimensionless"/>
<variable name="F" public_interface="in" units="C_per_mol"/>
<variable name="C_m" public_interface="in" units="fF"/>
<variable name="kappa_TCC" public_interface="in" units="fmol_per_sec"/>
<variable name="K_Cai" public_interface="in" units="per_fmol"/>
<variable name="K_Cae" public_interface="in" units="per_fmol"/>
<variable name="vol_o" public_interface="in" units="microm3"/>
<!-- state variables-->
<variable name="q_Cai" public_interface="in" units="fmol"/>
<variable name="q_Cae" public_interface="in" units="fmol"/>
<variable name="q_mem" public_interface="in" units="fC"/>
<variable name="v_TCC" public_interface="out" units="fmol_per_sec"/>
<variable name="I_mem" public_interface="out" units="fA"/>
<variable name="u_Cai" units="J_per_mol"/>
<variable name="u_Cae" units="J_per_mol"/>
<variable name="V_mem" units="J_per_C"/>
<variable name="Am_TCC" units="J_per_mol"/>
<variable name="Af_Ca" units="J_per_mol"/>
<variable name="Ar_Ca" units="J_per_mol"/>
<!-- Constitutive relations - Convention: positive flow from inside to outside-->
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>Am_TCC</ci>
<apply>
<times/>
<ci>F</ci>
<ci>V_mem</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_Cai</ci>
<apply>
<times/>
<ci>RT</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_Cai</ci>
<ci>q_Cai</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>u_Cae</ci>
<apply>
<times/>
<ci>RT</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_Cae</ci>
<ci>q_Cae</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Af_Ca</ci>
<apply>
<plus/>
<ci>mu_s21</ci>
<ci>u_Cai</ci>
<ci>Am_TCC</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>Ar_Ca</ci>
<apply>
<plus/>
<ci>mu_s21</ci>
<ci>u_Cae</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_TCC</ci>
<piecewise>
<piece>
<apply>
<times/>
<ci>kappa_TCC</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>Af_Ca</ci>
<ci>RT</ci>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>Ar_Ca</ci>
<ci>RT</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Am_TCC</ci>
<cn cellml:units="J_per_mol">0</cn>
</apply>
</piece>
<otherwise>
<apply>
<times/>
<apply>
<divide/>
<apply>
<divide/>
<apply>
<times/>
<ci>kappa_TCC</ci>
<ci>Am_TCC</ci>
</apply>
<ci>RT</ci>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>Am_TCC</ci>
<ci>RT</ci>
</apply>
</apply>
<cn cellml:units="dimensionless">1</cn>
</apply>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>Af_Ca</ci>
<ci>RT</ci>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>Ar_Ca</ci>
<ci>RT</ci>
</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</ci>
<apply>
<times/>
<ci>z</ci>
<ci>F</ci>
<ci>v_TCC</ci>
</apply>
</apply>
</math>
<!-- GATE-->
<variable name="v_s00" units="fmol_per_sec"/>
<variable name="v_s10" units="fmol_per_sec"/>
<variable name="v_s20" units="fmol_per_sec"/>
<variable name="v_s01" units="fmol_per_sec"/>
<variable name="v_s11" units="fmol_per_sec"/>
<variable name="v_s21" units="fmol_per_sec"/>
<variable name="v_b00" units="fmol_per_sec"/>
<variable name="v_b10" units="fmol_per_sec"/>
<variable name="v_b01" units="fmol_per_sec"/>
<variable name="v_b11" units="fmol_per_sec"/>
<variable name="v_g00" units="fmol_per_sec"/>
<variable name="v_g10" units="fmol_per_sec"/>
<variable name="v_g20" units="fmol_per_sec"/>
<variable name="mu_s00" units="J_per_mol"/>
<variable name="mu_s10" units="J_per_mol"/>
<variable name="mu_s20" units="J_per_mol"/>
<variable name="mu_s01" units="J_per_mol"/>
<variable name="mu_s11" units="J_per_mol"/>
<variable name="mu_s21" units="J_per_mol"/>
<variable name="Af_b00" units="J_per_mol"/>
<variable name="Ar_b00" units="J_per_mol"/>
<variable name="Af_b10" units="J_per_mol"/>
<variable name="Ar_b10" units="J_per_mol"/>
<variable name="Af_b01" units="J_per_mol"/>
<variable name="Ar_b01" units="J_per_mol"/>
<variable name="Af_b11" units="J_per_mol"/>
<variable name="Ar_b11" units="J_per_mol"/>
<variable name="Af_g00" units="J_per_mol"/>
<variable name="Ar_g00" units="J_per_mol"/>
<variable name="Af_g10" units="J_per_mol"/>
<variable name="Ar_g10" units="J_per_mol"/>
<variable name="Af_g20" units="J_per_mol"/>
<variable name="Ar_g20" units="J_per_mol"/>
<variable name="kappa_b00" public_interface="in" units="fmol_per_sec"/>
<variable name="kappa_b01" public_interface="in" units="fmol_per_sec"/>
<variable name="kappa_b10" public_interface="in" units="fmol_per_sec"/>
<variable name="kappa_b11" public_interface="in" units="fmol_per_sec"/>
<variable name="kappa_g00" public_interface="in" units="fmol_per_sec"/>
<variable name="kappa_g10" public_interface="in" units="fmol_per_sec"/>
<variable name="kappa_g20" public_interface="in" units="fmol_per_sec"/>
<variable name="K_S00" public_interface="in" units="per_fmol"/>
<variable name="K_S10" public_interface="in" units="per_fmol"/>
<variable name="K_S20" public_interface="in" units="per_fmol"/>
<variable name="K_S01" public_interface="in" units="per_fmol"/>
<variable name="K_S11" public_interface="in" units="per_fmol"/>
<variable name="K_S21" public_interface="in" units="per_fmol"/>
<variable name="z_bf" public_interface="in" units="dimensionless"/>
<variable name="z_gf" public_interface="in" units="dimensionless"/>
<variable name="z_br" public_interface="in" units="dimensionless"/>
<variable name="z_gr" public_interface="in" units="dimensionless"/>
<variable initial_value="0.999995" name="q_s00" units="fmol"/>
<variable initial_value="1e-6" name="q_s10" units="fmol"/>
<variable initial_value="1e-6" name="q_s20" units="fmol"/>
<variable initial_value="1e-6" name="q_s01" units="fmol"/>
<variable initial_value="1e-6" name="q_s11" units="fmol"/>
<variable initial_value="1e-6" name="q_s21" units="fmol"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>Af_b00</ci>
<apply>
<plus/>
<ci>mu_s00</ci>
<apply>
<times/>
<ci>z_bf</ci>
<ci>F</ci>
<ci>V_mem</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Ar_b00</ci>
<apply>
<plus/>
<ci>mu_s10</ci>
<apply>
<times/>
<ci>z_br</ci>
<ci>F</ci>
<ci>V_mem</ci>
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<apply>
<eq/>
<ci>Af_b10</ci>
<apply>
<plus/>
<ci>mu_s10</ci>
<apply>
<times/>
<ci>z_bf</ci>
<ci>F</ci>
<ci>V_mem</ci>
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</apply>
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<apply>
<eq/>
<ci>Ar_b10</ci>
<apply>
<plus/>
<ci>mu_s20</ci>
<apply>
<times/>
<ci>z_br</ci>
<ci>F</ci>
<ci>V_mem</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Af_b01</ci>
<apply>
<plus/>
<ci>mu_s01</ci>
<apply>
<times/>
<ci>z_bf</ci>
<ci>F</ci>
<ci>V_mem</ci>
</apply>
</apply>
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<apply>
<eq/>
<ci>Ar_b01</ci>
<apply>
<plus/>
<ci>mu_s11</ci>
<apply>
<times/>
<ci>z_br</ci>
<ci>F</ci>
<ci>V_mem</ci>
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<apply>
<eq/>
<ci>Af_b11</ci>
<apply>
<plus/>
<ci>mu_s11</ci>
<apply>
<times/>
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<ci>V_mem</ci>
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<eq/>
<ci>Ar_b11</ci>
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<plus/>
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<times/>
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<ci>V_mem</ci>
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<apply>
<eq/>
<ci>Af_g00</ci>
<apply>
<plus/>
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<apply>
<times/>
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<ci>F</ci>
<ci>V_mem</ci>
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<apply>
<eq/>
<ci>Ar_g00</ci>
<apply>
<plus/>
<ci>mu_s01</ci>
<apply>
<times/>
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<ci>V_mem</ci>
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<eq/>
<ci>Af_g10</ci>
<apply>
<plus/>
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<times/>
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<ci>Ar_g10</ci>
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<plus/>
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<plus/>
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<ci>v_b00</ci>
<apply>
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<divide/>
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<apply>
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<apply>
<divide/>
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<apply>
<eq/>
<ci>v_b10</ci>
<apply>
<times/>
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<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
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<ci>RT</ci>
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<apply>
<exp/>
<apply>
<divide/>
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<ci>RT</ci>
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<eq/>
<ci>v_b01</ci>
<apply>
<times/>
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<apply>
<minus/>
<apply>
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<divide/>
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<eq/>
<ci>v_b11</ci>
<apply>
<times/>
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<apply>
<minus/>
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<apply>
<divide/>
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<ci>v_g00</ci>
<apply>
<times/>
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<minus/>
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<divide/>
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<ci>v_g20</ci>
<apply>
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<apply>
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<ci>v_g00</ci>
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<apply>
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<apply>
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<eq/>
<ci>v_s11</ci>
<apply>
<plus/>
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<ci>mu_s10</ci>
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<eq/>
<ci>mu_s20</ci>
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<apply>
<eq/>
<ci>mu_s11</ci>
<apply>
<times/>
<ci>RT</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_S11</ci>
<ci>q_s11</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_s21</ci>
<apply>
<times/>
<ci>RT</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_S21</ci>
<ci>q_s21</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_s00</ci>
</apply>
<ci>v_s00</ci>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_s10</ci>
</apply>
<ci>v_s10</ci>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_s20</ci>
</apply>
<ci>v_s20</ci>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_s01</ci>
</apply>
<ci>v_s01</ci>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_s11</ci>
</apply>
<ci>v_s11</ci>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_s21</ci>
</apply>
<ci>v_s21</ci>
</apply>
</math>
</component>
<connection>
<map_components component_1="environment" component_2="TCC_channel"/>
<map_variables variable_1="time" variable_2="t"/>
<map_variables variable_1="RT" variable_2="RT"/>
<map_variables variable_1="z" variable_2="z"/>
<map_variables variable_1="F" variable_2="F"/>
<map_variables variable_1="q_Cai" variable_2="q_Cai"/>
<map_variables variable_1="q_Cae" variable_2="q_Cae"/>
<map_variables variable_1="q_mem" variable_2="q_mem"/>
<map_variables variable_1="C_m" variable_2="C_m"/>
<map_variables variable_1="vol_o" variable_2="vol_o"/>
<map_variables variable_1="v_TCC" variable_2="v_TCC"/>
<map_variables variable_1="I_mem" variable_2="I_mem"/>
</connection>
<connection>
<map_components component_1="TCC_parameters" component_2="TCC_channel"/>
<map_variables variable_1="kappa_TCC" variable_2="kappa_TCC"/>
<map_variables variable_1="kappa_b00" variable_2="kappa_b00"/>
<map_variables variable_1="kappa_b01" variable_2="kappa_b01"/>
<map_variables variable_1="kappa_b10" variable_2="kappa_b10"/>
<map_variables variable_1="kappa_b11" variable_2="kappa_b11"/>
<map_variables variable_1="kappa_g00" variable_2="kappa_g00"/>
<map_variables variable_1="kappa_g10" variable_2="kappa_g10"/>
<map_variables variable_1="kappa_g20" variable_2="kappa_g20"/>
<map_variables variable_1="K_Cai" variable_2="K_Cai"/>
<map_variables variable_1="K_Cae" variable_2="K_Cae"/>
<map_variables variable_1="K_S00" variable_2="K_S00"/>
<map_variables variable_1="K_S10" variable_2="K_S10"/>
<map_variables variable_1="K_S20" variable_2="K_S20"/>
<map_variables variable_1="K_S01" variable_2="K_S01"/>
<map_variables variable_1="K_S11" variable_2="K_S11"/>
<map_variables variable_1="K_S21" variable_2="K_S21"/>
<map_variables variable_1="z_bf" variable_2="z_bf"/>
<map_variables variable_1="z_gf" variable_2="z_gf"/>
<map_variables variable_1="z_br" variable_2="z_br"/>
<map_variables variable_1="z_gr" variable_2="z_gr"/>
</connection>
</model>