Location: BG_to_channel @ 950b3b004fb4 / BG_to.cellml
- Author:
- Shelley Fong <s.fong@auckland.ac.nz>
- Date:
- 2022-03-22 15:21:27+13:00
- Desc:
- Updating channel density to literature value (Fedida91)
- Permanent Source URI:
- https://models.cellml.org/workspace/82e/rawfile/950b3b004fb4e23b7a4177d7aaf1d7ec8062b261/BG_to.cellml
<?xml version='1.0' encoding='UTF-8'?>
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<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="microm3" units_ref="microm3"/>
<units name="fF" units_ref="fF"/>
<units name="fC" units_ref="fC"/>
<units name="fA" units_ref="fA"/>
</import>
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<variable name="time" public_interface="out" units="second"/>
<variable initial_value="1.0e6" name="C_m" public_interface="out" units="fF"/>
<variable initial_value="0.116325" name="q_K_o" public_interface="out" units="fmol"/>
<variable initial_value="3.65002" name="q_K_i" public_interface="out" units="fmol"/>
<variable initial_value="-8.5e4" 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_to" public_interface="in" units="fmol_per_sec"/>
<variable name="I_mem_to" public_interface="in" units="fA"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
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<eq/>
<apply>
<diff/>
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<eq/>
<apply>
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<divide/>
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<ci>C_m</ci>
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<component name="to_parameters">
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<variable initial_value="192.53" name="kappa_z00" public_interface="out" units="fmol_per_sec"/>
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<variable initial_value="1.38227" name="kappa_y20" public_interface="out" units="fmol_per_sec"/>
<variable initial_value="1.35902" name="kappa_y30" public_interface="out" units="fmol_per_sec"/>
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<variable initial_value="3.02293" name="K_S10_to" public_interface="out" units="per_fmol"/>
<variable initial_value="1.02489" name="K_S20_to" public_interface="out" units="per_fmol"/>
<variable initial_value="1.04242" name="K_S30_to" public_interface="out" units="per_fmol"/>
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<variable initial_value="152.67" name="K_S11_to" public_interface="out" units="per_fmol"/>
<variable initial_value="51.761" name="K_S21_to" public_interface="out" units="per_fmol"/>
<variable initial_value="52.6467" name="K_S31_to" public_interface="out" units="per_fmol"/>
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<variable initial_value="1" name="zK" public_interface="out" units="dimensionless"/>
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<component name="to">
<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="zK" public_interface="in" units="dimensionless"/>
<variable name="F" private_interface="out" public_interface="in" units="C_per_mol"/>
<variable name="C_m" public_interface="in" units="fF"/>
<!-- Parameters-->
<variable name="kappa_to" public_interface="in" units="fmol_per_sec"/>
<variable name="K_K_i" public_interface="in" units="per_fmol"/>
<variable name="K_K_o" 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_to" public_interface="out" units="fmol_per_sec"/>
<variable name="I_mem_to" 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" units="J_per_C"/>
<variable name="Am_to" units="J_per_mol"/>
<variable name="Af_K" units="J_per_mol"/>
<variable name="Ar_K" units="J_per_mol"/>
<!-- Conservation laws-->
<!-- Constitutive relations - Convention: positive flow from inside to outside-->
<math xmlns="http://www.w3.org/1998/Math/MathML">
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<apply>
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<times/>
<ci>K_K_i</ci>
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<eq/>
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<ln/>
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<times/>
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</apply>
</apply>
</apply>
</apply>
</math>
<!-- account for rvdv = exp(V/100) term-->
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<variable name="q_P" units="fmol"/>
<variable initial_value="1" name="K_P" units="per_fmol"/>
<variable name="mu_P" units="J_per_mol"/>
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<ln/>
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<plus/>
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<ci>Am_to</ci>
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<plus/>
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<apply>
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<apply>
<divide/>
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<times/>
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<times/>
<apply>
<divide/>
<apply>
<divide/>
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<apply>
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<apply>
<plus/>
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<times/>
<apply>
<minus/>
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<apply>
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<minus/>
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<ci>z_yf</ci>
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</apply>
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</math>
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<variable name="v_s00_to" units="fmol_per_sec"/>
<variable name="v_s10_to" units="fmol_per_sec"/>
<variable name="v_s20_to" units="fmol_per_sec"/>
<variable name="v_s30_to" units="fmol_per_sec"/>
<variable name="v_s01_to" units="fmol_per_sec"/>
<variable name="v_s11_to" units="fmol_per_sec"/>
<variable name="v_s21_to" units="fmol_per_sec"/>
<variable name="v_s31_to" units="fmol_per_sec"/>
<variable name="v_z00" units="fmol_per_sec"/>
<variable name="v_z10" units="fmol_per_sec"/>
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<variable name="v_z01" units="fmol_per_sec"/>
<variable name="v_z11" units="fmol_per_sec"/>
<variable name="v_z21" units="fmol_per_sec"/>
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<variable name="v_y10" units="fmol_per_sec"/>
<variable name="v_y20" units="fmol_per_sec"/>
<variable name="v_y30" units="fmol_per_sec"/>
<variable name="mu_s00_to" units="J_per_mol"/>
<variable name="mu_s10_to" units="J_per_mol"/>
<variable name="mu_s20_to" units="J_per_mol"/>
<variable name="mu_s30_to" units="J_per_mol"/>
<variable name="mu_s01_to" units="J_per_mol"/>
<variable name="mu_s11_to" units="J_per_mol"/>
<variable name="mu_s21_to" units="J_per_mol"/>
<variable name="mu_s31_to" units="J_per_mol"/>
<variable name="Af_z00" units="J_per_mol"/>
<variable name="Ar_z00" units="J_per_mol"/>
<variable name="Af_z10" units="J_per_mol"/>
<variable name="Ar_z10" units="J_per_mol"/>
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<variable name="Ar_z20" units="J_per_mol"/>
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<variable name="Ar_z01" units="J_per_mol"/>
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<variable name="Ar_z11" units="J_per_mol"/>
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<variable name="Af_y00" units="J_per_mol"/>
<variable name="Ar_y00" units="J_per_mol"/>
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<variable name="Ar_y10" units="J_per_mol"/>
<variable name="Af_y20" units="J_per_mol"/>
<variable name="Ar_y20" units="J_per_mol"/>
<variable name="Af_y30" units="J_per_mol"/>
<variable name="Ar_y30" units="J_per_mol"/>
<variable name="kappa_z00" public_interface="in" units="fmol_per_sec"/>
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<variable name="kappa_z11" public_interface="in" units="fmol_per_sec"/>
<variable name="kappa_z20" public_interface="in" units="fmol_per_sec"/>
<variable name="kappa_z21" public_interface="in" units="fmol_per_sec"/>
<variable name="kappa_y00" public_interface="in" units="fmol_per_sec"/>
<variable name="kappa_y10" public_interface="in" units="fmol_per_sec"/>
<variable name="kappa_y20" public_interface="in" units="fmol_per_sec"/>
<variable name="kappa_y30" public_interface="in" units="fmol_per_sec"/>
<variable name="K_S00_to" public_interface="in" units="per_fmol"/>
<variable name="K_S10_to" public_interface="in" units="per_fmol"/>
<variable name="K_S20_to" public_interface="in" units="per_fmol"/>
<variable name="K_S30_to" public_interface="in" units="per_fmol"/>
<variable name="K_S01_to" public_interface="in" units="per_fmol"/>
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<variable name="K_S21_to" public_interface="in" units="per_fmol"/>
<variable name="K_S31_to" public_interface="in" units="per_fmol"/>
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<variable name="z_yr" public_interface="in" units="dimensionless"/>
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<apply>
<eq/>
<ci>Ar_y20</ci>
<apply>
<plus/>
<ci>mu_s21_to</ci>
<apply>
<times/>
<ci>z_yr</ci>
<ci>F</ci>
<ci>V_mem</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Af_y30</ci>
<apply>
<plus/>
<ci>mu_s30_to</ci>
<apply>
<times/>
<ci>z_yf</ci>
<ci>F</ci>
<ci>V_mem</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Ar_y30</ci>
<apply>
<plus/>
<ci>mu_s31_to</ci>
<apply>
<times/>
<ci>z_yr</ci>
<ci>F</ci>
<ci>V_mem</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v_z00</ci>
<apply>
<times/>
<ci>kappa_z00</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>Af_z00</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>Ar_z00</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v_z10</ci>
<apply>
<times/>
<ci>kappa_z10</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>Af_z10</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>Ar_z10</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v_z20</ci>
<apply>
<times/>
<ci>kappa_z20</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>Af_z20</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>Ar_z20</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v_z01</ci>
<apply>
<times/>
<ci>kappa_z01</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>Af_z01</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>Ar_z01</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v_z11</ci>
<apply>
<times/>
<ci>kappa_z11</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>Af_z11</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>Ar_z11</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v_z21</ci>
<apply>
<times/>
<ci>kappa_z21</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>Af_z21</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>Ar_z21</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v_y00</ci>
<apply>
<times/>
<ci>kappa_y00</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>Af_y00</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>Ar_y00</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v_y10</ci>
<apply>
<times/>
<ci>kappa_y10</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>Af_y10</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>Ar_y10</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v_y20</ci>
<apply>
<times/>
<ci>kappa_y20</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>Af_y20</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>Ar_y20</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v_y30</ci>
<apply>
<times/>
<ci>kappa_y30</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>Af_y30</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>Ar_y30</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v_s00_to</ci>
<apply>
<minus/>
<apply>
<minus/>
<ci>v_z00</ci>
</apply>
<ci>v_y00</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_s10_to</ci>
<apply>
<minus/>
<apply>
<minus/>
<ci>v_z00</ci>
<ci>v_z10</ci>
</apply>
<ci>v_y10</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_s20_to</ci>
<apply>
<minus/>
<apply>
<minus/>
<ci>v_z10</ci>
<ci>v_z20</ci>
</apply>
<ci>v_y20</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_s30_to</ci>
<apply>
<minus/>
<ci>v_z20</ci>
<ci>v_y30</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_s01_to</ci>
<apply>
<minus/>
<ci>v_y00</ci>
<ci>v_z01</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_s11_to</ci>
<apply>
<plus/>
<apply>
<minus/>
<ci>v_z01</ci>
<ci>v_z11</ci>
</apply>
<ci>v_y10</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_s21_to</ci>
<apply>
<plus/>
<apply>
<minus/>
<ci>v_z11</ci>
<ci>v_z21</ci>
</apply>
<ci>v_y20</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_s31_to</ci>
<apply>
<plus/>
<ci>v_z21</ci>
<ci>v_y30</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_s00_to</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_S00_to</ci>
<ci>q_s00_to</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_s10_to</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_S10_to</ci>
<ci>q_s10_to</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_s20_to</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_S20_to</ci>
<ci>q_s20_to</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_s30_to</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_S30_to</ci>
<ci>q_s30_to</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_s01_to</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_S01_to</ci>
<ci>q_s01_to</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_s11_to</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_S11_to</ci>
<ci>q_s11_to</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_s21_to</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_S21_to</ci>
<ci>q_s21_to</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_s31_to</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_S31_to</ci>
<ci>q_s31_to</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_s00_to</ci>
</apply>
<ci>v_s00_to</ci>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_s10_to</ci>
</apply>
<ci>v_s10_to</ci>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_s20_to</ci>
</apply>
<ci>v_s20_to</ci>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_s30_to</ci>
</apply>
<ci>v_s30_to</ci>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_s01_to</ci>
</apply>
<ci>v_s01_to</ci>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_s11_to</ci>
</apply>
<ci>v_s11_to</ci>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_s21_to</ci>
</apply>
<ci>v_s21_to</ci>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_s31_to</ci>
</apply>
<ci>v_s31_to</ci>
</apply>
</math>
</component>
<connection>
<map_components component_1="environment" component_2="to"/>
<map_variables variable_1="time" 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_mem" variable_2="q_mem"/>
<map_variables variable_1="C_m" variable_2="C_m"/>
<map_variables variable_1="v_to" variable_2="v_to"/>
<map_variables variable_1="I_mem_to" variable_2="I_mem_to"/>
</connection>
<connection>
<map_components component_1="to" component_2="to_parameters"/>
<map_variables variable_1="kappa_to" variable_2="kappa_to"/>
<map_variables variable_1="kappa_z00" variable_2="kappa_z00"/>
<map_variables variable_1="kappa_z01" variable_2="kappa_z01"/>
<map_variables variable_1="kappa_z10" variable_2="kappa_z10"/>
<map_variables variable_1="kappa_z11" variable_2="kappa_z11"/>
<map_variables variable_1="kappa_z20" variable_2="kappa_z20"/>
<map_variables variable_1="kappa_z21" variable_2="kappa_z21"/>
<map_variables variable_1="kappa_y00" variable_2="kappa_y00"/>
<map_variables variable_1="kappa_y10" variable_2="kappa_y10"/>
<map_variables variable_1="kappa_y20" variable_2="kappa_y20"/>
<map_variables variable_1="kappa_y30" variable_2="kappa_y30"/>
<map_variables variable_1="K_K_i" variable_2="K_K_i"/>
<map_variables variable_1="K_K_o" variable_2="K_K_o"/>
<map_variables variable_1="K_S00_to" variable_2="K_S00_to"/>
<map_variables variable_1="K_S10_to" variable_2="K_S10_to"/>
<map_variables variable_1="K_S20_to" variable_2="K_S20_to"/>
<map_variables variable_1="K_S30_to" variable_2="K_S30_to"/>
<map_variables variable_1="K_S01_to" variable_2="K_S01_to"/>
<map_variables variable_1="K_S11_to" variable_2="K_S11_to"/>
<map_variables variable_1="K_S21_to" variable_2="K_S21_to"/>
<map_variables variable_1="K_S31_to" variable_2="K_S31_to"/>
<map_variables variable_1="z_zf" variable_2="z_zf"/>
<map_variables variable_1="z_yf" variable_2="z_yf"/>
<map_variables variable_1="z_zr" variable_2="z_zr"/>
<map_variables variable_1="z_yr" variable_2="z_yr"/>
<map_variables variable_1="zK" variable_2="zK"/>
</connection>
</model>