- Author:
- Shelley Fong <s.fong@auckland.ac.nz>
- Date:
- 2022-03-03 09:58:16+13:00
- Desc:
- Changing Xi to X_i, and adding python param finder code
- Permanent Source URI:
- https://models.physiomeproject.org/workspace/82c/rawfile/73d6bc1016edb1be3ceadf6cccc4aa05ef251e58/BG_Kr.cellml
<?xml version='1.0' encoding='UTF-8'?>
<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="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="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="27.9828" name="q_K_o" public_interface="out" units="fmol"/>
<variable initial_value="5510" name="q_K_i" public_interface="out" units="fmol"/>
<variable 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 initial_value="2494.34" name="RT" public_interface="out" units="J_per_mol"/>
<variable initial_value="96500" name="F" public_interface="out" units="C_per_mol"/>
<variable name="v_KGHK" 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_K_i</ci>
</apply>
<apply>
<minus/>
<ci>v_KGHK</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>q_K_o</ci>
</apply>
<ci>v_KGHK</ci>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>q_mem</ci>
</apply>
<apply>
<minus/>
<ci>I_mem</ci>
</apply>
</apply>
</math>
</component>
<component name="Kr_parameters">
<variable initial_value="740.548" name="kappa_Kr" public_interface="out" units="fmol_per_sec"/>
<variable initial_value="0.374318" name="kappa_rC3" public_interface="out" units="fmol_per_sec"/>
<variable initial_value="0.344937" name="kappa_rC2" public_interface="out" units="fmol_per_sec"/>
<variable initial_value="3.96058" name="kappa_rC1" public_interface="out" units="fmol_per_sec"/>
<variable initial_value="151.064" name="kappa_rC1IF" public_interface="out" units="fmol_per_sec"/>
<variable initial_value="23.2033" name="kappa_rOIF" public_interface="out" units="fmol_per_sec"/>
<variable initial_value="0.716132" name="K_K_i" public_interface="out" units="per_fmol"/>
<variable initial_value="5.25145" name="K_K_o" public_interface="out" units="per_fmol"/>
<variable initial_value="76.2011" name="K_C3" public_interface="out" units="per_fmol"/>
<variable initial_value="6.2968" name="K_C2" public_interface="out" units="per_fmol"/>
<variable initial_value="3.12231" name="K_C1" public_interface="out" units="per_fmol"/>
<variable initial_value="0.532948" name="K_O" public_interface="out" units="per_fmol"/>
<variable initial_value="2.24495" name="K_I" public_interface="out" units="per_fmol"/>
<variable initial_value="1.48177" name="z_fC3" public_interface="out" units="dimensionless"/>
<variable initial_value="-9.72572e-10" name="z_fC2" public_interface="out" units="dimensionless"/>
<variable initial_value="1.48177" name="z_fC1" public_interface="out" units="dimensionless"/>
<variable initial_value="0.025163" name="z_fC1IF" public_interface="out" units="dimensionless"/>
<variable initial_value="1.48177" name="z_fOIF" public_interface="out" units="dimensionless"/>
<variable initial_value="-0.977351" name="z_rC3" public_interface="out" units="dimensionless"/>
<variable initial_value="2.16033e-09" name="z_rC2" public_interface="out" units="dimensionless"/>
<variable initial_value="-0.576452" name="z_rC1" public_interface="out" units="dimensionless"/>
<variable initial_value="-0.628274" name="z_rC1IF" public_interface="out" units="dimensionless"/>
<variable initial_value="4.19344" name="z_rOIF" public_interface="out" units="dimensionless"/>
<variable initial_value="1" name="zK" public_interface="out" units="dimensionless"/>
</component>
<component name="BG_Kr">
<variable name="t" private_interface="out" public_interface="in" units="second"/>
<variable name="RT" private_interface="out" public_interface="in" units="J_per_mol"/>
<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"/>
<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"/>
<variable name="vol_o" public_interface="in" units="microm3"/>
<!-- 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_KGHK" public_interface="out" units="fmol_per_sec"/>
<variable name="I_mem" public_interface="out" units="fA"/>
<variable name="mu_K_i" units="J_per_mol"/>
<variable name="mu_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_K" units="J_per_mol"/>
<variable name="Ar_K" 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_Kr</ci>
<apply>
<times/>
<ci>zK</ci>
<ci>F</ci>
<ci>V_mem</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_K_i</ci>
<apply>
<times/>
<ci>RT</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_K_i</ci>
<ci>q_K_i</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_K_o</ci>
<apply>
<times/>
<ci>RT</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_K_o</ci>
<ci>q_K_o</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Af_K</ci>
<apply>
<plus/>
<ci>mu_sO</ci>
<ci>mu_K_i</ci>
<ci>Am_Kr</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>Ar_K</ci>
<apply>
<plus/>
<ci>mu_sO</ci>
<ci>mu_K_o</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_KGHK</ci>
<piecewise>
<piece>
<apply>
<times/>
<cn cellml:units="dimensionless">1</cn>
<ci>kappa_Kr</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>Af_K</ci>
<ci>RT</ci>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>Ar_K</ci>
<ci>RT</ci>
</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>
<ci>RT</ci>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>Am_Kr</ci>
<ci>RT</ci>
</apply>
</apply>
<cn cellml:units="dimensionless">1</cn>
</apply>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>Af_K</ci>
<ci>RT</ci>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>Ar_K</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>zK</ci>
<ci>F</ci>
<ci>v_KGHK</ci>
</apply>
</apply>
</math>
<!-- GATE-->
<variable initial_value="1.65881420e-4" name="q_sC3" units="fmol"/>
<variable initial_value="1.42042000e-5" name="q_sC2" units="fmol"/>
<variable initial_value="2.23800000e-5" name="q_sC1" units="fmol"/>
<variable initial_value="3.560000000e-5" name="q_sO" units="fmol"/>
<variable initial_value="2.03995940e-5" name="q_sI" units="fmol"/>
<variable name="v_sC3" units="fmol_per_sec"/>
<variable name="v_sC2" units="fmol_per_sec"/>
<variable name="v_sC1" units="fmol_per_sec"/>
<variable name="v_sO" units="fmol_per_sec"/>
<variable name="v_sI" units="fmol_per_sec"/>
<variable name="v_rC3" units="fmol_per_sec"/>
<variable name="v_rC2" units="fmol_per_sec"/>
<variable name="v_rC1" units="fmol_per_sec"/>
<variable name="v_rC1IF" units="fmol_per_sec"/>
<variable name="v_rOIF" units="fmol_per_sec"/>
<variable name="mu_sC3" units="J_per_mol"/>
<variable name="mu_sC2" units="J_per_mol"/>
<variable name="mu_sC1" units="J_per_mol"/>
<variable name="mu_sO" units="J_per_mol"/>
<variable name="mu_sI" units="J_per_mol"/>
<variable name="Af_rC3" units="J_per_mol"/>
<variable name="Ar_rC3" units="J_per_mol"/>
<variable name="Af_rC2" units="J_per_mol"/>
<variable name="Ar_rC2" units="J_per_mol"/>
<variable name="Af_rC1" units="J_per_mol"/>
<variable name="Ar_rC1" units="J_per_mol"/>
<variable name="Af_rC1IF" units="J_per_mol"/>
<variable name="Ar_rC1IF" units="J_per_mol"/>
<variable name="Af_rOIF" units="J_per_mol"/>
<variable name="Ar_rOIF" units="J_per_mol"/>
<variable name="kappa_rC3" public_interface="in" units="fmol_per_sec"/>
<variable name="kappa_rC2" public_interface="in" units="fmol_per_sec"/>
<variable name="kappa_rC1" public_interface="in" units="fmol_per_sec"/>
<variable name="kappa_rC1IF" public_interface="in" units="fmol_per_sec"/>
<variable name="kappa_rOIF" public_interface="in" units="fmol_per_sec"/>
<variable name="K_C3" public_interface="in" units="per_fmol"/>
<variable name="K_C2" public_interface="in" units="per_fmol"/>
<variable name="K_C1" public_interface="in" units="per_fmol"/>
<variable name="K_O" public_interface="in" units="per_fmol"/>
<variable name="K_I" public_interface="in" units="per_fmol"/>
<variable name="z_fC3" public_interface="in" units="dimensionless"/>
<variable name="z_fC2" public_interface="in" units="dimensionless"/>
<variable name="z_fC1" public_interface="in" units="dimensionless"/>
<variable name="z_fC1IF" public_interface="in" units="dimensionless"/>
<variable name="z_fOIF" public_interface="in" units="dimensionless"/>
<variable name="z_rC3" public_interface="in" units="dimensionless"/>
<variable name="z_rC2" public_interface="in" units="dimensionless"/>
<variable name="z_rC1" public_interface="in" units="dimensionless"/>
<variable name="z_rC1IF" public_interface="in" units="dimensionless"/>
<variable name="z_rOIF" public_interface="in" units="dimensionless"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>Af_rC3</ci>
<apply>
<plus/>
<ci>mu_sC3</ci>
<apply>
<times/>
<ci>z_fC3</ci>
<ci>F</ci>
<ci>V_mem</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Ar_rC3</ci>
<apply>
<plus/>
<ci>mu_sC2</ci>
<apply>
<times/>
<ci>z_rC3</ci>
<ci>F</ci>
<ci>V_mem</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Af_rC2</ci>
<apply>
<plus/>
<ci>mu_sC2</ci>
<apply>
<times/>
<ci>z_fC2</ci>
<ci>F</ci>
<ci>V_mem</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Ar_rC2</ci>
<apply>
<plus/>
<ci>mu_sC1</ci>
<apply>
<times/>
<ci>z_rC2</ci>
<ci>F</ci>
<ci>V_mem</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Af_rC1</ci>
<apply>
<plus/>
<ci>mu_sC1</ci>
<apply>
<times/>
<ci>z_fC1</ci>
<ci>F</ci>
<ci>V_mem</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Ar_rC1</ci>
<apply>
<plus/>
<ci>mu_sO</ci>
<apply>
<times/>
<ci>z_rC1</ci>
<ci>F</ci>
<ci>V_mem</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Af_rC1IF</ci>
<apply>
<plus/>
<ci>mu_sC1</ci>
<apply>
<times/>
<ci>z_fC1IF</ci>
<ci>F</ci>
<ci>V_mem</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Ar_rC1IF</ci>
<apply>
<plus/>
<ci>mu_sI</ci>
<apply>
<times/>
<ci>z_rC1IF</ci>
<ci>F</ci>
<ci>V_mem</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Af_rOIF</ci>
<apply>
<plus/>
<ci>mu_sO</ci>
<apply>
<times/>
<ci>z_fOIF</ci>
<ci>F</ci>
<ci>V_mem</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Ar_rOIF</ci>
<apply>
<plus/>
<ci>mu_sI</ci>
<apply>
<times/>
<ci>z_rOIF</ci>
<ci>F</ci>
<ci>V_mem</ci>
</apply>
</apply>
</apply>
<!-- -->
<apply>
<eq/>
<ci>v_rC3</ci>
<apply>
<times/>
<ci>kappa_rC3</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>Af_rC3</ci>
<ci>RT</ci>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>Ar_rC3</ci>
<ci>RT</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v_rC2</ci>
<apply>
<times/>
<ci>kappa_rC2</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>Af_rC2</ci>
<ci>RT</ci>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>Ar_rC2</ci>
<ci>RT</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v_rC1</ci>
<apply>
<times/>
<ci>kappa_rC1</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>Af_rC1</ci>
<ci>RT</ci>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>Ar_rC1</ci>
<ci>RT</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v_rC1IF</ci>
<apply>
<times/>
<ci>kappa_rC1IF</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>Af_rC1IF</ci>
<ci>RT</ci>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>Ar_rC1IF</ci>
<ci>RT</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v_rOIF</ci>
<apply>
<times/>
<ci>kappa_rOIF</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>Af_rOIF</ci>
<ci>RT</ci>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>Ar_rOIF</ci>
<ci>RT</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v_sC3</ci>
<apply>
<minus/>
<ci>v_rC3</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_sC2</ci>
<apply>
<minus/>
<ci>v_rC3</ci>
<ci>v_rC2</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_sC1</ci>
<apply>
<minus/>
<apply>
<minus/>
<ci>v_rC2</ci>
<ci>v_rC1</ci>
</apply>
<ci>v_rC1IF</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_sO</ci>
<apply>
<minus/>
<ci>v_rC1</ci>
<ci>v_rOIF</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_sI</ci>
<apply>
<plus/>
<ci>v_rC1IF</ci>
<ci>v_rOIF</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_sC3</ci>
<apply>
<times/>
<ci>RT</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_C3</ci>
<ci>q_sC3</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_sC2</ci>
<apply>
<times/>
<ci>RT</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_C2</ci>
<ci>q_sC2</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_sC1</ci>
<apply>
<times/>
<ci>RT</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_C1</ci>
<ci>q_sC1</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_sO</ci>
<apply>
<times/>
<ci>RT</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_O</ci>
<ci>q_sO</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_sI</ci>
<apply>
<times/>
<ci>RT</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_I</ci>
<ci>q_sI</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_sC3</ci>
</apply>
<ci>v_sC3</ci>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_sC2</ci>
</apply>
<ci>v_sC2</ci>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_sC1</ci>
</apply>
<ci>v_sC1</ci>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_sO</ci>
</apply>
<ci>v_sO</ci>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_sI</ci>
</apply>
<ci>v_sI</ci>
</apply>
</math>
</component>
<connection>
<map_components component_1="environment" component_2="BG_Kr"/>
<map_variables variable_1="time" variable_2="t"/>
<map_variables variable_1="RT" variable_2="RT"/>
<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="vol_o" variable_2="vol_o"/>
<map_variables variable_1="v_KGHK" variable_2="v_KGHK"/>
<map_variables variable_1="I_mem" variable_2="I_mem"/>
</connection>
<connection>
<map_components component_1="BG_Kr" component_2="Kr_parameters"/>
<map_variables variable_1="kappa_Kr" variable_2="kappa_Kr"/>
<map_variables variable_1="kappa_rC3" variable_2="kappa_rC3"/>
<map_variables variable_1="kappa_rC2" variable_2="kappa_rC2"/>
<map_variables variable_1="kappa_rC1" variable_2="kappa_rC1"/>
<map_variables variable_1="kappa_rC1IF" variable_2="kappa_rC1IF"/>
<map_variables variable_1="kappa_rOIF" variable_2="kappa_rOIF"/>
<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_C3" variable_2="K_C3"/>
<map_variables variable_1="K_C2" variable_2="K_C2"/>
<map_variables variable_1="K_C1" variable_2="K_C1"/>
<map_variables variable_1="K_O" variable_2="K_O"/>
<map_variables variable_1="K_I" variable_2="K_I"/>
<map_variables variable_1="z_fC3" variable_2="z_fC3"/>
<map_variables variable_1="z_fC2" variable_2="z_fC2"/>
<map_variables variable_1="z_fC1" variable_2="z_fC1"/>
<map_variables variable_1="z_fC1IF" variable_2="z_fC1IF"/>
<map_variables variable_1="z_fOIF" variable_2="z_fOIF"/>
<map_variables variable_1="z_rC3" variable_2="z_rC3"/>
<map_variables variable_1="z_rC2" variable_2="z_rC2"/>
<map_variables variable_1="z_rC1" variable_2="z_rC1"/>
<map_variables variable_1="z_rC1IF" variable_2="z_rC1IF"/>
<map_variables variable_1="z_rOIF" variable_2="z_rOIF"/>
<map_variables variable_1="zK" variable_2="zK"/>
</connection>
</model>
