- Author:
- Shelley Fong <sfon036@UoA.auckland.ac.nz>
- Date:
- 2022-05-20 17:11:50+12:00
- Desc:
- Init
- Permanent Source URI:
- https://models.cellml.org/workspace/880/rawfile/ea54a29b4c4bf7bb7d74ee6133e5e7fd8633973b/BG_NHE.cellml
<?xml version='1.0' encoding='UTF-8'?>
<model name="individual_NHE" 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="fF" units_ref="fF"/>
<units name="fC" units_ref="fC"/>
<units name="per_second" units_ref="per_second"/>
<units name="per_sec" units_ref="per_sec"/>
<units name="J_per_K_per_mol" units_ref="J_per_K_per_mol"/>
<units name="fmol_per_L" units_ref="fmol_per_L"/>
<units name="pL" units_ref="pL"/>
</import>
<import xlink:href="units_and_constants/constants_BG.cellml">
<component component_ref="constants" name="constants"/>
</import>
<component name="environment">
<variable name="time" public_interface="out" units="second"/>
<!-- initial values-->
<variable initial_value="2.69019E-06" name="q_H_i" public_interface="out" units="fmol"/>
<variable initial_value="2.06299E-07" name="q_H_o" public_interface="out" units="fmol"/>
<variable initial_value="481.46" name="q_Na_i" public_interface="out" units="fmol"/>
<variable initial_value="725.48" name="q_Na_o" public_interface="out" units="fmol"/>
<variable initial_value="1.666e-4" name="q_S1_NHE" public_interface="out" units="fmol"/>
<variable initial_value="1.666e-4" name="q_S2_NHE" public_interface="out" units="fmol"/>
<variable initial_value="1.666e-4" name="q_S3_NHE" public_interface="out" units="fmol"/>
<variable initial_value="1.666e-4" name="q_S4_NHE" public_interface="out" units="fmol"/>
<variable initial_value="1.666e-4" name="q_S5_NHE" public_interface="out" units="fmol"/>
<variable initial_value="1.666e-4" name="q_S6_NHE" public_interface="out" units="fmol"/>
<!-- From submodule-->
<variable name="v_R61_NHE" public_interface="in" units="fmol_per_sec"/>
<variable name="v_R12_NHE" public_interface="in" units="fmol_per_sec"/>
<variable name="v_R23_NHE" public_interface="in" units="fmol_per_sec"/>
<variable name="v_R34_NHE" public_interface="in" units="fmol_per_sec"/>
<variable name="v_R45_NHE" public_interface="in" units="fmol_per_sec"/>
<variable name="v_R56_NHE" public_interface="in" units="fmol_per_sec"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>q_H_i</ci>
</apply>
<apply>
<minus/>
<ci>v_R56_NHE</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>q_H_o</ci>
</apply>
<ci>v_R12_NHE</ci>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>q_Na_i</ci>
</apply>
<ci>v_R45_NHE</ci>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>q_Na_o</ci>
</apply>
<apply>
<minus/>
<ci>v_R23_NHE</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>q_S1_NHE</ci>
</apply>
<apply>
<minus/>
<ci>v_R61_NHE</ci>
<ci>v_R12_NHE</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>q_S2_NHE</ci>
</apply>
<apply>
<minus/>
<ci>v_R12_NHE</ci>
<ci>v_R23_NHE</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>q_S3_NHE</ci>
</apply>
<apply>
<minus/>
<ci>v_R23_NHE</ci>
<ci>v_R34_NHE</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>q_S4_NHE</ci>
</apply>
<apply>
<minus/>
<ci>v_R34_NHE</ci>
<ci>v_R45_NHE</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>q_S5_NHE</ci>
</apply>
<apply>
<minus/>
<ci>v_R45_NHE</ci>
<ci>v_R56_NHE</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>q_S6_NHE</ci>
</apply>
<apply>
<minus/>
<ci>v_R56_NHE</ci>
<ci>v_R61_NHE</ci>
</apply>
</apply>
</math>
<variable name="pH_i" units="dimensionless"/>
<variable name="pH_o" units="dimensionless"/>
<variable name="cH_i" units="mM"/>
<variable name="cH_o" units="mM"/>
<variable initial_value="38" name="w_i" units="pL"/>
<variable initial_value="5.182" name="w_o" units="pL"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>cH_i</ci>
<apply>
<divide/>
<ci>q_H_i</ci>
<ci>w_i</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>cH_o</ci>
<apply>
<divide/>
<ci>q_H_o</ci>
<ci>w_o</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>pH_i</ci>
<apply>
<minus/>
<apply>
<log/>
<ci>cH_i</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>pH_o</ci>
<apply>
<minus/>
<apply>
<log/>
<ci>cH_o</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="NHE_parameters">
<variable initial_value="3.97946" name="kappa_R61_NHE" public_interface="out" units="fmol_per_sec"/>
<variable initial_value="0.199355" name="kappa_R12_NHE" public_interface="out" units="fmol_per_sec"/>
<variable initial_value="46567.3" name="kappa_R23_NHE" public_interface="out" units="fmol_per_sec"/>
<variable initial_value="0.00101589" name="kappa_R34_NHE" public_interface="out" units="fmol_per_sec"/>
<variable initial_value="12689.2" name="kappa_R45_NHE" public_interface="out" units="fmol_per_sec"/>
<variable initial_value="54322.5" name="kappa_R56_NHE" public_interface="out" units="fmol_per_sec"/>
<variable initial_value="0.0427931" name="K_H_i" public_interface="out" units="per_fmol"/>
<variable initial_value="2034.44" name="K_H_o" public_interface="out" units="per_fmol"/>
<variable initial_value="0.183198" name="K_Na_i" public_interface="out" units="per_fmol"/>
<variable initial_value="0.00870946" name="K_Na_o" public_interface="out" units="per_fmol"/>
<variable initial_value="0.0217565" name="K_S1_NHE" public_interface="out" units="per_fmol"/>
<variable initial_value="12.5212" name="K_S2_NHE" public_interface="out" units="per_fmol"/>
<variable initial_value="18.9878" name="K_S3_NHE" public_interface="out" units="per_fmol"/>
<variable initial_value="69.6824" name="K_S4_NHE" public_interface="out" units="per_fmol"/>
<variable initial_value="0.297906" name="K_S5_NHE" public_interface="out" units="per_fmol"/>
<variable initial_value="0.0800162" name="K_S6_NHE" public_interface="out" units="per_fmol"/>
</component>
<component name="NHE">
<variable name="time" 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"/>
<!-- parameters-->
<variable name="kappa_R61_NHE" public_interface="in" units="fmol_per_sec"/>
<variable name="kappa_R12_NHE" public_interface="in" units="fmol_per_sec"/>
<variable name="kappa_R23_NHE" public_interface="in" units="fmol_per_sec"/>
<variable name="kappa_R34_NHE" public_interface="in" units="fmol_per_sec"/>
<variable name="kappa_R45_NHE" public_interface="in" units="fmol_per_sec"/>
<variable name="kappa_R56_NHE" public_interface="in" units="fmol_per_sec"/>
<variable name="K_H_i" public_interface="in" units="per_fmol"/>
<variable name="K_H_o" public_interface="in" units="per_fmol"/>
<variable name="K_Na_i" public_interface="in" units="per_fmol"/>
<variable name="K_Na_o" public_interface="in" units="per_fmol"/>
<variable name="K_S1_NHE" public_interface="in" units="per_fmol"/>
<variable name="K_S2_NHE" public_interface="in" units="per_fmol"/>
<variable name="K_S3_NHE" public_interface="in" units="per_fmol"/>
<variable name="K_S4_NHE" public_interface="in" units="per_fmol"/>
<variable name="K_S5_NHE" public_interface="in" units="per_fmol"/>
<variable name="K_S6_NHE" public_interface="in" units="per_fmol"/>
<!-- Input from global environment-->
<variable name="q_H_i" public_interface="in" units="fmol"/>
<variable name="q_H_o" public_interface="in" units="fmol"/>
<variable name="q_Na_i" public_interface="in" units="fmol"/>
<variable name="q_Na_o" public_interface="in" units="fmol"/>
<variable name="q_S1_NHE" public_interface="in" units="fmol"/>
<variable name="q_S2_NHE" public_interface="in" units="fmol"/>
<variable name="q_S3_NHE" public_interface="in" units="fmol"/>
<variable name="q_S4_NHE" public_interface="in" units="fmol"/>
<variable name="q_S5_NHE" public_interface="in" units="fmol"/>
<variable name="q_S6_NHE" public_interface="in" units="fmol"/>
<!-- Constitutive parameters-->
<variable name="mu_H_i" units="J_per_mol"/>
<variable name="mu_H_o" units="J_per_mol"/>
<variable name="mu_Na_i" units="J_per_mol"/>
<variable name="mu_Na_o" units="J_per_mol"/>
<variable name="mu_S1_NHE" units="J_per_mol"/>
<variable name="mu_S2_NHE" units="J_per_mol"/>
<variable name="mu_S3_NHE" units="J_per_mol"/>
<variable name="mu_S4_NHE" units="J_per_mol"/>
<variable name="mu_S5_NHE" units="J_per_mol"/>
<variable name="mu_S6_NHE" units="J_per_mol"/>
<variable name="v_R61_NHE" public_interface="out" units="fmol_per_sec"/>
<variable name="v_R12_NHE" public_interface="out" units="fmol_per_sec"/>
<variable name="v_R23_NHE" public_interface="out" units="fmol_per_sec"/>
<variable name="v_R34_NHE" public_interface="out" units="fmol_per_sec"/>
<variable name="v_R45_NHE" public_interface="out" units="fmol_per_sec"/>
<variable name="v_R56_NHE" public_interface="out" units="fmol_per_sec"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>mu_H_i</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_H_i</ci>
<ci>q_H_i</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_H_o</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_H_o</ci>
<ci>q_H_o</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_Na_i</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_Na_i</ci>
<ci>q_Na_i</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_Na_o</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_Na_o</ci>
<ci>q_Na_o</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_S1_NHE</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_S1_NHE</ci>
<ci>q_S1_NHE</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_S2_NHE</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_S2_NHE</ci>
<ci>q_S2_NHE</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_S3_NHE</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_S3_NHE</ci>
<ci>q_S3_NHE</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_S4_NHE</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_S4_NHE</ci>
<ci>q_S4_NHE</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_S5_NHE</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_S5_NHE</ci>
<ci>q_S5_NHE</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_S6_NHE</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_S6_NHE</ci>
<ci>q_S6_NHE</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v_R61_NHE</ci>
<apply>
<times/>
<ci>kappa_R61_NHE</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>mu_S6_NHE</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>mu_S1_NHE</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v_R12_NHE</ci>
<apply>
<times/>
<ci>kappa_R12_NHE</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>mu_S1_NHE</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>mu_S2_NHE</ci>
<ci>mu_H_o</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v_R23_NHE</ci>
<apply>
<times/>
<ci>kappa_R23_NHE</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>mu_S2_NHE</ci>
<apply>
<plus/>
<ci>mu_Na_o</ci>
</apply>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>mu_S3_NHE</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v_R34_NHE</ci>
<apply>
<times/>
<ci>kappa_R34_NHE</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>mu_S3_NHE</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>mu_S4_NHE</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v_R45_NHE</ci>
<apply>
<times/>
<ci>kappa_R45_NHE</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>mu_S4_NHE</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>mu_S5_NHE</ci>
<ci>mu_Na_i</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v_R56_NHE</ci>
<apply>
<times/>
<ci>kappa_R56_NHE</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>mu_S5_NHE</ci>
<ci>mu_H_i</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>mu_S6_NHE</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<connection>
<map_components component_1="environment" component_2="NHE"/>
<map_variables variable_1="time" variable_2="time"/>
<map_variables variable_1="q_H_i" variable_2="q_H_i"/>
<map_variables variable_1="q_H_o" variable_2="q_H_o"/>
<map_variables variable_1="q_Na_i" variable_2="q_Na_i"/>
<map_variables variable_1="q_Na_o" variable_2="q_Na_o"/>
<map_variables variable_1="q_S1_NHE" variable_2="q_S1_NHE"/>
<map_variables variable_1="q_S2_NHE" variable_2="q_S2_NHE"/>
<map_variables variable_1="q_S3_NHE" variable_2="q_S3_NHE"/>
<map_variables variable_1="q_S4_NHE" variable_2="q_S4_NHE"/>
<map_variables variable_1="q_S5_NHE" variable_2="q_S5_NHE"/>
<map_variables variable_1="q_S6_NHE" variable_2="q_S6_NHE"/>
<map_variables variable_1="v_R61_NHE" variable_2="v_R61_NHE"/>
<map_variables variable_1="v_R12_NHE" variable_2="v_R12_NHE"/>
<map_variables variable_1="v_R23_NHE" variable_2="v_R23_NHE"/>
<map_variables variable_1="v_R34_NHE" variable_2="v_R34_NHE"/>
<map_variables variable_1="v_R45_NHE" variable_2="v_R45_NHE"/>
<map_variables variable_1="v_R56_NHE" variable_2="v_R56_NHE"/>
</connection>
<connection>
<map_components component_1="NHE" component_2="NHE_parameters"/>
<map_variables variable_1="kappa_R61_NHE" variable_2="kappa_R61_NHE"/>
<map_variables variable_1="kappa_R12_NHE" variable_2="kappa_R12_NHE"/>
<map_variables variable_1="kappa_R23_NHE" variable_2="kappa_R23_NHE"/>
<map_variables variable_1="kappa_R34_NHE" variable_2="kappa_R34_NHE"/>
<map_variables variable_1="kappa_R45_NHE" variable_2="kappa_R45_NHE"/>
<map_variables variable_1="kappa_R56_NHE" variable_2="kappa_R56_NHE"/>
<map_variables variable_1="K_H_i" variable_2="K_H_i"/>
<map_variables variable_1="K_H_o" variable_2="K_H_o"/>
<map_variables variable_1="K_Na_i" variable_2="K_Na_i"/>
<map_variables variable_1="K_Na_o" variable_2="K_Na_o"/>
<map_variables variable_1="K_S1_NHE" variable_2="K_S1_NHE"/>
<map_variables variable_1="K_S2_NHE" variable_2="K_S2_NHE"/>
<map_variables variable_1="K_S3_NHE" variable_2="K_S3_NHE"/>
<map_variables variable_1="K_S4_NHE" variable_2="K_S4_NHE"/>
<map_variables variable_1="K_S5_NHE" variable_2="K_S5_NHE"/>
<map_variables variable_1="K_S6_NHE" variable_2="K_S6_NHE"/>
</connection>
<connection>
<map_components component_1="constants" component_2="NHE"/>
<map_variables variable_1="R" variable_2="R"/>
<map_variables variable_1="T" variable_2="T"/>
</connection>
</model>
