Location: Na+/H+ Exchanger @ 1a70e17462ba / BG / NHE3_BG.cellml
- Author:
- Soroush Safaei <ssaf006@aucklanduni.ac.nz>
- Date:
- 2016-11-26 15:39:29+13:00
- Desc:
- Adding bond graph version of NHE3
- Permanent Source URI:
- https://staging.physiomeproject.org/workspace/28f/rawfile/1a70e17462ba33f716f6ab6146d66694b9c32abb/BG/NHE3_BG.cellml
<?xml version='1.0'?>
<model name="NHE3_BG" 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.cellml">
<units name="per_mol" units_ref="per_mol"/>
<units name="J_per_mol" units_ref="J_per_mol"/>
<units name="mol_per_s" units_ref="mol_per_s"/>
</import>
<import xlink:href="Parameters-NHE3.cellml">
<component component_ref="param" name="param"/>
</import>
<component name="environment">
<variable name="time" public_interface="out" units="second"/>
</component>
<component name="main">
<variable name="t" public_interface="in" units="second"/>
<!-- Constants-->
<variable name="RT" public_interface="in" units="J_per_mol"/>
<!-- State variables-->
<variable initial_value="0.01" name="q_E_o" units="mole"/>
<variable initial_value="0.0" name="q_E_i" units="mole"/>
<variable initial_value="0.01" name="q_Na_o" units="mole"/>
<variable initial_value="0.0" name="q_Na_i" units="mole"/>
<variable initial_value="0.0" name="q_H_i" units="mole"/>
<variable initial_value="0.01" name="q_H_o" units="mole"/>
<variable initial_value="0.0" name="q_NH4_i" units="mole"/>
<variable initial_value="0.01" name="q_NH4_o" units="mole"/>
<variable initial_value="0.0" name="q_ENa_o" units="mole"/>
<variable initial_value="0.0" name="q_ENa_i" units="mole"/>
<variable initial_value="0.0" name="q_EH_i" units="mole"/>
<variable initial_value="0.0" name="q_EH_o" units="mole"/>
<variable initial_value="0.0" name="q_ENH4_i" units="mole"/>
<variable initial_value="0.0" name="q_ENH4_o" units="mole"/>
<variable name="nu_Re1" units="mol_per_s"/>
<variable name="nu_Re2" units="mol_per_s"/>
<variable name="nu_Re3" units="mol_per_s"/>
<variable name="nu_Re4" units="mol_per_s"/>
<variable name="nu_Re5" units="mol_per_s"/>
<variable name="nu_Re6" units="mol_per_s"/>
<variable name="nu_Re7" units="mol_per_s"/>
<variable name="nu_Re8" units="mol_per_s"/>
<variable name="nu_Re9" units="mol_per_s"/>
<variable name="mu_E_o" units="J_per_mol"/>
<variable name="mu_E_i" units="J_per_mol"/>
<variable name="mu_Na_o" units="J_per_mol"/>
<variable name="mu_Na_i" units="J_per_mol"/>
<variable name="mu_H_o" units="J_per_mol"/>
<variable name="mu_H_i" units="J_per_mol"/>
<variable name="mu_NH4_o" units="J_per_mol"/>
<variable name="mu_NH4_i" units="J_per_mol"/>
<variable name="mu_ENa_o" units="J_per_mol"/>
<variable name="mu_ENa_i" units="J_per_mol"/>
<variable name="mu_EH_o" units="J_per_mol"/>
<variable name="mu_EH_i" units="J_per_mol"/>
<variable name="mu_ENH4_o" units="J_per_mol"/>
<variable name="mu_ENH4_i" units="J_per_mol"/>
<variable name="mu_ExNa_o" units="J_per_mol"/>
<variable name="mu_ExNa_i" units="J_per_mol"/>
<variable name="mu_ExH_o" units="J_per_mol"/>
<variable name="mu_ExH_i" units="J_per_mol"/>
<variable name="mu_ExNH4_o" units="J_per_mol"/>
<variable name="mu_ExNH4_i" units="J_per_mol"/>
<!-- Constitutive parameters-->
<variable name="K_E_o" public_interface="in" units="per_mol"/>
<variable name="K_E_i" public_interface="in" units="per_mol"/>
<variable name="K_Na_o" public_interface="in" units="per_mol"/>
<variable name="K_Na_i" public_interface="in" units="per_mol"/>
<variable name="K_H_i" public_interface="in" units="per_mol"/>
<variable name="K_H_o" public_interface="in" units="per_mol"/>
<variable name="K_NH4_o" public_interface="in" units="per_mol"/>
<variable name="K_NH4_i" public_interface="in" units="per_mol"/>
<variable name="K_ENa_o" public_interface="in" units="per_mol"/>
<variable name="K_ENa_i" public_interface="in" units="per_mol"/>
<variable name="K_EH_i" public_interface="in" units="per_mol"/>
<variable name="K_EH_o" public_interface="in" units="per_mol"/>
<variable name="K_ENH4_o" public_interface="in" units="per_mol"/>
<variable name="K_ENH4_i" public_interface="in" units="per_mol"/>
<variable name="k_Re1" public_interface="in" units="mol_per_s"/>
<variable name="k_Re2" public_interface="in" units="mol_per_s"/>
<variable name="k_Re3" public_interface="in" units="mol_per_s"/>
<variable name="k_Re4" public_interface="in" units="mol_per_s"/>
<variable name="k_Re5" public_interface="in" units="mol_per_s"/>
<variable name="k_Re6" public_interface="in" units="mol_per_s"/>
<variable name="k_Re7" public_interface="in" units="mol_per_s"/>
<variable name="k_Re8" public_interface="in" units="mol_per_s"/>
<variable name="k_Re9" public_interface="in" units="mol_per_s"/>
<!-- Conservation laws-->
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>mu_ExNa_o</ci>
<apply>
<plus/>
<ci>mu_E_o</ci>
<ci>mu_Na_o</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_ExNa_i</ci>
<apply>
<plus/>
<ci>mu_Na_i</ci>
<ci>mu_E_i</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_ExH_o</ci>
<apply>
<plus/>
<ci>mu_H_o</ci>
<ci>mu_E_o</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_ExH_i</ci>
<apply>
<plus/>
<ci>mu_E_i</ci>
<ci>mu_H_i</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_ExNH4_o</ci>
<apply>
<plus/>
<ci>mu_E_o</ci>
<ci>mu_NH4_o</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_ExNH4_i</ci>
<apply>
<plus/>
<ci>mu_NH4_i</ci>
<ci>mu_E_i</ci>
</apply>
</apply>
<!-- Definitions-->
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_E_o</ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<ci>nu_Re6</ci>
<ci>nu_Re9</ci>
</apply>
<ci>nu_Re1</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_E_i</ci>
</apply>
<apply>
<minus/>
<apply>
<minus/>
<ci>nu_Re3</ci>
<ci>nu_Re4</ci>
</apply>
<ci>nu_Re7</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_Na_o</ci>
</apply>
<apply>
<minus/>
<ci>nu_Re1</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_Na_i</ci>
</apply>
<ci>nu_Re3</ci>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_H_i</ci>
</apply>
<apply>
<minus/>
<ci>nu_Re4</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_H_o</ci>
</apply>
<ci>nu_Re6</ci>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_NH4_i</ci>
</apply>
<apply>
<minus/>
<ci>nu_Re7</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_NH4_o</ci>
</apply>
<ci>nu_Re9</ci>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_ENa_o</ci>
</apply>
<apply>
<minus/>
<ci>nu_Re1</ci>
<ci>nu_Re2</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_ENa_i</ci>
</apply>
<apply>
<minus/>
<ci>nu_Re2</ci>
<ci>nu_Re3</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_EH_i</ci>
</apply>
<apply>
<minus/>
<ci>nu_Re4</ci>
<ci>nu_Re5</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_EH_o</ci>
</apply>
<apply>
<minus/>
<ci>nu_Re5</ci>
<ci>nu_Re6</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_ENH4_i</ci>
</apply>
<apply>
<minus/>
<ci>nu_Re7</ci>
<ci>nu_Re8</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_ENH4_o</ci>
</apply>
<apply>
<minus/>
<ci>nu_Re8</ci>
<ci>nu_Re9</ci>
</apply>
</apply>
<!-- Constitutive relations-->
<apply>
<eq/>
<ci>mu_E_o</ci>
<apply>
<times/>
<ci>RT</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_E_o</ci>
<ci>q_E_o</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_E_i</ci>
<apply>
<times/>
<ci>RT</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_E_i</ci>
<ci>q_E_i</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_Na_o</ci>
<apply>
<times/>
<ci>RT</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_Na_o</ci>
<ci>q_Na_o</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_Na_i</ci>
<apply>
<times/>
<ci>RT</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_Na_i</ci>
<ci>q_Na_i</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_H_o</ci>
<apply>
<times/>
<ci>RT</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_H_o</ci>
<ci>q_H_o</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_H_i</ci>
<apply>
<times/>
<ci>RT</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_H_i</ci>
<ci>q_H_i</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_NH4_o</ci>
<apply>
<times/>
<ci>RT</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_NH4_o</ci>
<ci>q_NH4_o</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_NH4_i</ci>
<apply>
<times/>
<ci>RT</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_NH4_i</ci>
<ci>q_NH4_i</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_ENa_o</ci>
<apply>
<times/>
<ci>RT</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_ENa_o</ci>
<ci>q_ENa_o</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_ENa_i</ci>
<apply>
<times/>
<ci>RT</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_ENa_i</ci>
<ci>q_ENa_i</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_EH_i</ci>
<apply>
<times/>
<ci>RT</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_EH_i</ci>
<ci>q_EH_i</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_EH_o</ci>
<apply>
<times/>
<ci>RT</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_EH_o</ci>
<ci>q_EH_o</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_ENH4_i</ci>
<apply>
<times/>
<ci>RT</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_ENH4_i</ci>
<ci>q_ENH4_i</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_ENH4_o</ci>
<apply>
<times/>
<ci>RT</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_ENH4_o</ci>
<ci>q_ENH4_o</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>nu_Re1</ci>
<apply>
<times/>
<ci>k_Re1</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>mu_ExNa_o</ci>
<ci>RT</ci>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>mu_ENa_o</ci>
<ci>RT</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>nu_Re2</ci>
<apply>
<times/>
<ci>k_Re2</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>mu_ENa_o</ci>
<ci>RT</ci>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>mu_ENa_i</ci>
<ci>RT</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>nu_Re3</ci>
<apply>
<times/>
<ci>k_Re3</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>mu_ENa_i</ci>
<ci>RT</ci>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>mu_ExNa_i</ci>
<ci>RT</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>nu_Re4</ci>
<apply>
<times/>
<ci>k_Re4</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>mu_ExH_i</ci>
<ci>RT</ci>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>mu_EH_i</ci>
<ci>RT</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>nu_Re5</ci>
<apply>
<times/>
<ci>k_Re5</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>mu_EH_i</ci>
<ci>RT</ci>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>mu_EH_o</ci>
<ci>RT</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>nu_Re6</ci>
<apply>
<times/>
<ci>k_Re6</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>mu_EH_o</ci>
<ci>RT</ci>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>mu_ExH_o</ci>
<ci>RT</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>nu_Re7</ci>
<apply>
<times/>
<ci>k_Re7</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>mu_ExNH4_i</ci>
<ci>RT</ci>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>mu_ENH4_i</ci>
<ci>RT</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>nu_Re8</ci>
<apply>
<times/>
<ci>k_Re8</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>mu_ENH4_i</ci>
<ci>RT</ci>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>mu_ENH4_o</ci>
<ci>RT</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>nu_Re9</ci>
<apply>
<times/>
<ci>k_Re9</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>mu_ENH4_o</ci>
<ci>RT</ci>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>mu_ExNH4_o</ci>
<ci>RT</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<connection>
<map_components component_1="main" component_2="param"/>
<map_variables variable_1="RT" variable_2="RT"/>
<map_variables variable_1="K_Na_o" variable_2="K_Na_o"/>
<map_variables variable_1="K_Na_i" variable_2="K_Na_i"/>
<map_variables variable_1="K_H_o" variable_2="K_H_o"/>
<map_variables variable_1="K_H_i" variable_2="K_H_i"/>
<map_variables variable_1="K_E_o" variable_2="K_E_o"/>
<map_variables variable_1="K_E_i" variable_2="K_E_i"/>
<map_variables variable_1="K_NH4_o" variable_2="K_NH4_o"/>
<map_variables variable_1="K_NH4_i" variable_2="K_NH4_i"/>
<map_variables variable_1="K_ENa_o" variable_2="K_ENa_o"/>
<map_variables variable_1="K_ENa_i" variable_2="K_ENa_i"/>
<map_variables variable_1="K_EH_o" variable_2="K_EH_o"/>
<map_variables variable_1="K_EH_i" variable_2="K_EH_i"/>
<map_variables variable_1="K_ENH4_o" variable_2="K_ENH4_o"/>
<map_variables variable_1="K_ENH4_i" variable_2="K_ENH4_i"/>
<map_variables variable_1="k_Re1" variable_2="k_Re1"/>
<map_variables variable_1="k_Re2" variable_2="k_Re2"/>
<map_variables variable_1="k_Re3" variable_2="k_Re3"/>
<map_variables variable_1="k_Re4" variable_2="k_Re4"/>
<map_variables variable_1="k_Re5" variable_2="k_Re5"/>
<map_variables variable_1="k_Re6" variable_2="k_Re6"/>
<map_variables variable_1="k_Re7" variable_2="k_Re7"/>
<map_variables variable_1="k_Re8" variable_2="k_Re8"/>
<map_variables variable_1="k_Re9" variable_2="k_Re9"/>
</connection>
<connection>
<map_components component_1="main" component_2="environment"/>
<map_variables variable_1="t" variable_2="time"/>
</connection>
</model>