- Author:
- Nima <nafs080@aucklanduni.ac.nz>
- Date:
- 2018-04-11 10:36:00+12:00
- Desc:
- Some Modifications in Modular Version
- Permanent Source URI:
- http://models.cellml.org/workspace/572/rawfile/9521df38ecbed3dc215d4f5501b9674b425087d3/AE1_flux.cellml
<?xml version='1.0'?>
<!--Link in Exposure: https://models.physiomeproject.org/e/2ff/Weinstein_2000_AE1.cellml/view
Original Paper: Weinstein, Alan M. "A mathematical model of the outer medullary collecting duct of the rat." American Journal of Physiology-Renal Physiology 279.1 (2000): F24-F45.-->
<model name="AE1_flux" xmlns="http://www.cellml.org/cellml/1.1#" xmlns:cellml="http://www.cellml.org/cellml/1.1#">
<component name="AE1">
<variable name="A_Apical" public_interface="in" units="m2"/>
<variable name="V_cell" public_interface="in" units="m3"/>
<variable name="q_HCO3_i" public_interface="in" units="M"/>
<variable name="q_HCO3_m" public_interface="in" units="M"/>
<variable name="q_Cl_i" public_interface="in" units="M"/>
<variable name="q_Cl_m" public_interface="in" units="M"/>
<variable name="J_AE1_HCO3" public_interface="out" units="umol_per_s"/>
<variable name="J_AE1_Cl" public_interface="out" units="umol_per_s"/>
<variable name="I_AE1_HCO3" public_interface="out" units="uA"/>
<variable name="I_AE1_Cl" public_interface="out" units="uA"/>
<variable initial_value="198e-3" name="K_HCO3_m" units="M"/>
<variable initial_value="198e-3" name="K_HCO3_i" units="M"/>
<variable initial_value="50e-3" name="K_Cl_s" units="M"/>
<variable initial_value="50e-3" name="K_Cl_i" units="M"/>
<variable initial_value="1247" name="P_HCO3_m" units="per_second"/>
<variable initial_value="135" name="P_HCO3_i" units="per_second"/>
<variable initial_value="562" name="P_Cl_s" units="per_second"/>
<variable initial_value="61" name="P_Cl_i" units="per_second"/>
<variable name="beta_ext" units="dimensionless"/>
<variable name="beta_int" units="dimensionless"/>
<variable name="gamma_ext" units="dimensionless"/>
<variable name="gamma_int" units="dimensionless"/>
<variable name="sigma" units="per_second"/>
<variable initial_value="2e-4" name="x_Tmax" units="M"/>
<variable initial_value="172e-3" name="K_I" units="M"/>
<variable name="x_T" units="M"/>
<variable name="F" public_interface="in" units="C_per_mol"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>x_T</ci>
<apply>
<divide/>
<ci>x_Tmax</ci>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<ci>q_HCO3_i</ci>
<ci>K_I</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>beta_ext</ci>
<apply>
<divide/>
<ci>q_HCO3_m</ci>
<ci>K_HCO3_m</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>beta_int</ci>
<apply>
<divide/>
<ci>q_HCO3_i</ci>
<ci>K_HCO3_i</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>gamma_ext</ci>
<apply>
<divide/>
<ci>q_Cl_m</ci>
<ci>K_Cl_s</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>gamma_int</ci>
<apply>
<divide/>
<ci>q_Cl_i</ci>
<ci>K_Cl_i</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>sigma</ci>
<apply>
<plus/>
<apply>
<times/>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<ci>beta_ext</ci>
<ci>gamma_ext</ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci>P_HCO3_i</ci>
<ci>beta_int</ci>
</apply>
<apply>
<times/>
<ci>P_Cl_i</ci>
<ci>gamma_int</ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<ci>beta_int</ci>
<ci>gamma_int</ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci>P_HCO3_m</ci>
<ci>beta_ext</ci>
</apply>
<apply>
<times/>
<ci>P_Cl_s</ci>
<ci>gamma_ext</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<!--1e9 is for unit conversion-->
<apply>
<eq/>
<ci>J_AE1_HCO3</ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless" type="e-notation">1<sep/>9</cn>
<ci>V_cell</ci>
<ci>x_Tmax</ci>
</apply>
<ci>sigma</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>P_HCO3_i</ci>
<ci>beta_int</ci>
<ci>P_Cl_s</ci>
<ci>gamma_ext</ci>
</apply>
<apply>
<times/>
<ci>P_HCO3_m</ci>
<ci>beta_ext</ci>
<ci>P_Cl_i</ci>
<ci>gamma_int</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>J_AE1_Cl</ci>
<ci>J_AE1_HCO3</ci>
</apply>
<apply>
<eq/>
<ci>I_AE1_HCO3</ci>
<apply>
<times/>
<ci>J_AE1_HCO3</ci>
<ci>F</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>I_AE1_Cl</ci>
<apply>
<times/>
<ci>J_AE1_Cl</ci>
<ci>F</ci>
</apply>
</apply>
</math>
</component>
</model>
