Location: A model of intracellular pH control @ 2704cb340f8a / Boron CO2 expts - original eqns - SS--RO--PH.cellml
- Author:
- David Nickerson <nickerso@users.sourceforge.net>
- Date:
- 2017-07-28 11:51:41+12:00
- Desc:
- Adding initial CellML model and SED-ML, received from Peter Hunter
- Permanent Source URI:
- https://models.physiomeproject.org/workspace/4a3/rawfile/2704cb340f8a72ba2b1dd87dd2e668cccc4f3519/Boron CO2 expts - original eqns - SS--RO--PH.cellml
<?xml version='1.0'?>
<model name="Boron_CO2_expts_original_eqns" xmlns="http://www.cellml.org/cellml/1.1#" xmlns:cellml="http://www.cellml.org/cellml/1.1#">
<units name="per_s">
<unit exponent="-1" units="second"/>
</units>
<units name="per_m">
<unit exponent="-1" units="metre"/>
</units>
<units name="m_per_s">
<unit units="metre"/>
<unit exponent="-1" units="second"/>
</units>
<units name="mol_per_m3">
<unit units="mole"/>
<unit exponent="-3" units="metre"/>
</units>
<units name="mol_per_m2_s">
<unit exponent="1" units="mole"/>
<unit exponent="-2" units="metre"/>
<unit exponent="-1" units="second"/>
</units>
<units name="mol_per_m3_s">
<unit exponent="1" units="mole"/>
<unit exponent="-3" units="metre"/>
<unit exponent="-1" units="second"/>
</units>
<units name="J_per_C">
<unit units="joule"/>
<unit exponent="-1" units="coulomb"/>
</units>
<units name="m3_per_mol">
<unit exponent="3" units="metre"/>
<unit exponent="-1" units="mole"/>
</units>
<component name="main">
<variable name="t" units="second"/>
<variable initial_value="-0.057" name="V_m" units="J_per_C"/>
<variable initial_value="0.0256796" name="RTF" units="J_per_C"/>
<variable name="epsilon" units="dimensionless"/>
<variable initial_value="0.0" name="TA_i" units="mol_per_m3"/>
<variable name="CO2_o" units="mol_per_m3"/>
<variable name="CO2_i" units="mol_per_m3"/>
<variable name="HCO3_i" units="mol_per_m3"/>
<variable name="HCO3_o" units="mol_per_m3"/>
<variable initial_value="3.981071705534970e-05" name="H_i" units="mol_per_m3"/>
<variable initial_value="1.995262314968879e-05" name="H_o" units="mol_per_m3"/>
<variable initial_value="3.981071705534970e-05" name="H_Lim" units="mol_per_m3"/>
<!--Note: 5.011872336272725e-05 (7.3); 3.981071705534970e-05 (7.4)-->
<variable name="M_CO2" units="mol_per_m2_s"/>
<variable name="M_HCO3" units="mol_per_m2_s"/>
<variable name="M_H" units="mol_per_m2_s"/>
<variable name="pH_i" units="dimensionless"/>
<variable name="pH_o" units="dimensionless"/>
<variable name="pH_Lim" units="dimensionless"/>
<variable initial_value="6e-5" name="P_CO2" units="m_per_s"/>
<variable initial_value="5e-9" name="P_HCO3" units="m_per_s"/>
<variable initial_value="0.0375" name="k" units="m_per_s"/>
<variable initial_value="1e-3" name="K_A" units="mol_per_m3"/>
<variable initial_value="8000" name="rho" units="per_m"/>
<variable name="alpha_i" units="dimensionless"/>
<variable initial_value="-26" name="beta" units="mol_per_m3"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>CO2_o</ci>
<piecewise>
<piece>
<cn cellml:units="mol_per_m3">0</cn>
<apply>
<lt/>
<ci>t</ci>
<cn cellml:units="second">100</cn>
</apply>
</piece>
<piece>
<cn cellml:units="mol_per_m3">1.1877</cn>
<apply>
<lt/>
<ci>t</ci>
<cn cellml:units="second">2800</cn>
</apply>
</piece>
<otherwise>
<cn cellml:units="mol_per_m3">0</cn>
</otherwise>
</piecewise>
</apply>
<apply>
<eq/>
<ci>HCO3_o</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>K_A</ci>
<ci>CO2_o</ci>
</apply>
<ci>H_o</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>epsilon</ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci>V_m</ci>
</apply>
<ci>RTF</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>M_CO2</ci>
<apply>
<times/>
<ci>P_CO2</ci>
<apply>
<minus/>
<ci>CO2_o</ci>
<ci>CO2_i</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>M_HCO3</ci>
<apply>
<divide/>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci>P_HCO3</ci>
<ci>V_m</ci>
</apply>
<ci>RTF</ci>
</apply>
<apply>
<minus/>
<ci>HCO3_o</ci>
<apply>
<times/>
<ci>HCO3_i</ci>
<ci>epsilon</ci>
</apply>
</apply>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<ci>epsilon</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>pH_Lim</ci>
<apply>
<minus/>
<apply>
<log/>
<apply>
<times/>
<cn cellml:units="m3_per_mol" type="e-notation">1<sep/>-3</cn>
<ci>H_Lim</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>M_H</ci>
<piecewise>
<piece>
<apply>
<times/>
<ci>k</ci>
<apply>
<minus/>
<ci>H_i</ci>
<ci>H_Lim</ci>
</apply>
</apply>
<apply>
<lt/>
<ci>pH_i</ci>
<ci>pH_Lim</ci>
</apply>
</piece>
<otherwise>
<cn cellml:units="mol_per_m2_s">0</cn>
</otherwise>
</piecewise>
</apply>
<apply>
<eq/>
<ci>pH_i</ci>
<apply>
<minus/>
<apply>
<log/>
<apply>
<times/>
<cn cellml:units="m3_per_mol" type="e-notation">1<sep/>-3</cn>
<ci>H_i</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>pH_o</ci>
<apply>
<minus/>
<apply>
<log/>
<apply>
<times/>
<cn cellml:units="m3_per_mol" type="e-notation">1<sep/>-3</cn>
<ci>H_o</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>alpha_i</ci>
<apply>
<divide/>
<ci>H_i</ci>
<apply>
<plus/>
<ci>H_i</ci>
<ci>K_A</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>CO2_i</ci>
<apply>
<times/>
<ci>alpha_i</ci>
<ci>TA_i</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>HCO3_i</ci>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<ci>alpha_i</ci>
</apply>
<ci>TA_i</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>TA_i</ci>
</apply>
<apply>
<times/>
<ci>rho</ci>
<apply>
<plus/>
<ci>M_CO2</ci>
<ci>M_HCO3</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>H_i</ci>
</apply>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">2.303</cn>
</apply>
<ci>H_i</ci>
</apply>
<ci>beta</ci>
</apply>
<ci>rho</ci>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<ci>alpha_i</ci>
</apply>
<ci>M_CO2</ci>
</apply>
<apply>
<times/>
<ci>alpha_i</ci>
<ci>M_HCO3</ci>
</apply>
</apply>
<ci>M_H</ci>
</apply>
</apply>
</apply>
</math>
</component>
</model>