Location: Intracellular pH regulation @ 920a714dbe07 / models / modules / Boron_acid_BG_V3_EA.cellml
- Author:
- Weiwei Ai <wai484@aucklanduni.ac.nz>
- Date:
- 2024-02-27 17:21:53+13:00
- Desc:
- Add H buffering in the acid BG model
- Permanent Source URI:
- https://staging.physiomeproject.org/workspace/b61/rawfile/920a714dbe070a8ab1215d82e465d4aaa7216a0a/models/modules/Boron_acid_BG_V3_EA.cellml
<?xml version='1.0' encoding='UTF-8'?>
<model name="BG51" xmlns="http://www.cellml.org/cellml/1.1#" xmlns:cellml="http://www.cellml.org/cellml/1.1#">
<!-- Intracellular pH regulation-->
<units name="dim">
<unit units="dimensionless"/>
</units>
<units name="per_s">
<unit exponent="-1" units="second"/>
</units>
<units name="mol_per_s">
<unit units="mole"/>
<unit exponent="-1" units="second"/>
</units>
<units name="per_mol">
<unit exponent="-1" units="mole"/>
</units>
<units name="per_mol2">
<unit exponent="-2" units="mole"/>
</units>
<units name="C_per_mol">
<unit units="coulomb"/>
<unit exponent="-1" units="mole"/>
</units>
<units name="J_per_mol">
<unit units="joule"/>
<unit exponent="-1" units="mole"/>
</units>
<units name="J_per_C">
<unit units="joule"/>
<unit exponent="-1" units="coulomb"/>
</units>
<units name="J_per_s">
<unit units="joule"/>
<unit exponent="-1" units="second"/>
</units>
<component name="main">
<variable name="t" units="second"/>
<variable initial_value="9.64853321e4" name="F" units="C_per_mol"/>
<variable initial_value="2462.1911" name="RT" units="J_per_mol"/>
<variable initial_value="-0.057" name="u_e_m" units="J_per_C"/>
<variable name="epsilon" units="dim"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>epsilon</ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<ci>F</ci>
<ci>u_e_m</ci>
</apply>
<ci>RT</ci>
</apply>
</apply>
</apply>
</math>
<!-- state variables-->
<variable initial_value="0.00765730077645094" name="q_CO2_i" units="mole"/>
<variable name="q_CO2_o" units="mole"/>
<variable initial_value="0.192342699223549" name="q_HCO3_i" units="mole"/>
<variable name="q_HCO3_o" units="mole"/>
<variable initial_value="3.981071705534970e-05" name="q_H_i" units="mole"/>
<variable initial_value="1.995262314968879e-05" name="q_H_o" units="mole"/>
<variable initial_value="1e-8" name="K_CO2_o" units="per_mol"/>
<variable initial_value="1e-8" name="K_CO2_i" units="per_mol"/>
<variable initial_value="1e-5" name="K_HCO3_o" units="per_mol"/>
<variable initial_value="1e-5" name="K_HCO3_i" units="per_mol"/>
<variable initial_value="1" name="K_H_o" units="per_mol"/>
<variable initial_value="1" name="K_H_i" units="per_mol"/>
<variable name="Q_CO2_o" units="dim"/>
<variable name="Q_CO2_i" units="dim"/>
<variable name="Q_HCO3_o" units="dim"/>
<variable name="Q_HCO3_i" units="dim"/>
<variable name="Q_H_o" units="dim"/>
<variable name="Q_H_i" units="dim"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>Q_CO2_o</ci>
<apply>
<times/>
<ci>K_CO2_o</ci>
<ci>q_CO2_o</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>Q_CO2_i</ci>
<apply>
<times/>
<ci>K_CO2_i</ci>
<ci>q_CO2_i</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>Q_HCO3_o</ci>
<apply>
<times/>
<ci>K_HCO3_o</ci>
<ci>q_HCO3_o</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>Q_HCO3_i</ci>
<apply>
<times/>
<ci>K_HCO3_i</ci>
<ci>q_HCO3_i</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>Q_H_o</ci>
<apply>
<times/>
<ci>K_H_o</ci>
<ci>q_H_o</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>Q_H_i</ci>
<apply>
<times/>
<ci>K_H_i</ci>
<ci>q_H_i</ci>
</apply>
</apply>
<!-- step change in external CO2-->
<apply>
<eq/>
<ci>q_CO2_o</ci>
<piecewise>
<piece>
<cn cellml:units="mole">0.00765730077645094</cn>
<apply>
<lt/>
<ci>t</ci>
<cn cellml:units="second">100</cn>
</apply>
</piece>
<piece>
<cn cellml:units="mole">1.1877</cn>
<apply>
<lt/>
<ci>t</ci>
<cn cellml:units="second">2800</cn>
</apply>
</piece>
<otherwise>
<cn cellml:units="mole">0.00765730077645094</cn>
</otherwise>
</piecewise>
</apply>
</math>
<variable name="v_CO2_m" units="mol_per_s"/>
<variable initial_value="1.490e+07" name="v_CO2_max" units="mol_per_s"/>
<variable initial_value="1.837e-01" name="gamma_CO2" units="dim"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v_CO2_m</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>v_CO2_max</ci>
<apply>
<minus/>
<ci>Q_CO2_o</ci>
<ci>Q_CO2_i</ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dim">2</cn>
<ci>gamma_CO2</ci>
</apply>
<apply>
<plus/>
<cn cellml:units="dim">1</cn>
<ci>gamma_CO2</ci>
</apply>
</apply>
<ci>Q_CO2_o</ci>
<ci>Q_CO2_i</ci>
<apply>
<times/>
<apply>
<divide/>
<cn cellml:units="dim">2</cn>
<apply>
<plus/>
<cn cellml:units="dim">1</cn>
<ci>gamma_CO2</ci>
</apply>
</apply>
<ci>Q_CO2_o</ci>
<ci>Q_CO2_i</ci>
</apply>
</apply>
</apply>
</apply>
</math>
<variable name="v_HCO3_m" units="mol_per_s"/>
<variable initial_value="10.01" name="kappa_HCO3_m" units="mol_per_s"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v_HCO3_m</ci>
<apply>
<times/>
<ci>kappa_HCO3_m</ci>
<apply>
<minus/>
<apply>
<times/>
<ci>Q_HCO3_o</ci>
<ci>epsilon</ci>
</apply>
<ci>Q_HCO3_i</ci>
</apply>
</apply>
</apply>
</math>
<variable name="v_H_m" units="mol_per_s"/>
<variable initial_value="10" name="kappa_H_m" units="mol_per_s"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v_H_m</ci>
<apply>
<times/>
<ci>kappa_H_m</ci>
<apply>
<minus/>
<ci>Q_H_o</ci>
<apply>
<times/>
<ci>Q_H_i</ci>
<ci>epsilon</ci>
</apply>
</apply>
</apply>
</apply>
</math>
<variable name="v_H2CO3_o" units="mol_per_s"/>
<variable name="v_H2CO3_i" units="mol_per_s"/>
<variable initial_value="1e8" name="kappa_H2CO3" units="mol_per_s"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v_H2CO3_o</ci>
<apply>
<times/>
<ci>kappa_H2CO3</ci>
<apply>
<minus/>
<ci>Q_CO2_o</ci>
<apply>
<times/>
<ci>Q_HCO3_o</ci>
<ci>Q_H_o</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v_H2CO3_i</ci>
<apply>
<times/>
<ci>kappa_H2CO3</ci>
<apply>
<minus/>
<ci>Q_CO2_i</ci>
<apply>
<times/>
<ci>Q_HCO3_i</ci>
<ci>Q_H_i</ci>
</apply>
</apply>
</apply>
</apply>
<!-- conservation equations-->
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_CO2_i</ci>
</apply>
<apply>
<minus/>
<ci>v_CO2_m</ci>
<ci>v_H2CO3_i</ci>
</apply>
</apply>
<!-- ode(q_HCO3_o, t) = -v_HCO3_m+v_H2CO3_o;-->
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_HCO3_i</ci>
</apply>
<apply>
<plus/>
<ci>v_HCO3_m</ci>
<ci>v_H2CO3_i</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>q_HCO3_o</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>K_HA</ci>
<ci>q_CO2_o</ci>
</apply>
<ci>q_H_o</ci>
</apply>
</apply>
<!-- ode(q_H_o, t) = -v_H_m+v_H2CO3_o;-->
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_H_i</ci>
</apply>
<apply>
<plus/>
<ci>v_H_m</ci>
<ci>v_H2CO3_i</ci>
</apply>
</apply>
</math>
<variable name="pH_i" units="dim"/>
<variable name="pH_o" units="dim"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>pH_i</ci>
<apply>
<minus/>
<apply>
<log/>
<apply>
<times/>
<cn cellml:units="per_mol" type="e-notation">1<sep/>-3</cn>
<ci>q_H_i</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>pH_o</ci>
<apply>
<minus/>
<apply>
<log/>
<apply>
<times/>
<cn cellml:units="per_mol" type="e-notation">1<sep/>-3</cn>
<ci>q_H_o</ci>
</apply>
</apply>
</apply>
</apply>
</math>
<variable name="alpha" units="dimensionless"/>
<variable initial_value="1e-3" name="K_HA" units="mole"/>
<variable initial_value="1" name="q_TA_i" units="mole"/>
<variable initial_value="5.011872336272725e-05" name="q_H_Lim" units="mole"/>
<variable name="pH_Lim" units="dim"/>
<variable initial_value="26" name="beta" units="mole"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>pH_Lim</ci>
<apply>
<minus/>
<apply>
<log/>
<apply>
<times/>
<cn cellml:units="per_mol" type="e-notation">1<sep/>-3</cn>
<ci>q_H_Lim</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_TA_i</ci>
</apply>
<apply>
<plus/>
<ci>v_CO2_m</ci>
<ci>v_HCO3_m</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>alpha</ci>
<apply>
<divide/>
<ci>q_H_i</ci>
<apply>
<plus/>
<ci>q_H_i</ci>
<ci>K_HA</ci>
</apply>
</apply>
</apply>
</math>
<!-- Power-->
<variable name="PC_CO2_i" units="J_per_s"/>
<variable name="PC_HCO3_i" units="J_per_s"/>
<variable name="PC_H_i" units="J_per_s"/>
<variable name="PC_CO2_o" units="J_per_s"/>
<variable name="PC_HCO3_o" units="J_per_s"/>
<variable name="PC_H_o" units="J_per_s"/>
<variable name="PRe_CO2_m" units="J_per_s"/>
<variable name="PRe_HCO3_m" units="J_per_s"/>
<variable name="PRe_H_m" units="J_per_s"/>
<variable name="PRe_HCO3_i" units="J_per_s"/>
<variable name="P_um" units="J_per_s"/>
<variable name="P_supply" units="J_per_s"/>
<variable name="P_absorb" units="J_per_s"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>PC_CO2_o</ci>
<apply>
<times/>
<apply>
<minus/>
<ci>RT</ci>
</apply>
<apply>
<ln/>
<ci>Q_CO2_o</ci>
</apply>
<ci>v_CO2_m</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>PC_CO2_i</ci>
<apply>
<times/>
<ci>RT</ci>
<apply>
<ln/>
<ci>Q_CO2_i</ci>
</apply>
<apply>
<minus/>
<ci>v_CO2_m</ci>
<ci>v_H2CO3_i</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>PC_HCO3_o</ci>
<apply>
<times/>
<apply>
<minus/>
<ci>RT</ci>
</apply>
<apply>
<ln/>
<ci>Q_HCO3_o</ci>
</apply>
<ci>v_HCO3_m</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>PC_HCO3_i</ci>
<apply>
<times/>
<ci>RT</ci>
<apply>
<ln/>
<ci>Q_HCO3_i</ci>
</apply>
<apply>
<plus/>
<ci>v_HCO3_m</ci>
<ci>v_H2CO3_i</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>PC_H_o</ci>
<apply>
<times/>
<apply>
<minus/>
<ci>RT</ci>
</apply>
<apply>
<ln/>
<ci>Q_H_o</ci>
</apply>
<ci>v_H_m</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>PC_H_i</ci>
<apply>
<times/>
<ci>RT</ci>
<apply>
<ln/>
<ci>Q_H_i</ci>
</apply>
<apply>
<plus/>
<ci>v_H_m</ci>
<ci>v_H2CO3_i</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>PRe_CO2_m</ci>
<apply>
<times/>
<apply>
<minus/>
<apply>
<times/>
<ci>RT</ci>
<apply>
<ln/>
<ci>Q_CO2_o</ci>
</apply>
</apply>
<apply>
<times/>
<ci>RT</ci>
<apply>
<ln/>
<ci>Q_CO2_i</ci>
</apply>
</apply>
</apply>
<ci>v_CO2_m</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>PRe_HCO3_m</ci>
<apply>
<times/>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<ci>RT</ci>
<apply>
<ln/>
<ci>Q_HCO3_o</ci>
</apply>
</apply>
<apply>
<times/>
<ci>F</ci>
<ci>u_e_m</ci>
</apply>
</apply>
<apply>
<times/>
<ci>RT</ci>
<apply>
<ln/>
<ci>Q_HCO3_i</ci>
</apply>
</apply>
</apply>
<ci>v_HCO3_m</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>PRe_H_m</ci>
<apply>
<times/>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<times/>
<ci>RT</ci>
<apply>
<ln/>
<ci>Q_H_o</ci>
</apply>
</apply>
<apply>
<times/>
<ci>F</ci>
<ci>u_e_m</ci>
</apply>
</apply>
<apply>
<times/>
<ci>RT</ci>
<apply>
<ln/>
<ci>Q_H_i</ci>
</apply>
</apply>
</apply>
<ci>v_H_m</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>P_um</ci>
<apply>
<minus/>
<apply>
<times/>
<ci>F</ci>
<ci>u_e_m</ci>
<ci>v_H_m</ci>
</apply>
<apply>
<times/>
<ci>F</ci>
<ci>u_e_m</ci>
<ci>v_HCO3_m</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>PRe_HCO3_i</ci>
<apply>
<times/>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<times/>
<ci>RT</ci>
<apply>
<ln/>
<ci>Q_CO2_i</ci>
</apply>
</apply>
<apply>
<times/>
<ci>RT</ci>
<apply>
<ln/>
<ci>Q_HCO3_i</ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci>RT</ci>
<apply>
<ln/>
<ci>Q_H_i</ci>
</apply>
</apply>
</apply>
<ci>v_H2CO3_i</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>P_supply</ci>
<apply>
<plus/>
<ci>PC_CO2_o</ci>
<ci>PC_HCO3_o</ci>
<ci>PC_H_o</ci>
<ci>P_um</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>P_absorb</ci>
<apply>
<plus/>
<ci>PC_CO2_i</ci>
<ci>PC_HCO3_i</ci>
<ci>PC_H_i</ci>
<ci>PRe_CO2_m</ci>
<ci>PRe_HCO3_m</ci>
<ci>PRe_H_m</ci>
<ci>PRe_HCO3_i</ci>
</apply>
</apply>
</math>
<!-- Activity-->
<variable initial_value="0" name="AC_CO2_i" units="joule"/>
<variable initial_value="0" name="AC_HCO3_i" units="joule"/>
<variable initial_value="0" name="AC_H_i" units="joule"/>
<variable initial_value="0" name="AC_CO2_o" units="joule"/>
<variable initial_value="0" name="AC_HCO3_o" units="joule"/>
<variable initial_value="0" name="AC_H_o" units="joule"/>
<variable initial_value="0" name="ARe_CO2_m" units="joule"/>
<variable initial_value="0" name="ARe_HCO3_m" units="joule"/>
<variable initial_value="0" name="ARe_H_m" units="joule"/>
<variable initial_value="0" name="ARe_HCO3_i" units="joule"/>
<variable initial_value="0" name="A_um" units="joule"/>
<variable initial_value="0" name="E_supply" units="joule"/>
<variable initial_value="0" name="E_absorb" units="joule"/>
<variable initial_value="0" name="A_supply" units="joule"/>
<variable initial_value="0" name="A_absorb" units="joule"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>AC_CO2_o</ci>
</apply>
<apply>
<abs/>
<ci>PC_CO2_o</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>AC_CO2_i</ci>
</apply>
<apply>
<abs/>
<ci>PC_CO2_i</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>AC_HCO3_o</ci>
</apply>
<apply>
<abs/>
<ci>PC_HCO3_o</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>AC_HCO3_i</ci>
</apply>
<apply>
<abs/>
<ci>PC_HCO3_i</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>AC_H_o</ci>
</apply>
<apply>
<abs/>
<ci>PC_H_o</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>AC_H_i</ci>
</apply>
<apply>
<abs/>
<ci>PC_H_i</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>ARe_CO2_m</ci>
</apply>
<apply>
<abs/>
<ci>PRe_CO2_m</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>ARe_HCO3_m</ci>
</apply>
<apply>
<abs/>
<ci>PRe_HCO3_m</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>ARe_H_m</ci>
</apply>
<apply>
<abs/>
<ci>PRe_H_m</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>A_um</ci>
</apply>
<apply>
<abs/>
<ci>P_um</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>ARe_HCO3_i</ci>
</apply>
<apply>
<abs/>
<ci>PRe_HCO3_i</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>E_supply</ci>
</apply>
<ci>P_supply</ci>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>E_absorb</ci>
</apply>
<ci>P_absorb</ci>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>A_supply</ci>
</apply>
<apply>
<abs/>
<ci>P_supply</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>A_absorb</ci>
</apply>
<apply>
<abs/>
<ci>P_absorb</ci>
</apply>
</apply>
</math>
</component>
</model>