Rendering of the source text
<?xml version='1.0' encoding='UTF-8'?>
<model name="my_model" xmlns="http://www.cellml.org/cellml/1.1#" xmlns:cellml="http://www.cellml.org/cellml/1.1#">
<!-- Simple model of epithelial cell with sodium, glucose and water transport-->
<units name="dim">
<unit units="dimensionless"/>
</units>
<units name="per_s">
<unit exponent="-1" units="second"/>
</units>
<units name="L_per_s">
<unit units="litre"/>
<unit exponent="-1" units="second"/>
</units>
<units name="kPa">
<unit units="joule"/>
<unit exponent="-1" units="litre"/>
</units>
<units name="kPa_s_per_L">
<unit units="kPa"/>
<unit units="second"/>
<unit exponent="-1" units="litre"/>
</units>
<units name="kPa_per_L">
<unit units="kPa"/>
<unit exponent="-1" units="litre"/>
</units>
<units name="L_per_s_per_kPa">
<unit units="L_per_s"/>
<unit exponent="-1" units="kPa"/>
</units>
<units name="per_mol">
<unit exponent="-1" units="mole"/>
</units>
<units name="mM">
<unit prefix="milli" units="mole"/>
<unit exponent="-1" units="litre"/>
</units>
<units name="mM2">
<unit exponent="2" units="mM"/>
</units>
<units name="per_mM">
<unit exponent="-1" units="mM"/>
</units>
<units name="millimols_per_mol">
<unit prefix="milli" units="mole"/>
<unit exponent="-1" units="mole"/>
</units>
<units name="mM_per_mol">
<unit units="mM"/>
<unit exponent="-1" units="mole"/>
</units>
<units name="mol_per_s">
<unit units="mole"/>
<unit exponent="-1" units="second"/>
</units>
<units name="mol_per_L">
<unit units="mole"/>
<unit exponent="-1" units="litre"/>
</units>
<units name="L_per_mol">
<unit units="litre"/>
<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="C_per_mol">
<unit units="coulomb"/>
<unit exponent="-1" units="mole"/>
</units>
<units name="C_per_J_per_s">
<unit units="coulomb"/>
<unit exponent="-1" units="joule"/>
<unit exponent="-1" units="second"/>
</units>
<units name="C2_per_J">
<unit exponent="2" units="coulomb"/>
<unit exponent="-1" units="joule"/>
</units>
<units name="per_s_per_V">
<unit units="per_s"/>
<unit exponent="-1" units="volt"/>
</units>
<component name="main">
<variable name="t" units="second"/>
<variable initial_value="0.1" name="pulse_time" units="second"/>
<variable initial_value="2.5e3" name="RT" units="J_per_mol"/>
<variable initial_value="0.965e5" name="F" units="C_per_mol"/>
<!-- ODEs for water storage -->
<variable initial_value="1" name="q_w_gut" units="litre"/>
<variable initial_value="1" name="q_w_epi" units="litre"/>
<variable initial_value="1" name="q_w_cap" units="litre"/>
<!-- ode(q_w_gut, t) = -v_w_epiApex;
ode(q_w_epi, t) = v_w_epiApex-v_w_epiBase;
ode(q_w_cap, t) = v_w_epiBase;-->
<variable name="q_w_tot" units="litre"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>q_w_tot</ci>
<apply>
<plus/>
<ci>q_w_gut</ci>
<ci>q_w_epi</ci>
<ci>q_w_cap</ci>
</apply>
</apply>
</math>
<!-- Sodium ion transport -->
<variable initial_value="0.1" name="q_Na_gut" units="mole"/>
<variable initial_value="0.001" name="q_Na_epi" units="mole"/>
<variable name="q_Na_cap" units="mole"/>
<variable initial_value="0.140" name="q_Na_cap_init" units="mole"/>
<variable initial_value="1.0" name="q_Na_cap_scale" units="dimensionless"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_Na_gut</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dim">2</cn>
</apply>
<ci>v_SGLT1</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_Na_epi</ci>
</apply>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<times/>
<cn cellml:units="dim">2</cn>
<ci>v_SGLT1</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dim">3</cn>
<ci>v_NKE</ci>
</apply>
</apply>
<ci>v_NKCC1</ci>
<ci>v_Na</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>q_Na_cap</ci>
<piecewise>
<piece>
<apply>
<times/>
<ci>q_Na_cap_init</ci>
<ci>q_Na_cap_scale</ci>
</apply>
<apply>
<gt/>
<ci>t</ci>
<ci>pulse_time</ci>
</apply>
</piece>
<otherwise>
<ci>q_Na_cap_init</ci>
</otherwise>
</piecewise>
</apply>
</math>
<!-- ode(q_Na_cap, t) = 3{dim}*v_NKE;-->
<variable name="c_Na_gut" units="mM"/>
<variable name="c_Na_epi" units="mM"/>
<variable name="c_Na_cap" units="mM"/>
<variable initial_value="1.e3" name="K_mm" units="millimols_per_mol"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>c_Na_gut</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>q_Na_gut</ci>
<ci>K_mm</ci>
</apply>
<ci>q_w_gut</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>c_Na_epi</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>q_Na_epi</ci>
<ci>K_mm</ci>
</apply>
<ci>q_w_epi</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>c_Na_cap</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>q_Na_cap</ci>
<ci>K_mm</ci>
</apply>
<ci>q_w_cap</ci>
</apply>
</apply>
</math>
<variable name="q_Na_tot" units="mole"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>q_Na_tot</ci>
<apply>
<plus/>
<ci>q_Na_gut</ci>
<ci>q_Na_epi</ci>
<ci>q_Na_cap</ci>
</apply>
</apply>
</math>
<!-- Potassium ion transport-->
<variable initial_value="0.130" name="q_K_epi" units="mole"/>
<variable initial_value="0.004" name="q_K_cap" units="mole"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_K_epi</ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<times/>
<cn cellml:units="dim">2</cn>
<ci>v_NKE</ci>
</apply>
<ci>v_K</ci>
</apply>
<ci>v_NKCC1</ci>
</apply>
<ci>v_KCC1</ci>
</apply>
</apply>
</math>
<variable name="c_K_epi" units="mM"/>
<variable name="c_K_cap" units="mM"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>c_K_epi</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>q_K_epi</ci>
<ci>K_mm</ci>
</apply>
<ci>q_w_epi</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>c_K_cap</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>q_K_cap</ci>
<ci>K_mm</ci>
</apply>
<ci>q_w_cap</ci>
</apply>
</apply>
</math>
<!-- Chloride ion transport-->
<variable initial_value="0.001" name="q_Cl_epi" units="mole"/>
<variable initial_value="0.100" name="q_Cl_cap" units="mole"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_Cl_epi</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<cn cellml:units="dim">2</cn>
<ci>v_NKCC1</ci>
</apply>
<ci>v_KCC1</ci>
</apply>
</apply>
</math>
<variable name="c_Cl_epi" units="mM"/>
<variable name="c_Cl_cap" units="mM"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>c_Cl_epi</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>q_Cl_epi</ci>
<ci>K_mm</ci>
</apply>
<ci>q_w_epi</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>c_Cl_cap</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>q_Cl_cap</ci>
<ci>K_mm</ci>
</apply>
<ci>q_w_cap</ci>
</apply>
</apply>
</math>
<!-- Charge balance-->
<variable initial_value="1e-5" name="q_e" units="coulomb"/>
<variable initial_value="-0.08" name="u_ee" units="J_per_C"/>
<variable name="u_e" units="J_per_C"/>
<variable initial_value="5e4" name="C_m" units="C2_per_J"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_e</ci>
</apply>
<apply>
<times/>
<ci>F</ci>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<times/>
<cn cellml:units="dim">2</cn>
<ci>v_SGLT1</ci>
</apply>
<ci>v_NKE</ci>
</apply>
<ci>v_K</ci>
</apply>
<ci>v_Na</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>u_e</ci>
<apply>
<divide/>
<ci>q_e</ci>
<ci>C_m</ci>
</apply>
</apply>
</math>
<!-- Glucose transport (assume glucose is immediately converted to ATP) -->
<variable name="q_Glc_gut" units="mole"/>
<variable initial_value="0.001" name="q_Glc_epi" units="mole"/>
<variable initial_value="0.01" name="q_Glc_cap" units="mole"/>
<variable initial_value="0.01" name="q_Glc_gut_init" units="mole"/>
<variable initial_value="1.0" name="q_Glc_gut_scale" units="dimensionless"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>q_Glc_gut</ci>
<piecewise>
<piece>
<apply>
<times/>
<ci>q_Glc_gut_init</ci>
<ci>q_Glc_gut_scale</ci>
</apply>
<apply>
<gt/>
<ci>t</ci>
<ci>pulse_time</ci>
</apply>
</piece>
<otherwise>
<ci>q_Glc_gut_init</ci>
</otherwise>
</piecewise>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_Glc_epi</ci>
</apply>
<apply>
<minus/>
<apply>
<minus/>
<ci>v_SGLT1</ci>
<ci>v_GLUT2</ci>
</apply>
<ci>v_AM</ci>
</apply>
</apply>
</math>
<variable name="c_Glc_gut" units="mM"/>
<variable name="c_Glc_epi" units="mM"/>
<variable name="c_Glc_cap" units="mM"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>c_Glc_gut</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>q_Glc_gut</ci>
<ci>K_mm</ci>
</apply>
<ci>q_w_gut</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>c_Glc_epi</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>q_Glc_epi</ci>
<ci>K_mm</ci>
</apply>
<ci>q_w_epi</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>c_Glc_cap</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>q_Glc_cap</ci>
<ci>K_mm</ci>
</apply>
<ci>q_w_cap</ci>
</apply>
</apply>
</math>
<!-- Hydraulic pressures (J/L)-->
<variable initial_value="1" name="u_w_gut" units="kPa"/>
<variable name="u_w_epi" units="kPa"/>
<variable initial_value="1" name="u_w_cap" units="kPa"/>
<variable initial_value="1" name="E_w_epi" units="joule"/>
<variable initial_value="0.5" name="U_w_epi" units="litre"/>
<variable initial_value="5" name="L_w_epi" units="litre"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>u_w_epi</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>E_w_epi</ci>
<apply>
<minus/>
<ci>q_w_epi</ci>
<ci>U_w_epi</ci>
</apply>
</apply>
<apply>
<power/>
<apply>
<minus/>
<ci>L_w_epi</ci>
<ci>q_w_epi</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</math>
<!-- Water fluxes (L/s)-->
<variable name="v_w_epiApex" units="L_per_s"/>
<variable name="v_w_epiBase" units="L_per_s"/>
<variable initial_value="1e-4" name="k_w_m" units="L_per_s_per_kPa"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v_w_epiApex</ci>
<apply>
<times/>
<ci>k_w_m</ci>
<apply>
<minus/>
<apply>
<minus/>
<ci>u_w_gut</ci>
<ci>u_w_epi</ci>
</apply>
<apply>
<times/>
<apply>
<divide/>
<ci>RT</ci>
<ci>K_mm</ci>
</apply>
<apply>
<minus/>
<ci>c_Na_gut</ci>
<ci>c_Na_epi</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v_w_epiBase</ci>
<apply>
<times/>
<ci>k_w_m</ci>
<apply>
<minus/>
<apply>
<minus/>
<ci>u_w_epi</ci>
<ci>u_w_cap</ci>
</apply>
<apply>
<times/>
<apply>
<divide/>
<ci>RT</ci>
<ci>K_mm</ci>
</apply>
<apply>
<minus/>
<ci>c_Na_epi</ci>
<ci>c_Na_cap</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
<!-- O2, CO2 & bicarbonate-->
<variable initial_value="9.25" name="c_O2" units="mM"/>
<variable initial_value="1.20" name="c_CO2" units="mM"/>
<variable initial_value="25.0" name="c_HCO3" units="mM"/>
<!-- ATP, ADP, Pi including flux from aerobic metabolism (conversion of 32 ADP & 32 Pi to 32 ATP for each mole of imported glucose)-->
<variable initial_value="0.003" name="q_ATP" units="mole"/>
<variable initial_value="0.0025" name="q_ADP" units="mole"/>
<variable initial_value="0.003" name="q_Pi" units="mole"/>
<variable initial_value="1e-7" name="q_H" units="mole"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_ATP</ci>
</apply>
<apply>
<plus/>
<apply>
<minus/>
<ci>v_NKE</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dim">32</cn>
<ci>v_AM</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_ADP</ci>
</apply>
<apply>
<minus/>
<ci>v_NKE</ci>
<apply>
<times/>
<cn cellml:units="dim">32</cn>
<ci>v_AM</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_Pi</ci>
</apply>
<apply>
<minus/>
<ci>v_NKE</ci>
<apply>
<times/>
<cn cellml:units="dim">32</cn>
<ci>v_AM</ci>
</apply>
</apply>
</apply>
</math>
<variable name="q_adenosine" units="mole"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>q_adenosine</ci>
<apply>
<plus/>
<ci>q_ATP</ci>
<ci>q_ADP</ci>
</apply>
</apply>
</math>
<variable name="c_ATP" units="mM"/>
<variable name="c_ADP" units="mM"/>
<variable name="c_Pi" units="mM"/>
<variable name="c_H" units="mM"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>c_ATP</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>q_ATP</ci>
<ci>K_mm</ci>
</apply>
<ci>q_w_epi</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>c_ADP</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>q_ADP</ci>
<ci>K_mm</ci>
</apply>
<ci>q_w_epi</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>c_Pi</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>q_Pi</ci>
<ci>K_mm</ci>
</apply>
<ci>q_w_epi</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>c_H</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>q_H</ci>
<ci>K_mm</ci>
</apply>
<ci>q_w_epi</ci>
</apply>
</apply>
</math>
<!-- SGLT1 flux (mol/s)-->
<variable initial_value="1e-2" name="kappa_SGLT1" units="mol_per_s"/>
<variable name="v_SGLT1" units="mol_per_s"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v_SGLT1</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>kappa_SGLT1</ci>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<power/>
<apply>
<divide/>
<ci>c_Na_gut</ci>
<ci>c_Na_epi</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>c_Glc_gut</ci>
</apply>
<ci>c_Glc_epi</ci>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dim">2</cn>
<ci>F</ci>
<ci>u_e</ci>
</apply>
<ci>RT</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<apply>
<plus/>
<cn cellml:units="dim">1</cn>
<apply>
<power/>
<apply>
<divide/>
<ci>c_Na_gut</ci>
<cn cellml:units="mM">20</cn>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dim">1</cn>
<apply>
<power/>
<apply>
<divide/>
<ci>c_Na_epi</ci>
<cn cellml:units="mM">100</cn>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
<!-- GLUT2 flux (mol/s)-->
<variable initial_value="1e1" name="kappa_GLUT2" units="mol_per_s"/>
<variable name="v_GLUT2" units="mol_per_s"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v_GLUT2</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>kappa_GLUT2</ci>
<apply>
<minus/>
<apply>
<divide/>
<ci>c_Glc_epi</ci>
<ci>c_Glc_cap</ci>
</apply>
<cn cellml:units="dim">1</cn>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dim">1</cn>
<apply>
<divide/>
<ci>c_Glc_epi</ci>
<cn cellml:units="mM">5</cn>
</apply>
<apply>
<divide/>
<ci>c_Glc_cap</ci>
<cn cellml:units="mM">10</cn>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>c_Glc_epi</ci>
<ci>c_Glc_cap</ci>
</apply>
<cn cellml:units="mM2">100</cn>
</apply>
</apply>
</apply>
</apply>
</math>
<!-- NKE flux (mol/s)-->
<variable initial_value="2e4" name="k_ATP_eq" units="mM2"/>
<variable initial_value="1e2" name="kappa_NKE" units="mol_per_s"/>
<variable name="v_NKE" units="mol_per_s"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v_NKE</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>kappa_NKE</ci>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<power/>
<apply>
<divide/>
<ci>c_Na_epi</ci>
<ci>c_Na_cap</ci>
</apply>
<cn cellml:units="dim">3</cn>
</apply>
<ci>c_ATP</ci>
<ci>k_ATP_eq</ci>
</apply>
<apply>
<times/>
<ci>c_ADP</ci>
<ci>c_Pi</ci>
<ci>c_H</ci>
</apply>
</apply>
<apply>
<times/>
<apply>
<power/>
<apply>
<divide/>
<ci>c_K_epi</ci>
<ci>c_K_cap</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<ci>F</ci>
<ci>u_e</ci>
</apply>
<ci>RT</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<apply>
<plus/>
<cn cellml:units="dim">1</cn>
<apply>
<power/>
<apply>
<divide/>
<ci>c_Na_epi</ci>
<cn cellml:units="mM">1</cn>
</apply>
<cn cellml:units="dim">3</cn>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dim">1</cn>
<apply>
<power/>
<apply>
<divide/>
<ci>c_Na_cap</ci>
<cn cellml:units="mM">100</cn>
</apply>
<cn cellml:units="dim">3</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
<!-- NKCC1 cotransporter flux (mol/s)-->
<variable initial_value="1e-1" name="kappa_NKCC1" units="mol_per_s"/>
<variable name="v_NKCC1" units="mol_per_s"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v_NKCC1</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>kappa_NKCC1</ci>
<apply>
<minus/>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<divide/>
<ci>c_Na_cap</ci>
<ci>c_Na_epi</ci>
</apply>
<ci>c_K_cap</ci>
</apply>
<ci>c_K_epi</ci>
</apply>
<apply>
<power/>
<apply>
<divide/>
<ci>c_Cl_cap</ci>
<ci>c_Cl_epi</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<cn cellml:units="dim">1</cn>
</apply>
</apply>
<apply>
<times/>
<apply>
<plus/>
<cn cellml:units="dim">1</cn>
<apply>
<divide/>
<ci>c_Na_cap</ci>
<cn cellml:units="mM">70</cn>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dim">1</cn>
<apply>
<divide/>
<ci>c_Na_epi</ci>
<cn cellml:units="mM">5</cn>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dim">1</cn>
<apply>
<divide/>
<ci>c_K_cap</ci>
<cn cellml:units="mM">2</cn>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dim">1</cn>
<apply>
<divide/>
<ci>c_K_epi</ci>
<cn cellml:units="mM">60</cn>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dim">1</cn>
<apply>
<power/>
<apply>
<divide/>
<ci>c_Cl_cap</ci>
<cn cellml:units="mM">50</cn>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dim">1</cn>
<apply>
<power/>
<apply>
<divide/>
<ci>c_Cl_epi</ci>
<cn cellml:units="mM">10</cn>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
<!-- v_NKCC1 = 0{mol_per_s};-->
<!-- KCC1 cotransporter flux (mol/s)-->
<variable initial_value="1e-1" name="kappa_KCC1" units="mol_per_s"/>
<variable name="v_KCC1" units="mol_per_s"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v_KCC1</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>kappa_KCC1</ci>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<divide/>
<ci>c_K_epi</ci>
<ci>c_K_cap</ci>
</apply>
<ci>c_Cl_epi</ci>
</apply>
<ci>c_Cl_cap</ci>
</apply>
<cn cellml:units="dim">1</cn>
</apply>
</apply>
<apply>
<times/>
<apply>
<plus/>
<cn cellml:units="dim">1</cn>
<apply>
<divide/>
<ci>c_Cl_cap</ci>
<cn cellml:units="mM">50</cn>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dim">1</cn>
<apply>
<divide/>
<ci>c_K_cap</ci>
<cn cellml:units="mM">2</cn>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dim">1</cn>
<apply>
<divide/>
<ci>c_Cl_epi</ci>
<cn cellml:units="mM">10</cn>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dim">1</cn>
<apply>
<divide/>
<ci>c_K_epi</ci>
<cn cellml:units="mM">60</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
<!-- v_KCC1 = 0 {mol_per_s};-->
<!-- Time-independent K channel flux (mol/s) using GHK-->
<variable initial_value="2e3" name="kappa_K" units="C_per_J_per_s"/>
<variable name="v_K" units="mol_per_s"/>
<variable name="GHKterm" units="J_per_C"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>GHKterm</ci>
<apply>
<divide/>
<ci>u_e</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<ci>F</ci>
<ci>u_e</ci>
</apply>
<ci>RT</ci>
</apply>
</apply>
<cn cellml:units="dim">1</cn>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v_K</ci>
<apply>
<times/>
<ci>kappa_K</ci>
<apply>
<minus/>
<apply>
<times/>
<ci>q_K_epi</ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<ci>F</ci>
<ci>u_e</ci>
</apply>
<ci>RT</ci>
</apply>
</apply>
</apply>
<ci>q_K_cap</ci>
</apply>
<ci>GHKterm</ci>
</apply>
</apply>
</math>
<!-- v_K = 0 {mol_per_s};-->
<!-- Sodium leakage current flux (mol/s) -->
<variable initial_value="0" name="kappa_Na" units="per_s_per_V"/>
<variable name="v_Na" units="mol_per_s"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v_Na</ci>
<apply>
<times/>
<ci>kappa_Na</ci>
<apply>
<minus/>
<ci>q_Na_cap</ci>
<apply>
<times/>
<ci>q_Na_epi</ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<ci>F</ci>
<ci>u_e</ci>
</apply>
<ci>RT</ci>
</apply>
</apply>
</apply>
</apply>
<ci>GHKterm</ci>
</apply>
</apply>
</math>
<!-- v_Na = 0 {mol_per_s};-->
<!-- AM (aerobic metabolism) flux (mol/s)-->
<variable initial_value="1e0" name="k_AM_eq" units="per_mM"/>
<variable initial_value="1e1" name="kappa_AM" units="mol_per_s"/>
<variable name="v_AM" units="mol_per_s"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v_AM</ci>
<apply>
<times/>
<ci>kappa_AM</ci>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<times/>
<ci>k_AM_eq</ci>
<ci>c_Glc_epi</ci>
<ci>c_ADP</ci>
</apply>
<ci>c_ATP</ci>
</apply>
<cn cellml:units="dim">1</cn>
</apply>
</apply>
</apply>
</math>
<!-- Reversal potential for SGLT1-->
<variable name="u_SGLT1_reversal" units="J_per_C"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>u_SGLT1_reversal</ci>
<apply>
<times/>
<apply>
<divide/>
<ci>RT</ci>
<apply>
<times/>
<cn cellml:units="dim">2</cn>
<ci>F</ci>
</apply>
</apply>
<apply>
<ln/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<power/>
<apply>
<divide/>
<ci>c_Na_gut</ci>
<ci>c_Na_epi</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>c_Glc_gut</ci>
</apply>
<ci>c_Glc_epi</ci>
</apply>
</apply>
</apply>
</apply>
</math>
<!-- Reversal potential for K channel-->
<variable name="u_K_reversal" units="J_per_C"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>u_K_reversal</ci>
<apply>
<times/>
<apply>
<divide/>
<ci>RT</ci>
<ci>F</ci>
</apply>
<apply>
<ln/>
<apply>
<divide/>
<ci>c_K_cap</ci>
<ci>c_K_epi</ci>
</apply>
</apply>
</apply>
</apply>
</math>
<!-- Reversal potential for Na channel-->
<variable name="u_Na_reversal" units="J_per_C"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>u_Na_reversal</ci>
<apply>
<times/>
<apply>
<divide/>
<ci>RT</ci>
<ci>F</ci>
</apply>
<apply>
<ln/>
<apply>
<divide/>
<ci>c_Na_cap</ci>
<ci>c_Na_epi</ci>
</apply>
</apply>
</apply>
</apply>
</math>
<!-- Threshold for gut sodium at which SGLT1 flux is zero-->
<variable name="c_Na_gutThreshold" units="mM"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>c_Na_gutThreshold</ci>
<apply>
<times/>
<ci>c_Na_epi</ci>
<apply>
<root/>
<apply>
<divide/>
<ci>c_Glc_epi</ci>
<ci>c_Glc_gut</ci>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<ci>F</ci>
<ci>u_e</ci>
</apply>
<ci>RT</ci>
</apply>
</apply>
</apply>
</apply>
</math>
<!-- Equilbrium value for epithelial sodium at which NKE flux is zero-->
<variable name="c_Na_epiEquilibrium" units="mM"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>c_Na_epiEquilibrium</ci>
<apply>
<times/>
<ci>c_Na_cap</ci>
<apply>
<power/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<divide/>
<ci>c_ADP</ci>
<ci>c_ATP</ci>
</apply>
<ci>c_Pi</ci>
<ci>c_H</ci>
</apply>
<ci>k_ATP_eq</ci>
</apply>
<cn cellml:units="dim">0.33334</cn>
</apply>
<apply>
<power/>
<apply>
<divide/>
<ci>c_K_epi</ci>
<ci>c_K_cap</ci>
</apply>
<cn cellml:units="dim">0.66667</cn>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<ci>F</ci>
<ci>u_e</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dim">3</cn>
<ci>RT</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
<!-- Equilibrium value for epithelial chloride at which NKCC1 flux is zero -->
<variable name="c_Cl_epiEquilibrium" units="mM"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>c_Cl_epiEquilibrium</ci>
<apply>
<times/>
<ci>c_Cl_cap</ci>
<apply>
<root/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<divide/>
<ci>c_Na_cap</ci>
<ci>c_Na_epi</ci>
</apply>
<ci>c_K_cap</ci>
</apply>
<ci>c_K_epi</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
</model>