- Author:
- Weiwei Ai <wai484@aucklanduni.ac.nz>
- Date:
- 2026-05-22 14:34:26+12:00
- Desc:
- update the params
- Permanent Source URI:
- https://staging.physiomeproject.org/workspace/cad/rawfile/464437442fe2529c8751a37cf98977cd34a4135b/models/NKE_pump_BG_6_states_v2.cellml
<?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#">
<!-- 6-state BG model of NKE ATPase based on the Post-Albers kinetic model
Note that volume is expressed in picoLitres (nL = 10^-9L), energy in femto-Joules (pJ = 10^-12J),
molar qtys in femto-moles (pmol = 10^-12mol), concentration in milli-moles per litre (mM = pmol_per_nL),
charge in nano-Coulombs (nC), voltage in milli-Volts (mV=pJ_per_nC), chemical potential in pJ_per_pmol (= J_per_mol)
Cell membrane capacitance of 10pF is 1e-5 nC^2/pJ -->
<units name="dim">
<unit units="dimensionless"/>
</units>
<units name="per_s">
<unit exponent="-1" units="second"/>
</units>
<units name="nL">
<unit prefix="nano" units="litre"/>
</units>
<units name="pmol">
<unit prefix="pico" units="mole"/>
</units>
<units name="mM">
<unit prefix="milli" units="mole"/>
<unit exponent="-1" units="litre"/>
</units>
<units name="mV">
<unit prefix="milli" units="volt"/>
</units>
<units name="per_pmol">
<unit exponent="-1" units="pmol"/>
</units>
<units name="pmol_per_s">
<unit units="pmol"/>
<unit exponent="-1" units="second"/>
</units>
<units name="pJ_per_s">
<unit units="pJ"/>
<unit exponent="-1" units="second"/>
</units>
<units name="mM_per_s">
<unit units="mM"/>
<unit exponent="-1" units="second"/>
</units>
<units name="pJ">
<unit prefix="pico" units="joule"/>
</units>
<units name="nC">
<unit prefix="nano" units="coulomb"/>
</units>
<units name="J_per_mol">
<unit units="joule"/>
<unit exponent="-1" units="mole"/>
</units>
<units name="J_per_K_per_mol">
<unit units="joule"/>
<unit exponent="-1" units="kelvin"/>
<unit exponent="-1" units="mole"/>
</units>
<units name="pJ_per_pmol">
<unit units="pJ"/>
<unit exponent="-1" units="pmol"/>
</units>
<units name="pJ_per_pmol_per_K">
<unit units="pJ"/>
<unit exponent="-1" units="pmol"/>
<unit exponent="-1" units="kelvin"/>
</units>
<units name="nC_per_pmol">
<unit units="nC"/>
<unit exponent="-1" units="pmol"/>
</units>
<units name="nC2_per_pJ">
<unit exponent="2" units="nC"/>
<unit exponent="-1" units="pJ"/>
</units>
<units name="pJ_per_nC">
<unit units="pJ"/>
<unit exponent="-1" units="nC"/>
</units>
<component name="main">
<variable name="t" units="second"/>
<variable initial_value="8.314" name="R" units="pJ_per_pmol_per_K"/>
<variable initial_value="308" name="T" units="kelvin"/>
<variable initial_value="96.4853321" name="F" units="nC_per_pmol"/>
<variable name="RT" units="pJ_per_pmol"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>RT</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</math>
<variable name="q_Na_o" units="pmol"/>
<variable name="q_Na_i" units="pmol"/>
<variable name="q_K_o" units="pmol"/>
<variable name="q_K_i" units="pmol"/>
<variable name="q_ATP" units="pmol"/>
<variable name="q_ADP" units="pmol"/>
<variable name="q_Pi" units="pmol"/>
<!-- var q_H: pmol;-->
<variable initial_value="140" name="c_Nao" units="mM"/>
<variable initial_value="12" name="c_Nai" units="mM"/>
<variable initial_value="5" name="c_Ko" units="mM"/>
<variable initial_value="140" name="c_Ki" units="mM"/>
<variable initial_value="0.001" name="c_ADP" units="mM"/>
<variable initial_value="10" name="c_ATP" units="mM"/>
<variable initial_value="0.001" name="c_Pi" units="mM"/>
<variable initial_value="1" name="W_o" units="nL"/>
<variable initial_value="1" name="W_i" units="nL"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>q_Na_o</ci>
<apply>
<times/>
<ci>c_Nao</ci>
<ci>W_o</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>q_Na_i</ci>
<apply>
<times/>
<ci>c_Nai</ci>
<ci>W_i</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>q_K_o</ci>
<apply>
<times/>
<ci>c_Ko</ci>
<ci>W_o</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>q_K_i</ci>
<apply>
<times/>
<ci>c_Ki</ci>
<ci>W_i</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>q_ATP</ci>
<apply>
<times/>
<ci>c_ATP</ci>
<ci>W_i</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>q_ADP</ci>
<apply>
<times/>
<ci>c_ADP</ci>
<ci>W_i</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>q_Pi</ci>
<apply>
<times/>
<ci>c_Pi</ci>
<ci>W_i</ci>
</apply>
</apply>
</math>
<!-- var pH: dim {init: 7.4};
q_H = pow(10{dim}, -pH)*1000{mM}*W_i;
q_H = 1 {pmol};-->
<!-- var q_m: nC {init: 0};
var C_m: nC2_per_pJ {init: 1e-5};-->
<variable initial_value="-50" name="u_e" units="pJ_per_nC"/>
<!-- var z_1: dim {init: -1.73847019e-01};-->
<variable initial_value="1.73847019e-01" name="z_1" units="dim"/>
<variable name="z_2" units="dim"/>
<!-- z_2 = -1{dim}-z_1; incorrect?-->
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>z_2</ci>
<apply>
<minus/>
<cn cellml:units="dim">1</cn>
<ci>z_1</ci>
</apply>
</apply>
</math>
<!-- ode(q_m, t) = z_1*F*v_5+z_2*F*v_5;
u_e = q_m/C_m;-->
<variable name="e_0" units="dim"/>
<variable name="e_1" units="dim"/>
<variable name="e_2" units="dim"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>e_0</ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<ci>F</ci>
<ci>u_e</ci>
</apply>
<ci>RT</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>e_1</ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<ci>z_1</ci>
<ci>F</ci>
<ci>u_e</ci>
</apply>
<ci>RT</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>e_2</ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<ci>z_2</ci>
<ci>F</ci>
<ci>u_e</ci>
</apply>
<ci>RT</ci>
</apply>
</apply>
</apply>
</math>
<variable initial_value="3" name="q_1" units="pmol"/>
<variable initial_value="0" name="q_2" units="pmol"/>
<variable initial_value="0" name="q_3" units="pmol"/>
<variable initial_value="0" name="q_4" units="pmol"/>
<variable initial_value="0" name="q_5" units="pmol"/>
<variable initial_value="0" name="q_6" units="pmol"/>
<variable name="Q_1" units="dim"/>
<variable name="Q_2" units="dim"/>
<variable name="Q_3" units="dim"/>
<variable name="Q_4" units="dim"/>
<variable name="Q_5" units="dim"/>
<variable name="Q_6" units="dim"/>
<!-- var K_1: per_pmol {init: 0.266655299};
var K_2: per_pmol {init: 0.733375971};
var K_3: per_pmol {init: 0.130777328};
var K_4: per_pmol {init: 0.981840672};
var K_5: per_pmol {init: 0.981840672};
var K_6: per_pmol {init: 0.981840672};-->
<variable initial_value="1" name="K_1" units="per_pmol"/>
<variable initial_value="1" name="K_2" units="per_pmol"/>
<variable initial_value="1" name="K_3" units="per_pmol"/>
<variable initial_value="1" name="K_4" units="per_pmol"/>
<variable initial_value="1" name="K_5" units="per_pmol"/>
<variable initial_value="1" name="K_6" units="per_pmol"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>Q_1</ci>
<apply>
<times/>
<ci>K_1</ci>
<ci>q_1</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>Q_2</ci>
<apply>
<times/>
<ci>K_2</ci>
<ci>q_2</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>Q_3</ci>
<apply>
<times/>
<ci>K_3</ci>
<ci>q_3</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>Q_4</ci>
<apply>
<times/>
<ci>K_4</ci>
<ci>q_4</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>Q_5</ci>
<apply>
<times/>
<ci>K_5</ci>
<ci>q_5</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>Q_6</ci>
<apply>
<times/>
<ci>K_6</ci>
<ci>q_6</ci>
</apply>
</apply>
</math>
<variable name="Q_Na_o" units="dim"/>
<variable name="Q_Na_i" units="dim"/>
<variable name="Q_K_o" units="dim"/>
<variable name="Q_K_i" units="dim"/>
<variable name="Q_ATP" units="dim"/>
<variable name="Q_ADP" units="dim"/>
<variable name="Q_Pi" units="dim"/>
<!-- var Q_H: dim;-->
<!-- var K_Ko: per_pmol {init: 0.009236};
var K_Ki: per_pmol {init: 0.0012595};
var K_ADP: per_pmol {init: 7.976e-05};
var K_ATP: per_pmol {init: 2.3715};
var K_Nao: per_pmol {init: 0.0061242};
var K_Nai: per_pmol {init: 0.00083514};
var K_Pi: per_pmol {init: 1};
var K_H: per_pmol {init: 1};-->
<variable initial_value="1" name="K_Ko" units="per_pmol"/>
<variable initial_value="1" name="K_Ki" units="per_pmol"/>
<variable initial_value="1" name="K_ADP" units="per_pmol"/>
<variable initial_value="1" name="K_ATP" units="per_pmol"/>
<variable initial_value="1" name="K_Nao" units="per_pmol"/>
<variable initial_value="1" name="K_Nai" units="per_pmol"/>
<variable initial_value="1" name="K_Pi" units="per_pmol"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>Q_Na_o</ci>
<apply>
<times/>
<ci>K_Nao</ci>
<ci>q_Na_o</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>Q_Na_i</ci>
<apply>
<times/>
<ci>K_Nai</ci>
<ci>q_Na_i</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>Q_K_o</ci>
<apply>
<times/>
<ci>K_Ko</ci>
<ci>q_K_o</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>Q_K_i</ci>
<apply>
<times/>
<ci>K_Ki</ci>
<ci>q_K_i</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>Q_ATP</ci>
<apply>
<times/>
<ci>K_ATP</ci>
<ci>q_ATP</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>Q_ADP</ci>
<apply>
<times/>
<ci>K_ADP</ci>
<ci>q_ADP</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>Q_Pi</ci>
<apply>
<times/>
<ci>K_Pi</ci>
<ci>q_Pi</ci>
</apply>
</apply>
</math>
<!-- Q_H = K_H *q_H;-->
<variable name="v_1" units="pmol_per_s"/>
<variable name="v_2" units="pmol_per_s"/>
<variable name="v_3" units="pmol_per_s"/>
<variable name="v_4" units="pmol_per_s"/>
<variable name="v_5" units="pmol_per_s"/>
<variable name="v_6" units="pmol_per_s"/>
<!-- var kappa_1: pmol_per_s {init: 9.77016607e+02};
var kappa_2: pmol_per_s {init: 3.16819036e+01};
var kappa_3: pmol_per_s {init: 3000};
var kappa_4: pmol_per_s {init: 6.65037715e-02};
var kappa_5: pmol_per_s {init: 6.65037715e+02};
var kappa_6: pmol_per_s {init: 6.65037715e+02};-->
<variable initial_value="100" name="kappa_1" units="pmol_per_s"/>
<variable initial_value="100" name="kappa_2" units="pmol_per_s"/>
<variable initial_value="10" name="kappa_3" units="pmol_per_s"/>
<variable initial_value="100" name="kappa_4" units="pmol_per_s"/>
<variable initial_value="100" name="kappa_5" units="pmol_per_s"/>
<variable initial_value="1" name="kappa_6" units="pmol_per_s"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v_1</ci>
<apply>
<times/>
<ci>kappa_1</ci>
<apply>
<minus/>
<apply>
<times/>
<ci>Q_1</ci>
<apply>
<power/>
<ci>Q_Na_i</ci>
<cn cellml:units="dim">3</cn>
</apply>
<ci>Q_ATP</ci>
</apply>
<ci>Q_2</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v_2</ci>
<apply>
<times/>
<ci>kappa_2</ci>
<apply>
<minus/>
<ci>Q_2</ci>
<apply>
<times/>
<ci>Q_3</ci>
<ci>Q_ADP</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v_3</ci>
<apply>
<times/>
<ci>kappa_3</ci>
<apply>
<minus/>
<ci>Q_3</ci>
<apply>
<times/>
<ci>Q_4</ci>
<apply>
<power/>
<ci>Q_Na_o</ci>
<cn cellml:units="dim">3</cn>
</apply>
<ci>e_1</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v_4</ci>
<apply>
<times/>
<ci>kappa_4</ci>
<apply>
<minus/>
<apply>
<times/>
<ci>Q_4</ci>
<apply>
<power/>
<ci>Q_K_o</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<ci>Q_5</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v_5</ci>
<apply>
<times/>
<ci>kappa_5</ci>
<apply>
<minus/>
<ci>Q_5</ci>
<apply>
<times/>
<ci>Q_6</ci>
<ci>Q_Pi</ci>
<ci>Q_H</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v_6</ci>
<apply>
<times/>
<ci>kappa_6</ci>
<apply>
<minus/>
<ci>Q_6</ci>
<apply>
<times/>
<ci>Q_1</ci>
<apply>
<power/>
<ci>Q_K_i</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>e_2</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_1</ci>
</apply>
<apply>
<minus/>
<ci>v_6</ci>
<ci>v_1</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_2</ci>
</apply>
<apply>
<minus/>
<ci>v_1</ci>
<ci>v_2</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_3</ci>
</apply>
<apply>
<minus/>
<ci>v_2</ci>
<ci>v_3</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_4</ci>
</apply>
<apply>
<minus/>
<ci>v_3</ci>
<ci>v_4</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_5</ci>
</apply>
<apply>
<minus/>
<ci>v_4</ci>
<ci>v_5</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_6</ci>
</apply>
<apply>
<minus/>
<ci>v_5</ci>
<ci>v_6</ci>
</apply>
</apply>
</math>
<variable name="q_tot" units="pmol"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>q_tot</ci>
<apply>
<plus/>
<ci>q_1</ci>
<ci>q_2</ci>
<ci>q_3</ci>
<ci>q_4</ci>
<ci>q_5</ci>
<ci>q_6</ci>
</apply>
</apply>
</math>
</component>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:about="#model">
<bqs:reference xmlns:bqs="http://www.cellml.org/bqs/1.0#" rdf:parseType="Resource" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<dc:subject xmlns:dc="http://purl.org/dc/elements/1.1/" rdf:parseType="Resource" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<bqs:subject_type xmlns:bqs="http://www.cellml.org/bqs/1.0#">keyword</bqs:subject_type>
<rdf:value xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Bag xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:li xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">protein-modules</rdf:li>
</rdf:Bag>
</rdf:value>
</dc:subject>
</bqs:reference>
</rdf:Description>
</rdf:RDF>
</model>
