Location: The cardiac Na+ /K+ ATPase: An updated, thermodynamically consistent model @ aa1b81aa5a9c / Code / CellML / Terkildsen_NaK_kinetic_Fig2.cellml
- Author:
- Michael <panm@student.unimelb.edu.au>
- Date:
- 2017-11-02 12:22:46+11:00
- Desc:
- Uploaded updated files for submission
- Permanent Source URI:
- https://models.cellml.org/workspace/579/rawfile/aa1b81aa5a9c284c8112459563e0dc1045b5ced2/Code/CellML/Terkildsen_NaK_kinetic_Fig2.cellml
<?xml version='1.0'?>
<model name="Terkildsen_NaK_kinetic" xmlns="http://www.cellml.org/cellml/1.1#" xmlns:cellml="http://www.cellml.org/cellml/1.1#">
<units name="mJ_per_K_per_mol">
<unit prefix="milli" units="joule"/>
<unit exponent="-1" units="kelvin"/>
<unit exponent="-1" units="mole"/>
</units>
<units name="C_per_mol">
<unit units="coulomb"/>
<unit exponent="-1" units="mole"/>
</units>
<units name="mM">
<unit prefix="milli" units="mole"/>
</units>
<units name="per_second">
<unit exponent="-1" units="second"/>
</units>
<units name="per_second3">
<unit exponent="-3" units="second"/>
</units>
<units name="per_second_per_mM">
<unit exponent="-1" units="second"/>
<unit exponent="-1" units="mM"/>
</units>
<units name="per_second_per_mM2">
<unit exponent="-1" units="second"/>
<unit exponent="-2" units="mM"/>
</units>
<units name="mV">
<unit prefix="milli" units="volt"/>
</units>
<units name="mV_per_sec">
<unit units="mV"/>
<unit exponent="-1" units="second"/>
</units>
<component name="environment">
<!-- Time-->
<variable initial_value="0" name="t" units="second"/>
<!-- Physical parameters-->
<variable initial_value="8314" name="R" units="mJ_per_K_per_mol"/>
<variable initial_value="310" name="T" units="kelvin"/>
<variable initial_value="96485" name="F" units="C_per_mol"/>
<!-- Model parameters-->
<variable initial_value="579.7295" name="K0d_nak_nai" units="mM"/>
<variable initial_value="0.0349" name="K0d_nak_nae" units="mM"/>
<variable initial_value="5.6399" name="Kd_nak_nai2" units="mM"/>
<variable initial_value="1.0617e4" name="Kd_nak_nae2" units="mM"/>
<variable initial_value="1.0817" name="Kd_nak_ke" units="mM"/>
<variable initial_value="1.6795e4" name="Kd_nak_ki" units="mM"/>
<variable initial_value="140.3709" name="Kd_nak_MgATP" units="mM"/>
<variable initial_value="1.4232e3" name="rate_f_nak_1" units="per_second"/>
<variable initial_value="1.1565e4" name="rate_f_nak_2" units="per_second"/>
<variable initial_value="194.4506" name="rate_f_nak_3" units="per_second"/>
<variable initial_value="3.0630e4" name="rate_f_nak_4" units="per_second"/>
<variable initial_value="225.9048" name="rate_r_nak_1" units="per_second_per_mM"/>
<variable initial_value="3.6355e4" name="rate_r_nak_2" units="per_second"/>
<variable initial_value="2.8104e5" name="rate_r_nak_3" units="per_second_per_mM2"/>
<variable initial_value="1.5740e6" name="rate_r_nak_4" units="per_second"/>
<variable initial_value="-0.0550" name="factor_nak_del" units="dimensionless"/>
<variable initial_value="6.7700" name="pKd_nak_hpi" units="dimensionless"/>
<variable initial_value="292" name="Kd_nak_kpi" units="mM"/>
<variable initial_value="224" name="Kd_nak_napi" units="mM"/>
<!-- Voltage and concentrations-->
<!-- Set Nae to one of these values: 1.5 mM, 50 mM, 100 mM, 150 mM to reproduce Fig 2a-->
<variable initial_value="1.5" name="Nae" units="mM"/>
<variable initial_value="-120" name="Vm" units="mV"/>
<variable initial_value="0" name="Ki" units="mM"/>
<variable initial_value="5.4" name="Ke" units="mM"/>
<variable initial_value="50" name="Nai" units="mM"/>
<variable initial_value="10" name="MgATP" units="mM"/>
<variable initial_value="0" name="MgADP" units="mM"/>
<variable initial_value="0" name="Pi_total" units="mM"/>
<variable initial_value="3.9811e-5" name="H" units="mM"/>
<variable name="Pi" units="mM"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>Pi</ci>
<apply>
<divide/>
<ci>Pi_total</ci>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<ci>Ki</ci>
<ci>Kd_nak_kpi</ci>
</apply>
<apply>
<divide/>
<ci>H</ci>
<apply>
<power/>
<cn cellml:units="dimensionless">10</cn>
<apply>
<minus/>
<cn cellml:units="dimensionless">3.0</cn>
<ci>pKd_nak_hpi</ci>
</apply>
</apply>
</apply>
<apply>
<divide/>
<ci>Nai</ci>
<ci>Kd_nak_napi</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>Vm</ci>
</apply>
<cn cellml:units="mV_per_sec">1</cn>
</apply>
</math>
<!-- Model equations-->
<variable name="Kd_nak_nae1" units="mM"/>
<variable name="Kd_nak_nai1" units="mM"/>
<variable name="Nae_bound1" units="dimensionless"/>
<variable name="Nai_bound1" units="dimensionless"/>
<variable name="Nae_bound2" units="dimensionless"/>
<variable name="Nai_bound2" units="dimensionless"/>
<variable name="Ke_bound" units="dimensionless"/>
<variable name="Ki_bound" units="dimensionless"/>
<variable name="MgATP_bound" units="dimensionless"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>Kd_nak_nae1</ci>
<apply>
<times/>
<ci>K0d_nak_nae</ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<plus/>
<cn cellml:units="dimensionless">1.0</cn>
<ci>factor_nak_del</ci>
</apply>
<ci>F</ci>
<ci>Vm</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Kd_nak_nai1</ci>
<apply>
<times/>
<ci>K0d_nak_nai</ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<ci>factor_nak_del</ci>
<ci>F</ci>
<ci>Vm</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Nae_bound1</ci>
<apply>
<divide/>
<ci>Nae</ci>
<ci>Kd_nak_nae1</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>Nai_bound1</ci>
<apply>
<divide/>
<ci>Nai</ci>
<ci>Kd_nak_nai1</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>Nae_bound2</ci>
<apply>
<divide/>
<ci>Nae</ci>
<ci>Kd_nak_nae2</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>Nai_bound2</ci>
<apply>
<divide/>
<ci>Nai</ci>
<ci>Kd_nak_nai2</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>Ke_bound</ci>
<apply>
<divide/>
<ci>Ke</ci>
<ci>Kd_nak_ke</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>Ki_bound</ci>
<apply>
<divide/>
<ci>Ki</ci>
<ci>Kd_nak_ki</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>MgATP_bound</ci>
<apply>
<divide/>
<ci>MgATP</ci>
<ci>Kd_nak_MgATP</ci>
</apply>
</apply>
</math>
<variable name="alpha_f_nak_1" units="per_second"/>
<variable name="alpha_f_nak_2" units="per_second"/>
<variable name="alpha_f_nak_3" units="per_second"/>
<variable name="alpha_f_nak_4" units="per_second"/>
<variable name="alpha_r_nak_1" units="per_second"/>
<variable name="alpha_r_nak_2" units="per_second"/>
<variable name="alpha_r_nak_3" units="per_second"/>
<variable name="alpha_r_nak_4" units="per_second"/>
<variable name="sig_nak" units="per_second3"/>
<variable name="v_cyc_nak" units="per_second"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>alpha_f_nak_1</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>rate_f_nak_1</ci>
<ci>Nai_bound1</ci>
<apply>
<power/>
<ci>Nai_bound2</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<ci>Nai_bound1</ci>
<apply>
<power/>
<ci>Nai_bound2</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<power/>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<ci>Nai_bound2</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<power/>
<apply>
<plus/>
<cn cellml:units="dimensionless">1.0</cn>
<ci>Ki_bound</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<cn cellml:units="dimensionless">1.0</cn>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>alpha_f_nak_2</ci>
<ci>rate_f_nak_2</ci>
</apply>
<apply>
<eq/>
<ci>alpha_f_nak_3</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>rate_f_nak_3</ci>
<apply>
<power/>
<ci>Ke_bound</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<ci>Nae_bound1</ci>
<apply>
<power/>
<ci>Nae_bound2</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<power/>
<apply>
<plus/>
<cn cellml:units="dimensionless">1.0</cn>
<ci>Nae_bound2</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<power/>
<apply>
<plus/>
<cn cellml:units="dimensionless">1.0</cn>
<ci>Ke_bound</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<cn cellml:units="dimensionless">1.0</cn>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>alpha_f_nak_4</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>rate_f_nak_4</ci>
<ci>MgATP_bound</ci>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless">1.0</cn>
<ci>MgATP_bound</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>alpha_r_nak_1</ci>
<apply>
<times/>
<ci>rate_r_nak_1</ci>
<ci>MgADP</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>alpha_r_nak_2</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>rate_r_nak_2</ci>
<ci>Nae_bound1</ci>
<apply>
<power/>
<ci>Nae_bound2</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<ci>Nae_bound1</ci>
<apply>
<power/>
<ci>Nae_bound2</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<power/>
<apply>
<plus/>
<cn cellml:units="dimensionless">1.0</cn>
<ci>Nae_bound2</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<power/>
<apply>
<plus/>
<cn cellml:units="dimensionless">1.0</cn>
<ci>Ke_bound</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<cn cellml:units="dimensionless">1.0</cn>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>alpha_r_nak_3</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>rate_r_nak_3</ci>
<ci>Pi</ci>
<ci>H</ci>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless">1.0</cn>
<ci>MgATP_bound</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>alpha_r_nak_4</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>rate_r_nak_4</ci>
<apply>
<power/>
<ci>Ki_bound</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<ci>Nai_bound1</ci>
<apply>
<power/>
<ci>Nai_bound2</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<power/>
<apply>
<plus/>
<cn cellml:units="dimensionless">1.0</cn>
<ci>Nai_bound2</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<power/>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<ci>Ki_bound</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<cn cellml:units="dimensionless">1</cn>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>sig_nak</ci>
<apply>
<plus/>
<apply>
<times/>
<ci>alpha_r_nak_1</ci>
<ci>alpha_r_nak_2</ci>
<ci>alpha_r_nak_3</ci>
</apply>
<apply>
<times/>
<ci>alpha_r_nak_1</ci>
<ci>alpha_r_nak_2</ci>
<ci>alpha_f_nak_4</ci>
</apply>
<apply>
<times/>
<ci>alpha_r_nak_1</ci>
<ci>alpha_f_nak_3</ci>
<ci>alpha_f_nak_4</ci>
</apply>
<apply>
<times/>
<ci>alpha_f_nak_2</ci>
<ci>alpha_f_nak_3</ci>
<ci>alpha_f_nak_4</ci>
</apply>
<apply>
<times/>
<ci>alpha_r_nak_2</ci>
<ci>alpha_r_nak_3</ci>
<ci>alpha_r_nak_4</ci>
</apply>
<apply>
<times/>
<ci>alpha_f_nak_1</ci>
<ci>alpha_r_nak_2</ci>
<ci>alpha_r_nak_3</ci>
</apply>
<apply>
<times/>
<ci>alpha_f_nak_1</ci>
<ci>alpha_r_nak_2</ci>
<ci>alpha_f_nak_4</ci>
</apply>
<apply>
<times/>
<ci>alpha_f_nak_1</ci>
<ci>alpha_f_nak_3</ci>
<ci>alpha_f_nak_4</ci>
</apply>
<apply>
<times/>
<ci>alpha_r_nak_1</ci>
<ci>alpha_r_nak_3</ci>
<ci>alpha_r_nak_4</ci>
</apply>
<apply>
<times/>
<ci>alpha_f_nak_2</ci>
<ci>alpha_r_nak_3</ci>
<ci>alpha_r_nak_4</ci>
</apply>
<apply>
<times/>
<ci>alpha_f_nak_1</ci>
<ci>alpha_f_nak_2</ci>
<ci>alpha_r_nak_3</ci>
</apply>
<apply>
<times/>
<ci>alpha_f_nak_1</ci>
<ci>alpha_f_nak_2</ci>
<ci>alpha_f_nak_4</ci>
</apply>
<apply>
<times/>
<ci>alpha_r_nak_1</ci>
<ci>alpha_r_nak_2</ci>
<ci>alpha_r_nak_4</ci>
</apply>
<apply>
<times/>
<ci>alpha_r_nak_1</ci>
<ci>alpha_f_nak_3</ci>
<ci>alpha_r_nak_4</ci>
</apply>
<apply>
<times/>
<ci>alpha_f_nak_2</ci>
<ci>alpha_f_nak_3</ci>
<ci>alpha_r_nak_4</ci>
</apply>
<apply>
<times/>
<ci>alpha_f_nak_1</ci>
<ci>alpha_f_nak_2</ci>
<ci>alpha_f_nak_3</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v_cyc_nak</ci>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<times/>
<ci>alpha_f_nak_1</ci>
<ci>alpha_f_nak_2</ci>
<ci>alpha_f_nak_3</ci>
<ci>alpha_f_nak_4</ci>
</apply>
<apply>
<times/>
<ci>alpha_r_nak_1</ci>
<ci>alpha_r_nak_2</ci>
<ci>alpha_r_nak_3</ci>
<ci>alpha_r_nak_4</ci>
</apply>
</apply>
<ci>sig_nak</ci>
</apply>
</apply>
</math>
</component>
</model>