Location: 12 L Platform 1 model codes @ 4c1ab73f48d7 / VSM_ftu / wang2010.cellml
- Author:
- aram148 <a.rampadarath@auckland.ac.nz>
- Date:
- 2021-11-04 16:02:42+13:00
- Desc:
- Updated USMC-Bursztyn model
- Permanent Source URI:
- http://models.cellml.org/workspace/6b0/rawfile/4c1ab73f48d7150c2094cf8017425482a1594ccf/VSM_ftu/wang2010.cellml
<?xml version='1.0' encoding='UTF-8'?>
<model name="wang_2010" xmlns="http://www.cellml.org/cellml/1.1#" xmlns:cellml="http://www.cellml.org/cellml/1.1#">
<!-- def import using "units.cellml" for
unit per_mM_per_sec using unit per_mM_per_sec;
unit mV using unit mV;
unit per_sec using unit per_sec;
unit mM using unit mM;
unit nS_per_mM using unit nS_per_mM;
unit C_per_mol using unit C_per_mol;
unit per_mM using unit per_mM;
unit mM_per_sec using unit mM_per_sec;
unit mJ_per_K_per_mol using unit mJ_per_K_per_mol;
unit uA_per_cmsq using unit uA_per_cmsq;
enddef;-->
<!-- def comp environment as
var time: second {pub: out};
enddef;-->
<component name="ca_parameters">
<variable initial_value="2000" name="k_1" public_interface="out" units="per_mM_per_sec"/>
<variable initial_value="1.0" name="k_2" public_interface="out" units="per_mM_per_sec"/>
<variable initial_value="2000" name="k_3" public_interface="out" units="per_mM_per_sec"/>
<variable initial_value="1.0" name="k_4" public_interface="out" units="per_mM_per_sec"/>
<variable initial_value="100" name="k_5" public_interface="out" units="per_mM_per_sec"/>
<variable initial_value="260" name="k_m1" public_interface="out" units="per_sec"/>
<variable initial_value="1.05" name="k_m2" public_interface="out" units="per_sec"/>
<variable initial_value="1886" name="k_m3" public_interface="out" units="per_sec"/>
<variable initial_value="0.145" name="k_m4" public_interface="out" units="per_sec"/>
<variable initial_value="8.2" name="k_m5" public_interface="out" units="per_sec"/>
<variable initial_value="0.0072" name="k_ryr0" public_interface="out" units="per_sec"/>
<variable initial_value="0.334" name="k_ryr1" public_interface="out" units="per_sec"/>
<variable initial_value="0.5" name="k_ryr2" public_interface="out" units="mM"/>
<variable initial_value="38" name="k_ryr3" public_interface="out" units="mM"/>
<variable initial_value="5.55" name="k_ipr" public_interface="out" units="per_sec"/>
<variable initial_value="5.0" name="k_RyR" public_interface="out" units="per_sec"/>
<variable initial_value="-50" name="Vm" public_interface="out" units="mV"/>
<variable initial_value="12" name="km" public_interface="out" units="mV"/>
<variable initial_value="9" name="gca" public_interface="out" units="nS_per_mM"/>
<variable initial_value="96485" name="F" public_interface="out" units="C_per_mol"/>
<variable initial_value="8345" name="R" public_interface="out" units="mJ_per_K_per_mol"/>
<variable initial_value="310" name="T" public_interface="out" units="kelvin"/>
<variable initial_value="0.05" name="alpha0" public_interface="out" units="mM_per_sec"/>
<variable initial_value="0.25" name="alpha1" public_interface="out" units="dimensionless"/>
<variable initial_value="1" name="alpha2" public_interface="out" units="per_sec"/>
<variable initial_value="0.1" name="Jer" public_interface="out" units="per_sec"/>
<variable initial_value="4.5" name="Ve" public_interface="out" units="mM_per_sec"/>
<variable initial_value="0.1" name="Ke" public_interface="out" units="mM"/>
<variable initial_value="4.5" name="Vp" public_interface="out" units="mM_per_sec"/>
<variable initial_value="0.4" name="Kp" public_interface="out" units="mM"/>
<variable initial_value="5.5" name="gamma" public_interface="out" units="dimensionless"/>
<variable initial_value="0.05" name="delta" public_interface="out" units="dimensionless"/>
</component>
<component name="asm_ca">
<variable name="time" public_interface="in" units="second"/>
<variable initial_value="0.112" name="c" public_interface="out" units="mM"/>
<variable name="J_release" units="mM_per_sec"/>
<variable name="J_serca" units="mM_per_sec"/>
<variable name="J_in" units="mM_per_sec"/>
<variable name="J_pm" units="mM_per_sec"/>
<variable name="k_ipr" public_interface="in" units="per_sec"/>
<variable name="P_ipr" units="dimensionless"/>
<variable name="k_RyR" public_interface="in" units="per_sec"/>
<variable name="P_RyR" units="dimensionless"/>
<variable name="Jer" public_interface="in" units="per_sec"/>
<variable initial_value="24" name="cs" units="mM"/>
<variable name="p" public_interface="out" units="mM"/>
<variable name="k_ryr0" public_interface="in" units="per_sec"/>
<variable name="k_ryr1" public_interface="in" units="per_sec"/>
<variable name="k_ryr2" public_interface="in" units="mM"/>
<variable name="k_ryr3" public_interface="in" units="mM"/>
<variable name="Ve" public_interface="in" units="mM_per_sec"/>
<variable name="Ke" public_interface="in" units="mM"/>
<variable name="Vp" public_interface="in" units="mM_per_sec"/>
<variable name="Kp" public_interface="in" units="mM"/>
<variable name="alpha0" public_interface="in" units="mM_per_sec"/>
<variable name="alpha1" public_interface="in" units="dimensionless"/>
<variable name="alpha2" public_interface="in" units="per_sec"/>
<variable name="F" public_interface="in" units="C_per_mol"/>
<variable initial_value="0" name="y" units="dimensionless"/>
<variable name="phi1" units="dimensionless"/>
<variable name="phi2" units="dimensionless"/>
<variable name="k_1" public_interface="in" units="per_mM_per_sec"/>
<variable name="k_2" public_interface="in" units="per_mM_per_sec"/>
<variable name="k_3" public_interface="in" units="per_mM_per_sec"/>
<variable name="k_4" public_interface="in" units="per_mM_per_sec"/>
<variable name="k_5" public_interface="in" units="per_mM_per_sec"/>
<variable name="k_m1" public_interface="in" units="per_sec"/>
<variable name="k_m2" public_interface="in" units="per_sec"/>
<variable name="k_m3" public_interface="in" units="per_sec"/>
<variable name="k_m4" public_interface="in" units="per_sec"/>
<variable name="k_m5" public_interface="in" units="per_sec"/>
<variable name="K1" units="dimensionless"/>
<variable name="K2" units="dimensionless"/>
<variable name="K3" units="dimensionless"/>
<variable name="K4" units="dimensionless"/>
<variable name="K5" units="dimensionless"/>
<variable name="delta" public_interface="in" units="dimensionless"/>
<variable name="V" units="mV"/>
<variable name="gamma" public_interface="in" units="dimensionless"/>
<variable name="R" public_interface="in" units="mJ_per_K_per_mol"/>
<variable name="T" public_interface="in" units="kelvin"/>
<variable name="I_ca" units="uA_per_cmsq"/>
<variable name="gca" public_interface="in" units="nS_per_mM"/>
<variable name="m" units="dimensionless"/>
<variable name="V_ca" units="mV"/>
<variable name="Vm" public_interface="in" units="mV"/>
<variable name="km" public_interface="in" units="mV"/>
<variable initial_value="0" name="ce" units="mM"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>V</ci>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="mV">60</cn>
</apply>
<apply>
<lt/>
<ci>time</ci>
<cn cellml:units="second">50</cn>
</apply>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="mV">30</cn>
</apply>
<apply>
<and/>
<apply>
<geq/>
<ci>time</ci>
<cn cellml:units="second">50</cn>
</apply>
<apply>
<leq/>
<ci>time</ci>
<cn cellml:units="second">400</cn>
</apply>
</apply>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="mV">60</cn>
</apply>
<apply>
<gt/>
<ci>time</ci>
<cn cellml:units="second">400</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>K1</ci>
<apply>
<divide/>
<ci>k_m1</ci>
<ci>k_1</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>K2</ci>
<apply>
<divide/>
<ci>k_m2</ci>
<ci>k_2</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>K3</ci>
<apply>
<divide/>
<ci>k_m3</ci>
<ci>k_3</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>K4</ci>
<apply>
<divide/>
<ci>k_m4</ci>
<ci>k_4</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>K5</ci>
<apply>
<divide/>
<ci>k_m5</ci>
<ci>k_5</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>I_ca</ci>
<apply>
<times/>
<ci>gca</ci>
<apply>
<power/>
<ci>m</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>V_ca</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>m</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<ci>V</ci>
<ci>Vm</ci>
</apply>
</apply>
<ci>km</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>V_ca</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>V</ci>
<apply>
<minus/>
<ci>c</ci>
<apply>
<times/>
<ci>ce</ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>V</ci>
<ci>F</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>V</ci>
<ci>F</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>J_pm</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>Vp</ci>
<apply>
<power/>
<ci>c</ci>
<cn cellml:units="dimensionless">4</cn>
</apply>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci>Kp</ci>
<cn cellml:units="dimensionless">4</cn>
</apply>
<apply>
<power/>
<ci>c</ci>
<cn cellml:units="dimensionless">4</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>J_serca</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>Ve</ci>
<apply>
<power/>
<ci>c</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci>Ke</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<power/>
<ci>c</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>J_release</ci>
<apply>
<times/>
<apply>
<plus/>
<apply>
<times/>
<ci>k_ipr</ci>
<ci>P_ipr</ci>
</apply>
<apply>
<times/>
<ci>k_RyR</ci>
<ci>P_RyR</ci>
</apply>
<ci>Jer</ci>
</apply>
<apply>
<minus/>
<ci>cs</ci>
<ci>c</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>J_in</ci>
<apply>
<times/>
<apply>
<plus/>
<apply>
<minus/>
<ci>alpha0</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>alpha1</ci>
<ci>I_ca</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>F</ci>
</apply>
</apply>
</apply>
<ci>alpha2</ci>
</apply>
<ci>p</ci>
<apply>
<lt/>
<ci>time</ci>
<cn cellml:units="second">100</cn>
</apply>
</apply>
</apply>
<!--+0{dimensionless}*(time >= 100{second});-->
<apply>
<eq/>
<ci>P_ipr</ci>
<apply>
<power/>
<apply>
<divide/>
<apply>
<times/>
<ci>p</ci>
<ci>c</ci>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<ci>y</ci>
</apply>
</apply>
<apply>
<times/>
<apply>
<plus/>
<ci>p</ci>
<ci>K1</ci>
</apply>
<apply>
<plus/>
<ci>c</ci>
<ci>K5</ci>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless">3</cn>
</apply>
</apply>
<apply>
<eq/>
<ci>P_RyR</ci>
<apply>
<divide/>
<apply>
<times/>
<apply>
<plus/>
<ci>k_ryr0</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>k_ryr1</ci>
<apply>
<power/>
<ci>c</ci>
<cn cellml:units="dimensionless">3</cn>
</apply>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci>k_ryr2</ci>
<cn cellml:units="dimensionless">3</cn>
</apply>
<apply>
<power/>
<ci>c</ci>
<cn cellml:units="dimensionless">3</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<power/>
<ci>cs</ci>
<cn cellml:units="dimensionless">4</cn>
</apply>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci>k_ryr3</ci>
<cn cellml:units="dimensionless">4</cn>
</apply>
<apply>
<power/>
<ci>c</ci>
<cn cellml:units="dimensionless">4</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>phi1</ci>
<apply>
<divide/>
<apply>
<times/>
<apply>
<plus/>
<apply>
<times/>
<ci>k_m4</ci>
<ci>K2</ci>
<ci>K1</ci>
</apply>
<apply>
<times/>
<ci>k_m2</ci>
<ci>K4</ci>
<ci>p</ci>
</apply>
</apply>
<ci>c</ci>
</apply>
<apply>
<times/>
<ci>K4</ci>
<ci>K2</ci>
<apply>
<plus/>
<ci>K1</ci>
<ci>p</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>phi2</ci>
<apply>
<divide/>
<apply>
<plus/>
<apply>
<times/>
<ci>k_m2</ci>
<ci>p</ci>
</apply>
<apply>
<times/>
<ci>k_m4</ci>
<ci>K3</ci>
</apply>
</apply>
<apply>
<plus/>
<ci>K3</ci>
<ci>p</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>y</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>phi1</ci>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<ci>y</ci>
</apply>
</apply>
<apply>
<times/>
<ci>phi2</ci>
<ci>y</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>c</ci>
</apply>
<apply>
<plus/>
<apply>
<minus/>
<ci>J_release</ci>
<ci>J_serca</ci>
</apply>
<apply>
<times/>
<ci>delta</ci>
<apply>
<minus/>
<ci>J_in</ci>
<ci>J_pm</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>cs</ci>
</apply>
<apply>
<times/>
<ci>gamma</ci>
<apply>
<minus/>
<ci>J_serca</ci>
<ci>J_release</ci>
</apply>
</apply>
</apply>
<!-- p = 0{dimensionless};-->
<apply>
<eq/>
<ci>p</ci>
<apply>
<times/>
<apply>
<divide/>
<cn cellml:units="dimensionless">0.35</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">0.0699</cn>
</apply>
<apply>
<minus/>
<ci>time</ci>
<cn cellml:units="second">50</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<gt/>
<ci>time</ci>
<cn cellml:units="second">50</cn>
</apply>
</apply>
</apply>
</math>
</component>
<component name="calcium">
<variable name="time" public_interface="in" units="second"/>
<variable name="k1" public_interface="out" units="per_sec"/>
<variable name="k2h" public_interface="out" units="per_sec"/>
<variable initial_value="0.5962" name="k1a" units="per_sec"/>
<variable name="c" public_interface="in" units="mM"/>
<variable initial_value="1.35" name="k1b" units="mM"/>
<variable initial_value="156.9" name="tau" units="second"/>
<variable initial_value="0" name="P" units="dimensionless"/>
<variable name="kon" units="dimensionless"/>
<variable name="koff" units="dimensionless"/>
<variable initial_value="242.14" name="k2b" units="per_sec"/>
<variable initial_value="0.000125" name="kon1" units="dimensionless"/>
<variable initial_value="0.8988" name="kon2" units="mM"/>
<variable initial_value="0.4629" name="koff1" units="dimensionless"/>
<variable initial_value="20.035" name="koff2" units="dimensionless"/>
<variable name="p" public_interface="in" units="mM"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>kon</ci>
<apply>
<plus/>
<ci>kon1</ci>
<apply>
<divide/>
<apply>
<power/>
<ci>c</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci>kon2</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<power/>
<ci>c</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>koff</ci>
<apply>
<plus/>
<ci>koff1</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>koff2</ci>
<ci>p</ci>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<ci>p</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>P</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<ci>tau</ci>
</apply>
<ci>kon</ci>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<ci>P</ci>
</apply>
</apply>
<apply>
<times/>
<ci>koff</ci>
<ci>P</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>k2h</ci>
<apply>
<times/>
<ci>k2b</ci>
<apply>
<power/>
<ci>P</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>k1</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>k1a</ci>
<apply>
<power/>
<ci>c</ci>
<cn cellml:units="dimensionless">4</cn>
</apply>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci>k1b</ci>
<cn cellml:units="dimensionless">4</cn>
</apply>
<apply>
<power/>
<ci>c</ci>
<cn cellml:units="dimensionless">4</cn>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<connection>
<map_components component_1="ca_parameters" component_2="asm_ca"/>
<map_variables variable_1="k_1" variable_2="k_1"/>
<map_variables variable_1="k_2" variable_2="k_2"/>
<map_variables variable_1="k_3" variable_2="k_3"/>
<map_variables variable_1="k_4" variable_2="k_4"/>
<map_variables variable_1="k_5" variable_2="k_5"/>
<map_variables variable_1="k_m1" variable_2="k_m1"/>
<map_variables variable_1="k_m2" variable_2="k_m2"/>
<map_variables variable_1="k_m3" variable_2="k_m3"/>
<map_variables variable_1="k_m4" variable_2="k_m4"/>
<map_variables variable_1="k_m5" variable_2="k_m5"/>
<map_variables variable_1="gamma" variable_2="gamma"/>
<map_variables variable_1="delta" variable_2="delta"/>
<map_variables variable_1="F" variable_2="F"/>
<map_variables variable_1="R" variable_2="R"/>
<map_variables variable_1="T" variable_2="T"/>
<map_variables variable_1="alpha0" variable_2="alpha0"/>
<map_variables variable_1="alpha1" variable_2="alpha1"/>
<map_variables variable_1="alpha2" variable_2="alpha2"/>
<map_variables variable_1="k_ipr" variable_2="k_ipr"/>
<map_variables variable_1="k_RyR" variable_2="k_RyR"/>
<map_variables variable_1="Jer" variable_2="Jer"/>
<map_variables variable_1="k_ryr0" variable_2="k_ryr0"/>
<map_variables variable_1="k_ryr1" variable_2="k_ryr1"/>
<map_variables variable_1="k_ryr2" variable_2="k_ryr2"/>
<map_variables variable_1="k_ryr3" variable_2="k_ryr3"/>
<map_variables variable_1="Ve" variable_2="Ve"/>
<map_variables variable_1="Ke" variable_2="Ke"/>
<map_variables variable_1="Vp" variable_2="Vp"/>
<map_variables variable_1="Kp" variable_2="Kp"/>
<map_variables variable_1="gca" variable_2="gca"/>
<map_variables variable_1="Vm" variable_2="Vm"/>
<map_variables variable_1="km" variable_2="km"/>
</connection>
<!-- def map between calcium and asm_ca for
vars c and c;
vars p and p;
enddef;-->
</model>