Location: Diabetes @ 65bfa15468fc / SI / 3-InsulinBindingLevel.cellml
- Author:
- Soroush Safaei <ssaf006@aucklanduni.ac.nz>
- Date:
- 2018-06-02 19:07:50+12:00
- Desc:
- adding new insulin model
- Permanent Source URI:
- https://models.cellml.org/workspace/483/rawfile/65bfa15468fcaadd309ed2ab64b2a4bd7771fa4c/SI/3-InsulinBindingLevel.cellml
<?xml version='1.0'?>
<model name="main3" xmlns="http://www.cellml.org/cellml/1.1#" xmlns:cellml="http://www.cellml.org/cellml/1.1#" xmlns:xlink="http://www.w3.org/1999/xlink">
<!-- in: INS,X_P
out: r1x2,r11x2,r1x22,r1x22d,r11x22,rendP,rPbasal-->
<import xlink:href="Parameters.cellml">
<component component_ref="param3" name="param"/>
</import>
<component name="environment">
<variable name="time" public_interface="out" units="second"/>
</component>
<component name="state">
<variable name="t" public_interface="in" units="second"/>
<!-- Parameters-->
<variable name="K_m" public_interface="in" units="dimensionless"/>
<variable name="d1" public_interface="in" units="per_s"/>
<variable name="d2" public_interface="in" units="per_s"/>
<variable name="K_cr" public_interface="in" units="per_s"/>
<variable name="K_ex" public_interface="in" units="per_s"/>
<variable name="K_end" public_interface="in" units="per_s"/>
<variable name="K_dp" public_interface="in" units="per_s"/>
<variable name="K_cat" public_interface="in" units="per_s"/>
<variable name="kfbasal" public_interface="in" units="per_s"/>
<variable name="krbasal" public_interface="in" units="per_s"/>
<variable name="K8" public_interface="in" units="per_s"/>
<variable name="a1" public_interface="in" units="per_M_s"/>
<variable name="a2" public_interface="in" units="per_M_s"/>
<variable name="K4" public_interface="in" units="per_M_s"/>
<!-- State variables-->
<!-- r0: inactive receptor state with no insulin bound
r1: inactive receptor state with 1 insulin molecule bound to site 1
r2: inactive receptor state with 1 insulin molecule bound to site 2
r11: inactive receptor state with 2 insulin molecules bound to site 1
r12: inactive receptor state with 2 insulin molecules bound to site 1 and 2 respectively
r22: inactive receptor state with 2 insulin molecules bound to site 2
r1x2: active receptor state with 2 insulin molecules bound to site 1 and 2 respectively
r11x2: active receptor state with 3 insulin molecules bound, 2 to site 1 and 1 to site 2
r1x22: active receptor state with 3 insulin molecules bound, 1 to site 1 and 2 to site 2
r1x22d: active receptor state with 1 insulin molecules bound to site 1 and an insulin dimer to site 2
r11x22: active receptor state with 4 insulin molecules bound, 2 to site 1 and 2 to site 2
rend: internalised receptor states
rendP: internalised and phosphorylated receptor states
iendIR: receptor bound internalised insulin molecules
iend: internalised insulin molecules
rPbasal: state that account for the basal phosphorylation of receptor states-->
<variable name="INS" public_interface="in" units="M"/>
<variable name="S1" public_interface="out" units="M"/>
<variable initial_value="0" name="S2" public_interface="out" units="M"/>
<variable name="X_P" public_interface="in" units="dimensionless"/>
<variable initial_value="9.9682" name="r0" public_interface="out" units="dimensionless"/>
<variable initial_value="0.02214" name="r1" public_interface="out" units="dimensionless"/>
<variable initial_value="0.00935" name="r2" public_interface="out" units="dimensionless"/>
<variable initial_value="1.22887e-5" name="r11" public_interface="out" units="dimensionless"/>
<variable initial_value="1.03764e-5" name="r12" public_interface="out" units="dimensionless"/>
<variable initial_value="2.18683e-6" name="r22" public_interface="out" units="dimensionless"/>
<variable initial_value="1.36476e-6" name="r1x2" public_interface="out" units="dimensionless"/>
<variable initial_value="1.51514e-9" name="r11x2" public_interface="out" units="dimensionless"/>
<variable initial_value="6.39352e-10" name="r1x22" public_interface="out" units="dimensionless"/>
<variable initial_value="5.59231e-20" name="r1x22d" public_interface="out" units="dimensionless"/>
<variable initial_value="1.78726e-14" name="r11x22" public_interface="out" units="dimensionless"/>
<variable initial_value="3.31712e-5" name="rend" public_interface="out" units="dimensionless"/>
<variable initial_value="0.0002125" name="rendP" public_interface="out" units="dimensionless"/>
<variable initial_value="7.25519e-6" name="iendIR" public_interface="out" units="dimensionless"/>
<variable initial_value="1.13228e-6" name="iend" public_interface="out" units="dimensionless"/>
<variable initial_value="3.8723e-5" name="rPbasal" public_interface="out" units="dimensionless"/>
<variable name="R1" public_interface="out" units="per_s"/>
<variable name="R2" public_interface="out" units="per_s"/>
<variable name="R3" public_interface="out" units="per_s"/>
<variable name="R4" public_interface="out" units="per_s"/>
<variable name="R5" public_interface="out" units="per_s"/>
<variable name="R6" public_interface="out" units="per_s"/>
<variable name="R7" public_interface="out" units="per_s"/>
<variable name="R8" public_interface="out" units="per_s"/>
<variable name="R9" public_interface="out" units="per_s"/>
<variable name="R10" public_interface="out" units="per_s"/>
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<variable name="R25" public_interface="out" units="per_s"/>
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<variable name="R27" public_interface="out" units="per_s"/>
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<variable name="R30" public_interface="out" units="per_s"/>
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<variable name="R39" public_interface="out" units="per_s"/>
<variable name="R40" public_interface="out" units="per_s"/>
<variable name="R41" public_interface="out" units="per_s"/>
<variable name="R42" public_interface="out" units="per_s"/>
<variable name="R43" public_interface="out" units="per_s"/>
<variable name="R44" public_interface="out" units="per_s"/>
<variable name="R45" public_interface="out" units="per_s"/>
<variable name="R46" public_interface="out" units="per_s"/>
<variable name="R47" public_interface="out" units="per_s"/>
<variable name="R48" public_interface="out" units="per_s"/>
<!-- Conservation laws-->
<math xmlns="http://www.w3.org/1998/Math/MathML">
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<!-- Internalisation Process-->
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<ci>r11x22</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>R36</ci>
<apply>
<times/>
<ci>d2</ci>
<ci>r11x22</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>R37</ci>
<apply>
<times/>
<ci>K_ex</ci>
<ci>rend</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>R38</ci>
<apply>
<times/>
<ci>K_ex</ci>
<ci>iend</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>R39</ci>
<apply>
<times/>
<ci>K_end</ci>
<ci>r1x2</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>R40</ci>
<apply>
<times/>
<ci>K_end</ci>
<ci>r11x2</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>R41</ci>
<apply>
<times/>
<ci>K_end</ci>
<ci>r1x22</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>R42</ci>
<apply>
<times/>
<ci>K_end</ci>
<ci>r1x22d</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>R43</ci>
<apply>
<times/>
<ci>K_end</ci>
<ci>r11x22</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>R44</ci>
<apply>
<times/>
<apply>
<plus/>
<ci>K_dp</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>K_cat</ci>
<ci>X_P</ci>
</apply>
<apply>
<plus/>
<ci>K_m</ci>
<ci>X_P</ci>
</apply>
</apply>
</apply>
<ci>rendP</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>R45</ci>
<apply>
<times/>
<apply>
<plus/>
<ci>K_dp</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>K_cat</ci>
<ci>X_P</ci>
</apply>
<apply>
<plus/>
<ci>K_m</ci>
<ci>X_P</ci>
</apply>
</apply>
</apply>
<ci>iendIR</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>R46</ci>
<apply>
<times/>
<ci>kfbasal</ci>
<ci>r0</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>R47</ci>
<apply>
<times/>
<ci>krbasal</ci>
<ci>rPbasal</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>R48</ci>
<apply>
<times/>
<ci>K_end</ci>
<ci>rPbasal</ci>
</apply>
</apply>
</math>
</component>
<connection>
<map_components component_1="state" component_2="param"/>
<map_variables variable_1="a1" variable_2="a1"/>
<map_variables variable_1="a2" variable_2="a2"/>
<map_variables variable_1="d1" variable_2="d1"/>
<map_variables variable_1="d2" variable_2="d2"/>
<map_variables variable_1="K_cr" variable_2="K_cr"/>
<map_variables variable_1="K_ex" variable_2="K_ex"/>
<map_variables variable_1="K_end" variable_2="K_end"/>
<map_variables variable_1="K_dp" variable_2="K_dp"/>
<map_variables variable_1="K_cat" variable_2="K_cat"/>
<map_variables variable_1="K_m" variable_2="K_m"/>
<map_variables variable_1="kfbasal" variable_2="kfbasal"/>
<map_variables variable_1="krbasal" variable_2="krbasal"/>
<map_variables variable_1="K4" variable_2="K4"/>
<map_variables variable_1="K8" variable_2="K8"/>
</connection>
<connection>
<map_components component_1="environment" component_2="state"/>
<map_variables variable_1="time" variable_2="t"/>
</connection>
</model>