Location: Diabetes @ 35523e4fa869 / 3-InsulinBindingLevel.cellml
- Author:
- Soroush Safaei <ssaf006@aucklanduni.ac.nz>
- Date:
- 2017-03-23 00:03:16+13:00
- Desc:
- finishing insulin model
- Permanent Source URI:
- https://models.cellml.org/workspace/483/rawfile/35523e4fa86913421c5b384f16fc95bf425e2e62/3-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="Units.cellml">
<units name="l_per_kg" units_ref="l_per_kg"/>
<units name="per_s" units_ref="per_s"/>
<units name="s_kg_per_pmol" units_ref="s_kg_per_pmol"/>
<units name="mg" units_ref="mg"/>
<units name="per_mg" units_ref="per_mg"/>
<units name="mg_per_kg_s" units_ref="mg_per_kg_s"/>
<units name="mg_l_per_kg_s_pmol" units_ref="mg_l_per_kg_s_pmol"/>
<units name="mg_per_s_pmol" units_ref="mg_per_s_pmol"/>
<units name="mg_per_kg" units_ref="mg_per_kg"/>
<units name="pmol_l_per_kg_mg" units_ref="pmol_l_per_kg_mg"/>
<units name="pmol_l_per_kg_mg_s" units_ref="pmol_l_per_kg_mg_s"/>
<units name="pmol_per_kg" units_ref="pmol_per_kg"/>
<units name="pmol_per_l" units_ref="pmol_per_l"/>
<units name="mg_per_l" units_ref="mg_per_l"/>
<units name="pmol_per_kg_s" units_ref="pmol_per_kg_s"/>
<units name="l_per_mol_s" units_ref="l_per_mol_s"/>
<units name="mol_per_l" units_ref="mol_per_l"/>
</import>
<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="a1" public_interface="in" units="l_per_mol_s"/>
<variable name="a2" public_interface="in" units="l_per_mol_s"/>
<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="K_m" 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="K4" public_interface="in" units="l_per_mol_s"/>
<variable name="K8" public_interface="in" units="per_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="pmol_per_l"/>
<variable name="S1" units="mol_per_l"/>
<variable initial_value="0" name="S2" units="mol_per_l"/>
<variable name="X_P" public_interface="in" units="dimensionless"/>
<variable initial_value="9.9682" name="r0" units="dimensionless"/>
<variable initial_value="0.02214" name="r1" units="dimensionless"/>
<variable initial_value="0.00935" name="r2" units="dimensionless"/>
<variable initial_value="1.22887e-5" name="r11" units="dimensionless"/>
<variable initial_value="1.03764e-5" name="r12" units="dimensionless"/>
<variable initial_value="2.18683e-6" name="r22" 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" units="dimensionless"/>
<variable initial_value="0.0002125" name="rendP" public_interface="out" units="dimensionless"/>
<variable initial_value="7.25519e-6" name="iendIR" units="dimensionless"/>
<variable initial_value="1.13228e-6" name="iend" units="dimensionless"/>
<variable initial_value="3.8723e-5" name="rPbasal" public_interface="out" units="dimensionless"/>
<variable name="R1" units="per_s"/>
<variable name="R2" units="per_s"/>
<variable name="R3" units="per_s"/>
<variable name="R4" units="per_s"/>
<variable name="R5" units="per_s"/>
<variable name="R6" units="per_s"/>
<variable name="R7" units="per_s"/>
<variable name="R8" units="per_s"/>
<variable name="R9" units="per_s"/>
<variable name="R10" units="per_s"/>
<variable name="R11" units="per_s"/>
<variable name="R12" units="per_s"/>
<variable name="R13" units="per_s"/>
<variable name="R14" units="per_s"/>
<variable name="R15" units="per_s"/>
<variable name="R16" units="per_s"/>
<variable name="R17" units="per_s"/>
<variable name="R18" units="per_s"/>
<variable name="R19" units="per_s"/>
<variable name="R20" units="per_s"/>
<variable name="R21" units="per_s"/>
<variable name="R22" units="per_s"/>
<variable name="R23" units="per_s"/>
<variable name="R24" units="per_s"/>
<variable name="R25" units="per_s"/>
<variable name="R26" units="per_s"/>
<variable name="R27" units="per_s"/>
<variable name="R28" units="per_s"/>
<variable name="R29" units="per_s"/>
<variable name="R30" units="per_s"/>
<variable name="R31" units="per_s"/>
<variable name="R32" units="per_s"/>
<variable name="R33" units="per_s"/>
<variable name="R34" units="per_s"/>
<variable name="R35" units="per_s"/>
<variable name="R36" units="per_s"/>
<variable name="R37" units="per_s"/>
<variable name="R38" units="per_s"/>
<variable name="R39" units="per_s"/>
<variable name="R40" units="per_s"/>
<variable name="R41" units="per_s"/>
<variable name="R42" units="per_s"/>
<variable name="R43" units="per_s"/>
<variable name="R44" units="per_s"/>
<variable name="R45" units="per_s"/>
<variable name="R46" units="per_s"/>
<variable name="R47" units="per_s"/>
<variable name="R48" units="per_s"/>
<!-- Conservation laws-->
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>S1</ci>
<apply>
<times/>
<apply>
<plus/>
<ci>INS</ci>
<cn cellml:units="pmol_per_l">5</cn>
</apply>
<cn cellml:units="dimensionless" type="e-notation">1<sep/>-12</cn>
</apply>
</apply>
<!-- Inactive Receptor States-->
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>r0</ci>
</apply>
<apply>
<plus/>
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<ci>R1</ci>
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</apply>
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<ci>R47</ci>
</apply>
</apply>
<apply>
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</apply>
<apply>
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<ci>R6</ci>
</apply>
<ci>R9</ci>
</apply>
<ci>R12</ci>
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</apply>
</apply>
<apply>
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<ci>r2</ci>
</apply>
<apply>
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<ci>R7</ci>
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<ci>R8</ci>
</apply>
<ci>R10</ci>
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<ci>R13</ci>
<ci>R16</ci>
<ci>R22</ci>
</apply>
</apply>
<apply>
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</bvar>
<ci>r11</ci>
</apply>
<apply>
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<ci>R3</ci>
<ci>R12</ci>
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<ci>R17</ci>
</apply>
<ci>R26</ci>
</apply>
</apply>
<apply>
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<!-- Active Receptor States-->
<apply>
<eq/>
<apply>
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<ci>r1x2</ci>
</apply>
<apply>
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<ci>R10</ci>
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<ci>R11</ci>
</apply>
<ci>R14</ci>
</apply>
<ci>R19</ci>
</apply>
<ci>R22</ci>
</apply>
<ci>R23</ci>
</apply>
<ci>R24</ci>
<ci>R25</ci>
<ci>R34</ci>
</apply>
<ci>R39</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
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<bvar>
<ci>t</ci>
</bvar>
<ci>r11x2</ci>
</apply>
<apply>
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<apply>
<plus/>
<apply>
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<apply>
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<apply>
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<ci>R11</ci>
<ci>R17</ci>
<ci>R20</ci>
</apply>
<ci>R24</ci>
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<ci>R26</ci>
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<ci>R31</ci>
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<ci>R40</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>r1x22</ci>
</apply>
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<ci>R14</ci>
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<ci>R33</ci>
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</apply>
<ci>R41</ci>
</apply>
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<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>r1x22d</ci>
</apply>
<apply>
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<apply>
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<apply>
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<apply>
<plus/>
<ci>R23</ci>
<ci>R32</ci>
</apply>
<ci>R33</ci>
</apply>
<ci>R34</ci>
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<ci>R42</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>r11x22</ci>
</apply>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<plus/>
<ci>R30</ci>
<ci>R31</ci>
</apply>
<ci>R35</ci>
</apply>
<ci>R36</ci>
</apply>
<ci>R43</ci>
</apply>
</apply>
<!-- Internalisation Process-->
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>rend</ci>
</apply>
<apply>
<plus/>
<apply>
<minus/>
<ci>R37</ci>
</apply>
<ci>R44</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>rendP</ci>
</apply>
<apply>
<plus/>
<apply>
<minus/>
<ci>R44</ci>
</apply>
<ci>R39</ci>
<ci>R40</ci>
<ci>R41</ci>
<ci>R42</ci>
<ci>R43</ci>
<ci>R48</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>iendIR</ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<ci>R39</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>R40</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>R41</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">3</cn>
<ci>R42</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">3</cn>
<ci>R43</ci>
</apply>
</apply>
<ci>R45</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>iend</ci>
</apply>
<apply>
<plus/>
<apply>
<minus/>
<ci>R38</ci>
</apply>
<ci>R45</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>rPbasal</ci>
</apply>
<apply>
<minus/>
<apply>
<minus/>
<ci>R46</ci>
<ci>R47</ci>
</apply>
<ci>R48</ci>
</apply>
</apply>
<!-- Reactions-->
<apply>
<eq/>
<ci>R1</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>a1</ci>
<ci>S1</ci>
<ci>r0</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>R2</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>a2</ci>
<ci>S1</ci>
<ci>r0</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>R3</ci>
<apply>
<times/>
<ci>a1</ci>
<ci>S1</ci>
<ci>r1</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>R4</ci>
<apply>
<times/>
<ci>a1</ci>
<ci>S1</ci>
<ci>r2</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>R5</ci>
<apply>
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<apply>
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<apply>
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<ci>r1</ci>
</apply>
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<apply>
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<ci>R7</ci>
<apply>
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<apply>
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<times/>
<ci>K8</ci>
<ci>r1x22d</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>R34</ci>
<apply>
<times/>
<ci>d2</ci>
<ci>r1x22d</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>R35</ci>
<apply>
<times/>
<ci>d1</ci>
<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>