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/>
                    <apply>
                        <minus/>
                        <apply>
                            <plus/>
                            <apply>
                                <minus/>
                                <apply>
                                    <minus/>
                                    <ci>R1</ci>
                                </apply>
                                <ci>R2</ci>
                            </apply>
                            <ci>R5</ci>
                            <ci>R8</ci>
                            <ci>R37</ci>
                        </apply>
                        <ci>R46</ci>
                    </apply>
                    <ci>R47</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>r1</ci>
                </apply>
                <apply>
                    <plus/>
                    <apply>
                        <minus/>
                        <apply>
                            <minus/>
                            <apply>
                                <minus/>
                                <apply>
                                    <minus/>
                                    <ci>R1</ci>
                                    <ci>R3</ci>
                                </apply>
                                <ci>R5</ci>
                            </apply>
                            <ci>R6</ci>
                        </apply>
                        <ci>R9</ci>
                    </apply>
                    <ci>R12</ci>
                    <ci>R15</ci>
                    <ci>R19</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>r2</ci>
                </apply>
                <apply>
                    <plus/>
                    <apply>
                        <minus/>
                        <apply>
                            <minus/>
                            <apply>
                                <minus/>
                                <apply>
                                    <minus/>
                                    <ci>R2</ci>
                                    <ci>R4</ci>
                                </apply>
                                <ci>R7</ci>
                            </apply>
                            <ci>R8</ci>
                        </apply>
                        <ci>R10</ci>
                    </apply>
                    <ci>R13</ci>
                    <ci>R16</ci>
                    <ci>R22</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>r11</ci>
                </apply>
                <apply>
                    <plus/>
                    <apply>
                        <minus/>
                        <apply>
                            <minus/>
                            <ci>R3</ci>
                            <ci>R12</ci>
                        </apply>
                        <ci>R17</ci>
                    </apply>
                    <ci>R26</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>r12</ci>
                </apply>
                <apply>
                    <plus/>
                    <apply>
                        <minus/>
                        <apply>
                            <minus/>
                            <apply>
                                <minus/>
                                <apply>
                                    <minus/>
                                    <apply>
                                        <plus/>
                                        <ci>R4</ci>
                                        <ci>R6</ci>
                                    </apply>
                                    <ci>R13</ci>
                                </apply>
                                <ci>R15</ci>
                            </apply>
                            <ci>R18</ci>
                        </apply>
                        <ci>R20</ci>
                    </apply>
                    <ci>R27</ci>
                    <ci>R28</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>r22</ci>
                </apply>
                <apply>
                    <plus/>
                    <apply>
                        <minus/>
                        <apply>
                            <minus/>
                            <ci>R7</ci>
                            <ci>R16</ci>
                        </apply>
                        <ci>R21</ci>
                    </apply>
                    <ci>R29</ci>
                </apply>
            </apply>
            <!-- Active Receptor States-->
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>r1x2</ci>
                </apply>
                <apply>
                    <minus/>
                    <apply>
                        <plus/>
                        <apply>
                            <minus/>
                            <apply>
                                <minus/>
                                <apply>
                                    <minus/>
                                    <apply>
                                        <minus/>
                                        <apply>
                                            <minus/>
                                            <apply>
                                                <plus/>
                                                <ci>R9</ci>
                                                <ci>R10</ci>
                                            </apply>
                                            <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>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>r11x2</ci>
                </apply>
                <apply>
                    <minus/>
                    <apply>
                        <plus/>
                        <apply>
                            <minus/>
                            <apply>
                                <minus/>
                                <apply>
                                    <minus/>
                                    <apply>
                                        <minus/>
                                        <apply>
                                            <plus/>
                                            <ci>R11</ci>
                                            <ci>R17</ci>
                                            <ci>R20</ci>
                                        </apply>
                                        <ci>R24</ci>
                                    </apply>
                                    <ci>R26</ci>
                                </apply>
                                <ci>R28</ci>
                            </apply>
                            <ci>R31</ci>
                        </apply>
                        <ci>R36</ci>
                    </apply>
                    <ci>R40</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>r1x22</ci>
                </apply>
                <apply>
                    <minus/>
                    <apply>
                        <plus/>
                        <apply>
                            <minus/>
                            <apply>
                                <minus/>
                                <apply>
                                    <minus/>
                                    <apply>
                                        <minus/>
                                        <apply>
                                            <minus/>
                                            <apply>
                                                <plus/>
                                                <ci>R14</ci>
                                                <ci>R18</ci>
                                                <ci>R21</ci>
                                            </apply>
                                            <ci>R25</ci>
                                        </apply>
                                        <ci>R27</ci>
                                    </apply>
                                    <ci>R29</ci>
                                </apply>
                                <ci>R30</ci>
                            </apply>
                            <ci>R32</ci>
                        </apply>
                        <ci>R33</ci>
                        <ci>R35</ci>
                    </apply>
                    <ci>R41</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>r1x22d</ci>
                </apply>
                <apply>
                    <minus/>
                    <apply>
                        <minus/>
                        <apply>
                            <minus/>
                            <apply>
                                <plus/>
                                <ci>R23</ci>
                                <ci>R32</ci>
                            </apply>
                            <ci>R33</ci>
                        </apply>
                        <ci>R34</ci>
                    </apply>
                    <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>
                    <times/>
                    <ci>d1</ci>
                    <ci>r1</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>R6</ci>
                <apply>
                    <times/>
                    <ci>a2</ci>
                    <ci>S1</ci>
                    <ci>r1</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>R7</ci>
                <apply>
                    <times/>
                    <ci>a2</ci>
                    <ci>S1</ci>
                    <ci>r2</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>R8</ci>
                <apply>
                    <times/>
                    <ci>d2</ci>
                    <ci>r2</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>R9</ci>
                <apply>
                    <times/>
                    <ci>K_cr</ci>
                    <ci>r1</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>R10</ci>
                <apply>
                    <times/>
                    <ci>K_cr</ci>
                    <ci>r2</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>R11</ci>
                <apply>
                    <times/>
                    <ci>a1</ci>
                    <ci>S1</ci>
                    <ci>r1x2</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>R12</ci>
                <apply>
                    <times/>
                    <cn cellml:units="dimensionless">2</cn>
                    <ci>d1</ci>
                    <ci>r11</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>R13</ci>
                <apply>
                    <times/>
                    <ci>d1</ci>
                    <ci>r12</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>R14</ci>
                <apply>
                    <times/>
                    <ci>a2</ci>
                    <ci>S1</ci>
                    <ci>r1x2</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>R15</ci>
                <apply>
                    <times/>
                    <ci>d2</ci>
                    <ci>r12</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>R16</ci>
                <apply>
                    <times/>
                    <cn cellml:units="dimensionless">2</cn>
                    <ci>d2</ci>
                    <ci>r22</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>R17</ci>
                <apply>
                    <times/>
                    <cn cellml:units="dimensionless">2</cn>
                    <ci>K_cr</ci>
                    <ci>r11</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>R18</ci>
                <apply>
                    <times/>
                    <ci>K_cr</ci>
                    <ci>r12</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>R19</ci>
                <apply>
                    <times/>
                    <ci>d2</ci>
                    <ci>r1x2</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>R20</ci>
                <apply>
                    <times/>
                    <ci>K_cr</ci>
                    <ci>r12</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>R21</ci>
                <apply>
                    <times/>
                    <cn cellml:units="dimensionless">2</cn>
                    <ci>K_cr</ci>
                    <ci>r22</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>R22</ci>
                <apply>
                    <times/>
                    <ci>d1</ci>
                    <ci>r1x2</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>R23</ci>
                <apply>
                    <times/>
                    <ci>a2</ci>
                    <ci>S2</ci>
                    <ci>r1x2</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>R24</ci>
                <apply>
                    <times/>
                    <ci>d1</ci>
                    <ci>r11x2</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>R25</ci>
                <apply>
                    <times/>
                    <ci>d2</ci>
                    <ci>r1x22</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>R26</ci>
                <apply>
                    <times/>
                    <ci>d2</ci>
                    <ci>r11x2</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>R27</ci>
                <apply>
                    <times/>
                    <ci>d2</ci>
                    <ci>r1x22</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>R28</ci>
                <apply>
                    <times/>
                    <ci>d1</ci>
                    <ci>r11x2</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>R29</ci>
                <apply>
                    <times/>
                    <ci>d1</ci>
                    <ci>r1x22</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>R30</ci>
                <apply>
                    <times/>
                    <ci>a1</ci>
                    <ci>S1</ci>
                    <ci>r1x22</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>R31</ci>
                <apply>
                    <times/>
                    <ci>a2</ci>
                    <ci>S1</ci>
                    <ci>r11x2</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>R32</ci>
                <apply>
                    <times/>
                    <ci>K4</ci>
                    <ci>S1</ci>
                    <ci>r1x22</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>R33</ci>
                <apply>
                    <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>