Location: Na+/K+-ATPase (sodium-potassium pump) @ ab05b632e8a8 / BG-full / StateDiagram.cellml

Author:
Soroush Safaei <ssaf006@aucklanduni.ac.nz>
Date:
2017-01-31 18:55:59+13:00
Desc:
adding the single file version of BG
Permanent Source URI:
https://staging.physiomeproject.org/workspace/294/rawfile/ab05b632e8a8bda23904da10c37a0a67e8a07a67/BG-full/StateDiagram.cellml

<?xml version='1.0'?>
<model name="StateDiagram" xmlns="http://www.cellml.org/cellml/1.1#" xmlns:cellml="http://www.cellml.org/cellml/1.1#">
    <component name="state">
        <variable name="t" public_interface="in" units="second"/>
        <variable name="RT" public_interface="in" units="J_per_mol"/>
        <variable name="z" public_interface="in" units="dimensionless"/>
        <variable name="F" public_interface="in" units="C_per_mol"/>
        <!-- Parameters-->
        <variable name="K_q1" public_interface="in" units="per_mM"/>
        <variable name="K_q2" public_interface="in" units="per_mM"/>
        <variable name="K_q3" public_interface="in" units="per_mM"/>
        <variable name="K_q4" public_interface="in" units="per_mM"/>
        <variable name="K_q5" public_interface="in" units="per_mM"/>
        <variable name="K_q6" public_interface="in" units="per_mM"/>
        <variable name="K_q7" public_interface="in" units="per_mM"/>
        <variable name="K_q8" public_interface="in" units="per_mM"/>
        <variable name="K_q9" public_interface="in" units="per_mM"/>
        <variable name="K_q10" public_interface="in" units="per_mM"/>
        <variable name="K_q11" public_interface="in" units="per_mM"/>
        <variable name="K_q12" public_interface="in" units="per_mM"/>
        <variable name="K_q13" public_interface="in" units="per_mM"/>
        <variable name="K_q14" public_interface="in" units="per_mM"/>
        <variable name="K_q15" public_interface="in" units="per_mM"/>
        <variable name="K_q16" public_interface="in" units="per_mM"/>
        <variable name="K_q17" public_interface="in" units="per_mM"/>
        <variable name="K_q18" public_interface="in" units="per_mM"/>
        <variable name="K_q19" public_interface="in" units="per_mM"/>
        <variable name="K_q20" public_interface="in" units="per_mM"/>
        <variable name="K_q21" public_interface="in" units="per_mM"/>
        <variable name="K_q22" public_interface="in" units="per_mM"/>
        <variable name="K_E" public_interface="in" units="per_mM"/>
        <variable name="K_Re1" public_interface="in" units="mM_per_s"/>
        <variable name="K_Re2" public_interface="in" units="mM_per_s"/>
        <variable name="K_Re3" public_interface="in" units="mM_per_s"/>
        <variable name="K_Re4" public_interface="in" units="mM_per_s"/>
        <variable name="K_Re5" public_interface="in" units="mM_per_s"/>
        <variable name="K_Re6" public_interface="in" units="mM_per_s"/>
        <variable name="K_Re7" public_interface="in" units="mM_per_s"/>
        <variable name="K_Re8" public_interface="in" units="mM_per_s"/>
        <variable name="K_Re9" public_interface="in" units="mM_per_s"/>
        <variable name="K_Re10" public_interface="in" units="mM_per_s"/>
        <variable name="K_Re11" public_interface="in" units="mM_per_s"/>
        <variable name="K_Re12" public_interface="in" units="mM_per_s"/>
        <variable name="K_Re13" public_interface="in" units="mM_per_s"/>
        <variable name="K_Re14" public_interface="in" units="mM_per_s"/>
        <variable name="K_Re15" public_interface="in" units="mM_per_s"/>
        <!-- State variables-->
        <variable name="q1_init" public_interface="in" units="mM"/>
        <variable name="q2_init" public_interface="in" units="mM"/>
        <variable name="q3_init" public_interface="in" units="mM"/>
        <variable name="q4_init" public_interface="in" units="mM"/>
        <variable name="q5_init" public_interface="in" units="mM"/>
        <variable name="q6_init" public_interface="in" units="mM"/>
        <variable name="q7_init" public_interface="in" units="mM"/>
        <variable name="q8_init" public_interface="in" units="mM"/>
        <variable name="q9_init" public_interface="in" units="mM"/>
        <variable name="q10_init" public_interface="in" units="mM"/>
        <variable name="q11_init" public_interface="in" units="mM"/>
        <variable name="q12_init" public_interface="in" units="mM"/>
        <variable name="q13_init" public_interface="in" units="mM"/>
        <variable name="q14_init" public_interface="in" units="mM"/>
        <variable name="q15_init" public_interface="in" units="mM"/>
        <variable name="q16_init" public_interface="in" units="mM"/>
        <variable name="q17_init" public_interface="in" units="mM"/>
        <variable name="q18_init" public_interface="in" units="mM"/>
        <variable name="q19_init" public_interface="in" units="mM"/>
        <variable name="q20_init" public_interface="in" units="mM"/>
        <variable name="q21_init" public_interface="in" units="mM"/>
        <variable name="q22_init" public_interface="in" units="mM"/>
        <!--        var q_E_init: mM {pub: in};-->
        <variable initial_value="0.0" name="q1_aux" units="mM"/>
        <variable initial_value="0.0" name="q2_aux" units="mM"/>
        <variable initial_value="0.0" name="q3_aux" units="mM"/>
        <variable initial_value="0.0" name="q4_aux" units="mM"/>
        <variable initial_value="0.0" name="q5_aux" units="mM"/>
        <variable initial_value="0.0" name="q6_aux" units="mM"/>
        <variable initial_value="0.0" name="q7_aux" units="mM"/>
        <variable initial_value="0.0" name="q8_aux" units="mM"/>
        <variable initial_value="0.0" name="q9_aux" units="mM"/>
        <variable initial_value="0.0" name="q10_aux" units="mM"/>
        <variable initial_value="0.0" name="q11_aux" units="mM"/>
        <variable initial_value="0.0" name="q12_aux" units="mM"/>
        <variable initial_value="0.0" name="q13_aux" units="mM"/>
        <variable initial_value="0.0" name="q14_aux" units="mM"/>
        <variable initial_value="0.0" name="q15_aux" units="mM"/>
        <variable initial_value="0.0" name="q16_aux" units="mM"/>
        <variable initial_value="0.0" name="q17_aux" units="mM"/>
        <variable initial_value="0.0" name="q18_aux" units="mM"/>
        <variable initial_value="0.0" name="q19_aux" units="mM"/>
        <variable initial_value="0.0" name="q20_aux" units="mM"/>
        <variable initial_value="0.0" name="q21_aux" units="mM"/>
        <variable initial_value="0.0" name="q22_aux" units="mM"/>
        <!--        var q_E_aux: mM {init: 0.0};-->
        <variable name="q1" public_interface="out" units="mM"/>
        <variable name="q2" public_interface="out" units="mM"/>
        <variable name="q3" public_interface="out" units="mM"/>
        <variable name="q4" public_interface="out" units="mM"/>
        <variable name="q5" public_interface="out" units="mM"/>
        <variable name="q6" public_interface="out" units="mM"/>
        <variable name="q7" public_interface="out" units="mM"/>
        <variable name="q8" public_interface="out" units="mM"/>
        <variable name="q9" public_interface="out" units="mM"/>
        <variable name="q10" public_interface="out" units="mM"/>
        <variable name="q11" public_interface="out" units="mM"/>
        <variable name="q12" public_interface="out" units="mM"/>
        <variable name="q13" public_interface="out" units="mM"/>
        <variable name="q14" public_interface="out" units="mM"/>
        <variable name="q15" public_interface="out" units="mM"/>
        <variable name="q16" public_interface="out" units="mM"/>
        <variable name="q17" public_interface="out" units="mM"/>
        <variable name="q18" public_interface="out" units="mM"/>
        <variable name="q19" public_interface="out" units="mM"/>
        <variable name="q20" public_interface="out" units="mM"/>
        <variable name="q21" public_interface="out" units="mM"/>
        <variable name="q22" public_interface="out" units="mM"/>
        <!--        var q_E: mM {pub: out};-->
        <variable name="v_Re1" public_interface="out" units="mM_per_s"/>
        <variable name="v_Re2" public_interface="out" units="mM_per_s"/>
        <variable name="v_Re3" public_interface="out" units="mM_per_s"/>
        <variable name="v_Re4" public_interface="out" units="mM_per_s"/>
        <variable name="v_Re5" public_interface="out" units="mM_per_s"/>
        <variable name="v_Re6" public_interface="out" units="mM_per_s"/>
        <variable name="v_Re7" public_interface="out" units="mM_per_s"/>
        <variable name="v_Re8" public_interface="out" units="mM_per_s"/>
        <variable name="v_Re9" public_interface="out" units="mM_per_s"/>
        <variable name="v_Re10" public_interface="out" units="mM_per_s"/>
        <variable name="v_Re11" public_interface="out" units="mM_per_s"/>
        <variable name="v_Re12" public_interface="out" units="mM_per_s"/>
        <variable name="v_Re13" public_interface="out" units="mM_per_s"/>
        <variable name="v_Re14" public_interface="out" units="mM_per_s"/>
        <variable name="v_Re15" public_interface="out" units="mM_per_s"/>
        <variable name="u1" public_interface="out" units="J_per_mol"/>
        <variable name="u2" public_interface="out" units="J_per_mol"/>
        <variable name="u3" public_interface="out" units="J_per_mol"/>
        <variable name="u4" public_interface="out" units="J_per_mol"/>
        <variable name="u5" public_interface="out" units="J_per_mol"/>
        <variable name="u6" public_interface="out" units="J_per_mol"/>
        <variable name="u7" public_interface="out" units="J_per_mol"/>
        <variable name="u8" public_interface="out" units="J_per_mol"/>
        <variable name="u9" public_interface="out" units="J_per_mol"/>
        <variable name="u10" public_interface="out" units="J_per_mol"/>
        <variable name="u11" public_interface="out" units="J_per_mol"/>
        <variable name="u12" public_interface="out" units="J_per_mol"/>
        <variable name="u13" public_interface="out" units="J_per_mol"/>
        <variable name="u14" public_interface="out" units="J_per_mol"/>
        <variable name="u15" public_interface="out" units="J_per_mol"/>
        <variable name="u16" public_interface="out" units="J_per_mol"/>
        <variable name="u17" public_interface="out" units="J_per_mol"/>
        <variable name="u18" public_interface="out" units="J_per_mol"/>
        <variable name="u19" public_interface="out" units="J_per_mol"/>
        <variable name="u20" public_interface="out" units="J_per_mol"/>
        <variable name="u21" public_interface="out" units="J_per_mol"/>
        <variable name="u22" public_interface="out" units="J_per_mol"/>
        <variable name="u23" public_interface="out" units="J_per_mol"/>
        <variable name="u24" public_interface="out" units="J_per_mol"/>
        <variable name="u25" public_interface="out" units="J_per_mol"/>
        <variable name="u26" public_interface="out" units="J_per_mol"/>
        <variable name="u27" public_interface="out" units="J_per_mol"/>
        <variable name="u28" public_interface="out" units="J_per_mol"/>
        <variable name="u29" public_interface="out" units="J_per_mol"/>
        <variable name="u30" public_interface="out" units="J_per_mol"/>
        <variable name="u31" public_interface="out" units="J_per_mol"/>
        <variable name="u32" public_interface="out" units="J_per_mol"/>
        <variable name="u33" public_interface="out" units="J_per_mol"/>
        <variable name="u34" public_interface="out" units="J_per_mol"/>
        <variable name="u35" public_interface="out" units="J_per_mol"/>
        <variable name="u36" public_interface="out" units="J_per_mol"/>
        <variable name="u_E" public_interface="in" units="J_per_C"/>
        <!-- Conservation laws-->
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>q1_aux</ci>
                </apply>
                <apply>
                    <plus/>
                    <ci>v_Re1</ci>
                    <ci>v_Re3</ci>
                    <ci>v_Re5</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>q2_aux</ci>
                </apply>
                <apply>
                    <minus/>
                    <apply>
                        <minus/>
                        <apply>
                            <minus/>
                            <ci>v_Re2</ci>
                        </apply>
                        <ci>v_Re4</ci>
                    </apply>
                    <ci>v_Re6</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>q3_aux</ci>
                </apply>
                <apply>
                    <minus/>
                    <apply>
                        <minus/>
                        <ci>v_Re7</ci>
                    </apply>
                    <ci>v_Re9</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>q4_aux</ci>
                </apply>
                <apply>
                    <plus/>
                    <ci>v_Re8</ci>
                    <ci>v_Re10</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>q5_aux</ci>
                </apply>
                <apply>
                    <minus/>
                    <ci>v_Re11</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>q6_aux</ci>
                </apply>
                <ci>v_Re12</ci>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>q7_aux</ci>
                </apply>
                <ci>v_Re13</ci>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>q8_aux</ci>
                </apply>
                <apply>
                    <minus/>
                    <ci>v_Re5</ci>
                    <ci>v_Re7</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>q9_aux</ci>
                </apply>
                <apply>
                    <minus/>
                    <ci>v_Re7</ci>
                    <ci>v_Re9</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>q10_aux</ci>
                </apply>
                <apply>
                    <minus/>
                    <ci>v_Re9</ci>
                    <ci>v_Re13</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>q11_aux</ci>
                </apply>
                <apply>
                    <minus/>
                    <ci>v_Re13</ci>
                    <ci>v_Re11</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>q12_aux</ci>
                </apply>
                <apply>
                    <minus/>
                    <ci>v_Re11</ci>
                    <ci>v_Re14</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>q13_aux</ci>
                </apply>
                <apply>
                    <minus/>
                    <ci>v_Re14</ci>
                    <ci>v_Re10</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>q14_aux</ci>
                </apply>
                <apply>
                    <minus/>
                    <ci>v_Re10</ci>
                    <ci>v_Re8</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>q15_aux</ci>
                </apply>
                <apply>
                    <minus/>
                    <ci>v_Re8</ci>
                    <ci>v_Re6</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>q16_aux</ci>
                </apply>
                <apply>
                    <minus/>
                    <ci>v_Re6</ci>
                    <ci>v_Re4</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>q17_aux</ci>
                </apply>
                <apply>
                    <minus/>
                    <ci>v_Re4</ci>
                    <ci>v_Re2</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>q18_aux</ci>
                </apply>
                <apply>
                    <minus/>
                    <ci>v_Re2</ci>
                    <ci>v_Re12</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>q19_aux</ci>
                </apply>
                <apply>
                    <minus/>
                    <ci>v_Re12</ci>
                    <ci>v_Re15</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>q20_aux</ci>
                </apply>
                <apply>
                    <minus/>
                    <ci>v_Re15</ci>
                    <ci>v_Re1</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>q21_aux</ci>
                </apply>
                <apply>
                    <minus/>
                    <ci>v_Re1</ci>
                    <ci>v_Re3</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>q22_aux</ci>
                </apply>
                <apply>
                    <minus/>
                    <ci>v_Re3</ci>
                    <ci>v_Re5</ci>
                </apply>
            </apply>
            <!--        ode(q_E_aux, t) = z*v_Re15;-->
            <apply>
                <eq/>
                <ci>q1</ci>
                <apply>
                    <plus/>
                    <ci>q1_aux</ci>
                    <ci>q1_init</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>q2</ci>
                <apply>
                    <plus/>
                    <ci>q2_aux</ci>
                    <ci>q2_init</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>q3</ci>
                <apply>
                    <plus/>
                    <ci>q3_aux</ci>
                    <ci>q3_init</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>q4</ci>
                <apply>
                    <plus/>
                    <ci>q4_aux</ci>
                    <ci>q4_init</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>q5</ci>
                <apply>
                    <plus/>
                    <ci>q5_aux</ci>
                    <ci>q5_init</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>q6</ci>
                <apply>
                    <plus/>
                    <ci>q6_aux</ci>
                    <ci>q6_init</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>q7</ci>
                <apply>
                    <plus/>
                    <ci>q7_aux</ci>
                    <ci>q7_init</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>q8</ci>
                <apply>
                    <plus/>
                    <ci>q8_aux</ci>
                    <ci>q8_init</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>q9</ci>
                <apply>
                    <plus/>
                    <ci>q9_aux</ci>
                    <ci>q9_init</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>q10</ci>
                <apply>
                    <plus/>
                    <ci>q10_aux</ci>
                    <ci>q10_init</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>q11</ci>
                <apply>
                    <plus/>
                    <ci>q11_aux</ci>
                    <ci>q11_init</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>q12</ci>
                <apply>
                    <plus/>
                    <ci>q12_aux</ci>
                    <ci>q12_init</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>q13</ci>
                <apply>
                    <plus/>
                    <ci>q13_aux</ci>
                    <ci>q13_init</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>q14</ci>
                <apply>
                    <plus/>
                    <ci>q14_aux</ci>
                    <ci>q14_init</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>q15</ci>
                <apply>
                    <plus/>
                    <ci>q15_aux</ci>
                    <ci>q15_init</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>q16</ci>
                <apply>
                    <plus/>
                    <ci>q16_aux</ci>
                    <ci>q16_init</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>q17</ci>
                <apply>
                    <plus/>
                    <ci>q17_aux</ci>
                    <ci>q17_init</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>q18</ci>
                <apply>
                    <plus/>
                    <ci>q18_aux</ci>
                    <ci>q18_init</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>q19</ci>
                <apply>
                    <plus/>
                    <ci>q19_aux</ci>
                    <ci>q19_init</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>q20</ci>
                <apply>
                    <plus/>
                    <ci>q20_aux</ci>
                    <ci>q20_init</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>q21</ci>
                <apply>
                    <plus/>
                    <ci>q21_aux</ci>
                    <ci>q21_init</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>q22</ci>
                <apply>
                    <plus/>
                    <ci>q22_aux</ci>
                    <ci>q22_init</ci>
                </apply>
            </apply>
            <!--        q_E = q_E_init;-->
            <apply>
                <eq/>
                <ci>u23</ci>
                <apply>
                    <plus/>
                    <ci>u1</ci>
                    <ci>u21</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u24</ci>
                <apply>
                    <plus/>
                    <ci>u1</ci>
                    <ci>u22</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u25</ci>
                <apply>
                    <plus/>
                    <ci>u1</ci>
                    <ci>u8</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u26</ci>
                <apply>
                    <plus/>
                    <ci>u3</ci>
                    <ci>u8</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u27</ci>
                <apply>
                    <plus/>
                    <ci>u3</ci>
                    <ci>u9</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u28</ci>
                <apply>
                    <plus/>
                    <ci>u11</ci>
                    <ci>u7</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u29</ci>
                <apply>
                    <plus/>
                    <ci>u11</ci>
                    <ci>u5</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u30</ci>
                <apply>
                    <plus/>
                    <ci>u4</ci>
                    <ci>u14</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u31</ci>
                <apply>
                    <plus/>
                    <ci>u4</ci>
                    <ci>u15</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u32</ci>
                <apply>
                    <plus/>
                    <ci>u2</ci>
                    <ci>u15</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u33</ci>
                <apply>
                    <plus/>
                    <ci>u2</ci>
                    <ci>u16</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u34</ci>
                <apply>
                    <plus/>
                    <ci>u2</ci>
                    <ci>u17</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u35</ci>
                <apply>
                    <plus/>
                    <ci>u19</ci>
                    <ci>u6</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u36</ci>
                <apply>
                    <minus/>
                    <ci>u19</ci>
                    <apply>
                        <times/>
                        <ci>z</ci>
                        <ci>F</ci>
                        <ci>u_E</ci>
                    </apply>
                </apply>
            </apply>
            <!-- Constitutive relations-->
            <apply>
                <eq/>
                <ci>u1</ci>
                <apply>
                    <times/>
                    <ci>RT</ci>
                    <apply>
                        <ln/>
                        <apply>
                            <times/>
                            <ci>K_q1</ci>
                            <ci>q1</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u2</ci>
                <apply>
                    <times/>
                    <ci>RT</ci>
                    <apply>
                        <ln/>
                        <apply>
                            <times/>
                            <ci>K_q2</ci>
                            <ci>q2</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u3</ci>
                <apply>
                    <times/>
                    <ci>RT</ci>
                    <apply>
                        <ln/>
                        <apply>
                            <times/>
                            <ci>K_q3</ci>
                            <ci>q3</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u4</ci>
                <apply>
                    <times/>
                    <ci>RT</ci>
                    <apply>
                        <ln/>
                        <apply>
                            <times/>
                            <ci>K_q4</ci>
                            <ci>q4</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u5</ci>
                <apply>
                    <times/>
                    <ci>RT</ci>
                    <apply>
                        <ln/>
                        <apply>
                            <times/>
                            <ci>K_q5</ci>
                            <ci>q5</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u6</ci>
                <apply>
                    <times/>
                    <ci>RT</ci>
                    <apply>
                        <ln/>
                        <apply>
                            <times/>
                            <ci>K_q6</ci>
                            <ci>q6</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u7</ci>
                <apply>
                    <times/>
                    <ci>RT</ci>
                    <apply>
                        <ln/>
                        <apply>
                            <times/>
                            <ci>K_q7</ci>
                            <ci>q7</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u8</ci>
                <apply>
                    <times/>
                    <ci>RT</ci>
                    <apply>
                        <ln/>
                        <apply>
                            <times/>
                            <ci>K_q8</ci>
                            <ci>q8</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u9</ci>
                <apply>
                    <times/>
                    <ci>RT</ci>
                    <apply>
                        <ln/>
                        <apply>
                            <times/>
                            <ci>K_q9</ci>
                            <ci>q9</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u10</ci>
                <apply>
                    <times/>
                    <ci>RT</ci>
                    <apply>
                        <ln/>
                        <apply>
                            <times/>
                            <ci>K_q10</ci>
                            <ci>q10</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u11</ci>
                <apply>
                    <times/>
                    <ci>RT</ci>
                    <apply>
                        <ln/>
                        <apply>
                            <times/>
                            <ci>K_q11</ci>
                            <ci>q11</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u12</ci>
                <apply>
                    <times/>
                    <ci>RT</ci>
                    <apply>
                        <ln/>
                        <apply>
                            <times/>
                            <ci>K_q12</ci>
                            <ci>q12</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u13</ci>
                <apply>
                    <times/>
                    <ci>RT</ci>
                    <apply>
                        <ln/>
                        <apply>
                            <times/>
                            <ci>K_q13</ci>
                            <ci>q13</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u14</ci>
                <apply>
                    <times/>
                    <ci>RT</ci>
                    <apply>
                        <ln/>
                        <apply>
                            <times/>
                            <ci>K_q14</ci>
                            <ci>q14</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u15</ci>
                <apply>
                    <times/>
                    <ci>RT</ci>
                    <apply>
                        <ln/>
                        <apply>
                            <times/>
                            <ci>K_q15</ci>
                            <ci>q15</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u16</ci>
                <apply>
                    <times/>
                    <ci>RT</ci>
                    <apply>
                        <ln/>
                        <apply>
                            <times/>
                            <ci>K_q16</ci>
                            <ci>q16</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u17</ci>
                <apply>
                    <times/>
                    <ci>RT</ci>
                    <apply>
                        <ln/>
                        <apply>
                            <times/>
                            <ci>K_q17</ci>
                            <ci>q17</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u18</ci>
                <apply>
                    <times/>
                    <ci>RT</ci>
                    <apply>
                        <ln/>
                        <apply>
                            <times/>
                            <ci>K_q18</ci>
                            <ci>q18</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u19</ci>
                <apply>
                    <times/>
                    <ci>RT</ci>
                    <apply>
                        <ln/>
                        <apply>
                            <times/>
                            <ci>K_q19</ci>
                            <ci>q19</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u20</ci>
                <apply>
                    <times/>
                    <ci>RT</ci>
                    <apply>
                        <ln/>
                        <apply>
                            <times/>
                            <ci>K_q20</ci>
                            <ci>q20</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u21</ci>
                <apply>
                    <times/>
                    <ci>RT</ci>
                    <apply>
                        <ln/>
                        <apply>
                            <times/>
                            <ci>K_q21</ci>
                            <ci>q21</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>u22</ci>
                <apply>
                    <times/>
                    <ci>RT</ci>
                    <apply>
                        <ln/>
                        <apply>
                            <times/>
                            <ci>K_q22</ci>
                            <ci>q22</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <!--        u_E = RT*K_E*q_E;-->
            <apply>
                <eq/>
                <ci>v_Re1</ci>
                <apply>
                    <times/>
                    <ci>K_Re1</ci>
                    <apply>
                        <minus/>
                        <apply>
                            <exp/>
                            <apply>
                                <divide/>
                                <ci>u20</ci>
                                <ci>RT</ci>
                            </apply>
                        </apply>
                        <apply>
                            <exp/>
                            <apply>
                                <divide/>
                                <ci>u23</ci>
                                <ci>RT</ci>
                            </apply>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>v_Re2</ci>
                <apply>
                    <times/>
                    <ci>K_Re2</ci>
                    <apply>
                        <minus/>
                        <apply>
                            <exp/>
                            <apply>
                                <divide/>
                                <ci>u34</ci>
                                <ci>RT</ci>
                            </apply>
                        </apply>
                        <apply>
                            <exp/>
                            <apply>
                                <divide/>
                                <ci>u18</ci>
                                <ci>RT</ci>
                            </apply>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>v_Re3</ci>
                <apply>
                    <times/>
                    <ci>K_Re3</ci>
                    <apply>
                        <minus/>
                        <apply>
                            <exp/>
                            <apply>
                                <divide/>
                                <ci>u21</ci>
                                <ci>RT</ci>
                            </apply>
                        </apply>
                        <apply>
                            <exp/>
                            <apply>
                                <divide/>
                                <ci>u24</ci>
                                <ci>RT</ci>
                            </apply>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>v_Re4</ci>
                <apply>
                    <times/>
                    <ci>K_Re4</ci>
                    <apply>
                        <minus/>
                        <apply>
                            <exp/>
                            <apply>
                                <divide/>
                                <ci>u33</ci>
                                <ci>RT</ci>
                            </apply>
                        </apply>
                        <apply>
                            <exp/>
                            <apply>
                                <divide/>
                                <ci>u17</ci>
                                <ci>RT</ci>
                            </apply>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>v_Re5</ci>
                <apply>
                    <times/>
                    <ci>K_Re5</ci>
                    <apply>
                        <minus/>
                        <apply>
                            <exp/>
                            <apply>
                                <divide/>
                                <ci>u22</ci>
                                <ci>RT</ci>
                            </apply>
                        </apply>
                        <apply>
                            <exp/>
                            <apply>
                                <divide/>
                                <ci>u25</ci>
                                <ci>RT</ci>
                            </apply>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>v_Re6</ci>
                <apply>
                    <times/>
                    <ci>K_Re6</ci>
                    <apply>
                        <minus/>
                        <apply>
                            <exp/>
                            <apply>
                                <divide/>
                                <ci>u32</ci>
                                <ci>RT</ci>
                            </apply>
                        </apply>
                        <apply>
                            <exp/>
                            <apply>
                                <divide/>
                                <ci>u16</ci>
                                <ci>RT</ci>
                            </apply>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>v_Re7</ci>
                <apply>
                    <times/>
                    <ci>K_Re7</ci>
                    <apply>
                        <minus/>
                        <apply>
                            <exp/>
                            <apply>
                                <divide/>
                                <ci>u26</ci>
                                <ci>RT</ci>
                            </apply>
                        </apply>
                        <apply>
                            <exp/>
                            <apply>
                                <divide/>
                                <ci>u9</ci>
                                <ci>RT</ci>
                            </apply>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>v_Re8</ci>
                <apply>
                    <times/>
                    <ci>K_Re8</ci>
                    <apply>
                        <minus/>
                        <apply>
                            <exp/>
                            <apply>
                                <divide/>
                                <ci>u14</ci>
                                <ci>RT</ci>
                            </apply>
                        </apply>
                        <apply>
                            <exp/>
                            <apply>
                                <divide/>
                                <ci>u31</ci>
                                <ci>RT</ci>
                            </apply>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>v_Re9</ci>
                <apply>
                    <times/>
                    <ci>K_Re9</ci>
                    <apply>
                        <minus/>
                        <apply>
                            <exp/>
                            <apply>
                                <divide/>
                                <ci>u27</ci>
                                <ci>RT</ci>
                            </apply>
                        </apply>
                        <apply>
                            <exp/>
                            <apply>
                                <divide/>
                                <ci>u10</ci>
                                <ci>RT</ci>
                            </apply>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>v_Re10</ci>
                <apply>
                    <times/>
                    <ci>K_Re10</ci>
                    <apply>
                        <minus/>
                        <apply>
                            <exp/>
                            <apply>
                                <divide/>
                                <ci>u13</ci>
                                <ci>RT</ci>
                            </apply>
                        </apply>
                        <apply>
                            <exp/>
                            <apply>
                                <divide/>
                                <ci>u30</ci>
                                <ci>RT</ci>
                            </apply>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>v_Re11</ci>
                <apply>
                    <times/>
                    <ci>K_Re11</ci>
                    <apply>
                        <minus/>
                        <apply>
                            <exp/>
                            <apply>
                                <divide/>
                                <ci>u29</ci>
                                <ci>RT</ci>
                            </apply>
                        </apply>
                        <apply>
                            <exp/>
                            <apply>
                                <divide/>
                                <ci>u12</ci>
                                <ci>RT</ci>
                            </apply>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>v_Re12</ci>
                <apply>
                    <times/>
                    <ci>K_Re12</ci>
                    <apply>
                        <minus/>
                        <apply>
                            <exp/>
                            <apply>
                                <divide/>
                                <ci>u18</ci>
                                <ci>RT</ci>
                            </apply>
                        </apply>
                        <apply>
                            <exp/>
                            <apply>
                                <divide/>
                                <ci>u35</ci>
                                <ci>RT</ci>
                            </apply>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>v_Re13</ci>
                <apply>
                    <times/>
                    <ci>K_Re13</ci>
                    <apply>
                        <minus/>
                        <apply>
                            <exp/>
                            <apply>
                                <divide/>
                                <ci>u10</ci>
                                <ci>RT</ci>
                            </apply>
                        </apply>
                        <apply>
                            <exp/>
                            <apply>
                                <divide/>
                                <ci>u28</ci>
                                <ci>RT</ci>
                            </apply>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>v_Re14</ci>
                <apply>
                    <times/>
                    <ci>K_Re14</ci>
                    <apply>
                        <minus/>
                        <apply>
                            <exp/>
                            <apply>
                                <divide/>
                                <ci>u12</ci>
                                <ci>RT</ci>
                            </apply>
                        </apply>
                        <apply>
                            <exp/>
                            <apply>
                                <divide/>
                                <ci>u13</ci>
                                <ci>RT</ci>
                            </apply>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>v_Re15</ci>
                <apply>
                    <times/>
                    <ci>K_Re15</ci>
                    <apply>
                        <minus/>
                        <apply>
                            <exp/>
                            <apply>
                                <divide/>
                                <ci>u36</ci>
                                <ci>RT</ci>
                            </apply>
                        </apply>
                        <apply>
                            <exp/>
                            <apply>
                                <divide/>
                                <ci>u20</ci>
                                <ci>RT</ci>
                            </apply>
                        </apply>
                    </apply>
                </apply>
            </apply>
        </math>
    </component>
</model>